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Investigation of thermoelectric properties ofmagnesium-based metal alloys coatings deposited by

sputtering processMahsasadat Safavi

To cite this version:Mahsasadat Safavi. Investigation of thermoelectric properties of magnesium-based metal alloys coat-ings deposited by sputtering process. Other. Université Bourgogne Franche-Comté, 2021. English.NNT : 2021UBFCA005. tel-03551787

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Investigation of thermoelectric properties of magnesium-based metal alloy coatings deposited by sputtering process

Mahsasadat SAFAVI

THESE DE DOCTORAT DE L’UNIVERSITE BOURGOGNE FRANCHE-COMTE

Université de Technologie Belfort-Montbéliard

Ecole doctorale n°37

Sciences Pour l'Ingénieur et Microtechniques

Doctorat en Sciences pour l’Ingénieur

Par

Mahsasadat SAFAVI

Investigation of thermoelectric properties of magnesium-based metal alloy coatings deposited by sputtering process

Présentée le 31 mars 2021

Devant le Jury :

Bertrand LENOIR Président Professeur des Universités, Université de Lorraine

Nicole FRETY Rapporteur Professeur des Universités, Université de Montpellier

Angélique BOUSQUET Rapporteur MCF (HDR), Université Clermont Auvergne

Corinne NOUVEAU Examinateur MCF (HDR), Arts et Métiers Sciences et Technologies, Paris

Alain BILLARD Examinateur Professeur des Universités, Université Bourgogne Franche-Comté

Nicolas MARTIN Directeur de thèse Professeur des Universités, Université Bourgogne Franche-Comté Mohammad ARAB POUR YAZDI Codirecteur de thèse Ingénieur de Recherche, Université Bourgogne Franche-Comté

http://www.theses.fr/s197865



ii

Titre : Etude des propriétés thermoélectriques de revêtements d’alliages métalliques à base de

magnésium déposés par pulvérisation cathodique.

Mots clés : thermoélectrique ; Mg2X; couche mince; solution solide, pulvérisation cathodique

Résumé : Les matériaux thermoélectriques ont

suscité un intérêt mondial, grâce à leur capacité à

convertir directement l’énergie thermique en

électrique de manière propre et renouvelable. Mg2X

(X = Si, Sn, Ge) et leurs solutions solides attirent plus

d’attention en raison de leur stabilité thermique, faible

coût, non-toxicité, abondance dans la croûte terrestre,

faible densité et leur potentiel pour fournir à la fois la

conduction de type n ou p pour des applications dans

une gamme de températures modérées. La plupart des

études menées sur ces matériaux sont limitées aux

matériaux de type n et en massif, tandis que pour le

développement d’un bon générateur thermoélectrique

les matériaux performants de type n et p sont

nécessaires. En plus, des matériaux développés en

couches minces sont essentiels pour réduire la taille

des dispositifs thermoélectriques actuels afin de les

utiliser dans des applications miniaturisées comme

microsystèmes électromécaniques et Internet des

objets. Cette thèse vise à développer et à améliorer les

performances thermoélectriques des alliages de type

p à base de Mg en utilisant différentes stratégies,

y compris la synthèse sous forme de couches minces,

déficientes en magnésium, ou dopées, et des solutions

solides. Dans ce travail, des films minces ont été

déposés par pulvérisation cathodique magnétron et le

rôle de la composition chimique et de la modification

structurale sur les propriétés électroniques et

thermoélectriques des films ont été étudiés.

L’influence du dopage en Cu sur les films Mg2Sn

stoechométriques et sur les couches minces

déficientes en Mg a été étudiée comme une stratégie

pour améliorer les performances thermoélectriques

dans le système Mg2Sn. De celle manière, les

performances thermoélectriques de Mg2Si1-xSnx, ont

été étudiées en fonction de la composition et la

microstructure du film. L’effet du dopage avec Ge sur

Mg2Si0.35Sn0.65 de type p a été discuté en détails. Les

couches minces Mg2Ge et Mg2Ge1-xSnx ont été

synthétisées pour explorer le rôle de la substitution de

Ge dans le transport électronique et les propriétés

thermoélectriques de ces composés. Enfin, la stabilité

thermique des films a été étudiée après recuit sous

vide (10-4 Pa) à des températures allant de l’ambiante

jusqu’au 600 °C.

Title: Investigation of thermoelectric properties of magnesium-based metal alloy coatings deposited

by sputtering process

Keywords: Thermoelectric; Mg2X; Thin Film; Solid Solution, Magnetron sputtering

Abstract: Thermoelectric materials have drawn

global interest, according to their ability to convert

directly thermal to electrical energy, thus providing a

clean and renewable supply of energy. Mg2X (X = Si,

Sn, Ge) and their solid solutions attract more

attention due to their thermal stability, low cost, non-

toxicity, constituent abundance in the earth’s crust,

low density and their potential for providing both n

and p-type conductions in a moderate temperature

range of applications. Most of the studies focused on

these materials are limited to n-type and as a bulk,

while for developing a good thermoelectric generator

both n- and p-type materials are required.

Furthermore, thin film materials are required to

reduce the size of current thermoelectric devices in

order to address them in miniaturized applications

like Micro Electro-Mechanical Systems and Internet

of Things.

This thesis aims at developing and improving

thermoelectric performances of p-type Mg-based by

employing different strategies, including thin films

synthesis, magnesium deficiency, doping, and solid

solutions. In this work, thin films were deposited by

magnetron sputtering and the role of chemical

composition and structural modification on their

electronic transport and thermoelectric properties

were investigated. The influence of Cu-doping on

stoichiometry and Mg-deficiency Mg2Sn thin films

were studied as a strategy to enhance thermoelectric

performances in the Mg2Sn system. Such

thermoelectric performances of Mg2Si1-xSnx, were

investigated as a function of the film composition and

microstructure. The effect of Ge-doping on p-type

Mg2Si0.35Sn0.65 was discussed in detail. Mg2Ge and

Mg2Ge1-xSnx thin films were synthesized to explore

the role of Ge substitution in electronic transport and

thermoelectric properties of these compounds.

Finally, the thermal stability of the films was studied

after annealing in vacuum (10-4 Pa) at different

temperatures from RT to 600°C.

Université Bourgogne Franche-Comté 32, avenue de l’Observatoire 25000 Besançon

iii

A mes parents,

A Mohammad

Et à tous ceux qui m’ont soutenu pendant ces années.

Remerciements

Je dois l’aboutissement de cette thèse au concours de mon directeur de thèse, de co-

directeur, des équipes de recherche qui m’ont accueilli, des membres du jury, de mon époux

et de toute ma famille. Je tiens à exprimer ma reconnaissance et ma gratitude à chacun

d’eux.

Je tiens en particulier à remercier Monsieur Nicolas MARTIN, directeur de thèse, pour avoir

dirigé mes travaux de thèse et m’avoir permis de réaliser l’ensemble de ces recherches et

aussi pour ses conseils et son suivi au cours de ma thèse.

Je remercie particulièrement, Monsieur Mohammad ARAB POUR YAZDI pour avoir co-dirigé

ces travaux et pour m'avoir fait bénéficier de son savoir et de sa rigueur méthodologique

dans l'avancement d'un projet scientifique.

Je tiens également à exprimer ma reconnaissance à Mesdames Nicole FRETY et Angélique

BOUSQUET, qui m’ont fait l’honneur d’être les rapporteurs de cette thèse. Mes gratitudes

portent également à Madame Corinne NOUVEAU, Monsieur Bertrand LENOIR et Monsieur

Alain BILLARD qui ont accepté d’être les examinateurs de cette thèse. Je leur exprime ma

gratitude pour s’être rendus disponibles en dépit de leurs occupations.

Mes remerciements vont également à tous les membres de l’équipe MINAMAS du

laboratoire Femto-ST, pour m’avoir accueilli dans leurs structures de recherche. Je souhaite

exprimer ma gratitude envers monsieur Pascal Briois, et monsieur Eric Aubry.

Je remercie également les techniciens, les ingénieurs et les secrétaires qui ont participé

directement ou indirectement au bon déroulement de ces travaux de recherche et à leur

aboutissement, praticulièrement : monsieur Christian Petitot, monsieur Khalid Neffaa,

Madame Emmanuelle Arcens.

Je remercie également mes collègues doctorants et mes amis pour les bons moments passés

ensemble, Huan Luo, Shutong Lai, Xiaolei Ye.

Je remercie tout naturellement et très chaleureusement mes parents pour leur patience,

leur soutien, leurs encouragements et leurs aides précieuses tout au long de ma vie. Sans

eux je n'en serais pas arrivé là.

Je ne saurais terminer sans dire un Grand Merci tout particulier à mon époux Mohammad

qui, à tout moment, même très difficile, a su m’apporter réconfort et amour durant toutes

ces années de thèse. Je ne peux pas oublier également toute ma famille, ma sœur, Mona,

mon frère, Mostafa, pour leur précieux soutien et leur encouragement sans cesse.

Respectueusement

Mahsa

v

Sommaire

Abbreviation and Symbols .............................................................................................................. vi

General Introduction ...........................................................................................................................1

Chapter 1 ...........................................................................................................................................3

Chapter 2 .........................................................................................................................................53

Chapter 3 .........................................................................................................................................75

Chapter 4 .......................................................................................................................................105

Conclusion and Perspectives ...........................................................................................................138

Scientific production .......................................................................................................................142

vi

Abbreviation and Symbols

a.m.u. Atomic Mass Unit (kg)

CBM Conduction Band Minimum

𝐶𝐻 Heavy Conduction Band

𝐶𝐿 Light Conduction Band

DOS Density Of States

EDS Energy-Dispersive X-ray Spectroscopy

IBAD Ion-Beam-Assisted Deposition

IOT Internet Of Things

MBE Molecular Beam Epitaxy

MEMS Micro-Electro-Mechanical Systems

MOCVD Metal-Organic Chemical Vapor Deposition

NIST National Institute of Standards and Technologies

PLD Pulsed Laser Deposition

PVD Physical Vapor Deposition

RF Radio Frequency

SEM Scanning Electron Microscope

TFA Thin Film Analyzer

VBM Valance Band Maximum

XRD X-Ray Diffraction

ZT Figure of merit

𝜎 Electrical conductivity (S m-1)

µ𝐻 Carrier Mobility (m2 V-1 s-1)

Magnetic field (T)

𝑒 Electronic charge (1.6 × 10-19 As)

𝐸𝑒𝑚𝑓 Electromotive force (V)

𝐸𝑔 Band gap energy (eV)

J Local current (A m-2)

𝐾𝐵 Boltzman Constant (6.63 × 10-34 J s)

𝑘𝑡 Total thermal conductivity (W m-1 K-1)

𝑘𝑒𝑙 Electronic thermal conductivity (W m-1 K-1)

𝑘𝑙𝑎𝑡 Lattice thermal conductivity (W m-1 K-1)

L Lornez number (2.4 × 10-8 J2 K-2 C-2)

𝑚∗ Effective mass (kg)

𝑛 Carrier concentration (m-3)

PF Power factor (W m-1 K-1)

𝑅𝐻 Hall coefficient (Ω m T-1)

S Seebeck coefficient (V K-1 or µV K-1)

sccm Standard cubic centimeters per minute

∆𝑉 Difference in voltage (V)

𝑉𝐻 Hall voltage (V)

General Introduction

Since 1800, with the Industrial Revolution, fossil fuel consumption has grown significantly and

in 2019 reached 135,807 terawatt-hours. Fossil fuel consumption was widely criticized as a

finite resource and being a contributor to climate change. Moreover, the statistical result shows

that more than 60% of energy waste, mostly in the form of heat. So, today the objective is not

only reducing fuel consumption, but also is extremely important to use energy more efficiently.

Thermoelectric materials enable to convert directly thermal to electrical energy and vice versa,

thus have drawn attention as a potential clean and renewable supply of energy for resolving the

power crisis. This conversion has several advantages due to their solid-state operation, gas free

emissions, maintenance-free operation without any moving parts, noise and chemical reaction,

no damage to the environment, small size, feasibility of application in the wide temperature

range and finally high reliability.

Nowadays, the wide variety of thermoelectric materials have been known, some of them have

been used for decades, while others are a result of more recent researches. The thermoelectric

materials can be classified based on different aspects such as their optimal operating

temperature range, crystal structure, cost, and conversion efficiency.

Intermetallic compounds of Mg2X (X = Si, Sn, Ge) and their solid solutions have attracted much

interest due to their thermoelectric performance in the middle-temperature range, low density,

their thermal stability, non-toxic elements, and providing both n and p-type conductions. Till

now most of the studies on these group of materials are limited to n-type and as a bulk, while

for developing a good thermoelectric generator both n- and p-type materials are required, and

it is important both of these can be fabricated from similar material system to reduce any

thermal stress mismatch which can lead to failure of thermoelectric module. On the other hand,

synthesis of the materials in form of thin films should be interesting as two points of view: first,

the overall thermoelectric performance could be improved by controlling the micro and nano

structure. Second, from the application perspective, the thermoelectric thin films reduce the size

of current thermoelectric devices in order to address them in miniaturized applications like

Micro Electronic and Mechanical Systems and Internet of Things.

Within this context, the main objective of this Ph.D. thesis is developing and improving

thermoelectric performances of p-type Mg-based by employing different strategies, including

thin films, magnesium deficiency, doping, and solid solutions.

This manuscript is divided into four chapters:

Chapter I introduces brief history of thermoelectricity, application, principles of

thermoelectric, and art of selecting thermoelectric materials. Mg2X (X= Si, Sn, Ge) compounds

and their solid solutions are entirely studied as potential candidates for thermoelectric

General Introduction 2

applications. Finally, the different strategies for enhancing the thermoelectric performances of

these groups of materials are discussed in detail.

Chapter II presents the principle of magnetron sputtering used for film preparation and the

experimental details and characterization techniques used in this Ph.D. project. Furthermore,

the deposition equipment, selected substrates, and measurements parameters are discussed.

Chapter III, Mg-Sn thin films (21 ≤ at. % Sn ≤ 42.5) are deposited by magnetron co-sputtering

of Mg and Sn targets in an argon atmosphere. This part aims at investigating the role of chemical

composition and structural modification on the films electronic transport and thermoelectric

properties. In parallel, thermal stability of the film has been studied after annealing in vacuum

(10-4 Pa) at different temperatures. Moreover, Cu-doping impact on stoichiometry and Mg-

deficiency thin films is chosen as a strategy to enhance thermoelectric performances of Mg2Sn

system. Two groups of Cu-doped thin films with different [Mg]/[Sn] atomic ratios are deposited

by magnetron co-sputtering of Mg, Sn and Cu targets in an argon atmosphere. Their structures

and morphologies are studied as a function of the Cu atomic concentration. The film charge

carrier’s concentration and mobility are measured to explain the electronic transport behavior

as a function of the film composition and morphology. The effects of Mg-deficiency and Cu-

doping on the thermoelectric properties of both groups are discussed in a range of temperatures:

30-200 °C.

Chapter IV is devoted to Mg2Si1-xSnx and Mg2Ge1-xSnx solid solutions. This chapter is

composed by three parts. In the first part, Mg2Si1-xSnx solid solutions are deposited by

magnetron co-sputtering of Mg, Si and Sn targets in an argon atmosphere in the aim of

investigating the influence of chemical composition on the films electronic transport and

thermoelectric properties. Moreover, thermal stability of the film is studied after annealing in

vacuum (10-4 Pa) at different temperatures. In the second part, p-type Mg2Si0.35Sn0.65 is selected

and doped by different Ge atomic concentrations, in order to enhance ZT in the system. The

Ge-doped Mg2Si0.35Sn0.65 thin films are synthesized by magnetron co-sputtering of Mg, Si, Sn

and Ge targets in an argon atmosphere. Their structures and morphologies are studied as a

function of the Ge atomic concentration. The film charge carrier concentration and their

mobility are measured to explain the electronic transport behavior as a function of the film

composition. The effects of Ge-doping on the thermoelectric properties of MgSi0.35Sn0.65 are

discussed in a range of temperatures: 30-200 °C. Thermal stability of the film is investigated

after annealing in vacuum (10-4 Pa) at different temperatures. In the last part, Mg2Ge and

Mg2Ge1-xSnx thin films are deposited by magnetron co-sputtering of Mg, Ge and Sn targets in

an argon atmosphere. The influence of chemical composition on the films electronic transport

and thermoelectric properties is discussed. Finally, thermal stability of the film is studied after

annealing in vacuum (10-4 Pa) at different temperatures.

Chapter 1

Introduction to thermoelectric: survey of the

state-of-the-art materials

Table of contents

I.1 Introduction .................................................................................................................................... 6

I.2 History ............................................................................................................................................ 6

I.3 Application of thermoelectric materials ......................................................................................... 8

I.4 Thermoelectric modules ............................................................................................................... 10

I.5 The principle of thermoelectric .................................................................................................... 11

I.5.1 The Seebeck effect : ............................................................................................................. 11

I.5.2 Peltier effect ......................................................................................................................... 12

I.6 Thermoelectric efficiency ............................................................................................................. 13

I.7 Factor affecting thermoelectricity ................................................................................................. 14

I.7.1 Seebeck coefficient .............................................................................................................. 14

I.7.2 Electrical conductivity ......................................................................................................... 14

I.7.3 Thermal conductivity ........................................................................................................... 15

I.7.4 Carrier concentration ........................................................................................................... 16

I.8 Thermoelectric Materials .............................................................................................................. 16

I.8.1 Low temperature (˂ 250 °C) ......................................................................................................... 17

I.8.2 Moderate temperature (250 °C- 650 °C) ...................................................................................... 18

I.8.3 High temperature (>650 °C) ......................................................................................................... 21

I.9 Magnesium-based thermoelectric materials ................................................................................. 24

I.9.1 Mg2Sn compounds ............................................................................................................... 26

I.9.2 Mg2Si compounds ................................................................................................................ 27

I.9.3 Mg2Ge compounds and its solid solutions ........................................................................... 29

I.9.4 Mg2Si1-XSnX compounds ...................................................................................................... 31

I.10 Strategies to improve ZT of Mg2X thermoelectric materials ........................................................ 32

I.10.1 Alloying ............................................................................................................................... 33

I.10.2 Solid solution ....................................................................................................................... 34

I.10.3 Dimension reduction ............................................................................................................ 34

I.10.4 Nanostructuring.................................................................................................................... 36

I.10.5 Band engineering ................................................................................................................. 36

I.10.6 Microstructural defects ........................................................................................................ 37

I.11 Conclusion .................................................................................................................................... 40

I.12 References .................................................................................................................................... 42

List of Figures

Figure I. 1: Evolution in the number of thermoelectric articles (source Web of Science/ last update:

07/01/2021). .................................................................................................................................... 8

Figure I. 2 : Evolution in the number of regard thin films in thermoelectric articles (source Web of

Science/ last update: 07/01/2021). .................................................................................................. 8

Figure I. 3 : Radio powered by thermoelectric module using the heat of kerosene lamp [Beretta et al.,

2019]. .............................................................................................................................................. 9

Figure I. 4 : Configuration of a general-purpose heat source radioisotope thermoelectric generators

(GPHS-RTG) using SiGe thermoelectric elements [Yang et al., 2006]. ........................................ 9

Figure I. 5 : Thermoelectric generator in BMW, [Ando Junior et al., 2018] ........................................ 10

Figure I. 6 : a) Schematic illustration of a TEG module power by body, b) Matrix power watch by

Boukai [Jaziri et al., 2020]. ........................................................................................................... 10

Figure I. 7 : Thermoelectric module showing of charge flow on both cooling and power generation

[Zebarjadi et al., 2012].................................................................................................................. 11

Figure I. 8 : Schematic of the Seebeck effect for the power generation. An applied temperature

difference causes charge carrier in the material (holes or electrons) to diffuse from the hot side to

cold side, leading to a current flux through the circuit [Zhang et al., 2015]. ................................ 12

Figure I. 9 : Schematic of Peltier effect for the active refrigeration. Heat develops at the upper junction

and is absorbed at lower junction when a current is made to flow the circuit [Zhang et al., 2015].

...................................................................................................................................................... 13

Figure I. 10 : Conversion efficiency of thermoelectric materials as a function of the average ZT

[Zhang et al., 2015]. ...................................................................................................................... 14

Figure I. 11 : Optimizing ZT through carrier concentration tuning [Gayner et al., 2016] .................... 16

Figure I. 12 : Layered structure of Bi2Te3.Bi are octahedrally coordinated by Te, residing on two

inequivalent sites, defining here by tone and notation [Witting et al., 2019]. .............................. 17

Figure I. 13 : ZT vs. temperature for bulk Bi2Te3 with different methods of preparation [Kanatzidis,

2010]. ............................................................................................................................................ 18

Figure I. 14 : Crystal structure of PbTe [Xiao et al., 2018] ................................................................... 19

Figure I. 15 : ZT vs. temperature for p and n-type PbTe [Xiao et al., 2018]......................................... 19

Figure I. 16 : Unit cell of the Skutterudite, defined by Oftedal et al. in 1928; a) crystalline structure

described by Kjekshus et al. in 1974, where the octahedral coordination of the metal atom is

drawn; b) for both images, transition metals are represented by red spheres, nonmetallic atoms by

yellow spheres and the voids in the structure or the filled atoms by light blue spheres [Rull-Bravo

et al., 2015]. .................................................................................................................................. 20

Figure I. 17 : ZT vs. temperature for p and n-type skutterudites: .......................................................... 20

Figure I. 18 : Crystal structure of type-I clathrates: polyhedral view showing two types of polyhedral

cages tetrakaidecahedra (yellow) and pentagonal dodechehedra (blue) [Dolyniuk et al., 2016]. 21

Figure I. 19 : ZT vs. temperature for some high-performance thermoelectric clathrates [Beretta et al.,

2019]. ............................................................................................................................................ 21

Figure I. 20 : The crystal structure of HH alloys [Shi et al., 2016]. ...................................................... 22

Figure I. 21 : ZT vs. temperature for several HH alloys [Shi et al., 2016]. ........................................... 22

Figure I. 22 : The crystal structure of NaxCoO2[Shi et al., 2016] .......................................................... 23

Figure I. 23 : ZT vs. temperature for several oxide compounds [Shi et al., 2016]. ............................... 23

Figure I. 24 : ZT vs. temperature for several SiGe-alloys [Shi et al., 2016] ......................................... 24

Figure I. 25 : Crystal structure of Mg2X (X=Si, Sn, Ge) ....................................................................... 24

Figure I. 26 : Simplified band structure of Mg2X (X=Si, Sn, Ge) compounds. CH, CL and V signify the

heavy conduction band, light conduction band and valence band, respectively [Santos et al.,

2018]. ............................................................................................................................................ 25

Figure I. 27 : Mg-Sn phase diagram [Nayeb-hashemi et al., 1984] ...................................................... 26

Figure I. 28 : Mg-Si phase diagram [Nayeb-hashemi et al., 1984] ....................................................... 27

Figure I. 29 : Mg-Ge phase diagram [Yan et al., 2010] ........................................................................ 29

Figure I. 30 : Calculated phase diagram of the Mg2Ge-Mg2Sn section with experimental data [Jung et

al., 2010] ....................................................................................................................................... 30

Figure I. 31 : Optimized phase diagram of the Mg2Sn-Mg2Si binary section in the Mg-Si-Sn system

[Jung et al., 2007] ......................................................................................................................... 31

Figure I. 32 : Lattice thermal conductivity as a function of the composition of magnesium-based

ternary alloys at room temperature [Bashir et al., 2014] .............................................................. 34

Figure I. 33 : Electronic density of states for a) a bulk 3D crystalline semiconductor, b) a 2D quantum

well, c) a 1D nanowire (nanotube), and d) 0D quantum dot [Dresselhaus et al., 2007]. .............. 35

Figure I. 34 : Schematic diagram illustrating various phonon scattering mechanism in nanograined

thermoelectric materials [Vineis et al., 2010]. .............................................................................. 36

Figure I. 35 : Relative position of the heavy and light conduction band vs. Sn content for Mg2Si1-XSnX.

The red dotted line shows energy variation for the heavy conduction band as the Sn content

increases, while the blue and black dotted lines represent the motions of the light conduction

band and the valence band, respectively. Colored dots present the calculated data for different Sn

Contents [Liu et al., 2012]. ........................................................................................................... 37

Figure I. 36 : Schematic views for (a) point defects, (b) dislocations, (c) stacking faults, (d) grain

boundaries, (e) twin boundary, and (f) nanoprecipitate [Mao et al., 2018] .................................. 38

Figure I. 37 : Atomic chemical potential (Mg or Sn) dependence of the calculated formation energies

for impurities (Cu, Ag, and Au) in Mg2Sn. The solid and dashed line refer to impurities are

substituted on Mg and Sn site, respectively [Tani et al., 2012]. ................................................... 39

List of Tables

Table I.1 : Heat source and temperature range of thermoelectric materials [Neeli et al., 2016] ........... 17

Table I.2 : Figure of merit ZT for some polymers [Neeli et al., 2016] ................................................. 18

Table I.3 : Properties of Mg2X (X=Si, Sn, Ge) [Zaitsev et al., 2006] ................................................... 25

Table I.4 : Some parameters of electron structure for Mg2X compounds [Zaitsev et al., 2016] ........... 25

Table I. 5 : Outline of studies focused on Mg2Sn compounds .............................................................. 26

Table I. 6 : Outline of published studies on Mg2Si compounds ............................................................ 28

Table I. 7 : Outline of published studies on Mg2Ge compounds ........................................................... 30

Table I. 8 : Outline of published studies on Mg2Si1-XSnX compounds .................................................. 32

Table I. 9 : Fermi level shift induced by the most stable defects in Mg2X (X= Si, Ge, Sn) ................. 38

Introduction to thermoelectric: survey of the state-of-the-art materials 6

I.1 Introduction

Nowadays, environmental problems such as global warming, climate-changing, greenhouse gas

emission, ozone layer depletion, acid rains are enlarged as a consequence of extensive fossil

fuel consumption. According to the statistical data, more than 60% of energy waste mostly in

the form of heat. Thermoelectric materials have attracted global interest due to their ability to

convert directly thermal to electrical energy and vice versa, thus providing a clean and

renewable supply of energy. This conversion has numerous advantages because of their solid-

state operation, gas free emissions, maintenance-free operation without any moving parts, noise

and chemical reaction, no damage to the environment, small size, feasibility of application in

the wide temperature range and finally high reliability [Lalonde et al., 2011].

This chapter is devoted to the brief history of thermoelectricity, application, principles of

thermoelectric, and selecting thermoelectric materials. In the following, the Mg-based alloys

are studied as potential candidates for thermoelectric applications and the different strategies

for improving the thermoelectric performances of these groups of materials will be discussed.

I.2 History

The thermoelectricity phenomenon was observed almost two centuries ago. In 1821, the

German scientist named Thomas Johann Seebeck discovered that a compass needle deflected

by a circuit made from two dissimilar metals with junctions at different temperatures. This

phenomenon is called the Seebeck effect. Later, in 1834, the French scientist named Jean-

Charles Athanase Peltier discovered the Peltier effect which is the reverse of the Seebeck effect.

In 1856, William Thomson explained that electrical current can be produced as a result of

temperature gradient in a single homogeneous conductor which is known as Thomson effect.

In 1912, for the first time, Edmund Altenkirch offered the concept of “thermoelectric figure of

merit”. He showed that good thermoelectric materials should exhibit high electrical

conductivity, large Seebeck coefficient value, and low thermal conductivity. The high Seebeck

coefficients certify a large thermovoltage, the high electrical conductivity is essential to

minimize the Joule heating effect and the low thermal conductivity is needed to create a large

temperature gradient. In 1928, Felix Bloch reported that the electrical conductivity in metals is

affected by the thermal vibration of the lattice and the existence of impurities. Later in 1931,

Alan Herries Wilson extended Bloch’s theory to semiconductors and insulators. He suggested

that, for these groups of materials, the electrical conductivity should be dependent on

temperature. At lower temperatures, the conductivity decreases due to the limited number of

carrier concentration. In the same year, Sommerfeld and Frank investigated thermoelectric

phenomena in metals based on the revised free-electron theory of metals. They obtained the

equations of thermal conductivity, electrical conductivity and Thomson coefficient [Bulusu et

al., 2008; Gayner et al., 2016].

In 1947, Maria Telkes invented a thermoelectric generator based on PbS and ZnSb, showing a

conversion efficiency higher than 5% when operating under a temperature difference of 400 K

[Telkes, 1947].


In 1952, Abram Ioffé stated that the thermal conductivity of semiconductors is related to their

position in the periodic table. In other words, elements with large atomic weights have low

thermal conductivity (also low thermal conductivity is observed for low-density materials).

Two years later, in 1954, Julian Goldsmid studied the variation of electrical conductivity with

the crystal structure and electron mobility. He found out that electron mobility affected the

thermoelectric properties of a material. He reported that the ratio of electron mobility to thermal

conductivity is a function of atomic weight. In 1956, Ioffé hypothesized that the figure of merit

for semiconducting thermoelectric material can be improved by alloying with an isomorphous

substance (materials having the same crystalline structures) by reducing the thermal

conductivity without affecting carrier concentrations. Ioffé proposed the figure of merit ZT as

a measure to quantify the performance of thermoelectric materials [Bulusu et al., 2008].

In 1959, Chasmar and Stratton defined a material factor, often referred to as the material quality

factor which is represented by β. The material factor is a parameter which depends only on the

physical properties of the semiconductors such as carrier mobility, effective mass, temperature,

doping, and thermal conductivity. They showed that a large bandgap semiconductor can’t be

considered as a good thermoelectric material duo to low carrier mobility and high thermal

conductivity [Chasmar et al., 1959]. In 1961, Howard Littman and Burton Davidson presented

the reason for the lack of an upper limit for ZT based on irreversible thermodynamics [Littman

et al., 1961].

In the same year, Nikitin at Ioffé Institute showed that the compounds of Mg2BIV (BIV =Si, Sn,

Ge) have favorable physical and chemical properties and can be considered as candidates for

the development of new efficient thermoelectric materials [Zaitsev et al., 2006].

In 1962, Simon studied the optimum ZT value in two band semiconductors as a function of the

minimum bandgap (Eg). Later, in 1993, Mildred Dresselhaus and Hicks remarked low

dimensional structures (materials with nanostructuration) have higher ZT value compared to

bulk materials according to their lower thermal conductivity [Hicks et al., 1993]. Consequently,

some thin film technologies were selected to miniaturized traditional bulk thermoelectric

devices. In 1994, Slack and Tsoukala proposed the concept of ‘Phonon-Glass Electron-Crystal’

(PGEC) related to the thermoelectric materials. According to this concept, the ideal

thermoelectric materials should conduct electricity and heat like crystal and glass, respectively

at the same time [Slack et al., 1994].

From 1995, NASA, Jet Propulsion Laboratory (JPL), Massachusetts Institute of Technology

(MIT-Lincoln Labs), Michigan states University and other organizations developed a new

generation of thermoelectric materials. These materials are generally small-sized structures,

such as two-dimensional like thin films, one-dimensional like nanowires to achieve a higher

figure of merit [Ando Junior et al., 2018]. In 1999, Stark and Strodeur produced thin films based

on bismuth telluride as new generation of thermoelectric materials in order to address them in

micro and sensor systems [Stark et al., 1999]. Nanocomposites were introduced as innovative

thermoelectric materials. In 2012, Biswas et al. presented an approach consisting in band


engineering and nanostructuring to produce high-performance bulk materials [Biswas et al.,

2012].

Since 2000, the number of publications in thermoelectric has grown exponentially except 2020

as a result of coronavirous pandemic. The figure I.1 and I.2 present the rate of published papers

in thermoelectric and regard thin films in thermoelectric by year, respectively.

Figure I. 1: Evolution in the number of thermoelectric articles (source Web of Science/ last update:

07/01/2021).

Figure I. 2: Evolution in the number of regard thin films in thermoelectric articles (source Web of

Science/ last update: 07/01/2021).

I.3 Application of thermoelectric materials

Thermoelectric materials are currently used in different temperature ranges in diverse

applications. They have numerous applications such as automotive waste heat recovery [Choi

et al., 2007], deep space exploration probes [Lukowicz et al., 2016], military system [Champier,

2017], domestic applications [Tassou et al., 2010], cooling computers and recharging devices

[Taylor et al., 2008] and internet of things [Lopez et al., 2017]. Some examples of applications

will be presented below.


In 1948, U.S.S.R. introduced radio which can function with heat provided by the kerosene lamp.

As it is shown in figure I.3 a tube consisting of thermo-elements (ZnSb/Constantan) is located

above the kerosene lamp which provides a large amount of heat as lighting. As a result, the

inside of the tube is heated by the hot combustion gases and the outside is cooled by means of

a set of radiators. The temperature difference created in this way is about 250-300 °C, which

gives a few watts of electrical energy for feeding a radio receiver set [Ioffe, 1957].

Figure I. 3: Radio powered by thermoelectric module using the heat of kerosene lamp [Beretta et al.,

2019].

Since 1961, the National Aeronautics and Space Administration’s (NASA) Spacecraft and deep

space probes benefit Radioisotope Thermoelectric Generators (RTGs). RTGs generate the

electrical power using a thermoelectric converter which is able to convert the heat released from

nuclear decay of radioisotope (Plutonium-238) into electricity. RTGs have been successfully

used in several space mission like Apollo lunar mission; Pioneer 10 and 11; Voyager 1 and 2

(launched in 1977); Ulysses; Galileo and Cassini [Yang et al., 2006].

Figure I. 4: Configuration of a general-purpose heat source radioisotope thermoelectric generators

(GPHS-RTG) using SiGe thermoelectric elements [Yang et al., 2006].

In 2005, the BMW company introduced BMW series 5 E60, which benefits thermoelectric

materials located in its exhaust with the capability to generate electric power of 500 W, with a

temperature gradient of 207 °C, in order to recharge the batteries. The thermoelectric materials

were embedded in the engine, where the temperature is higher, in order to obtain higher electric

power [Ando Junior et al., 2018].


Figure I. 5: Thermoelectric generator in BMW, [Ando Junior et al., 2018]

In 2017, Boukai introduced “Matrix Power Watch” as the first smart watch monitoring powered

by Thermoelectric Generator (TEG) [Jaziri et al., 2020].

Figure I. 6: a) Schematic illustration of a TEG module power by body, b) Matrix power watch by

Boukai [Jaziri et al., 2020].

The thermoelectric materials are also promising for micro-source power devices such as

wireless sensors, portable devices, and so on. In these cases, the thermoelectric modules are not

only suitable, but they are also the best possible choice in some of devices.

I.4 Thermoelectric modules

The Peltier and Seebeck effects are origin of thermoelectric refrigerant and thermoelectric

power generation devices, respectively. A thermoelectric module is consisting of p (containing

free holes) and n (containing free electron) legs which are connected thermally in parallel and

electrically in series. The p and n legs are attached by an interconnect metal with Seebeck

coefficient almost zero (like copper) and the series of legs are set in between a heat source and

heat absorbent (figure I.7). Each thermoelectric module consists of several tens to hundreds of

pairs of thermoelectric couples. Once an electrical current is passed through the thermoelectric

module, heat is absorbed at the cold side of the module and rejected at the hot side, so the device

acts as a cooler. On the other hand, if an external temperature difference applied to the module,

electrical power will be given to an external load and device acts as a power generation

[Zebarjadi et al., 2012].


Figure I. 7: Thermoelectric module showing of charge flow on both cooling and power generation

[Zebarjadi et al., 2012].

I.5 The principle of thermoelectric

The thermoelectric effect is based on two fundamental principles: the Seebeck effect and the

Peltier effect, which are related to the principle of energy conversion, from thermal energy to

electricity or vice versa [Ahmed et al., 2015].

I.5.1 The Seebeck effect :

The Seebeck effect observed where an applied temperature drives the charge carriers (electrons

or holes) in the material to diffuse from the hot side to the cold side, leads to a current flux

through the circuit. This current and electromotive force existing in the joint circuit is called

the thermo-current and thermo-electromotive force, respectively. Increasing the voltage

difference (ΔV) rises the temperature difference (ΔT) between the two dissimilar material

joints. It worth noting that the relation between the Seebeck voltage and the temperature is

linear only for small changes of temperature. For larger temperature ranges, it becomes non-

linear.

The Seebeck coefficient is related to the intrinsic properties of the materials. This coefficient is

relatively low for materials like metals, 10 µV K-1, or less, while it would be much larger around

± 100 µV K-1 and higher for most of the semiconductors.

𝐽 = 𝜎(∆𝑉 + 𝐸𝑒𝑚𝑓) (I.1)


Where J, 𝜎, 𝛥𝑉,𝐸𝑒𝑚𝑓 are local current (A m-2), electrical conductivity (S m-1), the difference in

voltage (V) and electromotive force (V), respectively.

In general, Seebeck effect is described locally by the creation of an electromotive force:

𝐸𝑒𝑚𝑓 = −𝑆𝛻𝑇 (I.2)

Where S is the Seebeck coefficient (V K-1) and ∇T the temperature gradient.

If the system reaches steady-state, J=0 (A m-2), then the voltage is given simply by the

electromotive force:

−∆𝑉 = 𝑆∆𝑇 (I.3)

Where 𝛥𝑉 is the difference in voltage (V), and 𝛥𝑇 the difference in temperature (K). [Bell,

2008; Szczech et al., 2011; Elskeikh et al., 2014].

Figure I. 8: Schematic of the Seebeck effect for the power generation. An applied temperature

difference causes charge carrier in the material (holes or electrons) to diffuse from the hot side to cold

side, leading to a current flux through the circuit [Zhang et al., 2015].

I.5.2 Peltier effect

Peltier effect observed when the current exists in the circuit, the joint of two dissimilar

conductors rejects or absorbs the heat depending on the direction of the current. This

phenomenon is mainly due to the difference of the Fermi energies between two materials. The

capacity of the heat rejection or absorption is related to the property of the two dissimilar

conductors and the temperature of the joint.

= (𝛱𝐴 − 𝛱𝐵)𝐼 (I.4)

Where is the heat generated at the junction per unit time (W), 𝛱𝐴(𝛱𝐵) the Peltier coefficient

of conductors A and B (V m-1), and 𝐼 the electric current (A) [Szczech et al., 2011; He et al.,

2015].


Figure I. 9: Schematic of Peltier effect for the active refrigeration. Heat develops at the upper junction

and is absorbed at lower junction when a current is made to flow the circuit [Zhang et al., 2015].

I.6 Thermoelectric efficiency

The efficiency of a material in thermoelectric generator (cooler) is defined by their power

factor, which is calculated by its Seebeck coefficient and its electrical conductivity for a given

temperature difference:

𝑃𝑜𝑤𝑒𝑟𝑓𝑎𝑐𝑡𝑜𝑟 = 𝑃𝐹 = 𝑠2𝜎 (I.5)

As equation I.5 indicates the dimension of power factor should be in W m−1 K−2 where S is the

Seebeck coefficient (V K−1), σ the electrical conductivity (S m−1), respectively.

The dimensionless figure of merit (ZT) has been considered as a design parameter to show the

efficiency of the thermoelectric materials (equation I.6).

𝑍𝑇 =𝑆2𝜎

𝐾𝑇𝑇

(I.6)

Where S is the Seebeck coefficient (V K−1), σ the electrical conductivity (S m−1), 𝐾𝑇 the total

thermal conductivity (W m−1 K−1) and T the absolute temperature (K).

For the thermoelectric module, the maximum efficiency (𝜂𝑚𝑎𝑥) is given by equation I.7:

𝜂 =𝑇ℎ − 𝑇𝑐

𝑇ℎ

√1 + 𝑍𝑇𝑚 − 1

√1 + 𝑍𝑇𝑚 +𝑇𝑐𝑇ℎ

(I.7)

Where 𝑍𝑇𝑚 is the average ZT of temperature drop, 𝑇ℎ the temperature of the heat source (hot

side), and 𝑇𝑐 the temperature of the cold side [Zebarjadi et al., 2012; Liu et al., 2019].

Figure I.10 indicates that a higher average ZT accompanied by a large temperature difference

will lead to the highest conversion efficiency, which can be comparable to traditional heat

engines [Zhang et al., 2015].


Commercial thermoelectric materials exhibit ZT about the unit. At the laboratory scale, ZT

reaches about 2. As can be seen in figure I.10, only thermoelectric materials with ZT value

above 2, are able to convert waste heat to a useful electrical energy [Han et al., 2014].

Figure I. 10: Conversion efficiency of thermoelectric materials as a function of the average ZT [Zhang

et al., 2015].

I.7 Factor affecting thermoelectricity

The thermoelectric figure of merit ZT determines the performance of thermoelectric material.

To obtain a high value of ZT, a large power factor and low thermal conductivity are inquired.

The figure of merit ZT is a function of S, 𝜎, and 𝚱 which are coupled and strongly dependent

on many fundamental properties such as electronic structure, material’s crystal structure, and

carrier concentration. Harmonizing the effects of these overlapping dependencies to improve

ZT is a significant challenge [Madsen, 2006; Zheng, 2008].

I.7.1 Seebeck coefficient

The figure of merit ZT is proportional to the square of the Seebeck coefficient. Therefore,

enhancing the Seebeck coefficient plays an important role on improving ZT. The Seebeck

coefficient relies on the electronic band structure of the materials and the density of states

(DOS) in the range of Fermi level. Higher DOS and moderate carrier concentration will

generate a larger Seebeck coefficient. The sign of Seebeck coefficient is determined by the type

of the charge carriers (holes or electrons) [Sharma et al., 2017].

I.7.2 Electrical conductivity

The electrical conductivity of a material is given by the following equation:

𝜎 = 𝑛𝑒µ (I.8)

Where, σ is the electrical conductivity (S m−1), n the charge carrier concentration (m-3), e the

electronic charge (1.6×10-19 A s) and µ the mobility of the charge carriers (m2 V-1 s-1) which are

determined from Hall experiments. The charge mobility expressed as the following equation:


µ =𝑞(𝜏)

𝑚∗

(I.9)

Where, q is the elementary charge (1.6× 10−19 A s), 𝜏 the relaxation time (s) and 𝑚∗ the effective

mass (kg).

The carrier mobility and concentration depend on the temperature. In semiconductors,

conductivity rises with temperature. The conductivity is also affected by various types of

impurities in the material which act as a barrier to the flow of the electrons and scatters them in

the crystal lattice [Pichanuskorn et al., 2010; Sharma et al., 2017].

I.7.3 Thermal conductivity

Thermal conductivity is defined as the ability of a material to conduct heat by lattice vibrations

or phonons. Thermal conductivity is also a function of temperature and can be stated as:

𝑄 = −𝐾𝑙 (𝑑𝑇

𝑑𝑥)

(I.10)

Where Q is the amount of the heat flow through the material, 𝑑𝑇

𝑑𝑥 is the thermal gradient across

the material and 𝐾𝑙 is the coefficient of thermal conductivity of the material. The negative sign

shows that heat flows from the hot to the cold side. The total thermal conductivity 𝐾𝑇 (W m−1

K−1) of a material is given by:

𝐾𝑇 = 𝐾𝑒𝑙 + 𝐾𝑙𝑎𝑡 (I.11)

Where 𝐾𝑒𝑙 is the electronic contribution to the thermal conductivity of the material and 𝐾𝑙𝑎𝑡 is

owing to the lattice vibrations.

The Weidemann-Franz law expresses that electronic thermal conductivity is related to the

Lorenz number according to the relation (I.12):

𝐾𝑒𝑙 = 𝐿𝜎𝑇 = 𝐿𝑛𝑒µ𝑇 (I.12)

Where σ is electrical conductivity (S m-1), T the absolute temperature (K), and L the Lorenz

number (2.4×10-8 J2 K-2 C-2). It can be noticed that 𝐾𝑒𝑙 is a function of σ and T and thus from

equation I.8, the 𝐾𝑒𝑙 also depends on charge carrier concentration (m-3) and carrier mobility (m2

V-1 s-1) .

The lattice contribution of thermal conductivity depends on the phonon vibration

characteristics. According to the kinetic theory of the gases:

𝐾𝑙𝑎𝑡 =1

3𝐶𝑣𝑙

(I.13)


Where C is the heat capacity of the metal (J K-1), v the velocity of phonon vibrations (m s-1) and

l is the mean scattering free path of phonons (m) [Sharma et al., 2017].

I.7.4 Carrier concentration

Figure I.11 indicates the evaluation of thermoelectric properties as a function of the carrier

concentration in insulators, semiconductors, and metals. The electrical conductivity increases

with carrier concentration, limited by mobility at high concentrations. The Seebeck coefficient

decreases with carrier concentration as it is inversely proportional to the carrier concentration.

The thermal conductivity is almost constant and determined by lattice scattering phenomena

until at high concentration charge carriers, they contribute to increase the thermal conductivity.

High conductivity in metals leads to lower Seebeck coefficient which creates lower power

factor compare to semiconductors. On the other hand, an increase in the electronic thermal

conductivity of metals when temperature rises as high electron carrier concentration degrades

the ZT value. The low electrical conductivity in insulators make them unsuitable for

thermoelectric applications. The high charge carrier mobility and moderate carrier

concentration (1018 - 1020 cm-3) in semiconductors make them appropriate for thermoelectric

applications [Wood, 1988; Gayner et al., 2016].

Figure I. 11: Optimizing ZT through carrier concentration tuning [Gayner et al., 2016]

I.8 Thermoelectric Materials

Nowadays, by increasing the number of potential fields of application, thermoelectric materials

are now facing a new challenge which is introducing and developing more efficient, non-toxic

and sustainable compounds to obtain more practical and green technology.

Today, there is a wide variety known of thermoelectric materials. Some of them have been used

for decades while others are the result of more recent researches. Thermoelectric materials can

be categorized by considering different aspects such as their crystal structure, conversion

efficiency, cost, and temperature range.


According to the optimal working temperature, the thermoelectric materials can be classified

into three classes. The table I.1 shows the temperatures classes and the source of heat for each

temperature range [Neeli et al., 2016]:

Table I.1: Heat source and temperature range of thermoelectric materials [Neeli et al., 2016]

Temperature range (°C) Heat source

Low temperature

(˂250 °C)

Condenser ovens, air compressors, air conditioning/ refrigeration,

furnace doors, electric circuits, etc.

Moderate temperature

(250 °C- 650 °C)

Gas turbines exhaust, steam boilers exhaust, drying and baking

ovens, automobile exhausts, etc.

High temperature

(>650 °C)

Steal heating furnace, metal refining furnace, satellite launching

places, aerospace applications and natural decay of radio-isotope

(Pu238)

In the following parts, we briefly review some thermoelectric materials as a function of their

operation temperatures.

I.8.1 Low temperature (˂ 250 °C)

• (Bi,Sb)2(Te,Se)3 based materials: Bi2Te3, Sb2Te3, Bi2Se3 have been known as very

effective semiconductor with a narrow band gap of approximately 0.15 eV, for energy

conversion in the room temperature range. They adopt the tetradymite structure, which is

in the rhombohedral crystal system 𝑅3𝑚 space group. This material is often described as

having a distorted rock-salt structure with a repeat of five layers Te (1)-Bi-Te (2)-Bi-Te (1)

that are held together via van der Waals interactions. Figure I.12 present crystal structure of

these groups of materials [Chen et al., 2014; Witting et al., 2019].

Figure I. 12: Layered structure of Bi2Te3.Bi are octahedrally coordinated by Te, residing on two

inequivalent sites, defining here by tone and notation [Witting et al., 2019].

The high ZT = 1.56 at 27 °C have been reported for the bulk p-type Bi0.53Sb1.48Te3 synthesized

by melt spinning technique followed by a quick spark plasma sintering [Xie et al., 2009].

The ZT vs. temperature for bulk Bi2Te3 with different methods of preparation is summarized in

figure I.13.


Figure I. 13: ZT vs. temperature for bulk Bi2Te3 with different methods of preparation [Kanatzidis,

2010].

They are limited by their toxicity and thermal stability. The bismuth telluride is vaporized at

400 °C as the following reaction:

𝐵𝑖2𝑇𝑒3 → 2𝐵𝑖𝑇𝑒(𝑔) +1

2𝑇𝑒(𝑔)

(I.14)

Which limited its performance up to 300 °C [Skomedal, 2016].

• Polymers: For developing flexible and bio-compatible thermoelectric devices, a special

class of materials such as an electronic conducting polymer is required. This group of

materials is limited due to their low efficiency in energy conversion. It is possible to

improve the ZT value of polymers through enhancing the electronic properties of polymers

via doping with suitable elements and produce organic/inorganic nanocomposite. Table I.2

summarizes ZT values for some polymers at room temperature [Sun et al., 2015].

Table I.2: Figure of merit ZT for some polymers [Neeli et al., 2016]

Polymer ZT (room temperature)

Polythiophene 0.0066

Polypyrole 0.002

Polyaniline 0.051

Polyacetylene 0.47-0.38

Poly (3,4, ethylene dioxytiophen) PEDOT 0.25

Poly (styrnesulphonate) doping in PEDOT 0.42

I.8.2 Moderate temperature (250 °C- 650 °C)

• Group IV-VI tellurides: PbTe has adopted the NaCl-type crystal structure with a space

group of 𝐹𝑚3𝑚. The unit cell is a face-centered cube and all sites have six-coordinate atoms

as presented in figure I.14. It has a direct bandgap ranging about 0.27-041 eV [Xiao et al.,

2018, Beretta et al., 2019].


Figure I. 14: Crystal structure of PbTe [Xiao et al., 2018]

To obtain p-type PbTe, alkali metals like Li, Na, K can be used as acceptor dopants. In n-type

PbTe, elements such as I and Br (doping on Te sites) and Sb, Bi, Al, Ga, and In (doping on Pb

sites) are selected as donor dopants. The ZT vs. temperature for those p and n-type PbTe is

summarized in figure I.15. These materials are limited due to the toxicity of Pb and Te [Pei et

al., 2010; Xiao et al., 2018; Beretta et al., 2019].

Figure I. 15: ZT vs. temperature for p and n-type PbTe [Xiao et al., 2018]

• Skutterudites: Their name is derived from a town called Skuterdasen in Norway where

minerals with this structure such as CoAs3 were discovered in the middle 18th century, used

as a cobalt-blue pigment in the porcelain industry. The general formula of skutterudites is

TPn3 where T is a group IX transition metal such as Co, Rh, or Ir and Pn a nonmetallic atom

such as P, As, or Sb. These compounds are crystallized in the body-centered-cubic structure

(space group: Im3). The unit cell is composed of 32 atoms. The crystal structure of these

atoms has two large voids per unit cells which can be filled by a variety of foreign atoms.

The foreign element acts as a rattle and reduces thermal conductivity due to decreasing the

group velocity of phonons. The filler atoms are selected from lanthanides, actinides, alkali

earth, and even from boron or carbon groups. This generates are called filled or partially

filled skutterudite with general formula RxT4Pn12 where R is filler atom and x shows the

fractional occupancy on the available void site. Figure I.16 presents the crystal structure of

skutterudite [Nolas et al., 1998; Rull-Bravo et al., 2015].


Figure I. 16: Unit cell of the Skutterudite, defined by Oftedal et al. in 1928; a) crystalline structure

described by Kjekshus et al. in 1974, where the octahedral coordination of the metal atom is drawn; b)

for both images, transition metals are represented by red spheres, nonmetallic atoms by yellow spheres

and the voids in the structure or the filled atoms by light blue spheres [Rull-Bravo et al., 2015].

The ZT vs. temperature for those p and n-type skutterudites which reach a significantly high ZT

is summarized in figure I.17.

Figure I. 17: ZT vs. temperature for p and n-type skutterudites:

DD0.7Fe3CoSb12*, DD0.59Fe2.7Co1.3Sb11.8Sn0.2*: DD stand for didymium a natural double filler

consisting of 4.76 % Pr and 95.24 % Nd [Rogl et al., 2017].

• Clathrates: The terms “Clathrates” comes from the Latin word for lattice “Clathri” and the

term “Clatratus” which means protected by a cross bar. Clathrates are periodic solids in

which tetrahedrally coordinated atoms form cages that surround a metal atom. The general

formula AxByC46-Y, where B and C are tetrahedrally bonded to make a framework that forms

cages around the guest atoms A. These materials are considered as “PGCE” materials, as

the metal atoms rattle inside its cage, which reduces the lattice thermal conductivity, while

the electrical conductivity takes place mostly through the frame and not affected by the

guest atom. The clathrates are divided into nine class (I-IX) according to their cage

structure, space group, and intermetallic representing. The most interesting type of


clathrates in thermoelectric applications is type-I, which its crystal structure is shown in

figure I.18 [Iversen et al., 2000; Takabatake et al., 2014; Dolyniuk et al., 2016].

Figure I. 18 : Crystal structure of type-I clathrates: polyhedral view showing two types of polyhedral

cages tetrakaidecahedra (yellow) and pentagonal dodechehedra (blue) [Dolyniuk et al., 2016].

The ZT vs. temperature for some clathrates is presented in figure I.19.

Figure I. 19: ZT vs. temperature for some high-performance thermoelectric clathrates [Beretta et al.,

2019].

• Mg2BIV (Si, Sn, Ge) -Solid solution: As this thesis devoted to Mg-based alloys and their

solid solution, a review of their principle properties, including their thermoelectric

properties, will be presented in detail in section I.9.

I.8.3 High temperature (>650 °C)

• Half-Heussler compounds: Half-Heussler (HH) alloys are semiconducting structure with

the general formula of XYZ, where X is a transition metal, a noble metal or a rare-earth

element, Y is a noble metal or a transition metal and Z is the main group element. They

crystallized in the MgAgAs-type structure with the space group 𝐹43𝑚(figure I.20) while its

bandgap is in the range of 0.1-0.5 eV.


Figure I. 20: The crystal structure of HH alloys [Shi et al., 2016].

The cubic structure in HH, guaranties the high electronic transport properties and also large

thermal conductivity. Therefore, for optimizing the thermoelectric performance of HH alloys,

some techniques such as introducing nano-scale composite and increasing the phonon scattering

on the boundaries are used to degrade their thermal conductivity [Yan et al., 2012; Alam et al.,

2013; Rogl et al., 2017; Shi et al., 2016 ]. The ZT vs. temperature for some HH alloys is

presented in figure I.21.

Figure I. 21: ZT vs. temperature for several HH alloys [Shi et al., 2016].

• Oxides: The most obvious characters of oxide compounds are their thermal and chemical

stability at elevated temperatures. Despite the low thermal conductivity, they have never been

considered as a positional candidate for thermoelectric application due to their low electrical

conductivity till NaCo2O4-like oxide discovered that show good promising thermoelectric

properties.

The oxide compound examined for thermoelectric applications includes both narrow bandgap

(NaxCoO2, BiCuSeO, Ca3Co4O9, CaMnO3, SrTiO3), and wide bandgap (ZnO-based, SnO2-

based, In2O3-based). The electronic properties can be tuned from insulator behavior to metallic

behavior by manipulating their chemical composition via doping and their crystal structure. The

current research is focused on Co-based layered oxides such as Ca3Co4O9 and BiSr3Co2Oy that

crystallize in misfit-layered structures. Na2Co2O4 is the simplest type of layered structure

(figure I.22), with an alternating layer of CoO2 and disordered Na atoms. The CoO2 layers act


as good electron conductors while the sodium layer disturbs phonon transport through the

matrix [Shi et al., 2016].

Figure I. 22: The crystal structure of NaxCoO2[Shi et al., 2016]

The ZT vs. temperature for some oxide compounds is presented in figure I.23.

Figure I. 23: ZT vs. temperature for several oxide compounds [Shi et al., 2016].

• Silicon-Germanium-based alloys: SiGe alloys are broadly used as thermoelectric material for

high-temperature applications such as RTGs due to their high thermal stability. They have the

same crystal structure as diamond. They crystallize in the 𝐹𝑑3𝑚 space group, possessing the

face-centered cubic Bravais lattice. Doping with boron, phosphorus (or arsenic) leads to p-type

and n-type, respectively [Shi et al., 2016].

The ZT vs. temperature for several SiGe-alloys is presented in figure I.24.


Figure I. 24: ZT vs. temperature for several SiGe-alloys [Shi et al., 2016]

I.9 Magnesium-based thermoelectric materials

Mg2X (X= Si, Sn, Ge) compounds receive huge interest regarding their thermal stability, low

cost, non-toxicity, constituent abundance in the earth’s crust, environmentally friendly, low

density, and providing both n and p-type conductions.

According to the classical theory of the thermoelectric materials presented by Vining, the figure

of merit ZT is proportional to parameter given by the following equation:

= (𝑇

300)(𝑚

∗

𝑚𝑒⁄ )

32⁄ (

µ𝐾𝑙𝑎𝑡

⁄ ) (I.15)

Where T is the absolute temperature (K), 𝑚∗effective mass (Kg), 𝑚𝑒 carrier mass, µ carrier

mobility (m2 V-1 s-1), and 𝐾𝑙𝑎𝑡 lattice thermal conductivity (W m-1 K-1), respectively. For

simplicity, the unit of will be omitted throughout this paragraph. The value of the factor of

Mg2X (3.7-14) is larger than 𝛽-FeSi2 (0.05-0.8) and SiGe (1.2-2.6). Therefore, it is expected

that the Mg2X system will achieve a higher ZT [Tani, et al. 2008; Gao et al., 2011].

Mg2X compounds are crystallized in the anti-fluorite structure (space group: 𝐹𝑚3𝑚), CaF2-

type. The unit cell is composed of 12 atoms. In Mg2X structures, the X-4 occupies the face-

centered cubic (fcc) and Mg place in the tetrahedral site. Therefore, each atom of the X group

is surrounded by eight magnesium atoms in a regular cube [Grosch et al., 1996; Liu et al.,

2012].

Figure I. 25: Crystal structure of Mg2X (X=Si, Sn, Ge)


Table I.3 shows the basic properties of Mg2X compounds. These compounds especially Mg2Si,

have very low density. Therefore, the ratio of (ZT/density) for Mg2Si is the highest among

commercial thermoelectric materials. This is an advantage for applications, where weight is a

significant factor.

Table I.3: Properties of Mg2X (X=Si, Sn, Ge) [Zaitsev et al., 2006]

Compound Density

gcm-3

Melting point

K

Spacing

A°

Klat*, (300K)

Wm-1K-1

Mg2Si 1.88 1375 6.338 7.9

Mg2Ge 3.09 1388 6.3839 6.6

Mg2Sn 3.59 1051 6.756 5.9

Table I. 4 shows some electron structure parameters of Mg2X (X = Si, Sn, Ge) compounds. The

band structure of these compounds was studied theoretically and experimentally. Their valence

band is similar to silicon or germanium, with the valence band maximum (VBM) and the Ƭ

point in the Brillouin zone and the conduction band minimum (CBM) at X. The CBM is

considered as having a split band, where the light (CL) and heavy (CH) band are separated by

an energy offset (ΔE). The figure I.26 presents the simplified band structure of Mg2X

compounds [Zaitsev et al., 2006; Santos et al., 2018].

Table I.4: Some parameters of electron structure for Mg2X compounds [Zaitsev et al., 2016]

Compound E0 (0 K)

eV

E0

eV

E1

eV

E2

eV mn/m0 mp/m0

µn (300 K)

cm2V-1s-1

µp (300 K)

cm2V-1s-1

Mg2Si 0.77 - 0.4 - 0.5 0.9 405 65

Mg2Ge 0.74 1.8 0.58 0.20 0.18 0.31 530 110

Mg2Sn 0.35 - 0.16 - 1.2 1.3 320 260

Figure I. 26: Simplified band structure of Mg2X (X=Si, Sn, Ge) compounds. CH, CL and V signify the

heavy conduction band, light conduction band and valence band, respectively [Santos et al., 2018].

The high ZT in Mg2Si can be related to high electron and low hole mobility. Mg2Ge has the

highest electron mobility, but the electron to hole mobility ratio is lower in comparison with

Mg2Si. Mg2Sn has the highest effective mass of DOS (Density Of States). Among Mg2X

compounds, Mg2Sn has the highest hole mobility with a small difference between electron and

hole mobility. This suggests that p-type thermoelectric based on Mg2X alloys should contain a

large fraction of Mg2Sn.


I.9.1 Mg2Sn compounds

The Mg2Sn compound belongs to the class of Zintl phases. The Zintl phases are compounds

which contain two (or more) main groups metals with a large difference in electronegativity

according to Zintl, Klemm and Busmann concept. It has numerous applications such as

Hydrogenation catalyst, Li-ion batteries, and so on [Claus et al., 2006]. Figure I.27 shows the

Mg-Sn phase diagram.

Figure I. 27: Mg-Sn phase diagram [Nayeb-hashemi et al., 1984]

Table I. 5: Outline of studies focused on Mg2Sn compounds

Author

[Ref.]

Compound Dopant Method of

preparation

Type ZT

Max

PF Max

Wm-1K-1

Temperature °C

Song et

al.,

2007

Mg2Sn - Bulk mechanical

alloying, hot

pressing

p 0.02 - 147

Chen et

al.,

2009

Mg2Sn Ag

(2 at. %)

Modified vertical

Bridgman

p - 4×10-3 147

Chen et

al.,

2010

Mg2Sn Ag

(0.5 at. %)

Rocking

Bridgman

furnace

p 0.3 - 200

Le-

Quoc et

al.,

2011

Mg2Sn Ag

(1 at. %)

Co-sputtering

assisted by multi-

dipolar

microwave

plasma

p - 5×10-3 Room

temperature

Choi et

al.,

2012

Mg2Sn Ag

Vacuum melting

and spark plasma

sintering (SPS)

p 0.18 327


An et

al.,

2012

Mg2Sn

Ag

(1 mol%)

Spark plasma

sintering (SPS)

p - 1.4×10-3 52

Varma

et al.,

2018

Mg2Sn Ag

Radio frequency

induction casting

under Ar

atmosphere

p 0.055 - 50

Tani et

al.,

2019

Mg2Sn Li2CO3

(2.5 mol. %)

Chemical

reduction and

spark plasma

sintering (SPS)

p 0.25 - 401

Tani et

al.,

2019

Mg2Sn Sb2O3

(2.5 mol. %)

Chemical

reduction and

spark plasma

sintering (SPS)

n 0.058 - 301

Tani et

al.,

2019

Mg2Sn

- Radio frequency

magnetron

sputtering

p - 8.5×10-4 246

I.9.2 Mg2Si compounds

Mg2Si is a dark blue compound [Stathokostopoulos et al., 2013]. The density is relatively low

(1.88 gcm-3) for this compound while its melting point is rather high (1081 °C). According to

its light weight and high thermophysical properties (such as high melting point and Young’s

modulus (120 GPa), it can be considered as a promising candidate for applications in

electrochemical devices as alternative anode material in rechargeable lithium batteries,

photovoltaic, near-infrared sensing and thermoelectric energy conversion at temperatures

ranging from 227 to 527 °C [Ioannou et al., 2012; Li et al., 2012; Gordin et al., 2018]. Figure

I.28 shows the Mg-Si phase diagram.

Figure I. 28: Mg-Si phase diagram [Nayeb-hashemi et al., 1984]


Table I. 6 : Outline of published studies on Mg2Si compounds

Author

[Ref.] Compound Dopant Method of preparation Type ZT Max

Temperature

°C

Tani et al.,

2005 Mg2Si

Bi

spark plasma sintering

(SPS) n 0.86 589

Song et al.,

2007 Mg2Si -

Bulk mechanical

alloying, hot pressing n 0.13 380

Tani et al.,

2007 Mg2Si

P


(SPS) n 0.33 592

Akasaka et

al., 2007 Mg2Si - Vertical Bridgman n 0.17 383

Zhang et

al., 2008 Mg2Si -

Vacuum melting & Hot

pressing n 0.41 387

Zhang et

al., 2008 Mg2Si Ca

Vacuum melting & Hot

pressing n 0.34 387

Choi et al.,

2011 Mg2Si

Bi (2 a.t. %)

Vacuum melting &


(SPS)

n 0.74 567

Meng et

al., 2011

Mg2Si

Y

(2000 ppm)

Filed- activated &

pressure- assisted

synthesis (FAPAS)

n 0.23 327

Zhou et al.,

2011 Mg2Si

-

Solid state reaction &

Microwave radiation

techniques

n 0.13 327

You et al.,

2011 Mg2Si Bi

Solid state reaction,

Mechanical radiations,

Consolidation via hot

pressing (HP)

n 0.7 550

Sakamoto

et al., 2011 Mg2Si -

Plasma activated

sintering technique n 0.6 588

Bux et al.,

2011 Mg2Si

Bi

Ball milling, high-

pressure sintering n 0.7 502

Fiameni et

al., 2012 Mg2Si

Bi,

SWCNHs*

Ball milling, thermal

treatment & spark

plasma sintering (SPS)

n 0.39 600

Hayastu et

al., 2012 Mg2Si

Ni (5Wt %),

Sb

Plasma activated

sintering n 0.97 577

Berthebaud

et al., 2013 Mg2Si Ag

Microwave irradiation

followed spark plasma

sintering

p 0.35 497

Berthebaud

et al., 2013 Mg2Si Sb

Microwave irradiation

followed spark plasma

sintering

n 0.7 497

Tani et al.,

2013 Mg2Si Al

Reduction reaction with

Al2O3 and SPS n 0.58 592

Tani et al.,

2013 Mg2Si Bi


Bi2O3 and SPS n 0.68 592


Tani et al.,

2013 Mg2Si Sb


Sb2O3 and SPS n 0.63 592

Hu et al.,

2014 Mg2Si Al

Solid state reaction and

SPS n 0.58 571

Ioannou et

al., 2014 Mg2Si Bi

Ball milling, thermal

treatment n 0.68 537

Arai et al.,

2015 Mg2Si0.995Ge0.05 Sb, Ge

Spark plasma sintering

(SPS) n 0.74 483

Chen et al.,

2015 Mg2Si Bi (1 a.t. %)

Spark plasma sintering

(SPS) n 0.6 502

Kim et al.,

2016 Mg2Si Al, Bi


spark plasma sintering,

hot press

n 1.02 600

Kim et al.,

2017 Mg2Si Bi, Al

Hot pressing, spark

plasma sintering (SPS) n 0.98 600

Kitagawa et

al., 2018 Mg2Si Sb

Si sludge, pulse-current


Li et al.,

2018 Mg2Si Sb

High pressure spark

plasma sintering (SPS) n 0.94 602

SWCNHs*: Single Wall Carbon Nanohorns

I.9.3 Mg2Ge compounds and its solid solutions

Mg2Ge compound is an interesting material for technological applications as an infrared

detector in the wavelength range 1.2-1.8 µm for optical fibers and also thermoelectric

applications [Kaur et al., 2016]. Figure I.29 shows the Mg-Ge phase diagram.

Figure I. 29: Mg-Ge phase diagram [Yan et al., 2010]


Mg2Ge compounds are limited due to their deliquescent problem, which leads to decompose in

water or humid air, and should be stored with special care [Gao et al., 2015]. Mg2Ge1-xSix and

Mg2Ge1-xSnx are investigated as potential thermoelectric candidates. Among the solid solutions

Mg2Ge1-xSnx, despite their high thermal conductivity, are most interesting p-type candidate due

to their favorable hole to electron mobility ratio [Fedorov et al., 2006]. The bandgap of Mg2Ge1-

xSnx decrease with raising x, i.e. the bandgap is about 0.52 eV for Mg2Ge0.4Sn0.6, and 0.46 eV

for Mg2Ge0.2Sn0.8, respectively [Jiang et al., 2013; Ryu et al., 2019]. The best band convergence

for Mg2Ge1-xSnx is observed while the x=0.75[Liu et al., 2015].

Figures I.30 shows the Mg2Ge-Mg2Sn phase diagram [Jung et al., 2010].

Figure I. 30: Calculated phase diagram of the Mg2Ge-Mg2Sn section with experimental data [Jung et

al., 2010]

Table I. 7 : Outline of published studies on Mg2Ge compounds and its solid solutions

Author

[Ref.]

Compound Dopant Method of

preparation

Type ZT PF

Wm-1K-1

Temperature °C

Mars et

al.,

2009

Mg2Si0.6Ge0.4Bi0.02 Bi Tantalum-tube

weld melting in

and hot pressing

n 1.0 - 527

Mars et

al.,

2009

Mg2Si0.6Ge0.4Ag0.02 Ag

Melting in

tantalum crucibles

and hot pressing

p 0.26 - 647

Chuang

et al.,

2010

Mg2Ge Ag

Magnetron co-

sputtering

p - 10-5 427

Jiang et

al.,

2013

Mg2Ge0.6Sn0.4 Ag Ta-tube melting,

pulverized and hot

pressing

p 0.38 - 402

Gao et

al.,

2015

Mg2.2Ge1-xSbx Sb

Tantalum-tube

weld melting in

and hot pressing

n 0.2 - 467


Liu et

al.,

2015

Mg2Sn0.75Ge0.25 -

Ball milling and

Hot pressing

n 1.4 - 450

Santos

et al.,

2017

Mg2Ge

Bi One step reaction

Ge with MgH2 and

Spark plasma

sintering (SPS)

n 0.32 - 477

Yuan et

al.,

2019

Mg2Ge0.6Sn0.4 Li

Ball milling and

Hot pressing

p 0.75 - 450

I.9.4 Mg2Si1-XSnX solid solutions

The Mg2(Si, Sn) is a solid solution formed by two isostructural Mg2Si and Mg2Sn. The solid

solution Mg2Si1-XSnX form while some of the Si atoms in the Mg2Si unit cell are replaced by

Sn atoms. As Mg2Si1-XSnX follows Vegard’s law, the lattice constant and band gap of it can be

calculated by a linear combination of the properties of Mg2Si and Mg2Sn [Bahk et al., 2014;

Jang et al., 2018].

In the equilibrium phase diagram of the Mg2Si-Mg2Sn pseudo binary system, the Mg2Si1−xSnx

has an immiscibility gap between x = 0.4-0.6 or x = 0.2-0.7 and the Sn-rich phase coexists with

the Si-rich phase in this composition range as shown in figure I.31 [Kim, 2018].

Figure I. 31 : Optimized phase diagram of the Mg2Sn-Mg2Si binary section in the Mg-Si-Sn system

[Jung et al., 2007]

The power output per unit mass of Mg2Si1-XSnX compounds can be also higher than many

known thermoelectric material systems. For example, the density of Mg2Si0.4Sn0.6 is only 2.9 g

cm-3, much lower than that of PbTe (8.27 g cm-3), Bi2Te3 (7.93 g cm-3) and CoSb3 (7.625 g cm-

3) and it can be compared with Si0.8Ge0.2 (2.93 g cm-3) [Bashir et al., 2014].


Table I. 8: Outline of published studies on Mg2Si1-XSnX compounds

Author

[Ref.] Compound Dopant

Method of

preparation Type ZT Max

Temperature

°C

Song et

al., 2007 Mg2Si0.6Sn0.4 -

Bulk mechanical

alloying, hot pressing P 0.13 380

Zhang et

al., 2008 Mg2Si0.6Sn0.4 Sb

Melting, Ball milling,

hot pressing n 1.1 507

Zhang et

al., 2008 Mg2-xLax(SiSn)

La

X=0.005

Melting, Ball milling,

hot pressing n 0.81 537

Tani et al.,

2008 Mg2Si0.9Sn0.1 Al

Spark plasma


Liu et al.,

2011 Mg2(1+x)Si0.5Sn0.5 Sb


spark plasma sintering n 1.25 527

Gao et al.,

2011 Mg2Si0.7Sn0.3 Sb

Melting, Solid-state

reaction, Hot press

sintering

n 0.55 347

Gao et al.,

2011 Mg2Si0.5-XSn0.5

Sb

X=0.013 B2O3 flux in air n 0.9 507

Khan et

al., 2013 Mg2Si0.55Sn0.4Ge0.05

Bi

Powder method, ball-

milling n 1.4 480

Khan et

al., 2013 Mg2Si0.55Sn0.4Ge0.05

Sb

Powder method, ball-

milling n 1.2 489

Zhang et

al.,2013 Mg2Si0.6Sn0.4 Bi

Melt spinning, Spark

plasma sintering

(SPS)

n 1.2 300

Liu et al.,

2013 Mg2.16Si0.4Sn0.6 Bi


spark plasma sintering n 1.4 527

Gao et al.,

2014 Mg2.2Si0.7Sn0.3 Sb

B2O3 flux, Hot-

pressing n 1.1 487

Du et al.,

2015 Mg2(1+x)Si0.2Ge0.1Sn0.7 Sb B2O3 flux and SPS n 0.94 507

Zheng et

al., 2016 Mg2Si0.6Sn0.4 Sb

Mechanical alloying,

Spark plasma

sintering (SPS)

n 1.4 400

Tang et al.,

2016 Mg2(1-x)Li2xSi0.4Sn0.6

Li

X=0.07

Melt spining, Spark

plasma sintering

(SPS)

p 0.58 487

Tang et al.,

2017 Mg2-xAgxSi0.4Sn0.6

Ag

X=0.05

Melt spining, Spark

plasma sintering

(SPS)

p 0.45 417

Jang et al.,

2018 Mg2Si0.6Sn0.4

Sb

B2O3 encapsulation

method

n 0.55 480

Li et al.,

2018 Mg2Si0.35Sn0.65 Sb

High temperature-

gradient solidification n 1.3 457

I.10 Strategies to improve ZT of Mg2X thermoelectric materials

The enhancement of ZT in thermoelectric materials is challenging due to the interdependency

of thermoelectric parameters. Most of the strategies are developed to improve ZT by means of


the power factor (𝑆2𝜎) by optimizing carrier concentration or reducing lattice thermal

conductivity) by introducing the scattering centers or creating a combined effect of both factors.

These parameters are the function of scattering factor (r), carrier effective mass (𝑚∗), and

carrier mobility (µ), and their interdependency limit ZT ≈ 1 in bulk materials. Based on the

kinetic definition the Seebeck coefficient is the energy difference between the Fermi energy

and the average energy of the mobile carrier. If the carrier concentration (n) is increased, the

Fermi energy, as well as the average energy, rises. However, the Fermi energy increases more

quickly than the average energy when carrier concentration is raised. As a result, the Seebeck

coefficient decreases, dragging the power factor down rapidly. Therefore, in attempting to

improve ZT for most homogeneous materials, the carrier concentration increases the electrical

conductivity but reduces the Seebeck coefficient.

The individual relationships between the Seebeck coefficient, electrical conductivity, thermal

conductivity, and carrier concentration (electrons or holes) in a degenerate semiconductor can

be expressed as:

𝑆 =8𝜋2𝐾𝐵

2

3𝑒ℎ2𝑚∗𝑇 (

𝜋

3𝑛)

23

(I.16)

where 𝐾𝐵 is the Boltzmann constant (1.38×10-23 J K-1), e the electronic charge (1.6×10-19 A s),

ℎ the Planck’s constant (6.63×10-34 J s), 𝑚∗ effective mass (kg) and n the charge carrier

concentration (m-3). By considering equations (I.8), (I.9), and (I.12), the importance of

controlling carrier concentration is highlighted. Therefore, a good thermoelectric material must

have a large power factor, high effective mass, high mobility, and low lattice thermal

conductivity which are forming the concept of ‘Phonon-Glass Electron-Crystal’ previously

discussed in section I.2. This generally occurs in heavily doped semiconductors with optimum

carrier concentration between 1019 and 1021 cm-3 [Slack et al., 1994; Alam et al., 2013; Bashir

et al., 2014; Kim et al., 2020].

For improving ZT of Mg-based thermoelectric materials some methods are suggested such as

alloying [Gayner et al., 2016], solid solutions [Jiang et al., 2014], nanostructuring [Cederkrantz

et al., 2012], band engineering [Liu et al., 2012], magnesium deficiency [Santos et al., 2017]

and dimension reduction [Vineis et al., 2010; Arab Pour Yazdi et al., 2018] which are discussed

in this section.

I.10.1 Alloying

Alloying is known as atomic substitution of one element by one or more isoelectronic elements

by aiming of creating point defects. In this way, the crystal structure is remaining, while the

increased atomic mass contrast favors phonon scattering which can reduce the thermal

conductivity without affecting the electrical conductivity due to the difference in the

wavelength of phonon and electrons [Alam et al., 2013; Gayner et al., 2016; Kaur et al., 2017;

Santos et al., 2018].


The dominated scattering mechanism can be determined by the Hall mobility dependence forms

as a function of the temperature. The Hall mobility changes with temperature following form

µ~𝑇3

2⁄ or µ~𝑇−3

2⁄ , while the ionized impurity and acoustical phonon scattering are dominated,

respectively. The Hall mobility changes with temperature following µ~𝑇1

2⁄ or µ~𝑇−1

2⁄ , if the

alloy or optical phonon scattering are dominated, respectively. The Hall mobility changes with

temperature following µ~𝑇0 in the case of neutral impurity scattering [Bashir et al., 2014; Chen

et al., 2015; Mao et al., 2018].

I.10.2 Solid solution

Historically, the most successful strategy to improve ZT has been to modify the promising

compound by introducing point defects through the synthesis of isostructural solid solutions.

The solid solution features make changes in the crystal lattice (i.e., disorder) which produces

strong phonon scattering centers and reduce thermal conductivity [Kanatzidis, 2010].

Solid solutions of Mg2X (X= Si, Sn, Ge) pseudo-binary compounds: Mg2Si1-XSnX, Mg2Si1-

XGeX, and Mg2Ge1-XSnX have attracted interest due to huge effect of alloying on their lattice

thermal conductivity. The mass-difference scattering considers as the main mechanism for

decreasing the lattice thermal conductivity. Therefore, the large mass difference between Si

(28.1 a.m.u), Ge (72.6 a.m.u) and Sn (118.71 a.m.u) guaranties the reduction of thermal

conductivity. Figure I.32 shows the thermal conductivity reduction for magnesium-based

ternary alloys. The most significant thermal conductivity reduction occurs while the atomic

mass difference is greater.

Mg2Si-Mg2Sn pseudo-binaries are the most interesting compounds for thermoelectric

applications.

Figure I. 32: Lattice thermal conductivity as a function of the composition of magnesium-based

ternary alloys at room temperature [Bashir et al., 2014]

I.10.3 Dimension reduction

As previously mentioned in section I.2, Dresselhaus and Hicks, brought up the new concept of

selectively and separately modifying thermoelectric material properties based on the dimension

reduction of materials from bulk (3D) to thin film (2D), wire (1D) and dot (0D). They


theoretically showed that by using two-, one-, or zero-dimensional structures made of

conventional one could obtain a significant increase in the figure of merit (ZT ≈ 2.6).

By reduction of the dimension of the materials, the new physical phenomenon appeared which

is offering the possibility of varying independently Seebeck coefficient, electrical conductivity,

and thermal conductivity. In their theory, the improvement of ZT is mainly based on two effects:

• Quantum confinement effect on electronic density of states (D.O.S.) which enhances

the Seebeck coefficient.

• Scattering of phonons which reduces the thermal conductivity.

Figure I.33 shows that the reduction of materials dimension from bulk (3D) to quantum dot

(0D) is enhanced by the density of states (DOS) given by the presence of peaks displaying the

quantum confinement.

By considering the Beth-Sommerfeld expansion for the Seebeck coefficient:

𝑆 =𝜋2

3

𝐾𝐵

𝑒(𝐾𝐵𝑇) [

1

𝑛(𝐸)

𝑑𝑛(𝐸)

𝑑(𝐸)+

1

µ(𝐸)

𝑑µ(𝐸)

𝑑𝐸]𝐸=𝐸𝐹

(I.17)

where 𝐾𝐵 is the Boltzmann constant (1.38×10-23 J K-1) , e the elementary charge (1.6× 10−19 A

s), n(E) the carrier density (m3) at the energy E, 𝜇(𝐸) the mobility, and the 𝐸𝐹 presents the Fermi

energy. Based on equation (I.17), the Seebeck coefficient is directly proportional to the

derivative of the density of states which is dependent on the energy. So the enhancement of the

state density allows increasing the Seebeck coefficient [Dresselhaus et al., 2007].

Figure I. 33: Electronic density of states for a) a bulk 3D crystalline semiconductor, b) a 2D quantum

well, c) a 1D nanowire (nanotube), and d) 0D quantum dot [Dresselhaus et al., 2007].

In two dimensional (2D) materials like thin films, the layer interfaces can act as scatter centers

for phonons which end in the reduction of thermal conductivity, but the thickness of the layer

should be less than the phonon mean free path. Therefore, thin films offer higher ZT value

compared to bulk materials [Vineis et al., 2010].

Besides, thin film materials with optimized ZT are capable to reduce the size of current

thermoelectric devices in order to address them in miniaturized applications like Micro


Electronic and Mechanical Systems (MEMS) [Gould et al., 2011] and Internet of Things (IoT)

[Lopez et al., 2017].

Different methods were suggested for producing thermoelectric thin films such as flash

evaporation [Zhao et al., 2012], pulsed laser deposition (PLD) [Yamada et al., 2007; Chen et

al., 2016], electrochemical deposition [Park et al., 2009], metal-organic chemical vapor

deposition (MOCVD) [You et al., 2012], sputtering [Liu et al., 2011; Zhao et al., 2014; Zhao

et al., 2015; Bellanger et al., 2015; Arab Pour Yazdi et al., 2018] and molecular beam epitaxy

(MBE) [Daniel et al., 2015].

I.10.4 Nanostructuring

Nanoscience and nanotechnology are developing fields which give information about materials

containing building blocks with at least one dimension in size less than 100 nm.

Nanostructuring is a set of structure modifications at the nanoscale and also known as the one

of the most effective approaches to improve the thermoelectric properties of the materials. This

approach includes nanocomposite, reduction of grain size, and super lattices.

Nanostructuring can raise the density of states near the Fermi level through quantum

confinement thus enhancing the Seebeck coefficient. Besides, as mean free path of the electrons

is much shorter than that of phonons in heavily doped semiconductors, nanostructuring aims at

introducing a large density of interfaces in which phonons over a large mean free path range

can be scattered more effectively than electrons as presented in figure I.34 [Vineis et al., 2010;

Chen et al., 2012].

Figure I. 34: Schematic diagram illustrating various phonon scattering mechanism in nanograined

thermoelectric materials [Vineis et al., 2010].

I.10.5 Band engineering

In low dimensional materials, band engineering considers as quantum confinement effect which

leads to the modification of band structure. Band engineering such as resonant level and band

convergence can be obtained as a result of alloying or chemical doping in bulk materials

[Bourgeois et al., 2013; Saparamadu et al., 2017; Mao et al., 2018]. Doping offers to control

the semiconducting properties through adjusting carrier concentration which has a direct

influence on electrical conductivity and Seebeck coefficient [Ioannou et al., 2014].


Mg2X (X= Si, Sn, Ge) compounds have two conduction bands with a small band offset. In

Mg2Sn, the relative positions of the light (CL) and heavy (CH) conduction bands are inversed

comparing to Mg2Si and Mg2Ge, so by tuning the chemical composition of Mg2Si1-XSnX,

Mg2Si1-XGeX solid solutions, the band offset can be controlled and at certain composition like

Mg2Sn0.7Si0.3 effective band convergence is obtained as shown in figure I.35 [Liu et al., 2012;

Liu et al., 2015; Mao et al., 2018; Kim et al., 2020].

Figure I. 35: Relative position of the heavy and light conduction band vs. Sn content for Mg2Si1-XSnX.

The red dotted line shows energy variation for the heavy conduction band as the Sn content increases,

while the blue and black dotted lines represent the motions of the light conduction band and the

valence band, respectively. Colored dots present the calculated data for different Sn Contents [Liu et

al., 2012].

Band engineering was used too for Mg2Sn1-xGex compounds and in bulk Mg2Sn0.75Ge0.25, high

ZT = 1.4 at 450 °C was obtained as a result of effective band convergence [Liu et al., 2015].

I.10.6 Microstructural defects

Microstructural defects such as point defects, dislocations, stacking faults, grain boundaries,

twin boundaries and nanoprecipitate (figure I.36) can directly impact the thermoelectric

parameters due to their influence on the transport of electrons and phonons. They can disrupt

the phonon propagation by distorting the ideal crystal structures.

The microstructural defects can cause shortening the phonon mean free path which could span

from a few angstroms up to several hundred nanometers. By designing defects with

characteristic dimensions in a board range, phonons with different wavelengths can be

effectively scattered, thus the lattice thermal conductivity can be reduced [Mao et al., 2018].


Figure I. 36: Schematic views for (a) point defects, (b) dislocations, (c) stacking faults, (d) grain

boundaries, (e) twin boundary, and (f) nanoprecipitate [Mao et al., 2018]

Kato et al. [Kato et al., 2009] studied the point defects in Mg2Si by density functional theory

and proposed the major defect points in both Mg-poor and Mg-rich system as donor-like Mg

interstitials.

Viennois et al. [Viennois et al., 2012] discussed the stability of the native defects in the parent

compounds Mg2X (X=Si, Sn, Ge) with antifluorite structures. They have calculated the

formation energy of:

1. Interstitial defects in the center of the supercell of 96 atoms

2. Vacancies (mono-, bi-, and tri- vacancies)

3. Antisite defects

The calculations have been carried out for the neutral case, for example without adding any

additional charge on the defects. The favorable defects in the Mg2X are not the same as a result

of the difference in the nature of X. The favorable defects for Mg2X compounds are summarized

in table I.9.

Table I. 9: Fermi level shift induced by the most stable defects in Mg2X (X= Si, Ge, Sn)

Compounds Defect type in Mg2X Fermi level shift (eV)

Mg2Si

𝑉𝑀𝑔𝑆𝑖 : bi-vacancies

𝐼𝑀𝑔: Interstitial defect

𝑉𝑀𝑔2𝑆𝑖: tri-vacancies

0

0.46

-0.14

Mg2Ge

𝑉𝑀𝑔: Mg vacancy

𝑉𝑀𝑔𝐺𝑒: bi-vacancies

𝐺𝑒𝑀𝑔: Antisite defect

-0.2

-0.16

0

Mg2Sn

𝑉𝑀𝑔: Mg vacancy

𝑆𝑛𝑀𝑔: Antisite defect

𝐼𝑀𝑔: Interstitial defect

-0.17

0

0.125


They noted that when going from X=Si to X=Sn the 𝑉𝑀𝑔 becomes more favorable. They also

found out that the p-type doping is induced by 𝑉𝑀𝑔 vacancy and the 𝑉𝑀𝑔2𝑋 tri-vacancies and that

n-type doping is induced by the 𝐼𝑀𝑔 Interstitial defect. The intrinsic n-type doping in pure Mg2Si

can be attributed to the presence of Mg atoms in the interstitial positions because it is the most

stable defect, while in the cases of Mg2Ge and Mg2Sn another type of the defects is more stable,

p-type doping becomes more possible for them which is not naturally probable for pure Mg2Si.

Liu et al. reported on the influence of intrinsic point defects on the electronic transport

properties of Mg2X (X = Si, Ge, Sn) systems. They showed that Mg vacancies and interstitial

Mg are assumed to be the main defects in Mg2X compounds according to their relatively low

formation energies. Mg vacancies and interstitial Mg behave as acceptor and donor sites,

respectively, so it can tune the carrier concentration [Liu et al., 2016].

Tani and Kido studied the formation energy and the atomic structure of impurities in Mg2Sn

using first-principles plane-wave total energy calculations. In the Mg-site substitution, the order

of the formation energies of these impurities was Au < Ag < Cu. In the Sn-site substitution, the

order of the formation energies of these impurities was Au < (Ag, Cu). Figure I.37 shows the

atomic chemical potential (Mg or Sn) dependence of the calculated formation energies for

group IB impurities (Cu, Ag, and Au) in Mg2Sn. In Mg-rich system the Cu substitution occurs

on Sn-site mainly, as it has lower formation energy, while in Sn-rich system the Cu substitution

on Mg-site becomes more probable [Tani et al., 2012] .

Figure I. 37: Atomic chemical potential (Mg or Sn) dependence of the calculated formation energies

for impurities (Cu, Ag, and Au) in Mg2Sn. The solid and dashed line refer to impurities are substituted

on Mg and Sn site, respectively [Tani et al., 2012].


I.11 Conclusion

Extensive fossil fuel consumption lead to environmental problems such as global warming,

climate-changing, greenhouse gas emission, ozone layer depletion, acid rains are enlarged.

Thermoelectric materials have attracted global interest according to their ability to convert

directly thermal to electrical energy and vice versa, thus providing a clean and renewable supply

of energy.

The efficiency of thermoelectric materials refers to their dimensionless figure of merit (ZT),

which depends on the temperature (K), the square of the Seebeck coefficient (V K-1), the

electrical conductivity (S m-1), and the inverse of total thermal conductivity (W m-1 K-1).

In this chapter, thermoelectric phenomena and materials development were discussed.

According to the optimal working temperature, the thermoelectric materials can be classified

into three classes; low temperature, moderate temperature and high temperature.

The Mg2X (X = Si, Sn, Ge) and their solid solutions attract more attention due to their thermal

stability, low cost, none toxicity, constituent abundance in the earth’s crust, low density and

their potential for providing both n and p-type conductions and so on in moderate temperature

range.

Some strategies are developed to improve ZT of Mg-based thermoelectric materials such as

alloying, solid solutions, dimension reduction, nanostructuring, band engineering, and micro

structural defects. Alloying and solid solution lead to lower thermal conductivity without

affecting the electrical conductivity by introducing the point defects. Many works are focused

on bulk materials, while thin films are required for the integration of thermoelectric materials

in miniaturized devices and optimizing ZT in compliance with the low thermal conductivity of

low dimensional structures. Different methods were proposed for producing thermoelectric thin

films such as flash evaporation, pulsed laser deposition, electrochemical deposition, metal-

organic chemical vapor deposition, sputtering and molecular beam epitaxy. Nanostructuring

includes nanocomposite, reduction of grain size, and super lattices. This approach can raise the

density of states near the Fermi level through quantum confinement thus enhanced the Seebeck

coefficient. Moreover, as mean free path of the electrons is much shorter than that of phonons

in heavily doped semiconductors, nanostructuring employs to introduce a large density of

interfaces in which phonons over a large mean free path range can be scattered more effectively

than electrons. Band engineering includes band convergence, doping and resonant states.

Doping offers to control the semiconducting properties through adjusting carrier concentration

which has a direct influence on electrical conductivity and Seebeck coefficient. Microstructural

defects such as point defects, dislocations, stacking faults, twin boundaries, grain boundaries,

and nanostructures which can directly impact the thermoelectric parameters due to their

influence on the transport of electrons and phonons. They can disrupt the phonon propagation

by distorting the ideal crystal structures. The influence of intrinsic point defects on the

electronic transport properties of Mg2X (X = Si, Ge, Sn) systems was discussed. Mg vacancies

and interstitials are assumed to be the main defects in Mg2X compounds according to their


relatively low formation energies. Mg vacancies and interstitials behave as acceptor and donor

sites, respectively, so it can tune the carrier concentration.


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Chapter 2

Thin films synthesis technique and

characterization devices

Table of contents

II.1 Introduction .................................................................................................................................. 55

II.2 Physical vapor deposition (PVD) ................................................................................................. 55

II.3 Magnetron sputtering .................................................................................................................... 56

II.3.1 Principle of magnetron sputtering ........................................................................................ 56

II.3.2 Description of the experimental device used in this study ................................................... 57

II.4 Characterization devices ............................................................................................................... 58

II.4.1 Measurement of film’s thickness ......................................................................................... 58

II.4.2 Morphological characterization and determination of the film composition ....................... 58

II.4.3 Structural characterization ................................................................................................... 58

II.4.4 Electronic transport properties ............................................................................................. 59

II.4.4.1 Principle of Hall effect measurement .......................................................................... 59

II.4.4.2 Description of the experimental device of Hall measurement ..................................... 60

II.4.5 Measurements of the thermoelectric properties of the coatings ........................................... 61

II.4.5.1 Electrical conductivity measurement .......................................................................... 61

II.4.5.2 Thermal conductivity measurement............................................................................. 63

II.4.5.3 Seebeck coefficient measurement: ............................................................................... 65

II.4.6 Thin Film Analyzer (TFA) for thermoelectric properties .................................................... 66

II.4.6.1 The second-generation chip: ....................................................................................... 66

II.4.6.2 Electrical conductivity measurement by TFA ............................................................. 67

II.4.6.3 Thermal conductivity measurement by TFA ................................................................ 68

II.4.6.4 Seebeck measurements by TFA ................................................................................... 68

II.4.6.5 Calculation of the figure of merit ZT........................................................................... 69

II.4.6.6 Description of the thermoelectric properties by TFA ................................................. 70

II.4.7 Bandgap measurement: ........................................................................................................ 70

II.5 Conclusion .................................................................................................................................... 71

II.6 References .................................................................................................................................... 72

List of Figures

Figure II. 1 : PVD processing techniques: (a) vacuum evaporation, (b) and (c) sputter deposition in a

plasma environment, (d) sputter deposition in a vacuum, (e) Ion plating in a plasma with a

thermal evaporation source, (f) Ion plating with a sputtering source, (g) Ion plating with an arc

vaporization source, and (h) Ion Beam-Assisted Deposition (IBAD) with a thermal evaporation

source and ion bombardment from an ion gun [Mattox, 2010] .................................................... 55

Figure II. 2 : Schematic diagram of the working principle of cathodic magnetron sputtering .............. 57

Figure II. 3 : a) magnetron sputtering device (Alcatel 604): 1- deposition chamber, 2- pulsed DC

supply, 3- gas flow control system, 4- vacuum system control, 5- DC supply (MDX 500,

Advanced Energy), b) internal deposition chamber with four targets and rotative substrate holder

...................................................................................................................................................... 58

Figure II. 4 : The applied external magnetic field, Bz, perpendicular to the direction of charge flow,

leads to accumulation of negative charges to gather on the left side and positive charges on the

right side. This induces an electric field Ey which balances Bz. The voltage across the sides is the

Hall voltage, VH , which is obviously different from the bar voltage, Vx , measured across the

length of the bar [Mirza et al., 2013]. ........................................................................................... 59

Figure II. 5 : Homemade Hall effect vs. Temperature setup with 4 probe configuration van der Pauw

method (NIST procedure) ............................................................................................................. 61

Figure II. 6 : Four-point probe configuration for electrical resistivity measurement of a) bulk samples

b) thin films on an insulating substrate. ........................................................................................ 62

Figure II. 7 : Sample of arbitrary shape with contacts for van der Pauw method ................................. 62

Figure II. 8 : Schematic of the experimental configuration for 3ω traditional method [Wang et al.,

2019] ............................................................................................................................................. 64

Figure II. 9 : TFA setup : 1) K-REG, 2) Electric Rack, 3) Turbo Pump 4) TFA unit, 5) PC and Monitor

...................................................................................................................................................... 66

Figure II. 10 : a) Front view of chip with functional structures for the Seebeck coefficient, van der

Pauw and 3ω thermal conductivity, b) chip covered by metal mask, c) chip with sample

deposited, ready to be measured. .................................................................................................. 67

Figure II. 11 : Setup with sample for thermal conductivity measurements [Manual-TFA] .................. 68

Figure II. 12 : Van der Pauw setup with heater and resistance thermometer on the larger membrane

[Manual-TFA] .............................................................................................................................. 69

Thin films synthesis technique and characterization devices 55

II.1 Introduction

In this chapter, the pulsed DC magnetron sputtering, and its principle will be discussed as one

of the physical vapor deposition technique used in this study for synthesis of thin films. The

characterization devices which are employed for the study of the structure and microstructure

of the thin films will be presented and finally, the different techniques for electronic transport

and thermoelectric properties measurements will be discussed in details.

II.2 Physical vapor deposition (PVD)

Physical vapor deposition (PVD) describes a variety of vacuum deposition methods which can

be used to develop thin films and coatings. PVD technique, as its name implies involves

physical deposition process in which atoms, ions or molecules of materials from its source are

vaporized by physical means (high-temperature vacuum or gaseous plasma) and transport in

the form of vapor through the vacuum or low-pressure gaseous environment from its source to

the substrate and the vapor undergoes condensation on the substrate to form a thin film.

There are several PVD methods, but the main categories of PVD processing can be classified

in arc vacuum deposition (evaporation), sputter deposition and ion plating as shown in figure

II.1.

Figure II. 1: PVD processing techniques: (a) vacuum evaporation, (b) and (c) sputter deposition in a

plasma environment, (d) sputter deposition in a vacuum, (e) Ion plating in a plasma with a thermal

evaporation source, (f) Ion plating with a sputtering source, (g) Ion plating with an arc vaporization

source, and (h) Ion Beam-Assisted Deposition (IBAD) with a thermal evaporation source and ion

bombardment from an ion gun [Mattox, 2010]


II.3 Magnetron sputtering

Magnetron sputtering method is an improved film deposition technology, using direct current,

pulsed direct current or radio frequency (RF) as power supply, and has been widely employed

to large-scale producing of high-quality films [Huang et al., 2009; Fang et al., 2013]. It can be

used to deposit a very large number of metals, alloys, polymers, ceramic thin films onto a wide

range of substrate materials. The thickness of the deposited film by this technique can vary from

nanometer to a few tens of micrometers [Swan et al., 1988]. Magnetron sputtering has

numerous advantages such as high deposition rate, good reproducibility, obtaining films with a

high adhesion, easy way to control the film composition and homogeneity on a large-area

substrate, environmentally friendly [Mattox, 2010]. Furthermore, by magnetron sputtering the

deposition of materials with metastable phase is possible as it is able to synthesize materials

outside of thermodynamic equilibrium. Therefore, it finds a wide range of applications such as

hard, wear-resistance coatings, corrosion resistance coating, low friction coatings, decorative

coatings, and coating with specific electrical or optical properties for application in energy and

environment [Kelly et al., 2000; Constantin et al., 2011].

II.3.1 Principle of magnetron sputtering

Figure II.2 illustrates the schematic illustration of the cathodic magnetron sputtering. The

targets are placed parallel to the substrate holder. The reactor is pumped down by using the

pumping group (primary and secondary pumps) until the residual vacuum reaches a residual

pressure below 10−4 Pa before gas injection. For sputtering, low pressures are required for

several reasons as maintaining high ion energies, preventing too many atom-gas collisions after

ejection from the target, and provides reducing gaseous contamination of deposited films. The

inert gas (typically Ar) feeds into the reactor with a controlled flow rate in order to ignite a

plasma. Generally, the working pressure is kept between 0.1-10 Pa. The plasma is created since

the power supply generates the difference of potential between the target and the wall of the

reactor which acts as the anode. Due to the electrical field, the Ar+ ions are attracted by the

target (cathode), and makes the atoms ejected from the target. On the other hand, the secondary

electrons are produced which cause a further ionization of the Ar gas and maintains the plasma.

Two magnets are placed behind the target which help to constrain secondary electron motion

to the vicinity of the target as the magnetic field is parallel to the target surface and

perpendicular to the electrical field. Therefore, a dense plasma in the target region is obtained

as a result of the high ionization of the Ar. So, the ion bombardment of the target increases

which leads to a higher sputtering rate and deposition rate as well. Furthermore, by increasing

the ionization efficiency in the magnetron sputtering, some advantages exist such as lower

operating voltages (500 V, compared to 2 - 3 kV) than is possible in the basic sputtering method

and the discharge can be maintained at lower operating pressures (10-1 Pa, compared to 1 Pa).

However, two drawbacks appear during magnetron sputtering: first heterogeneous erosion of

the target. In fact, the magnetic field lines are confined right to the top of the magnets and the

sputtering of the target takes place preferentially at this place. Second, the significant


bombardment of plasma ions causes heating of the target and damages the magnets. Therefore,

a cooling system is required [Kelly et al., 2000; Billard et al., 2005; Constantin et al., 2011].

Figure II. 2: Schematic diagram of the working principle of cathodic magnetron sputtering

II.3.2 Description of the experimental device used in this study

Figure II.3 shows the magnetron sputtering device (Alcatel 604) which was used for deposition

of all thin films in this work. The reactor was a 90 L cylinder Alcatel 604 SCM (CIT Alcatel,

Annecy, France) pumped down via a turbo molecular pump system that permitted a residual

vacuum below 10−4 Pa. Argon flow rate was controlled with a Brooks flowmeter and the

working pressure was measured by using a MKS Baratron gauge. There is possibility to use

four targets (ø 50 mm × 3 mm) at the same time in the sputtering process. The chamber was

equipped with circular planar and water-cooled magnetron sources and the rotating substrate

holder was placed parallel to these sources at about 60 mm. The targets were supplied with a

pulsed DC supply (Advanced Energy Pinnacle +) and DC supply (MDX 500, Advanced

Energy).

In this work, a special chip (second-generation chip) produced by Linseis, fused quartz (Verre

equipment) (76 mm × 26 mm × 1 mm), glass microscope slides (Rogo-Sampaic (RS) France)

(76 mm × 26 mm × 1 mm), and Alumina pellet (Keral 99- Kerafol Gmbh) were used as

substrates. Before each set, all substrates except the special chip were cleaned with alcohol,

soap and then rinsed with water.

The substrates were placed on the substrate holder at about 45 mm from the substrate holder

axis and all depositions were carried out at floating temperature (Tsubstrate < 70 °C).


Figure II. 3: a) magnetron sputtering device (Alcatel 604): 1- deposition chamber, 2- pulsed DC

supply, 3- gas flow control system, 4- vacuum system control, 5- DC supply (MDX 500, Advanced

Energy), b) internal deposition chamber with four targets and rotative substrate holder

II.4 Characterization devices

II.4.1 Measurement of film’s thickness

The film’s thickness was measured by step method with an Altysurf Profilometer (Altysurf 500)

manufactured by Altimet society. Before each measurement, the calibration of the experimental

device was realized with a reference sample number 787569 accredited by CETIM

organization. The accuracy of the thickness measurement by Altysurf Profilometer is about ±

10 nm.

II.4.2 Morphological characterization and determination of the film composition

The morphology of the coatings on brittle fracture cross-section and on their top surface were

observed by a Scanning Electron Microscopy (Jeol JSM 7800F) Field Emission Gun Scanning

Electron Microscope (FEG-SEM). The microscope was equipped with Energy-Dispersive X-

ray Spectroscopy (EDS) for estimating the chemical composition of the films. For determining

the composition of the film, three different locations were randomly selected for EDS

measurements. Such measurements were obtained keeping constant all setting parameters. For

all selected zone magnification (×2000), probe current (2 nA) and working distance (100 mm)

were kept constant. The average atomic concentration was reported with addition of the errors

bar.

II.4.3 Structural characterization

The structural characterization of coatings was performed by Bragg-Brentano configuration X-

ray diffraction (XRD) using a BRUKER D8 focus diffractometer with a cobalt X-ray tube

(CoKα1+α2 radiations λ = 0.178897 nm) and equipped with a LynxEye linear detector.

Diffractograms were collected in air for 10 min in the 20°–80°, 2 angle range at a scan rate of

0.1°s-1.


II.4.4 Electronic transport properties

In 1987, Edwin Hall discovered that when an electrical current passed through a metal or

semiconductor placed in a magnetic field, a voltage difference proportional to the current and

to the magnetic field is created across the material in a direction perpendicular to both the

current and magnetic fields. For the first time, he determined the sign of the charge carriers in

a conductor by this measurement.

By means of the Hall effect, the following items can be determined in the semiconductor

materials:

• Hall voltage (𝑉𝐻)

• Hall coefficient (𝑅𝐻)

• The nature of the majority type of charge carriers (whether a semiconductor is p-type or

n-type)

• The charge carrier density (carrier concentration per unit volume) in the semiconductor

crystal.

• The mobility of the charge carrier (µ𝐻)

II.4.4.1 Principle of Hall effect measurement

If the electric current along the x-axis and a magnetic field perpendicular along the z-axis are

applied to the conducting bar as shown in figure II.4, the charge carriers experience the Lorentz

force which is given by following equation:

𝐹 = 𝑒(𝑣 × ) (II.1)

Where e is the elementary charge (1.6 × 10-19 As), 𝑣 the charge velocity (m s-1) and the

magnetic field (T). Under the influence of the Lorentz force, the charge carrier’s path is

deflected to the one side of the bar, while the equal and opposite charge accumulate at the other

end. As a result of the accumulation of the charges at the ends of the bar, the electric field

developed along the y-axis which cancel out the magnetic field. At this point, charge begins to

flow straight line giving rise to the Hall voltage 𝑉𝐻 (V).

Figure II. 4: The applied external magnetic field, 𝑩𝒛, perpendicular to the direction of charge flow,

leads to accumulation of negative charges to gather on the left side and positive charges on the right

side. This induces an electric field 𝑬𝒚 which balances 𝑩𝒛. The voltage across the sides is the Hall

voltage, 𝑽𝑯 , which is obviously different from the bar voltage, 𝑽𝒙 , measured across the length of the

bar [Mirza et al., 2013].


The Hall coefficient (𝑅𝐻) (Ω m T-1) is determined by measuring the developed field across the

y-axis:

𝑅𝐻 =𝐸𝑦

𝐵𝑧𝐽𝑥=

𝑉𝐻

𝐵

𝑑

𝐼 (II.2)

Where 𝐸𝑦 is the electric field (N C-1), which is known as the Hall field, 𝐵𝑧 the magnetic field

(T), 𝐽𝑥 the current density (A m-2) (y, z and x indicate the different directions), d the thickness

of the sample (m), I the supplied current (A) and finally B the applied magnetic field (T).

In metals or semiconductors with one type of carriers (electrons or holes) the carrier

concentration (n or 𝑝) (m-3) and the carrier mobility ( µ𝐻 ) (m2 V-1 s-1) are related to the Hall

coefficient and are given by the following equations:

𝑛(𝑝) = ±1

𝑒𝑅𝐻 (II.3)

and,

µ𝐻 = 𝑅𝐻𝜎 (II.4)

Where 𝜎 is the electrical conductivity (S m-1) of the sample [Mirza et al., 2013].

II.4.4.2 Description of the experimental device of Hall measurement

DC electrical resistivity, free carrier concentration and mobility were performed in air in the

temperature range 30-200 °C for the films deposited on glass slides by means of a homemade

system (figure II.5) based on the van der Pauw method (accuracy of measurement is about ±

5%). In order to warrant the ohmic behavior of the four contacts, I-V curves were systematically

plotted, and the linear evolution was checked for all van der Pauw combinations. Two cycles

of measurements were carried out on each sample. The first cycle started at 30 °C and the

sample was heated up to 200 °C with a ramp of 2 °C min-1 followed by 10 min stabilization at

200 °C. Afterward, the temperature was decreased with the same ramp down to 30 °C and the

second cycle continued with the same temperature profile as the first cycle. For charge carrier’s

mobility and concentration, a magnetic field of 0.8 T was perpendicularly applied to the sample

surface.


Figure II. 5: Homemade Hall effect vs. Temperature setup with 4 probe configuration van der Pauw

method (NIST procedure)

II.4.5 Measurements of the thermoelectric properties of the coatings

As previously discussed in the chapter I, the efficiency of thermoelectric materials is determined

by the dimensionless figure of merit ZT which is defined by the following equation:

𝑍𝑇 =𝑆2𝜎

𝑘𝑡𝑇 (II.5)

Where S is the Seebeck coefficient (µV K−1), σ the electrical conductivity (S m−1), 𝑘𝑡 the total

thermal conductivity (Wm−1K−1) and T the absolute temperature (K). Therefore, for a complete

thermoelectric characterization, these parameters should be evaluated accurately as developing

thermoelectric materials for enhancing their ZT.

II.4.5.1 Electrical conductivity measurement

For measuring the electrical conductivity in bulk materials and thin films, the four-point probe

method and the van der Pauw technique can be used.

In-plane electrical conductivity can be determined via a four-point probe measurement. The

van der Pauw method is mostly known as one of the most effective and widely used methods

for measuring the resistivity of materials in the form of thin films.

• Four-point probe method:

In this case, the measurement is taken using four contacts. The schematic of four-point probe

method is shown in figure II.6 (a) and (b) for bulk and thin film samples, respectively. In this

method, the direct current is applied at the outer pads, while the voltage is measured at the inner

pads.


Figure II. 6: Four-point probe configuration for electrical resistivity measurement of a) bulk samples

b) thin films on an insulating substrate.

The most common geometry is the in-line probes arrangement with equal probes spacing (s).

For a bulk material of semi-infinite thickness and probes far away from any boundary (figure

II.4. a), resistivity 𝜌 (Ω m) is simply calculated by:

𝜌 = 2𝜋𝑠∆𝑉

𝐼 (II.6)

where s is the probe spacing (m), I the applied current (A), and ∆𝑉 the measured voltage (V).

For thin semiconducting film on an insulating substrate (figure II.4. b) the equation II.6 is

replaced by:

𝜌 = 4.532𝑡∆𝑉

𝐼 (II.7)

For equation above to be valid, the thickness of the thin film (t) must be smaller than the half

of the probe spacing (𝑡 <𝑠

2).

This method eliminates errors from contact and spreading resistances [Li et al., 2012].

• van der Pauw method:

The main advantage of van der Pauw method is that it can accurately measure the electrical

resistivity of a sample with arbitrary shape as shown in figure II.7.

Figure II. 7: Sample of arbitrary shape with contacts for van der Pauw method

Apart from electrical resistivity, it can be also employed for mobility and sheet carrier density

measurements and for determining the type of the semiconductor (n- or p- type). Four contacts

are used again, which are placed in the periphery of the sample. Current is applied at two


adjacent contacts and the voltage is measured in the remaining pads. Then, the resistivity of a

uniform sample with a defined thickness (t) is given by following equation:

𝜌 =𝜋𝑡

𝑙𝑛2

𝑅𝐴 + 𝑅𝐵

2𝑓 (II.8)

where 𝑅𝐴 =𝑉3−𝑉4

𝐼1,2, 𝑅𝐵 =

𝑉4−𝑉1

𝐼2,3, and f a correction factor, which is a function of the ratio:

(𝑅𝑓 − 1)

(𝑅𝑓 + 1)=

𝑓

2𝑎𝑟𝑐𝑐𝑜𝑠ℎ (

𝑒𝑥𝑝 (𝑙𝑛2𝑓)

2) (II.9)

With 𝑅𝑓 is given by:

𝑅𝑓 =𝑅𝐴

𝑅𝐵 (II.10)

In the case of symmetrical geometries, 𝑅𝐴 = 𝑅𝐵, and then 𝑅𝑓 = 1, and 𝑓 = 1, equation II. 10 is

simplified following:

𝜌 =𝜋𝑡

𝑙𝑛2𝑅𝐴 (II.11)

It’s worth to note that the electrical resistivity measurements are carried out in order to

characterize thermoelectric materials, thus the thermoelectric effects should be taken into

account during the measurements. Peltier effect can be significant during the electrical

measurement, presenting temperature gradients along the sample. This fact enforces an

additional thermoelectric potential at the contacts where the voltage is measured (Vmeasured) such

that:

𝑉𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 = 𝑉𝐼𝑅 + 𝑆∆𝑇 (II.12)

where VIR is the resistive voltage (V) and SΔΤ the thermovoltage induced by the temperature

difference that Peltier effect generates. For eliminating such errors, relatively fast

measurements should be developed (~ 2- 3 s) or altering the current direction during the

measurement, either using a fast-switching DC or AC current source. In this way, the Seebeck

voltage is practically subtracted if we get the average of measurements in two opposite

directions [Van der Pauw, 1958]

II.4.5.2 Thermal conductivity measurement

Based on the Fourier’s law, thermal conduction is defined as the rate of heat flow through a

square meter of a solid sample where a temperature gradient exists in the direction of heat flow

and it is given by following equation:


𝑘 =−

𝑇 (II.13)

Where k is the thermal conductivity (W m-1 K-1), the heat flux (W m-2) across a unit section

perpendicular to the , and T is the absolute gradient temperature (K m-1).

There are several techniques to measure thermal conductivity, each is suitable for a limited

range of materials. There are two main categories of measurement techniques: steady-state and

transient. Steady-state techniques derive the thermal conductivity from measurements on the

state of a material once a steady-state temperature profile has been reached, whereas transient

techniques function on the instantaneous state of a system during the close to steady state. In

general, in all measurement methods the sample is heated (electrically or optically) and then

heat transport through the sample is measured. For accurate measurement of thermal

conductivity in thin films, electrothermal and optical measurement techniques can be employed.

The most common electrothermal approach is the 3-omega method (3𝜔 method) which was

established by Cahill and Pohl in 1980s. The 3𝜔 method is well-established method for

determining the thermal conductivity in thin films (> 100 nm) or superlattices and nanowires

[Jacquot et al., 2010].

• Principle of 3𝜔 method:

3𝜔 can be employed in both two or four probe configuration as shown in figure II.8.

Figure II. 8: Schematic of the experimental configuration for 3𝝎 traditional method [Wang et al.,

2019]

In the 3𝜔 method, a thin metallic strip which acts as a heater and thermometer laying on the

surface of the sample and according to the following equation:

𝐼ℎ(𝑡) = 𝐼ℎ𝑜(𝜔𝑡) (II.14)

An alternative current (ac) with angular frequency 𝜔 (rad s-1), and amplitude 𝐼ℎ𝑜 (A) is applied

to the strip. As a result of Joule heating, this current generates an oscillating heat source given

by the following equation:

(𝑡) =1

2𝐼ℎ𝑜2 (1 + 𝑐𝑜𝑠(2𝜔𝑡)) (II.15)


Where 𝑅ℎ𝑜 is the resistance of the metallic resistor (Ω) at the reference temperature. The related

temperature rise is composed of two parts: dc part (∆𝑇𝐷𝐶 and a 2𝜔 modulated part) where 𝜑 is

the phase shift between the excitation current and temperature oscillations.

Considering linear dependence of the resistance of the metallic strip on temperature, the steady-

state harmonic oscillations in the heater generate harmonic variations in the resistance given

by:

𝑅ℎ(𝑡) = 𝑅ℎ𝑜 (II.16)

Where 𝛽ℎis the temperature coefficient of resistance (TCR) of the heater. The voltage drop

across the heater can be determined from Ohm’s law as:

𝑉ℎ(𝑡) = 𝐼ℎ𝑜𝑅ℎ𝑜 [(1 + 𝛽ℎ∆𝑇𝐷𝐶)𝑐𝑜𝑠(𝜔𝑡) +1

2𝛽ℎ|∆𝑇𝐴𝐶|𝑐𝑜𝑠(𝜔𝑡 + 𝜑)

+1

2𝛽ℎ|∆𝑇𝐴𝐶|𝑐𝑜𝑠 (3𝜔 + 𝜑)]

(II.17)

The 3ω voltage components are measured with a lock-in amplifier and used to determine

relating in-phase and out-of-phase temperature oscillations, from which the thermal

conductivity of the sample is extracted [Wang et al., 2019].

II.4.5.3 Seebeck coefficient measurement:

The Seebeck coefficient is the most significant parameter for enhancement of thermoelectric

property, since the ZT is proportional to the square of Seebeck coefficient. To measure the

Seebeck coefficient for both bulk and thin films, conventional methodology is used to set up a

temperature gradient across the sample under the test and measure the temperature and voltage

differences. The Seebeck coefficient given by following equation:

𝑆 =−𝛥𝑉

𝛥𝑇 (II.18)

Where 𝛥𝑉 is the difference in voltage (V), and 𝛥𝑇 the difference in temperature (K).

The basic conditions for obtaining an accurate Seebeck coefficient measurement are:

• Good electrical and thermal contacts

• Synchronous measurement of temperature and voltage

• Accurate measurement of small voltages and temperatures with removing external

parasitic contributions

Extracting reliably of Seebeck coefficient, especially when the sample is in the form of the thin

film, is not an easy task. Thus, a few factors are essential to take into account the accurate

Seebeck coefficient measurement in thin films:

• Thin films need a supporting substrate as they are not free-standing, which might affect

the temperature distribution.


• For monitoring the thermovoltage in low dimensional systems, the finite-size metal

electrodes are needed.

• For high temperature measurement, the standard reference samples are lacking in

National Institute of Standards and Technology (NIST).

Since the superlattices are anisotropic, the direction of measurement (in-plane or perpendicular)

is vital. To obtain reliable results, all parameter measurements should be carried out in the same

direction [Borup et al., 2015; Wang et al., 2018].

II.4.6 Thin Film Analyzer (TFA) for thermoelectric properties

In the present work, Thin Film Analyzer (TFA) (figure II.9) designed by Linseis Co. was used to

measure all thermoelectric properties on the same sample and in one measurement run in order to

calculate in-plan ZT value. Linseis [Linseis et al., 2018] claimed that many error sources, like a

different sample deposition, which leads to composition, structure or thickness variations and heat

profiles difference, can be avoided and a high reliability of the results is possible to achieve while

all of the thermoelectric properties were measured on the same sample and in one measurement run.

In order to use TFA, all sample were deposited on the second-generation chips produced by

Linseis Co. In the following section, the structure of the 2nd generation chip and principle of

thermoelectric properties measurement by TFA will be discussed.

Figure II. 9: TFA setup: 1) K-REG, 2) Electric Rack, 3) Turbo Pump 4) TFA unit, 5) PC and Monitor

II.4.6.1 The second-generation chip:

The pre-structured measurement chips are used as the substrates for the thin film deposition.

These chips are 10 mm in the width and length (figure II.10 a). They are also called van der

Pauw (vdP) chip. The second-generation chips are produced with several lithographic

structuring and deposition steps such as reactive ion etching (RIE), atomic layer deposition

(ALD) and anisotropic etching of silicon in a clean room process. The chips are based on a

(100) Si substrate covered by Al2O3 passivation layer. The platinum electrodes and contact

material are used. The brown areas are only 100 nm thin SiNx membranes, which are used for

the Seebeck coefficient and thermal conductivity measurements. The pads 2, 3, 8, 9 are used

for van der Pauw measurements and they should be directly connected to the deposited samples.


The pad 8 is also used for the Seebeck coefficient measurement and should be connected to

pads 1, 4, 5, 6 via the small contact VTH,H at the resistance located on large membrane. When

measuring an empty chip for determine the zero curve for thermal conductivity, these pads

should not be connected (open circuit). As noted, the pads 1, 4, 5, 6 are used to measure the

Seebeck coefficient. They act as a 4-terminal connected resistance thermometer, which

measures the temperature at the hot thermovoltage measurement point, located in the center of

the large membrane. The pads 7, 10, 11, 12, 13, 14 are used for the thermal conductivity

measurement. They are linked to measure the resistance of the heating stripes in 4-terminal

method. During the sample deposition, the contacts must be protected with foil or metal mask,

and only the active areas has to be left free for the film deposition (figure II.10 b).

Figure II. 10: a) Front view of chip with functional structures for the Seebeck coefficient, van der

Pauw and 𝟑𝝎 thermal conductivity, b) chip covered by metal mask, c) chip with sample deposited,

ready to be measured.

II.4.6.2 Electrical conductivity measurement by TFA

For measuring the electrical conductivity (𝜎) the van der Pauw method is employed in

combination with the needle contacts 2, 3, 8 and 9 as shown in figure II.10. For obtaining an

accurate measurement result, the thickness of the sample must be measured very precisely and

must be homogeneous.

For the electrical conductivity measurement, a current is applied between two contacts at one

edge and then the resultant voltage drop at the other edge is determined between the remaining

two contacts. The resistivity (𝜌 can be determined using the van der Pauw formula given by the

following equation:

𝑒𝑥𝑝 (−𝜋𝑑

𝜌. 𝑅23,98) + 𝑒𝑥𝑝 (

−𝜋𝑑

𝜌. 𝑅39,82) = 1 (II.19)

with,

𝑅23,98 =𝑉98

𝐼23 (II.20)

Where 𝑉98 = 𝜑9 − 𝜑8 is the corresponding voltage drop between the contacts 9 and 8 with their

electric potential 𝜑𝑖, 𝐼23 the applied current starting in contact 2 and ending in contact 3. Since

the electrical conductivity is the inverse value of the resistivity, it can be simply obtained from


equation II.19. The accuracy of electrical resistivity measurement by TFA is ± 6% for most

materials.

II.4.6.3 Thermal conductivity measurement by TFA

To determine the thermal conductivity of thin film, a hotwire setup with a suspended membrane

is used as shown in small membrane in figure II.11. The membrane setup allows the

measurement of the in-plane thermal transport properties, which can be important data, when it

comes to anisotropic behavior, which most thin films show. Properties of the membrane such

as its thermal conductivity and thickness (t) should be considered due to the measurement

principle which is a differential measurement of covered chip by thin film (𝑘𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑𝑡𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑)

and the empty membrane (𝑘𝑀𝑡𝑀+𝑘𝑝𝑡𝑝). The membrane part can be corrected either with a zero

curve, which comes with the software, or can be measured independently with every empty

chip.

𝑘𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 × 𝑡𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑=𝑘𝑀𝑡𝑀 + (𝑘𝑆𝑡𝑆 + 𝑘𝑃𝑡𝑃) (II.21)

Figure II. 11: Setup with sample for thermal conductivity measurements [Manual-TFA]

In this setup, the hot wire acts as a heater and temperature sensor at the same time. When a

certain heating power is applied to the hot strip, a heat flux in the direction from the hot wire to

surrounding border will be produced due to the Joule heating effect. The temperature rise of the

hot wire can be determined from their resistance, using a calibration curve, which will be

recorded by a thermocouple in the sample holder through the measurement procedure. The

thermal conductivity can be determined by knowing the applied heating power, the

corresponding temperature increase and the chip geometry. The same setup can also be used

for 3𝜔 technique which is more precise and faster than the DC method. The accuracy of thermal

conductivity measurements by TFA is ± 10 % for most materials.

II.4.6.4 Seebeck measurements by TFA

To determine the Seebeck coefficient of thin films, a resistance thermometer with a small

sample contact 𝑉𝑇𝐻,𝐻 has been structured near the heating stripe on the big membrane as shown

in figure II.12. This contact is electrically connected to contact 1, which is operated as the hot

contact for the thermovoltage measurement. Contact 8 is used as the cold contact, which is

placed on the bulk silicon and remains at 𝑇0, even when a temperature gradient is applied to the


membrane. For the measurement, a current is applied to the heating stripe between the contacts

7 and 10, creating a temperature gradient along the membranes x-axis, starting at the heating

stripe and ending at the platinum border. For the temperature determination of the hot contact,

the resistance of the thermometer is measured in a 4-point configuration using the contacts 1,

4, 5, 6 (𝑇ℎ𝑜𝑡). The temperature coefficient of resistance is calibrated using a thermocouple

directly under the chip at thermal equilibrium conditions during the measurement routine. The

same thermocouple is also used for the determination of the cold contact temperature 𝑇𝑐𝑜𝑙𝑑 =

𝑇0.

𝑇ℎ𝑜𝑡 𝑉14

𝐼56 (II.22)

For the Seebeck measurement procedure at a certain temperature point, various temperature

gradients in the x-direction of the membrane are applied, and the temperature difference (∆𝑇 =

𝑇ℎ𝑜𝑡 − 𝑇𝑐𝑜𝑙𝑑 ) between contacts 1 (𝑉𝑇𝐻,𝐻) and 8 (𝑉𝑇𝐻,𝐶) is measured. The Seebeck coefficient can

then be evaluated using following equation:

𝑆 − 𝑆𝑝𝑡 =−𝑉𝑡ℎ

∆𝑇=

−(𝑉𝑇𝐻,𝐻 − 𝑉𝑇𝐻,𝐶)

𝑇ℎ𝑜𝑡 − 𝑇𝑐𝑜𝑙𝑑 (II.23)

where 𝑆𝑃𝑡 signifies the Seebeck coefficient of the platinum contacts. When the applied

temperature increase, at a certain temperature measurement point, is small enough to stay within

the constant regime of the samples Seebeck coefficient over temperature, the evaluation can

also be done by plotting the measured thermovoltage over the applied temperature gradient and

taking the slope of this graph as the Seebeck coefficient. The accuracy of the Seebeck

coefficient measurement by TFA is ± 7 % for most materials [Linseis et al., 2016; Linseis et

al., 2018].

Figure II. 12: Van der Pauw setup with heater and resistance thermometer on the larger membrane

[Manual-TFA]

II.4.6.5 Calculation of the figure of merit ZT

The figure of merit ZT can be calculated using equation II.5. By considering the accuracy of

the temperature measurement by TFA is ± 0.5 %, and equation II.5, and following equations:


𝑙𝑛𝑍𝑇 = 2𝑙𝑛𝑆 + 𝑙𝑛𝜎 + 𝑙𝑛𝑇 − 𝑙𝑛𝐾 (II.24)

and,

𝛥𝑍𝑇

𝑍𝑇= 2

𝛥𝑆

𝑆+

𝛥𝜎

𝜎+

𝛥𝑇

𝑇−

𝛥𝐾

𝐾 (II.25)

Error for calculated ZT is given by:

∆𝑍𝑇 = 𝑍𝑇 [2𝛥𝑆

𝑆+

𝛥𝜎

𝜎+

𝛥𝑇

𝑇−

𝛥𝐾

𝐾] (II.26)

II.4.6.6 Description of the thermoelectric properties by TFA

Thin Film Analyzer (TFA) designed by Linseis Co. was used to measure all thermoelectric

properties of thin films deposited on the second-generation chips. In order to get a stabilization

of the film’s properties, all measurements related to thermoelectric properties were carried out

in three cycles consisting of a heating and cooling run in the temperature range from 30 °C to

200 °C in vacuum at about 10-4 Pa.

After inserting chip in the TFA, the correct installation of chip should be checked. It can be

tasted using the “Check connection” test from the TFA software. While the sample is connected

correctly to the chip and the chip is connected to the electronics, all 6 parameters should be

checked successfully. Afterward the appropriate current for the measurement run is determined.

For obtaining the accurate results in each run of the measurement, the resistance homogeneity

of the sample in eight different points in both vertical and horizontal directions is controlled. If

the test of the resistance homogeneity is successful, the chip is ready to be measured.

In each cycle of measurement, the sample was heated with a ramp of 1 °C.min-1. Afterward the

temperature decreased with the same ramp down to 30 °C. The second and third cycles

continued with the same temperature profile as the first cycle. The films electrical conductivity,

thermal conductivity and Seebeck coefficient were recorded for each 10 °C step. After three-

cycles of measurements (heating and cooling cycles) films was completely educated. In first

and second cycles, the difference was observed between heating and cooling curves which can

be explained by the microstructure changes and stress relaxation occurs during the annealing.

From the second cycle, following cycles are reproducible and the thermoelectric properties

follow the same dependence with temperature both during heating and cooling. To avoid some

confusing data, in this thesis, only the results collected for the third cycle of cooling were

reported.

II.4.7 Bandgap measurement:

The bandgap of the samples was estimated by using the normalized Kubelka-Munk function

representing the absorption coefficient, which was calculated from equation II.27.


𝐹(𝑅(𝜆)) =(1 − 𝑅(𝜆))2

2𝑅(𝜆) (II.27)

Where R is the reflectance and the light wavelength (nm). Considering an indirect transition,

the band gap energy was determined by extrapolating to the energy-axis the straight portion of

the curve defined by the following formula:

(𝐹(𝑅)ℎ) = 𝐴(ℎ − 𝐸𝑔)2 (II.28)

Where h is the Plank’s constant (J s), the light frequency (s-1) and Eg the band-gap energy

(eV) [Guthrie et al., 1988].

The diffuse reflectance of the coating in the IR range was measured with a UV-visible-NIR

spectrophotometer (UV 3600, produced by Shimadzu) equipped with ISR-3100 integrating

sphere. Standard white board BaSO4 was used for the baseline.

II.5 Conclusion

In this chapter, the two main sections have been devoted to the thin film synthesis and

characterization. In the first part, the principle of magnetron sputtering is given, which is used

for thin film deposition in this work and the details of the sputtering reactor and the type of the

substrates that are used was explained.

In the second part, the methods and experimental instruments for characterization of thin films

were discussed in detail. The primary features of the films that have to be investigated are film’s

thickness (Profilometer), morphology (SEM), chemical composition (EDS), as well as the

crystalline structure (XRD), so these different characterizations device. The special attention

was paid to Hall effect measurement principle for determining the electronic transport

properties of the films. The Thin Film Analyzer (TFA) which is used for thermoelectric

properties measurement in this work, was presented. TFA was employed to measure all

thermoelectric properties on the same sample and in one measurement run in order to calculate

in-plan ZT value. It benefits van der Pauw and 3𝜔 methods for determining the electrical and

thermal conductivity, respectively. Finally, the bandgap measurement via normalized Kubelka-

Munk function is briefly discussed.


II.6 References

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l’Ingénieur, M 1 645, 1-17.

Borup, K. A., De Boor, J., Wang, H., Drymiotis, F., Gascoin, F., Shi, X., Chen, L., Fedorov,

M. I., Müller, E., Iversen, B. B., & Snyder, G. J. (2015). Measuring thermoelectric transport

properties of materials. Energy and Environmental Science, 8, 423-435.

Constantin, D. G., Apreutesei, M., Arvinte, R., Marin, A., Andrei, O. C., & Munteanu, D.

(2011). magnetron sputtering technique used for coatings deposition; technologies and

applications. 7th International conference on Materials Science and Engineering, 29-33.

Fang, B., Zeng, Z., Yan, X., & Hu, Z. (2013). Effects of annealing on thermoelectric properties

of Sb2Te3 thin films prepared by radio frequency magnetron sputtering. Journal of Material

Science: Materials in Electronics, 24, 1105-1111.

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Chapter 3 Investigation of Mg-deficiency and Cu-doping

impacts on Mg2Sn thin films properties

Table of contents

III.1 Introduction .................................................................................................................................. 77

III.2 Stoichiometry and Mg-deficiency Mg2Sn thin films .................................................................... 77

III.2.1 Structural and morphological characterization of Mg-Sn thin films .......................................... 78

III.2.2. Measurement of electronic transport properties of Mg2Sn thin films ................................... 81

III.2.3. Measurement of thermoelectric properties of Mg2Sn thin film ............................................ 84

III.2.4. Thermal stability of the Mg2Sn thin films ............................................................................. 86

III.3. Cu-doping impact on stoichiometry and Mg-deficiency thin films.............................................. 89

III.3.1. Structural and morphological characterization of Cu-doped Mg2Sn thin films .................... 90

III.3.2. Measurement of electronic transport properties of Cu-doped Mg2Sn thin films .................. 92

III.3.3. Measurement of optic bandgap of Cu-doped Mg2Sn thin films ............................................ 95

III.3.4. Measurement of thermoelectric properties of Cu-doped Mg2Sn thin films .......................... 97

III.4. Conclusion .................................................................................................................................. 101

III.5. References .................................................................................................................................. 103

List of Figures

Figure III. 1 : Evolution of the Sn atomic concentration in the films measured by Energy-Dispersive

X-ray Spectroscopy (EDS) vs. sputtering power ratio applied to each target. The red dotted line

is a guide for the eye. .................................................................................................................... 78

Figure III. 2 : a) XRD patterns of Mg-Sn coatings deposited on glass substrate as a function of the

atomic concentration of Sn. b) zoom area of 2θ = 34°-38°. c) zoom area of 2θ = 35°-50°. ......... 79

Figure III. 3 : SEM micrographs of Mg-Sn as-deposited films on glass substrate: Top surface images

vs. composition. ............................................................................................................................ 80

Figure III. 4 : SEM cross section micrographs of Mg-Sn thin films deposited on glass substrate. ....... 81

Figure III. 5 : DC electrical resistivity of Mg2Sn thin films vs. temperature ........................................ 82

Figure III. 6 : Carrier concentration of Mg2Sn thin films vs. temperature ............................................ 82

Figure III. 7 : Carrier mobility of Mg2Sn thin films vs. temperature .................................................... 83

Figure III. 8 : Carrier mobility vs. carrier concentration for Mg2Sn thin films ..................................... 83

Figure III. 9 : Electrical conductivity of Mg2Sn thin films measured by TFA device under vacuum vs.

temperature ................................................................................................................................... 84

Figure III. 10 : Seebeck coefficient of Mg2Sn thin films measured by TFA device in vacuum vs.

temperature ................................................................................................................................... 85

Figure III. 11 : Thermal conductivity of Mg2Sn thin films measured by TFA device in vacuum vs.

temperature ................................................................................................................................... 85

Figure III. 12 : Figure of merit ZT of Mg2Sn thin films measured by TFA device in vacuum vs.

temperature ................................................................................................................................... 86

Figure III. 13 : X-ray diffraction patterns of the film with 33.5 at. % Sn deposited on glass substrate

and post annealed in vacuum (10-4 Pa) for 2 h at different temperatures. .................................... 87

Figure III. 14 : X-ray diffraction patterns of the film with 36 at. % Sn deposited on glass substrate and

post annealed in vacuum (10-4 Pa) for 2 h at different temperatures. ........................................... 88

Figure III. 15 : (a) Top surface observation and (b) X-ray mapping of the film with 36 at. % Sn

deposited on glass substrate after 2 h annealing at 600°C under vacuum (10-4 Pa). .................... 88

Figure III. 16 : X-ray diffraction patterns of the film with 38 at. % Sn deposited on glass substrate and

post annealed under vacuum (10-4 Pa) for 2 h at different temperatures. ..................................... 89

Figure III. 17 : Evolution of the Sn atomic concentration in the films measured by Energy-Dispersive

X-ray Spectroscopy (EDS) vs. sputtering power ratio applied to Mg and Sn targets (figure III.1 was

repeated). The red dotted line is a guide for the eye. Sputtering parameters of closed symbols are

used in this part to investigate the effect of the Cu doping on stoichiometry and Mg deficiency thin

films. ............................................................................................................................................. 90

Figure III. 18 : XRD patterns of Mg-Sn coatings deposited on glass substrate as a function of the

atomic concentration of Cu. a) group I with ⌈Mg⌉Sn = 2, b) group II with ⌈Mg⌉Sn = 1.75 ....... 91

Figure III. 19 :SEM micrographs of deposited films on glass substrate and SEM cross section

micrographs vs. atomic concentration of Cu. a) group I with ⌈Mg⌉Sn = 2, b) group II with

⌈Mg⌉Sn = 1.75. ............................................................................................................................ 92

Figure III. 20 : Electrical conductivity of Cu doped (0, 0.5 and 1.5 at. % Cu) thin films of group I and

group II vs. temperature. ............................................................................................................... 93

Figure III. 21 : Carrier concentration of Cu doped Mg-Sn (0, 0.5 and 1.5 at. % Cu) thin films in groups

I and II vs. temperature. ................................................................................................................ 94

Figure III. 22 : Carrier mobility of Cu doped Mg-Sn (0, 0.5 and 1.5 at. % Cu) thin films in group I and

II vs. temperature. ......................................................................................................................... 95

Figure III. 23 : plot of lnσT1.3 as a function of reciprocal temperature for un-doped Mg2Sn in group I

(MgSn = 2) ................................................................................................................................... 96

Figure III. 24 : Kubelka-Munk transformed absorption spectra used to estimate the bandgap of Cu-

doped Mg-Sn (0, 0.5 and 1.5 at. % Cu) thin films a) in group I and b) in group II. ..................... 96

Figure III. 25 : Electrical conductivity of Cu doped Mg-Sn (0, 0.5 and 1.5 at. % Cu) thin films in

group I and II vs. temperature. ...................................................................................................... 97

Figure III. 26 : SEM micrographs of deposited films with 0.5 and 1.5 at. % Cu of group II on glass

substrate: As deposited and after 2h annealing in air and in vacuum. .......................................... 98

Figure III. 27 : a) X-ray diffraction patterns of the deposited films with 0.5 and 1.5 at. % Cu of group

II on glass substrate: As deposited and after 2h annealing in air and in vacuum, b) grain size of

the films with 0.5 and 1.5 at. % Cu of group II after 2h annealing in air and under vacuum. ...... 98

Figure III. 28 : Seebeck coefficient of Cu doped Mg-Sn (0, 0.5 and 1.5 at. % Cu) thin films in group I

and II vs. temperature. .................................................................................................................. 99

Figure III. 29 : Thermal conductivity of Cu doped Mg-Sn (0, 0.5 and 1.5 at. % Cu) thin films in group

I and II vs. temperature. .............................................................................................................. 100

Figure III. 30 : Figure of merit ZT of Cu doped Mg-Sn (0, 0.5 and 1.5 at. % Cu) thin films in group I

and II vs. temperature. ................................................................................................................ 101

List of Tables

Table III. 1 : Sputtering parameters used during deposition of Mg-Sn coatings. .................................. 78

Table III. 2: Sputtering parameters used during deposition of Cu-doped Mg2Sn coatings. .................. 89

Table III. 3 : Composition and thickness of deposited Cu-doped Mg2Sn thin films ............................. 90

Table III. 4 : Bandgap of thin films obtained by the Kubelka-Munk’s method (± 0.02 eV) ................. 96

Investigation of Mg-deficiency and Cu-doping impacts on Mg2Sn thin films properties 77

III.1 Introduction

Different strategies for improving ZT in chapter I, were discussed. Among these strategies, three

of them will be chosen in this chapter for studying their impacts on morphological, structural,

electronic and thermoelectric properties of Mg2Sn compound. These strategies will be:

• Thin film synthesis,

• Stoichiometry and Mg-deficiency thin films,

• Cu doping impact on stoichiometry and Mg-deficiency thin films.

In the first part, Mg-Sn thin films (21 ≤ at. % Sn ≤ 42.5) were successfully synthesized by

magnetron co-sputtering of Mg and Sn targets in an argon atmosphere. This part aims at

investigating the role of chemical composition and structural modification on the films

electronic transport and thermoelectric properties. In parallel, thermal stability of the film has

been studied after annealing in vacuum (10-4 Pa) at different temperatures.

In the second part, Cu-doping impact on stoichiometry and Mg-deficiency thin films is chosen

as a strategy to enhance ZT in the Mg2Sn system. Different elements such as Ni, Cu, Ag, Zn,

and In have been suggested as acceptor dopant in Mg2Sn. So far, the effect of Ag-doping on

thermoelectric properties of Mg2Sn have been studied by several groups as it effectively

enhanced the carrier concentration compared to undoped Mg2Sn [Choi et al., 2012; An et al.,

2012]. Two groups of thin films with different [Mg]/[Sn] atomic ratios were deposited by

magnetron co-sputtering of Mg, Sn and Cu targets in an argon atmosphere. Group I with

stoichiometric ratio [Mg]

[Sn]= 2 and group II with Mg-deficiency,

[Mg]

[Sn]= 1.75 were doped with Cu

concentrations of 0, 0.5 and 1.5 at.%. Their structures and morphologies were investigated as a

function of the Cu atomic concentration. The film charge carrier’s concentration and mobility

were measured to explain the electronic transport behavior as a function of the film composition

and morphology. The effects of Mg-deficiency and Cu-doping on the thermoelectric properties

of both groups were discussed in a range of temperatures: 30-200 °C.

III.2 Stoichiometry and Mg-deficiency Mg2Sn thin films

Mg-Sn thin films (21 ≤ at. % Sn ≤ 42.5) were successfully synthesized by magnetron co-

sputtering of Mg and Sn metallic targets in an argon atmosphere. The power was fixed at 70 W

for Mg target and was systematically changed on Sn target from 25 to 52 W to tune the coating

composition. Argon flow rate was 50 sccm and working pressure was kept at 0.41 Pa during

deposition. The substrates (Special chip produced by Linseis, as well as fused quartz and glass

microscope slides) were placed on the substrate holder at 60 mm from the substrate holder axis

and all depositions were carried out at floating temperature (Tsubstrate < 70 °C). The main

sputtering parameters are summarized in Table III.1.


Table III. 1 : Sputtering parameters used during deposition of Mg-Sn coatings.

Figure III.1 shows the evolution of the atomic concentration of Sn measured by EDS analyses

for each coating deposited on fused quartz as a function of the power ratio applied to each target

(PSn/PMg) during the sputtering process. Three different zones of each coating were selected for

EDS measurements and the average concentration was calculated. It can be noted that EDS

analyses show relatively homogeneous composition on the entire surface of deposited thin

films. These results show that as the power ratio applied to each target (PSn/PMg) increases, films

become Sn- rich following a linear evolution.

Figure III. 1: Evolution of the Sn atomic concentration in the films measured by Energy-Dispersive X-

ray Spectroscopy (EDS) vs. sputtering power ratio applied to each target. The red dotted line is a guide

for the eye.

III.2.1 Structural and morphological characterization of Mg-Sn thin films

Figure III.2 presents the X-ray diffraction patterns of as-deposited coatings with different

atomic concentrations of Sn. The XRD results indicate that for coatings containing 21 ≤ at. %

Sn ≤ 25, cubic Mg2Sn (fcc) structure coexists with secondary phase of Mg with hexagonal

close-packed (hcp) structure related to (002) diffracted peak at 2 41°. For coatings containing

30 at. % up to 33.5 at. % Sn, the Mg (hcp) phase vanishes and well-crystallized stable Mg2Sn

(fcc) structure is obtained. For coatings with 35 ≤ at. % Sn ≤ 37.4, the existence of (211)

diffracted signal at 2 28.05° confirms the presence of a metastable orthorhombic Mg2Sn

structure in addition to the fcc Mg2Sn structure. In this range of compositions and because of

orthorhombic and cubic structures coexistence, the Full Width at Half Maximum (FWHM) of

the peaks increases, which corresponds to films with a poor crystallized state. The stoichiometry

Target

Discharge

Power Frequency Toff

Ar Flow

Rate

Working

Pressure

Run

Duration

Draw Distance

(DT-S)

(W) (kHz) (µs) (sccm) (Pa) (min) (mm)

Sn 25–52 50 4 50 0.41 20 60

Mg 70


related to this second phase is close to Mg62Sn38. The metastable phases have been reported in

Mg-Sn thin films [Le-Quoc et al., 2011], or as a result of mechanical alloying via high-energy

ball milling in an Mg-Sn bulk system [Urretavizcaya et al., 2002]. Samples containing 37.6 ≤

at. % Sn ≤ 38, are crystallized in metastable orthorhombic structure (jcpds 00-031-0812) with

no diffraction peaks related to the fcc structure. Finally, for coatings with 39.5 ≤ at. % Sn ≤

42.5 metastable orthorhombic Mg2Sn co-existed with the body centered tetragonal (bct) Sn

phase as shown from the (200) diffracted signal at 2 35.7°. The crystallite size estimated by

Scherrer’s formula and it ranging from 130 nm (film with 21 at. % Sn) to about 70 nm (film

with 33.5 at. % Sn).

Figure III. 2: a) XRD patterns of Mg-Sn coatings deposited on glass substrate as a function of the

atomic concentration of Sn. b) zoom area of 2θ = 34°-38°. c) zoom area of 2θ = 35°-50°.

Top surface morphology observations by SEM of thin films deposited on glass substrate are

shown in figure III.3, as-deposited Mg-Sn coatings with Sn content of 21 at. % up to 42.5 at. %

were selected. It is evident that all as-deposited films perfectly cover the surface of the substrate

and no cracks and delamination were detected on top surface of the films. It can be observed in

figure III.3 that the separated granular morphology becomes more compact with a lower

porosity while Sn content increases. Films obtained with a higher concentration of Sn (35 ≤ at.

% Sn ≤ 38) present a cone-like shape microstructure. Looking at the morphology of the films

with 38 at. % Sn, smooth surface with cone-like shape microstructures co-exist, especially for

this sample. Finally, the film morphology returns to granular form with rising of Sn content to

about 42.5 at. %.


Figure III. 3: SEM micrographs of Mg-Sn as-deposited films on glass substrate: Top surface images

vs. composition.

Figure III.4 reveals brittle fracture cross section observations of the films as a function of Sn

atomic concentration. It can be seen that coatings containing 21 ≤ at. % Sn ≤ 25 present a

relatively more porous granular aspect compared to other samples. By increasing the atomic

concentration of Sn until 30-35 at. %, the morphology changes to slight columnar and becomes

denser. The coating with 36 at. % Sn exhibits a relatively dense columnar morphology with

submicron in-plan featured sizes. The coatings containing 38 ≤ at. % Sn ≤ 42.5 show a

completely dense and compact morphology. No cracks are detected and a good adhesion

between coating and substrate is observed. It is well known that, regarding to high energy of

sputtered atoms, adhesion of the films deposited by sputtering is much better than those

obtained with other deposition methods, e.g. by thermal evaporation [Le-Quoc et al., 2011].

The films thickness measured by SEM is relatively homogeneous with an average of about 1

µm. This value is in good agreement with those measured by profilometry. The deposition rate

is about 0.05 (µm. min-1).


Figure III. 4: SEM cross section micrographs of Mg-Sn thin films deposited on glass substrate.

III.2.2. Measurement of electronic transport properties of Mg2Sn thin films

The electronic transport properties of Mg-Sn thin films vs. temperature, were measured by Hall

effect and in the air. Figure III.5 illustrates the dependency of DC electrical resistivity of the

films with Sn content of 33.5 at. % up to 42.5 at. % as a function of temperature. As shown for

the films with 33.5 at. % Sn, which are well-crystallized in fcc Mg2Sn structure, the electrical

resistivity decreases as the temperature rises. It is well known that the electrical resistivity of

semiconductor materials decreases with increasing temperature [Lardjane et al., 2015]. For the

films with 35 ≤ at. % Sn ≤ 37.6, where the crystal structure changes from cubic to orthorhombic

structure, the variation of electrical resistivity becomes quite constant as a function of the

temperature. For the coatings containing 39.5 ≤ at. % Sn ≤ 42.5 with the orthorhombic structure

and presence of Sn secondary phase, the electrical resistivity is enhanced by the temperature,

that is associated to the metallic behavior related to the excess of Sn atoms. It is important to

note that, especially for the sample with 36 at. % Sn, the electrical resistivity remains relatively

constant vs. temperature (between 30 °C and 200 °C) with a value of about 2.31×10-5 Ω m.


Figure III. 5: DC electrical resistivity of Mg2Sn thin films vs. temperature

The variation of carrier concentration vs. temperature for the film with different Sn

concentrations is shown in figure III.6. It is important to highlight that the film carrier

concentration increases with Sn content in the films. Liu et al. [Liu et al., 2016] reported the

influence of intrinsic point defects on electronic transport properties of Mg2X (X = Si, Ge, Sn)

systems. They showed that Mg vacancies and interstitial Mg are assumed to be the main defects

in Mg2X compounds according to their relatively low formation energies. Mg vacancies and

interstitials Mg behave as acceptor and donor sites, respectively. We suppose that the increase

of carrier concentration in Mg2Sn films, while Sn content rises, can be explained by the

formation of Mg vacancies. The carrier concentration for all coatings is enhanced by increasing

the temperature and reaches the highest values (more than 1027 m-3) for the films containing

42.5 at. % Sn (the same order of magnitude of carrier concentrations in metals).

Figure III. 6: Carrier concentration of Mg2Sn thin films vs. temperature


Figure III.7 shows the variation of carrier mobility of the films vs. temperature. The carrier

mobility of all films decreases while the temperature rises. The carrier mobility is relatively

low for the films adopting the Mg2Sn cubic structure (33.5 at. % Sn). As the formation of

metastable orthorhombic Mg2Sn begins, carrier mobility increases (35 ≤ at. % Sn ≤ 37.6) and

the highest carrier mobility is obtained for the single phase orthorhombic Mg2Sn with 37.6 at.

% Sn. Finally, a further increase of the Sn content (≥ 39.5 at. %) leads to a drastic decrease of

the film carrier mobility. It is assigned to the presence of secondary Sn phase in these samples

as detected by XRD patterns (figure III.2).

Figure III. 7: Carrier mobility of Mg2Sn thin films vs. temperature

Figure III.8 reveals the variation of carrier mobility as a function of the carrier concentration.

For all films, this ratio decreases by increasing the temperature. It is clear that the highest ratios

of carrier mobility to carrier concentration are obtained for the films exhibiting the

orthorhombic structure. With the presence of Sn secondary phase in the films (at. % Sn ≥ 39.5),

this ratio starts to decrease and the films tend to behave like a metallic compound.

Figure III. 8 : Carrier mobility vs. carrier concentration for Mg2Sn thin films


III.2.3. Measurement of thermoelectric properties of Mg2Sn thin film

The thermoelectric properties were measured in vacuum (about 10-4 Pa) at different

temperatures using TFA device, on Linseis chips covered by Mg-Sn thin films.

Figure III.9 shows electrical conductivity of Mg2Sn thin films vs. temperature. The film

electrical conductivity decreases by increasing the atomic concentration of Sn from 21 to 33.5

at. % (Mg2Sn fcc structure). Then, the films conductivity enhances while the concentration of

Sn increases up to 42.5 at. % and the crystal structure changes to orthorhombic Mg2Sn structure.

Both samples with an excess of Mg or Sn show the highest values of electrical conductivity

(films with Sn = 21 at. % and Sn = 42.5 at. %, respectively). The highest electrical conductivity

is related to the coating containing 21 at. % Sn (6.2×106 S m-1 at 30 °C).

Figure III. 9: Electrical conductivity of Mg2Sn thin films measured by TFA device under vacuum vs.

temperature

Figure III.10 shows the variations of Seebeck coefficient vs. temperature. For all coatings,

Seebeck coefficient is positive throughout the measured temperature range. All films are p-type

semiconductors [Du et al., 2015]. The Seebeck coefficient and carrier concentration are

inversely proportional. This can be explained based on the following equation:

𝑆 ∝ ±𝑘𝐵 (𝑟 − ln 𝑛) / 𝑒 (III.1)

Where kB is the Boltzmann’s constant (1.38×10-23 J K-1), e the elementary charge (1.6×10-19 A

s), r is the scattering factor, and n the carrier concentration (m-3). The scattering factor r signifies

the exponent of the relaxation time vs. energy and is supposed to be constant. Therefore, as the

carrier concentration rises, the Seebeck coefficient decreases [Gao et al., 2011; An et al., 2012].

With respect to Le-Quoc et al. [Le-Quoc et al., 2012], the films with lower atomic concentration

of Sn, exhibits lower Seebeck coefficient and higher electrical conductivity. At room

temperature, the Seebeck coefficient varies from 2.1 µV K−1 to 174 µV K−1, which is at least

three times smaller than the value reported for the bulk Mg2Sn materials in the same

temperature range [Chen et al., 2009; Chen et al., 2010]. The films containing secondary phases

of Mg or Sn show relatively low Seebeck values compared to single phase Mg2Sn films. The


coating with 35 ≤ at. % Sn ≤ 36 and containing a mixture of cubic and orthorhombic structures

exhibits the highest Seebeck coefficient (152 µV K−1) at high temperature. The sample with

cubic structure (at. % Sn ≈ 33.5) present the highest value of Seebeck coefficient (174 µV K−1)

at low temperature and while temperature rises, the coefficient decreases.

Figure III. 10: Seebeck coefficient of Mg2Sn thin films measured by TFA device in vacuum vs.

temperature

Figure III.11 represents the evolution of thermal conductivity of thin films vs. temperature. It

is clear that while eliminating the secondary phase of Mg and rising Sn concentration, the

thermal conductivity significantly reduces. The highest thermal conductivity is related to the

coating containing 21 at. % Sn (7.9 W m−1 K−1). The thermal conductivity for coating with 42.5

at. % Sn is more affected by the variation of temperature. As previously noted, lower thermal

conductivity value can be expected for deposited thin films with polycrystalline structure

compared to the same materials in bulk form. Chen and Savvides [Chen et al., 2010] reported

the thermal conductivity about 5-15 Wm-1K-1 for bulk Mg2Sn.

Figure III. 11: Thermal conductivity of Mg2Sn thin films measured by TFA device in vacuum vs.

temperature


Figure III.12 indicates the variation of figure of merit (ZT) as a function of the temperature for

Mg-Sn thin films. The samples containing 21 at. % Sn up to 25 at. % Sn show low ZT values

as they behave like metal compounds due to the presence of Mg secondary phase. By increasing

the content of Sn from 30 at. % to 33.5 at. %, (samples with fcc structure and without secondary

phase of Sn), ZT values slightly enhance but remain relatively stable vs. temperature. By

changing the crystal structure from cubic to orthorhombic, (35 ≤ at. % Sn ≤ 38), the ZT values

notably enhance and as shown in figure III.12, ZT increases with temperature. The maximum

ZT value is obtained for thin films containing 36 at. % Sn with Mg2Sn cubic and orthorhombic

mixed crystal structures (ZT ~ 0.26 at 200 °C). The ZT slightly decreases for the film with 38

at. % Sn (with only the orthorhombic Mg2Sn structure) and drops in the case of the film with

42.5 at. % Sn (orthorhombic Mg2Sn structure + Sn secondary phase).

Figure III. 12: Figure of merit ZT of Mg2Sn thin films measured by TFA device in vacuum vs.

temperature

III.2.4. Thermal stability of the Mg2Sn thin films

As shown in section III.2.1, the Mg-Sn films structure is affected by the Sn atomic

concentration. It was shown that Mg2Sn structure was changed from stable face-centered cubic

to metastable orthorhombic structure while the content of Sn in the films increased. Three films

with different Sn atomic concentrations and crystal structure deposited on glass substrate were

selected and annealed in vacuum (10-4 Pa) at different temperatures (from 50 °C up to 600 °C

with an incremental step of 50 °C) with a dwell time of 2 hours. These films are:

• Mg-Sn (33.5 at. % Sn) with face centered cubic structure

• Mg-Sn (36 at. % Sn) with mixture of face centered cubic and orthorhombic structure

• Mg-Sn (38 at. % Sn) with orthorhombic structure

Such treatments were performed to determine the stability and structural decomposition

temperature limit for each sample.


• Mg2Sn (Sn 33.5 at. %):

Figure III.13 shows the XRD patterns of the film with 33.5 at. % Sn after annealing treatments

up to 600 °C under vacuum. Until 500 °C, the face centered cubic structure (jcpds 03-065-2997)

remains. As the annealing temperature rises to 500 °C, the slight right shift of the diffraction

peaks appears in this film, which might be related to the stress relaxation during annealing

treatment. For temperatures higher than 500 °C, the cubic Mg2Sn structure vanishes and

decomposition of Mg2Sn phase occurs which is leading to Mg and Sn formation. The (200)

diffracted signal related to Sn phase (jcpds 03-065-0296) coexists with (100) and (110)

diffracted peaks of Mg related to (hcp) and (bcc) phases, respectively.

Figure III. 13: X-ray diffraction patterns of the film with 33.5 at. % Sn deposited on glass substrate

and post annealed in vacuum (10-4 Pa) for 2 h at different temperatures.

• Mg2Sn (36 at. % Sn):

Figure III.14 shows the XRD patterns of film with 36 at. % Sn, annealed in vacuum at different

temperatures up to 600 °C. Until 300 °C, the cubic Mg2Sn structure coexists with (211)

diffracted peak related to the metastable orthorhombic Mg2Sn phase. For temperatures in-

between 350-500 °C, the metastable orthorhombic phase disappears and the well-crystallized

stable cubic Mg2Sn structure is obtained. As this sample has a non-stoichiometric composition

(Sn-rich content) in the temperature above 350 °C, the excess of Sn begins to release with the

appearance of Sn secondary phase as shown by (200) diffracted signal related to Sn phase at 2θ

≈ 37°. For temperatures higher than 500 °C, the cubic Mg2Sn structure vanishes (decomposition

of Mg2Sn phase leading to Mg and Sn formation). The (200) diffracted signal related to Sn

phase (jcpds 03-065-0296) coexists with (100) and (110) diffracted peaks of Mg related to (hcp)

and (bcc) phases, respectively.


Figure III. 14: X-ray diffraction patterns of the film with 36 at. % Sn deposited on glass substrate and

post annealed in vacuum (10-4 Pa) for 2 h at different temperatures.

Figure III.15 shows the top surface observation (a) and X-ray mapping (b) of the film with 36

at. % Sn deposited on a glass substrate after 2 h annealing at 600 °C under vacuum (10-4 Pa). It

is noticeable that the film morphology completely changed. Sn atoms segregated from Mg2Sn

layer and an entirely film decomposition happened. As confirmed by X-ray mapping image

heterogeneous Sn and Mg areas are formed. This result is in good agreement with XRD patterns

of this sample after an annealing at the temperature above 500 °C (figure III.14).

Figure III. 15 : (a) Top surface observation and (b) X-ray mapping of the film with 36 at. % Sn

deposited on glass substrate after 2 h annealing at 600°C under vacuum (10-4 Pa).

• Mg2Sn (38 at. % Sn):

Figure III.16 shows the XRD patterns of the film with 38 at. % Sn after annealing treatments

up to 600 °C under vacuum. Until 150 °C, the orthorhombic Mg2Sn structure remains. As this

sample has a non-stoichiometric composition (Sn-rich content) in the temperature above 200

°C, the excess of Sn begins to release with the appearance of Sn secondary phase ((200)

diffracted signal related to Sn phase is detected at 2θ ≈ 37°). For temperatures in-between 300-


400 °C, the cubic Mg2Sn structure coexists with (211) and (200) diffracted peaks related to the

metastable orthorhombic Mg2Sn phase and Sn secondary phase, respectively.

For temperatures 450-500 °C, the cubic Mg2Sn structure coexists with the metastable

orthorhombic Mg2Sn phase and body centered tetragonal Sn phase. Furthermore, the diffracted

peaks (100) and (110) related to Mg (hcp) and (bcc) phases respectively, appear in this

temperature range.

For temperatures higher than 550 °C, the cubic and orthorhombic Mg2Sn structures vanish

(decomposition of Mg2Sn phase leading to Mg and Sn formation). The (200) diffracted signal

related to Sn phase (jcpds 03-065-0296) coexists with (100) and (110) diffracted peaks of Mg

related to (hcp) and (bcc) phases, respectively.

Figure III. 16: X-ray diffraction patterns of the film with 38 at. % Sn deposited on glass substrate and

post annealed under vacuum (10-4 Pa) for 2 h at different temperatures.

III.3. Cu-doping impact on stoichiometry and Mg-deficiency thin films

Cu-doped Mg-Sn coatings were synthesized by co-sputtering of Mg, Sn and Cu (purity 99.9 at.

%, = 50 mm, thickness= 3 mm) targets in a pure argon atmosphere. The Mg and Sn targets

were powered by pulsed (DC) power supplies (Pinnacle, Advanced Energy). The Cu target was

powered by DC power supply (MDX 500, Advanced Energy). The main sputtering parameters

are summarized in Table III.2

Table III. 2: Sputtering parameters used during deposition of Cu-doped Mg2Sn coatings.

Target

Discharge

Power Frequency Toff

Ar Flow

Rate

Working

Pressure

Run

Duration

Draw

Distance

(DT-S)

(W) (kHz) (µs) (sccm) (Pa) (min) (mm)

Sn 50 and 56 50

50

0

4

4

0

50 0.41 20 60 Mg

Cu

73

0→1


Figure III.17 repeats the evolution of the atomic concentration of Sn measured by EDS analyses

for each coating deposited on fused quartz as a function of the power ratio applied to each target

(PSn/PMg) presented in the previous part of this study (figure III.1). In this part, the sputtering

parameters of closed symbols are selected and the power discharge on Cu target was adjusted

to investigate the effect of the Cu doping (0, 0.5 and 1.5 at. % Cu) on stoichiometry and Mg

deficiency thin films.

Figure III. 17: Evolution of the Sn atomic concentration in the films measured by Energy-Dispersive

X-ray Spectroscopy (EDS) vs. sputtering power ratio applied to Mg and Sn targets (figure III.1 was

repeated). The red dotted line is a guide for the eye. Sputtering parameters of closed symbols are used in

this part to investigate the effect of the Cu doping on stoichiometry and Mg deficiency thin films.

Table III.3 shows the thickness and composition of both groups of samples. The chemical

composition of coatings deposited on fused quartz were measured by EDS analyses. Three

different zones of each coating were selected for EDS measurements and the average

concentration was calculated. EDS analyses show relatively homogeneous composition on the

entire surface of deposited thin films.

Table III. 3 : Composition and thickness of deposited Cu-doped Mg2Sn thin films

Group no. Sample

no.

Mg content

(at. %)

Sn content

(at. %)

⌈𝑴𝒈⌉

[𝑺𝒏]

Cu content

(at. %)

Thickness

(±20 nm)

Group I

Sample # 1 67±1 33±1 2 0.0 1000

Sample # 2 67±1 33±1 2 0.5 970

Sample # 3 66±1 33±1 2 1.5 1200

Group II

Sample # 4 64±1 36±1 1.75 0.0 1000

Sample # 5 63±1 36±1 1.75 0.5 1100

Sample # 6 63±1 35±1 1.75 1.5 1100

III.3.1. Structural and morphological characterization of Cu-doped Mg2Sn thin films

Figure III.18 displays the X-ray diffraction patterns of both groups as a function of Cu atomic

concentrations. The XRD results show a well-crystallized stable cubic (fcc) Mg2Sn structure

for undoped films of group I. For Cu doped films of group I, the diffracted peaks of cubic

Mg2Sn phase (jcpds 03-065-2997) coexists with (422) and (221) very weak diffracted signals


related to the metastable orthorhombic Mg2Sn phase (jcpds 00-031-0812). For all samples of

group II, the diffracted peaks of cubic Mg2Sn (jcpds 03-065-2997) coexist with (400), (221)

and (422) diffracted signals corresponding to the metastable orthorhombic phase (jcpds 00-031-

0812). Assuming a stoichiometry close to Mg62Sn38, the proportion of orthorhombic phase

determined from the chemical content of the film is less than 5% in the undoped samples of

group I and reaches 57 % in the undoped sample of group II. In addition, it is worth of noting

that the cubic phase in group I crystallizes mostly along the (111) preferential direction while

this preferential direction becomes less important in group II. For all doped films of both

groups, even with a large amount of Cu (as high as 1.5 at. %), no traces of secondary phase

related to Cu is observed.

Figure III. 18: XRD patterns of Mg-Sn coatings deposited on glass substrate as a function of the

atomic concentration of Cu. a) group I with ⌈Mg⌉

[Sn]= 2, b) group II with

⌈Mg⌉

[Sn]= 1.75

Figure III.19 reveals top surface morphology and brittle fracture cross-section observations of

thin films deposited on glass substrates by SEM. For group I, the granular morphology with a

lateral grain size of about 70 nm is evident for the undoped samples and by raising the content

of Cu, separated granular morphology becomes more compact with a lower porosity and cone-

like shape microstructures. The brittle fracture cross section observation of undoped film in

group I, shows a relatively dense morphology with some porosities and open spaces. The

structure becomes more columnar with a less porous microstructures for the films with 0.5 and

1.5 at. % of Cu of group I.

The small cone-like morphology can be seen for undoped films of group II. By Cu-doping, the

smooth surface with a larger cone-like shape is observed for the other films of group II. The

undoped thin film of group II, exhibits a relatively dense and columnar morphology. The films

with 0.5 and 1.5 at. % Cu of group II show a more compact and larger columnar morphology.

It is worth noting that all samples perfectly cover the surface of the substrate and no cracks and

delamination were detected on the top surface of the films, and a good adhesion between films

and substrate was observed.


Figure III. 19: SEM micrographs of deposited films on glass substrate and SEM cross section

micrographs vs. atomic concentration of Cu. a) group I with ⌈Mg⌉

[Sn]= 2, b) group II with

⌈Mg⌉

[Sn]= 1.75.

III.3.2. Measurement of electronic transport properties of Cu-doped Mg2Sn thin films

The electronic transport properties of Cu-doped Mg2Sn thin films vs. temperature were

measured in air by Hall effect. The temperature dependence of electrical conductivity is shown

in figure III.20. For all films, the electrical conductivity increases with the temperature. No

changes corresponding to some chemical or structural modifications occur in the films. In group

I, by raising the Cu content in the films, the electrical conductivity increases. For the film with

1.5 at. % Cu of group I, the electrical conductivity reaches 1.89×104 S m-1 at 200 °C while for

undoped sample of this group, it does not exceed 1.53×104 S m-1 at 200 °C. It is worth to note

that for all samples of group I, the electrical conductivity increases with temperature which

indicates a semiconducting-like behaviors. In group II, undoped and doped films with 1.5 at. %

Cu show the highest electrical conductivity (4.5×104 S m-1 at 200 °C). The film with 0.5 at. %

Cu has a relatively low electrical conductivity (2.26×104 S m-1 at 200 °C) in group II. For the

undoped film of group II, the electrical conductivity remains constant vs. temperature.


Figure III. 20 : Electrical conductivity of Cu doped (0, 0.5 and 1.5 at. % Cu) thin films of group I and

group II vs. temperature.

Figure III.21 shows the variation of carrier concentration vs. temperature for all samples. For

the undoped films of group I, the carrier concentration is relatively constant while for Cu-doped

samples, the carrier concentration increases with temperature. The carrier concentration is close

to 4×1026 m-3 at 200 °C for the film of group I with 1.5 at. % Cu. Surprisingly, the undoped

sample of group II exhibits the highest carrier concentration when increasing temperature and

the lowest carrier concentration is obtained for the sample with 0.5 at. % Cu in this group. The

carrier concentration gradually increases with temperature for all films of group II. As

previously discussed in III.2.2., Liu et al. [Liu et al., 2016] reported the effect of intrinsic point

defects on electronic transport properties of Mg2X (X = Si, Ge, Sn) systems. They showed that

Mg vacancies and interstitial Mg are supposed to be the main defects in Mg2X compounds due

to their relatively low formation energies. Mg vacancies and interstitials behave as acceptor and

donor sites, respectively. As a consequence, the higher value of carrier concentration for

undoped Mg2Sn films of group II compared with the undoped films of group I can be explained

by the formation of Mg vacancies which is more probable in the films containing an excess of

Sn. Furthermore, Tani and Kido [Tani et al., 2012] studied the formation energy of impurities

in Mg2Sn. They reported the Cu-substitution preference on Mg-site or Sn-site is highly

dependent on Sn content in Mg2Sn system. In the case of Sn-rich Mg2Sn materials (such

compounds are similar to that of group II), Cu substitution occurs mainly in Mg-sites and

reduces the carrier concentration. Choi et al. [Choi et al., 2012] assumed that in Sn-rich systems,

Cu atoms are trapped at the grain boundary and do not react with the Mg2Sn matrix which

probably happens for the films of group II as the grain boundary increases due to the coexistence

of two phases in this group. They also supposed that Cu atoms do not substitute to Sn atoms,

but react with Sn atoms, forming CuxSny trace phase. Furthermore, the formation of this new

second phase disturbs the formation of the p-type Mg-deficient in Mg2Sn phase. As shown in

figure III.18.b, by increasing the Cu-doping in films of group II, the intensity of the cubic phase

increases compared to the undoped films of this group. It can be assumed that by forming


CuxSny trace phase (not detectable by XRD analysis), the Mg/Sn ratio changes, and these

samples are not Sn-rich enough compared to the undoped films of this group. These may also

explain why there is no enhancement of the carrier concentration in the films of group II by Cu

doping. In group I, it is supposed that Cu reacts with Mg and leads to Mg-deficient state. The

orthorhombic phase is formed (figure III.18.a) and consequently improves the carrier

concentration in films of group I. Despite these considerations, the evolution of the carrier

concentration with the Cu content in group II is still an open question.

Figure III. 21: Carrier concentration of Cu doped Mg-Sn (0, 0.5 and 1.5 at. % Cu) thin films in groups

I and II vs. temperature.

The temperature dependence of carrier mobility for all samples is shown in figure III.22. The

higher carrier mobility is observed for the films of group II explaining the higher electrical

conductivity of the group II. It was already observed in section III.2.2. that the metastable

orthorhombic phase exhibits a higher carrier mobility than the cubic Mg2Sn phase. The carrier

mobility for the undoped film of group I containing the fcc structure is nearly unaffected by the

temperature while it slightly decreases for doped-films of this group, probably due to the charge

carriers scattering on the Cu ions with their increasing content, and/or because of their “open”

morphology. As a result, carrier mobility in Cu-doped or Mg-deficient thin films is more

sensitive to the film composition and defects than temperature.

The electronic transport mechanisms are then ruled by chemical and structural defects than

electron-phonon scattering as typically described in many semiconducting materials containing

a low concentration of defects. That’s explain why the conductivity slope is smaller for the

coating containing 1.5 at. % Cu than for the undoped coating. In undoped Mg2Sn systems, the

carrier mobility is relatively low for the films with the cubic structure (group I), carrier mobility

increases in undoped films of group II because of the formation of metastable orthorhombic

Mg2Sn. It is important to remember that the highest carrier mobility is observed for the single

phase orthorhombic Mg2Sn (figure III.7). In group II, the lowest carrier mobility is obtained for


undoped films, and in contrary with the behavior of the films in group I, it can be observed that

the Cu doping in the films of group II leads to an enhancement of the carrier mobility.

Figure III. 22: Carrier mobility of Cu doped Mg-Sn (0, 0.5 and 1.5 at. % Cu) thin films in group I and

II vs. temperature.

III.3.3. Measurement of optic bandgap of Cu-doped Mg2Sn thin films

From Hall effects measurements, resistivity and Hall coefficient are connected via the following

relation:

𝜌 =1

𝑅𝐻𝑒 (III.2)

Where RH is the Hall coefficient (Ω m T-1), e the elementary charge (1.6×10-19 As) and ρ the

hole carrier concentration (m-3) which is extracted from the measured Hall coefficient. The Hall

mobility µH (m2 V-1 s-1) is given by the following equation:

µ𝐻 = 𝑅𝐻 . 𝜎 (III.3)

Where σ is the electrical conductivity (S m-1). Assuming that in the intrinsic temperature range,

the hole concentration ρ of a semiconductor is almost equal to the electron concentration:

𝜌 = 𝑛 = 2(𝐾𝐵 𝑇

2𝜋ћ2)3

2⁄ (𝑚𝑒 𝑚ℎ)3

4⁄ exp(−𝐸𝑔

2𝐾𝐵 𝑇) (III.4)

Where KB is the Boltzmann constant (1.38×10-23 J K-1), ћ the reduced Planck’s constant

(1.05×10-34 J s), me the effective mass of electron (kg), mhthe effective mass of hole and Eg the

bandgap (eV). The hole and electron mobilities both vary as Tr. Then by combining equations

(III.3-III.4), plotting ln[σT-(r+1.5)] vs. T-1 is linear with -Eg

2KB as the slope [Chen et al., 2010]. By

using the experimental data, the undoped sample in group I, r takes -2.8 and by plotting the


ln[σT1.3] vs. 1000/T, the bandgap energy is about 0.30 eV, which is in good agreement with the

literature (figure III.23) [Savvides et al., 2010].

Figure III. 23 : plot of ln(σT1.3) as a function of reciprocal temperature for un-doped Mg2Sn in group I

([Mg]

[Sn]= 2)

For other samples, the calculated bandgap energy is not relevant. Figure III.24 shows the

Kubelka-Munk transformed absorption spectra for both groups.

Figure III. 24 : Kubelka-Munk transformed absorption spectra used to estimate the bandgap of Cu-

doped Mg-Sn (0, 0.5 and 1.5 at. % Cu) thin films a) in group I and b) in group II.

The optical bandgap estimation for all samples by using the Kubelka-Munk method are

summarized in table III.4.

Table III. 4 : Bandgap of thin films obtained by the Kubelka-Munk’s method (± 0.02 eV)

Samples Group I Bandgap (eV) Samples Group II Bandgap (eV)

0 at. % Cu 0.46 0 at. % Cu 0.47

0.5 at. % Cu 0.47 0.5 at. % Cu 0.48

1.5 at. % Cu 0.48 1.5 at. % Cu 0.47

The optical bandgap energy of undoped stoichiometric Mg2Sn is about 0.46 eV, which is a little

higher than previously reported values (0.33-0.36 eV) [Tani et al., 2012]. When the charge


carrier concentration increases with the Cu content in stoichiometric films of group I, the

apparent optical bandgap energy slightly increases as well. In the case of group II, the optical

bandgap remains quite constant with Cu doping. Again, the optical bandgap behavior vs. Cu

doping is unclear, probably due to the alteration of the optical properties with the crystallization

of the orthorhombic phase induced by the Mg content lowering.

III.3.4. Measurement of thermoelectric properties of Cu-doped Mg2Sn thin films


temperatures by means of TFA device on Linseis chip covered by undoped or Cu-doped Mg-

Sn thin films.

For group I, the electrical conductivity increases by raising the Cu concentration (figure III.25).

For group II, the conductivity is relatively the same for undoped films and sample doped with

0.5 at. % Cu but surprisingly in the case of the film doped with 1.5 at. % Cu, the electrical

conductivity decreases. It is right to note that all samples of group II display the highest

electrical conductivity over the entire temperature range compared to the samples of group I.

Electrical conductivity of the films measured in vacuum displays lower values compare to

measurements performed in air.

Figure III. 25: Electrical conductivity of Cu doped Mg-Sn (0, 0.5 and 1.5 at. % Cu) thin films in group

I and II vs. temperature.

The same dependencies of the film’s electrical conductivity vs. temperature are observed in

vacuum and air for the films of group I. The films are thermally activated, and Cu doping in

stoichiometric compounds leads to higher electrical conductivity. However, in the groups II,

the electrical conductivity variations vs. temperature in air and vacuum do not exhibit the

similar behaviors while Cu concentration increases. Therefore, samples with 0.5 and 1.5 at. %

Cu of group II, deposited on glass substrate were annealed in vacuum (10-4 Pa) and in air at 200

°C for 2 hours. Such treatments were performed to better understand the difference between


electrical conductivity values measured in air and in vacuum in this group. Figure III.26

illustrates top surface morphology observations by SEM of annealed films. The film containing

0.5 at. % Cu remains compact after annealing (air and vacuum) while the sample with 1.5 at.

% Cu only remains compact in air. With 1.5 at. % Cu and after annealing under vacuum, the

films become more columnar with separated open spaces. As expected, the film with a compact

morphology should lead to a better electrical and thermal conductivity [Le-Quoc et al., 2012].

Figure III. 26: SEM micrographs of deposited films with 0.5 and 1.5 at. % Cu of group II on glass

substrate: As deposited and after 2h annealing in air and in vacuum.

The crystallographic structure of samples with 0.5 and 1.5 at. % Cu of group II, after annealing

at 200 °C for 2 hours under in air and vacuum was checked by XRD analysis as shown in figure

III.27. The crystallite size was estimated using Scherrer's formula. In the case of the sample

with 1.5 at. % Cu annealed under vacuum, the crystallite size decreases when annealing

temperature rises. Consequently, the difference between electrical conductivity values

measured in air and in vacuum can be related to this unusual variation of crystallite size.

Figure III. 27 : a) X-ray diffraction patterns of the deposited films with 0.5 and 1.5 at. % Cu of group

II on glass substrate: As deposited and after 2h annealing in air and in vacuum, b) grain size of the

films with 0.5 and 1.5 at. % Cu of group II after 2h annealing in air and under vacuum.


Figure III.28 presents the variation of the Seebeck coefficient vs. temperature. All samples can

be considered as p-type conductors since the Seebeck coefficient is positive throughout the

temperature range. The highest value of Seebeck coefficient belongs to undoped films with S

close to 174 µV K-1 at 30 °C. The Seebeck coefficient decreases with temperature for undoped

Mg2Sn films of group I. For the sample containing 0.5 at. % Cu (group I), the Seebeck

coefficient first slightly increases up to 100 °C and then decreases. The Seebeck coefficient for

sample with 0.5 at. % Cu of group I reaches the same value as the undoped film at 120 °C and

remains higher than it for the upper temperature. For the film with 1.5 at. % Cu of group I, the

Seebeck coefficient increases with temperature and never exceeds 97 µV K-1. This sample

shows the lowest Seebeck coefficient, despite Cu doping. In group II, the undoped sample and

the film with 0.5 at. % Cu show relatively the same Seebeck coefficient through the temperature

range. The sample with 1.5 at. % Cu presents the highest Seebeck coefficient of group II with

S = 130 µV K-1 at 30 °C. It is also interesting to note some correlations between the evolution

of the carrier concentration (Figure III.21) and Seebeck coefficient (Figure III.27) as a function

of the temperature and Cu concentration. It is commonly reported that the Seebeck coefficient

of semiconductors typically decreases when the concentration of charge carriers increases

[Levin, 2016]. Assuming a simple model of electron transport, Seebeck coefficient S is

inversely proportional to the hole concentration p (S 1/p2/3) for a given temperature [Snyder

et al., 2008]. Our results well agree with these theoretical models where Cu-doped Mg2Sn films

exhibit a clear decrease of Seebeck coefficient as the hole concentration rises and by changing

the temperature, particularly for the films of group I.

Figure III. 28: Seebeck coefficient of Cu doped Mg-Sn (0, 0.5 and 1.5 at. % Cu) thin films in group I

and II vs. temperature.

Figure III.29 illustrates the thermal conductivity for all samples as a function of the temperature.

For group I, the thermal conductivity increases with Cu doping. The sample with 1.5 at. % Cu

shows the highest thermal conductivity of about 1.85 W m-1 K-1. For undoped sample, the


thermal conductivity raises with temperature. The film with 0.5 at. % Cu exhibits a relatively

constant thermal conductivity until 140 °C. In group II, the thermal conductivity of undoped

sample drops with temperature till 150 °C and goes up again. For the sample with 0.5 at. % Cu

of group II, the thermal conductivity rises as the temperature reaches 140 °C and then reduces.

The sample containing 1.5 at. % Cu offers the lowest thermal conductivity. For this sample, the

thermal conductivity decreases till 60 °C and then for temperature above goes up.

Figure III. 29: Thermal conductivity of Cu doped Mg-Sn (0, 0.5 and 1.5 at. % Cu) thin films in group I


Figure III.30 shows the variation of figure of merit ZT vs. temperature for all thin films. For the

samples of group I, ZT is the highest with 0.07 at 200 °C. This ZT value is related to the sample

with 0.5 at. % Cu, which is about four times more than the ZT for undoped sample of this group.

This enhanced ZT value is related to a high and stable Seebeck coefficient combined with

moderate electrical conductivity. The ZT value of the film containing 1.5 at. % Cu of group I is

almost the same as the undoped film of the same group, because of the limited Seebeck

coefficient. The samples of group II show higher ZT values. The highest ZT of group II is

obtained for undoped and doped with 0.5 at. % Cu which is about 0.27 at 200 °C. The sample

with 1.5 at. % Cu shows higher ZT values at a lower temperature compared with other samples

of the same group. It is believed that these ZT improvements of group II are due to the

metastable phase exhibiting higher electrical mobility rather than the change in the preferential

orientation of the cubic phase.


Figure III. 30: Figure of merit ZT of Cu doped Mg-Sn (0, 0.5 and 1.5 at. % Cu) thin films in group I


III.4. Conclusion

In the first part of this chapter, Mg-Sn thin films (21 ≤ at. % Sn ≤ 42.5) were successfully

deposited by magnetron co-sputtering in an argon atmosphere. The film structure is strongly

affected by the Sn atomic concentration. Thin films containing 21≤ at. % Sn ≤ 25 have fcc

Mg2Sn structure with a secondary phase of Mg. The latter vanishes and fcc Mg2Sn structure

remains stable in the range of 30 ˂ at. % Sn < 33.5. Thin films with 35 ≤ at. % Sn ≤ 37.4 exhibit

a mixture of cubic and orthorhombic Mg2Sn phases. Films with 37.6 up to 38 at. % Sn adopt

the orthorhombic Mg2Sn structure and finally for the coatings containing 39.5≤ at. % Sn ≤ 42.5,

orthorhombic Mg2Sn structure with secondary phase of Sn co-exist. Thermal stability of the

Mg-Sn films with different crystal structure was studied under vacuum. Such treatments were

performed to determine the stability and structural decomposition temperature limit for each

sample. In this group the film with 33.5 at. % Sn (fcc) showed the highest thermal stability. For,

this sample till 500 °C, the face centered cubic structure remains. For temperatures higher than

500 °C, the cubic Mg2Sn structure vanishes and decomposition of Mg2Sn phase occurs which

is leading to Mg and Sn formation. For the film with 36 at. % Sn (fcc + orthorhombic) until

300°C, the mixed structure remains stable. The orthorhombic phase transforms to cubic while

annealing temperature increases from 350 °C to 500 °C and the secondary phase of Sn began

to form. Finally, at temperatures higher than 500 °C, Mg2Sn thin film completely decomposes

into Mg and Sn. For the sample with 38 at. % Sn (orthorhombic), till 150 °C, the orthorhombic

Mg2Sn structure remains. As this sample has a non-stoichiometric composition (Sn-rich

content) in the temperature above 200 °C, the excess of Sn begins to release as Sn secondary

phase. For temperatures in-between 300-400 °C, the cubic Mg2Sn structure coexists with the

metastable orthorhombic Mg2Sn phase and Sn secondary phase, respectively. For temperatures

450-500 °C, the cubic Mg2Sn structure coexists with the metastable orthorhombic Mg2Sn phase


and body centered tetragonal Sn phase. For temperatures higher than 550 °C, the cubic and

orthorhombic Mg2Sn structures vanish and decomposition of Mg2Sn phase was leading to Mg

and Sn formation.

Thermoelectric properties of the films with different structures were discussed as a function of

the temperature. With formation of orthorhombic Mg2Sn structure, ZT value is enhanced

compared to that of the film with cubic Mg2Sn structure. ZT values increase with temperature

for orthorhombic Mg2Sn coatings. The highest values of ZT = 0.26 is obtained at 200 °C while

cubic and orthorhombic Mg2Sn phases (36 at. % Sn) coexist in the films.

In the second part of this chapter, two groups of Mg-Sn thin films were deposited by co-

sputtering of Mg, Sn and Cu targets in an argon atmosphere. The effect of Mg-deficiency and

Cu-doping on thermoelectric properties of Mg-Sn was studied. Group I with ⌈Mg⌉/[Sn] =2 and

group II with ⌈Mg⌉/[Sn] =1.75 were doped by different Cu concentrations (0, 0.5 and 1.5 at.

%). Only the film with 0 at. % Cu of group I showed a stable face-centered cubic structure. For

other samples in both groups, a mixture of face-centered cubic and metastable orthorhombic

phases coexists. The thermoelectric properties of both groups were discussed in a wide range

of temperatures (30-200 °C) to investigate the influence of Cu-doping. It is shown that the Cu

introduction in stoichiometric and cubic Mg2Sn compound improves the electronic properties,

as expected, but also the thermal conductivity and in contrast to the decrease of the Seebeck

coefficients leading to the improvement of the thermoelectric properties in a restraint range.

The highest ZT value of about 0.07 was obtained at 200 °C with 0.5 at. % of Cu in group I. The

films of group II with a Mg-deficiency shows a different behavior. They exhibit higher

electrical conductivities due to a better carrier mobility. Thermal conductivities and Seebeck

coefficients of the same order of magnitude than in stoichiometric films were obtained in group

II. These features develop higher thermoelectric properties, almost 4 times higher (ZT = 0.27 at

200 °C for the film doped with 0.5 at. % of Cu). It is believed that the mixture of cubic and

orthorhombic phases contributes to the achievement of a higher carrier mobility.

Thermoelectric properties of the Mg2Sn films improved while a mixture of cubic and

orthorhombic coexist.


III.5. References

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Chen, H. Y., Savvides, N., Dasgupta, T., Stiewe, C., & Mueller, E. (2010). Electronic and

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intrinsic point defects in Mg2X (X = Si, Ge, Sn) thermoelectric materials. Advanced Electronic

Materials, 2, 1500284-1500294.

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Mg2Sn: Ag crystals. Journal of Electronic Materials, 39, 2136–2141.


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Chapter 4

Thermoelectric performance of Mg2Si1-xSnx

and Mg2Ge1-xSnx solid solutions

Table of contents

IV.1. Introduction ................................................................................................................................ 108

IV.2. Mg2Si1-xSnx thin films ................................................................................................................ 108

IV.2.1 Structural and morphological characterization of Mg2Si1-xSnx thin films ................................ 110

IV.2.2. Measurement of electronic transport properties of Mg2Si1-xSnx thin films ......................... 111

IV.2.3. Measurement of thermoelectric properties of Mg2Si1-xSnx thin film .................................. 113

IV.2.4. Thermal stability of the Mg2Si1-xSnx thin films .................................................................. 116

IV.3. Ge-doped Mg2Si0.35Sn0.65 thin films ........................................................................................... 117

IV.3.1. Structural and morphological characterization of Ge-doped Mg2Si0.35Sn0.65 thin films ...... 117

IV.3.2. Measurement of electronic transport properties of Ge-doped Mg2Si0.35Sn0.65 thin films .... 119

IV.3.3. Measurement of thermoelectric properties of Ge-doped Mg2Si0.35Sn0.65 thin films ............ 121

IV.3.4. Thermal stability of the Ge-doped Mg2Si0.35Sn0.65 thin films .............................................. 123

IV.4. Mg2Ge1-xSnx thin films ............................................................................................................... 124

IV.4.1 Structural characterization and thermal stability of the Mg2Ge1-xSnx thin films .................. 125

IV.4.2 Morphological characterization of Mg2Ge1-xSnx thin films ................................................. 127

IV.4.3. Measurement of electronic transport properties of Mg2Ge1-xSnx thin films........................ 128

IV.4.4. Measurement of thermoelectric properties of Mg2Ge1-xSnx thin films ............................... 130

IV.5. Conclusion ................................................................................................................................. 133

IV.6. References .................................................................................................................................. 135

List of Figures

Figure IV. 1: Evolution of stoichiometric ratio of Mg, Si, and Sn in Mg2Si1-xSnx thin films vs. sputtering power ratio applied on each target ............................................................................. 109

Figure IV. 2: a) X-ray diffraction patterns for thin films of Mg2Si1-xSnx, b) Evolution of Mg2Si1-xSnx

lattice parameters (a) vs. Sn concentration, and c) Evolution of Mg2Si1-xSnx crystallite size

estimated by Scherrer's formula vs. Sn concentration ................................................................ 110

Figure IV. 3: SEM micrographs of films deposited on glass substrate (a-c) and SEM cross section

micrographs (d-f) of Mg2Si1-xSnx with different compositions. .................................................. 111

Figure IV. 4: DC electrical resistivity vs. temperature of Mg2Si1-xSnx thin films measured in air. .... 112

Figure IV. 5: Carrier concentration vs. temperature of Mg2Si1-xSnx thin films in air. ......................... 112

Figure IV. 6: Carrier mobility vs. temperature of Mg2Si1-xSnx thin films in air. ................................. 113

Figure IV. 7: Electrical conductivity vs. temperature of Mg2Si1-xSnx thin films measured in vacuum by

TFA device. ................................................................................................................................ 113

Figure IV. 8: X-ray diffraction patterns for thin films after 2 h annealing in air and in vacuum: a)

Mg2Si0.7Sn0.3, b) Mg2Si0.35Sn0.65 and c) Mg2Si0.3Sn0.7 ................................................................. 114

Figure IV. 9: Seebeck coefficient vs. temperature of Mg2Si1-xSnx thin films measured by TFA device

in vacuum. .................................................................................................................................. 114

Figure IV. 10: Thermal conductivity vs. temperature of Mg2Si1-xSnx thin films measured by TFA

device in vacuum. ....................................................................................................................... 115

Figure IV. 11: Figure of merit (ZT) of Mg2Si1-xSnx thin films measured by TFA device in vacuum vs.

temperature (a) Zoom area of ZT variation vs. Temperature (b) ................................................ 115

Figure IV. 12: X-ray diffraction patterns of the Mg2Si1-xSnx thin films deposited on glass substrate and

post annealed in vacuum (10-4 Pa) for 2 h at different temperatures: a) Mg2Si0.7Sn0.3, b)

Mg2Si0.35Sn0.65, and c) Mg2Si0.3Sn0.7 ........................................................................................... 116

Figure IV. 13: XRD patterns of Ge-doped Mg2Si0.35Sn0.65 coatings deposited on glass substrate as a

function of the Ge atomic concentration. ................................................................................... 118

Figure IV. 14: SEM micrographs of Mg2Si0.35Sn0.65 thin films doped with different Ge concentrations

deposited on glass substrate (a-d) and SEM cross section micrographs (e-h) vs. Ge atomic

concentration. ............................................................................................................................. 119

Figure IV. 15: DC electrical conductivity of Ge-doped Mg2Si0.35Sn0.65 thin films vs. temperature

measured in air by hall effect ...................................................................................................... 120

Figure IV. 16: Carrier concentration vs. temperature of Ge-doped Mg2Si0.35Sn0.65 thin films in air. .. 120

Figure IV. 17: Carrier mobility vs. temperature of Ge-doped Mg2Si0.35Sn0.65 thin films in air. .......... 121

Figure IV. 18: Electrical conductivity vs. temperature of Ge-doped Mg2Si0.35Sn0.65 thin films measured

by TFA device in vacuum........................................................................................................... 121

Figure IV. 19: Seebeck coefficient vs. temperature of Ge-doped Mg2Si0.35Sn0.65 thin films measured by

TFA device in vacuum. .............................................................................................................. 122

Figure IV. 20: Thermal conductivity of Ge-doped Mg2Si0.35Sn0.65 thin films measured by TFA device

in vacuum vs. temperature .......................................................................................................... 123

Figure IV. 21 : Figure of merit (ZT) vs. temperature of Ge-doped Mg2Si0.35Sn0.65 thin films measured

by TFA device in vacuum (a) and zoom of ZT variation vs. temperature (b) ............................ 123

Figure IV. 22: X-ray diffraction patterns of the Ge-doped Mg2Si0.35Sn0.65 thin films deposited on glass

substrate and post annealed in vacuum (10-4 Pa) for 2 h at different temperatures. Doped with: a)

1 at. % Ge, b) 4 at. % Ge, and c) 7 at. % Ge .............................................................................. 124

Figure IV. 23: X-ray diffraction patterns of as deposited Mg2Ge1-xSnx on glass substrate and post

annealed in vacuum (10-4 Pa) for 2 h at different temperatures. a) Mg2Ge, b) Mg2Ge0.5Sn0.5, c)

Mg2Ge0.3Sn0.7, and d) Mg2Sn. ..................................................................................................... 126

Figure IV. 24 : X-ray diffraction patterns for thin films of Mg2Ge1-xSnx. ........................................... 127

Figure IV. 25: SEM micrographs of films deposited on glass substrate (a-d) and SEM cross section

micrographs (e-h) of Mg2Ge1-xSnx with different compositions. ................................................ 128

Figure IV. 26: DC electrical conductivity of Mg2Ge1-xSnx thin films vs. temperature ....................... 129

Figure IV. 27: Carrier concentration of Mg2Ge1-xSnx thin films vs. temperature ................................ 129

Figure IV. 28: Carrier mobility vs. temperature of Mg2Ge1-xSnx thin films. ....................................... 130

Figure IV. 29: Electrical resistivity vs. temperature of Mg2Ge1-xSnx thin films measured by TFA

device under vacuum. ................................................................................................................. 131

Figure IV. 30 : Seebeck coefficient vs. temperature of Mg2Ge1-xSnx thin films measured by TFA

device in vacuum. ....................................................................................................................... 131

Figure IV. 31 : Thermal conductivity vs. temperature of Mg2Ge1-xSnx thin films measured by TFA

device in vacuum. ....................................................................................................................... 132

Figure IV. 32: Figure of merit (ZT) vs. temperature of Mg2Ge1-xSnx thin films measured by TFA

device in vacuum. ....................................................................................................................... 132

List of Tables

Table IV. 1 : Sputtering parameters used during deposition of Mg2Si1-xSnx coatings. ....................... 108

Table IV. 2 : Composition and thickness of deposited Mg2Si1-xSnx thin films ................................... 109

Table IV. 3 : Bandgap of Mg2Si1-xSnx thin films obtained by Kubelka-Munk’s method ( 0.02 eV) 109

Table IV. 4 : Sputtering parameters used during deposition of Ge-doped Mg2Si0.35Sn0.65 coatings. ... 117

Table IV. 5 : Composition and thickness of Ge-doped Mg2Si0.35Sn0.65 ............................................... 117

Table IV. 6 : Sputtering parameters used during deposition of Mg2Ge1-xSnx coatings. ...................... 125

Table IV. 7 : Composition and thickness of Mg2Ge1-xSnx thin films .................................................. 125

Thermoelectric performance of Mg2Si1-xSnx and Mg2Sn1-xGex solid solutions 108

IV.1. Introduction

Different strategies for improving ZT was discussed in chapter I.9. As previously noted, one of

the strategies to improve ZT was the structural modification of promising compounds by

introducing point defects through the isostructural solid solutions formation. The solid solution

features make changes in the crystal lattice (i.e., disorder) which produces strong phonon

scattering centers and reduce thermal conductivity [Kanatzidis, 2010].

In the first part of this chapter, Mg2Si1-xSnx solid solutions thin films were synthesized by

magnetron co-sputtering of Mg, Sn and Si targets in an argon atmosphere. The aim of this

investigation is to understand the influence of chemical composition on the films electronic

transport and thermoelectric properties. Thermal stability of the films was studied after

annealing in vacuum (10-4 Pa) at different temperatures.

In the second part Mg2Si0.35Sn0.65 has been selected and doped by different atomic

concentrations of Ge (0, 1, 4, and 7 at. %), in order to improve ZT in the system. The structure

and morphology of the films were investigated as a function of the Ge atomic concentration.

The film charge carrier concentration and mobility were measured to explain the electronic

transport behavior and the effect of Ge-doping on thermoelectric properties of Mg2Si0.35Sn0.65

were discussed in a range of temperatures: 30-200 °C. Thermal stability of Ge doped films were

explored after annealing in vacuum (10-4 Pa) at different temperatures.

In the last part, Mg2Ge1-xSnx (x = 0, 0.5, 0.7) thin films were deposited by magnetron co-

sputtering of Mg, Sn and Ge targets in an argon atmosphere. The thermal stability of the film

was examined after annealing in vacuum (10-4 Pa) at different temperatures. The influence of

chemical composition and crystal structure on the films electronic transport and thermoelectric

properties was discussed.

IV.2. Mg2Si1-xSnx thin films

For obtaining thin films Mg2Si1-xSnx (x= 0.3, 0.65, 0.7) with different chemical compositions,

the power was fixed at 50 W for Mg target, 20 W for Sn target and was systematically changed

on Si target from 44 to 85 W to tune the coating composition. Argon flow rate was 50 sccm and

working pressure was kept at 0.41 Pa during deposition. Substrates (Special chip produced by

Linseis, as well as alumina pellet and glass microscope slides) were placed on the substrate

holder at 60 mm from the substrate holder axis and all depositions were carried out at floating

temperature (Tsubstrate < 70 °C). The main sputtering parameters are summarized in Table IV.1.

Table IV. 1: Sputtering parameters used during deposition of Mg2Si1-xSnx coatings.

Ar flow rate (sccm) 50 Target Mg Sn Si

Working pressure (Pa) 0.41 Discharge power (W) 50 20 44→85

Draw distance (DT-S) (mm) 60 Frequency (kHz) 50 50 50

Run duration (min) 25 𝑻𝒐𝒇𝒇 (µs) 4 4 4


Table IV.2 shows the chemical composition and thickness of all coatings measured by EDS

analyses and profilometer, respectively. Three different zones of each coating deposited on

alumina pellet were selected for EDS measurements and the average concentration was

calculated. It can be noted that EDS analyses show relatively homogeneous composition on the

entire surface of deposited thin films. According to the film thickness the average rate of

deposition is about 2.5 µm h-1.

Table IV. 2: Composition and thickness of deposited Mg2Si1-xSnx thin films

Sample no. Mg content

(at. %)

Si content

(at. %)

Sn content

(at. %)

Nominal

composition

Thickness

(±20 nm)

Sample # 1 67 ±1 22 ± 0.5 11± 0.5 Mg2Si0.7Sn0.3 0.82

Sample # 2 67 ± 1 12 ± 0.5 21 ± 0.5 Mg2Si0.35Sn0.65 0.87

Sample # 3 67 ± 1 11 ± 0.5 22 ± 0.5 Mg2Si0.3Sn0.7 0.87

Figure IV.1 illustrates the stoichiometric ratio of Mg, Si, and Sn of all films deposited on

alumina pellet measured by EDS measurements as a function of applied power to each target

𝑃𝑆𝑖/(𝑃𝑀𝑔 + 𝑃𝑆𝑛) during sputtering process. For all films [Mg]/([Si]+[Sn]) is kept almost about

2. These results show that as the applied power ratio 𝑃𝑆𝑖/(𝑃𝑀𝑔 + 𝑃𝑆𝑛) increases, films become

Si-rich following a linear evolution.

Figure IV. 1: Evolution of stoichiometric ratio of Mg, Si, and Sn in Mg2Si1-xSnx thin films vs. sputtering power ratio applied on each target

The optical bandgap estimation for Mg2Si1-xSnx thin films by using the Kubelka-Munk method

are summarized in table IV.3.

Table IV. 3 : Bandgap of Mg2Si1-xSnx thin films obtained by Kubelka-Munk’s method ( 0.02 eV)

Sample Bandgap (eV) by Kubelka-

Munk

Bandgap (eV)

[Santos et al., 2018]

Mg2Si0.7Sn0.3 0.54 0.5 Mg2Si0.35Sn0.65 0.46 0.46 Mg2Si0.3Sn0.7 0.48 0.5


For the antifluorite structure of Mg2Sn and Mg2Si the band gap energy is reported about 0.35

eV and 0.77 eV, respectively. The bandgap energy, highly depends on the composition in solid

solution Mg2Si1-xSnx and has a nonlinear character. Theoretically, the lower bandgap energy

can be expected for the Sn-rich films [Zaitsev et al, 2006; Liu et al., 2012; Santos et al., 2018].

As it is shown in table IV.3, the best bandgap convergence occurs in Mg2Si0.35Sn0.65 films with

the same value reported by Santos et al. [Santos et al., 2018].

IV.2.1 Structural and morphological characterization of Mg2Si1-xSnx thin films

Figure IV.2 a presents the X-ray diffraction patterns of as-deposited coatings. All diffraction

peaks are related to the face centered cubic (fcc) antifluorite structure with the space group

𝐹𝑚3𝑚 (jcpds: 01-089-4254). The most intense peak (2𝜃 ≈ 27°) is positioned between those

of Mg2Sn (jcpds: 03-065-2997) (2𝜃 ≈ 26°) and Mg2Si (jcpds: 03-065-9365) (2𝜃 ≈ 28°),

confirming the formation of the solid solutions. The peaks gradually shift towards lower angle

by increasing Sn content, as Sn has larger ionic radius than Si. The lattice parameter (a) is

calculated using Bragg’s equation and approximately follow Vegard’s law. The lattice

parameter increases almost linearly with raising the Sn content in the films (figure IV.2 b)

[Kamila et al., 2019]. Figure IV.2 c presents the evolution of crystallite size estimated by

Scherrer's formula for as-deposited films vs. Sn concentration (at. %). Mg2Si0.35Sn0.65 has the

largest crystallite size (~57 nm). Mg2Si0.3Sn0.7 and Mg2Si0.7Sn0.3 have relatively the same

crystallite size about 40 nm.

Figure IV. 2: a) X-ray diffraction patterns for thin films of Mg2Si1-xSnx, b) Evolution of Mg2Si1-xSnx

lattice parameters (a) vs. Sn concentration, and c) Evolution of Mg2Si1-xSnx crystallite size estimated

by Scherrer's formula vs. Sn concentration

Figure IV.3 reveals top surface morphology and brittle fracture cross section observations by

SEM of thin films deposited on glass substrates. The smooth surface with granular features was

observed for the film Mg2Si0.7Sn0.3. The granular morphology with some porosities and open

spaces can be seen for Mg2Si0.35Sn0.65. By increasing the Sn content, the morphology becomes


more compact for Mg2Si0.3Sn0.7. Brittle fracture cross section observations show a relatively

dense columnar morphology for films Mg2Si0.7Sn0.3 and Mg2Si0.35Sn0.65. The film Mg2Si0.3Sn0.7

presents a dense featureless microstructure with no growing defects. All samples perfectly

cover the surface of the substrate and no cracks and delamination are detected on the top surface

of the films. A good adhesion between films and substrate is also observed.

Figure IV. 3: SEM micrographs of films deposited on glass substrate (a-c) and SEM cross section

micrographs (d-f) of Mg2Si1-xSnx with different compositions.

IV.2.2. Measurement of electronic transport properties of Mg2Si1-xSnx thin films

The electronic transport properties of Mg2Si1-xSnx thin films vs. temperature were measured in

air by Hall effect. Figure IV.4 presents the dependency of DC electrical conductivity of the

Mg2Si1-xSnx films as a function of the temperature. For all films, the electrical conductivity

increases with the temperature, which indicates a semiconducting-like behavior [Khan et al.,

2013]. Mg2Si0.7Sn0.3 shows the lowest electrical conductivity value. It does not exceed 1.4×103

S m-1 at 200 °C because in Mg2Si1-xSnx solid solution electrical conductivity decreases by Si

content [Le-Quoc et al., 2012]. Surprisingly, Mg2Si0.35Sn0.65, displays higher electrical

conductivity throughout the measured temperature range compared with Mg2Si0.3Sn0.7 while the

Sn content is lower. This unusual behavior could be explained by the larger crystallite size of


Mg2Si0.35Sn0.65 thin film (figure IV.2 c). The electrical conductivity value for this film is about

1.26×103 S m-1 at 30 °C and reaches to 4.31×103 S m-1 at 200 °C.

Figure IV. 4: DC electrical resistivity vs. temperature of Mg2Si1-xSnx thin films measured in air.

The variation of carrier concentration vs. temperature for the Mg2Si1-xSnx films is shown in

figure IV.5. The carrier concentration is improved by temperature for all films. For

Mg2Si0.3Sn0.7 and Mg2Si0.35Sn0.65, almost the same carrier concentration, about 7.5×1025 m-3 is

obtained at 40 °C. For the film Mg2Si0.35Sn0.65, the carrier concentration increases with sharper

slope, and reaches 5.6×1026m-3 at 170 °C. The Mg2Si0.7Sn0.3 film shows the lowest carrier

concentration throughout the measured temperature, and do not exceed 7.63×1025 m-3 at 200

°C.

Figure IV. 5: Carrier concentration vs. temperature of Mg2Si1-xSnx thin films in air.

Figure IV.6 presents the variation of carrier mobility vs. temperature for the Mg2Si1-xSnx films.

Mg2Si0.35Sn0.65 has the lowest carrier mobility (4.4×10-5 m2 V-1 s-1 at 30 °C). The highest carrier

mobility obtained for Mg2Si0.7Sn0.3 is about 9.9 × 10-5 m2 V-1 s-1 at 200 °C. As it can be seen in

figure IV.6, the variation of carrier mobility by temperature is insignificant for all samples. So,

we can conclude that electrical conductivity is ruled by the carrier concentration rather than

carrier mobility in these samples.


Figure IV. 6: Carrier mobility vs. temperature of Mg2Si1-xSnx thin films in air.

IV.2.3. Measurement of thermoelectric properties of Mg2Si1-xSnx thin film


temperatures using TFA device, on Linseis chips covered by Mg2Si1-xSnx thin films. The

temperature dependence of electrical conductivity for Mg2Si1-xSnx under vacuum are plotted in

figure IV.7. The electrical conductivity measured under vacuum raises with temperature for all

samples with the same trend of the electrical conductivity measured in air (figure IV.4).

Mg2Si0.35Sn0.65 shows the highest electrical conductivity (𝜎 ≈1.5×103 S m-1 at 200 °C) and

Mg2Si0.7Sn0.3 exhibits the lowest electrical conductivity for the whole investigated temperature

range.

Figure IV. 7: Electrical conductivity vs. temperature of Mg2Si1-xSnx thin films measured in vacuum by

TFA device.

Mg2Si0.35Sn0.65 and Mg2Si0.3Sn0.7 exhibit a lower electrical conductivity in vacuum compared to

the same measurements performed in air. The crystallographic structure of all samples after

annealing at 200 °C for 2 hours in air and in vacuum was checked by XRD (figure IV.8). For

all samples, the films structures are relatively similar after annealing in air and in vacuum and

no secondary phases are observed. The average crystallite size was estimated using Scherrer's

formula. For Mg2Si0.35Sn0.65, the size is about 69 and 83 nm after annealing in vacuum and in

air, respectively. It is well known that, the electrical conductivity decreases by reducing the

crystallite size because of the carrier scattering enhancement at the grain boundaries [Satyala,

et al., 2012]. For Mg2Si0.3Sn0.7 and Mg2Si0.7Sn0.3 the average crystallite size was not changed


significantly. Consequently, the difference between electrical conductivity values measured in

air and in vacuum for these samples should not be related to the variation of the average

crystallite size.

Figure IV. 8: X-ray diffraction patterns for thin films after 2 h annealing in air and in vacuum: a)

Mg2Si0.7Sn0.3, b) Mg2Si0.35Sn0.65 and c) Mg2Si0.3Sn0.7

The temperature dependence of Seebeck coefficient for Mg2Si1-xSnx are presented in figure

IV.9. The Seebeck coefficient is positive for Mg2Si0.3Sn0.7 and Mg2Si0.35Sn0.65 films showing

the p-type conduction. For these samples, the Seebeck coefficient value increases with

temperature up to 100 °C and then decreases. The Seebeck coefficient is negative throughout

the investigated temperature range for the film Mg2Si0.7Sn0.3, indicating an n-type conduction

for this film. For this sample, the absolute Seebeck coefficient value increases with temperature.

It is well known that the absolute Seebeck coefficient is proportional to the average energy of

electrons above the Fermi level. So the increase of the absolute Seebeck coefficient with

temperature occurs for the n-type sample of Mg2Si0.7Sn0.3. It can be related to this decrease of

Fermi level as the temperature raising [Gao et al., 2011]. The highest absolute Seebeck

coefficient of about 244 µV K-1 at 180 °C is obtained for n-type Mg2Si0.7Sn0.3.

Figure IV. 9: Seebeck coefficient vs. temperature of Mg2Si1-xSnx thin films measured by TFA device in

vacuum.

Figure IV.10 indicates the variation of thermal conductivity measured under vacuum by TFA

device vs. temperature for Mg2Si1-xSnx. The lowest thermal conductivity is observed for Mg2Si1-

xSnx compare to Mg2Sn thin films (paragraph III.2.3, figure III.11) due to effect of alloying on

their lattice thermal conductivity. The mass-difference scattering is considered as the main


mechanism for decreasing the lattice thermal conductivity. Therefore, the large mass difference

between Si (28.1 a.m.u) and Sn (118.71 a.m.u) guaranties the reduction of thermal conductivity

[Bashir et al., 2014]. The lowest thermal conductivity of the solid solution (~ 1.8 W m-1 K-1) is

reported with a composition of 0.6 ≤ x ≤0.7, which is related to strong alloy scattering. The low

thermal conductivity can be expected for the thin films compared to the bulk material with the

same composition as the layer interfaces and the low grain size in thin films can act as scatter

centers for phonons [Vineis et al., 2010]. As shown by this figure, the thermal conductivity is

increased with temperature for Mg2Si0.3Sn0.7 and Mg2Si0.35Sn0.65 films. For Mg2Si0.7Sn0.3,

thermal conductivity is enhanced till 130 °C and then decreases drastically. This sample

exhibits the lowest thermal conductivity about 0.37 W m-1 K-1 at 30 °C, and it reaches 0.57 W

m-1 K-1 at 200 °C.

Figure IV. 10: Thermal conductivity vs. temperature of Mg2Si1-xSnx thin films measured by TFA

device in vacuum.

Figure IV.11 presents the temperature dependency of the figure of merit ZT of Mg2Si1-xSnx thin

films. The evolution of the ZT vs. temperature exhibits an exponential form for n-type

Mg2Si0.7Sn0.3 and reaches 3.6×10-2 at 200 °C. The p-type Mg2Si0.3Sn0.7 has the lowest ZT all

over the temperature range. The ZT increases with temperature for this sample till 150 °C and

reaches 0.8×10-3 and then decreases. For another p-type Mg2Si0.35Sn0.65 film, the ZT enhances

with temperature till 160 °C and then remains quite constant (4×10-3 at 200 °C) for the rest of

the measured temperature range.

Figure IV. 11: Figure of merit (ZT) of Mg2Si1-xSnx thin films measured by TFA device in vacuum vs.

temperature (a) Zoom area of ZT variation vs. Temperature (b)


IV.2.4. Thermal stability of the Mg2Si1-xSnx thin films

Mg2Si1-xSnx thin films deposited on glass substrate were annealed in vacuum (10-4 Pa) at

different temperatures (from 50 °C to 600 °C with an incremental step of 50 °C) with a dwell

time of 2 hours. Such treatments were performed to determine the stability and structural

decomposition temperature limit for each sample. Figure IV.12 illustrates the X-ray patterns of

the Mg2Si1-xSnx thin films after annealing treatments in vacuum up to 600 °C. Until 500 °C, the

face centered cubic structure (jcpds 01-089-4254) remains stable for all samples no matter of

their compositions. For the temperature in-between 300-450 °C, the (020) diffracted signal

related to Si phase (jcpds 01-089-9054) at 2θ ≈ 43° is only observed for Mg2Si0.7Sn0.3. At 550

°C, the cubic Mg2Si0.4Sn0.6 structure vanishes and decomposition of Mg2Si1-xSnx phase occurs

which corresponds to Mg, Si and Sn formation. The (200) diffracted signal related to Sn phase

(jcpds 03-065-0296) coexists with (110) diffracted peak of Mg related to (bcc) phase (jcpds 03-

065-0296) and (002) diffracted signal Si related to based-centered orthorhombic phase (jcpds

01-089-9054). For Mg2Si0.7Sn0.3 and Mg2Si0.3Sn0.7, the (200) diffracted peak of Si related to

hexagonal (jcpds 01-075-0841) is also observed.

Figure IV. 12: X-ray diffraction patterns of the Mg2Si1-xSnx thin films deposited on glass substrate and

post annealed in vacuum (10-4 Pa) for 2 h at different temperatures: a) Mg2Si0.7Sn0.3, b) Mg2Si0.35Sn0.65,

and c) Mg2Si0.3Sn0.7

As previously discussed, in paragraph I.9.4. (table I.8), many works have been focused on n-

type Mg2Si1-xSnx, while for developing a good thermoelectric generator, both n- and p-type

materials are required. It is important that both materials can be fabricated from similar


compounds to reduce any thermal stress mismatch which can lead to failure of thermoelectric

module [An et al., 2012]. Therefore, for the next step, as Mg2Si0.35Sn0.65 shows p-type character

with higher ZT compare with other p-type film, this composition is selected and doped with Ge,

in order to improve its thermoelectric properties.

IV.3. Ge-doped Mg2Si0.35Sn0.65 thin films

For obtaining Ge-doped Mg2Si0.35Sn0.65 with different Ge concentrations, the power was fixed

at 50 W, 20 W, 50 W for Mg, Sn and Si targets, respectively. It was systematically changed on

Ge target from 2 to 4 W to tune the coating composition. The Mg, Si and Sn targets were

powered by pulsed direct current (DC) power supplies (Pinnacle, Advanced Energy), while the

Ge target was powered by DC power supply (MDX 500, Advanced Energy). The main

sputtering parameters are summarized in Table IV.4.

Table IV. 4 : Sputtering parameters used during deposition of Ge-doped Mg2Si0.35Sn0.65 coatings.

Ar flow rate (sccm) 50 Target Mg Sn Si Ge

Working pressure (Pa) 0.41 Discharge power (W) 50 20 50 2→4

Draw distance (DT-S) (mm) 60 Frequency (kHz) 50 50 50 0

Run duration (min) 25 𝑻𝒐𝒇𝒇 (µs) 4 4 4 0

Table IV.5 shows the chemical composition and thickness of each coatings measured by EDS

analyses and profilometer, respectively. Results obtained by EDS analyses confirms that a

relatively homogeneous composition is produced on the entire surface of deposited thin films.

Table IV. 5: Composition and thickness of Ge-doped Mg2Si0.35Sn0.65

Sample no. Mg Content

(at. %)

Si Content

(at .%)

Sn Content

(at. %)

Ge Content (at

.%)

Thickness

(µm) (±20nm)

Sample # 1 67±1 12±0.5 21±0.5 0 0.873

Sample # 2 67±1 10±0.5 22±0.5 1 ± 0.1 0.876

Sample # 3 65±1 10±0.5 21±0.5 4 ± 0.1 0.821

Sample # 4 64±1 11±0.5 18±0.5 7 ± 0.15 0.817

The optical bandgap energy for Ge-doped Mg2Si0.35Sn0.65 was determined by the Kubelka-

Munk’s method. The bandgap of undoped Mg2Si0.35Sn0.65 and the film with 1 at. % Ge is about

0.46 eV, which is in good agreement with literature [Santos et al., 2018]. By increasing Ge

content, the apparent optical bandgap energy increases as well. For the sample with 4 and 7 at.

% Ge, the bandgap values are about 0.56 and 0.52 eV, respectively.

IV.3.1. Structural and morphological characterization of Ge-doped Mg2Si0.35Sn0.65 thin

films

Figure IV.13 shows X-ray diffraction patterns of deposited films as a function of the Ge atomic

concentration. All diffraction peaks correspond to the face-centered cubic (fcc) antifluorite

structure with the space group 𝐹𝑚3𝑚 (jcpds: 01-089-4254). The most intense peak (2𝜃 ≈ 27°)

is located between those of Mg2Sn (jcpds: 03-065-2997) (2𝜃 ≈ 26°) and Mg2Si (jcpds: 03-065-

9365) (2𝜃 ≈ 28°), confirming the formation of the solid solutions. For all doped films and


despite a large amount of Ge (as high as 7 at. %), no traces of a secondary phase related to Ge

is observed.

Figure IV. 13: XRD patterns of Ge-doped Mg2Si0.35Sn0.65 coatings deposited on glass substrate as a

function of the Ge atomic concentration.

Figure IV.14 reveals top surface morphology and brittle fracture cross section observations of

thin films deposited on glass substrates by SEM. The granular morphology with some porosities

and open spaces can be seen for undoped sample and film with 1 at. % of Ge. By increasing the

Ge content , the morphology becomes more compact.

Brittle fracture cross section observations show a relatively dense columnar morphology for

undoped and doped film with 1 at. % Ge. The film with 4 at. % of Ge has a denser microstructure

without distinct columns. For the film with 7 at. % Ge, the structure exhibits a dense and slightly

columnar structure. All samples perfectly cover the surface of the substrate and no cracks and

delamination were detected on the top surface of the films. A good adhesion between films and

substrate is also observed. The films’ thickness measured by SEM is relatively homogeneous,

and in good agreement with those measured by profilometry.


Figure IV. 14: SEM micrographs of Mg2Si0.35Sn0.65 thin films doped with different Ge concentrations

deposited on glass substrate (a-d) and SEM cross section micrographs (e-h) vs. Ge atomic

concentration.

IV.3.2. Measurement of electronic transport properties of Ge-doped Mg2Si0.35Sn0.65 thin

films

The electronic transport properties of Ge-doped Mg2Si0.35Sn0.65 thin films vs. temperature were

measured in air by Hall effect. Figure IV.15 shows the variation of electrical conductivity as a

function of the temperature for Ge-doped Mg2Si0.35Sn0.65. For all films, the electrical

conductivity rises with the temperature, indicating a semiconducting-like behavior. With

addition of only 1 at. % of Ge, the film electrical conductivity decreases by about one order of

magnitude. This film shows the lowest electrical conductivity all over the measured temperature

range and finally reaches 1.31×103 S m-1 at 200 °C. The undoped Mg2Si0.35Sn0.65 and the film

with 7 at. % Ge show almost the same electrical conductivity throughout the measured

temperature. The film with 4 at. % Ge exhibits the highest electrical conductivity at low

temperature and all over the measured temperature range. The highest electrical conductivity

for this sample is about 5.6×103 S m-1 at 200 °C.


Figure IV. 15: DC electrical conductivity of Ge-doped Mg2Si0.35Sn0.65 thin films vs. temperature

measured in air by hall effect

Figure IV.16 illustrates the temperature dependence of the carrier concentration of the thin

films. The carrier concentration rises with temperature for all samples. The undoped film

exhibits the highest carrier concentration value through the measured temperature range. The

lowest carrier concentration is obtained for the film with 1 at. % Ge at lower temperature and

does not exceed 3.0×1025 m-3. The carrier concentration increases with a sharp slope for the

sample with 7 at. % Ge and reaches to the same value as reported for the film with 4 at. % Ge

(7.7×1025 m-3 at 200 °C).

Figure IV. 16: Carrier concentration vs. temperature of Ge-doped Mg2Si0.35Sn0.65 thin films in air.

The variation of carrier mobility vs. temperature is shown in figure IV.17. The carrier mobility

rises by increasing Ge content. The film with 7 at. % Ge exhibits the highest carrier mobility at

the lower temperature while it drastically reduces with rising temperature. For the undoped

films and sample with 4 at. % Ge, the Hall mobility follows the form µ~𝑇0, determining neutral

impurity scattering mechanism, while for the film with 1 at. % Ge, the Hall mobility fits with

the µ~𝑇−1

2⁄ , signifying an optical phonon scattering mechanism. For the film with 7 at. % Ge,

the Hall mobility approximately follows µ~𝑇−3

2⁄ indicating that acoustical phonon is the

dominate scattering mechanism for this sample, respectively [Bashir et al., 2014; Chen et al.,

2015; Mao et al., 2018]. The highest carrier mobility is about 1.2×10-3 m2 V-1 S-1 at 30 °C for

the film with 7 at. % Ge.


Figure IV. 17: Carrier mobility vs. temperature of Ge-doped Mg2Si0.35Sn0.65 thin films in air.

IV.3.3. Measurement of thermoelectric properties of Ge-doped Mg2Si0.35Sn0.65 thin films

The thermoelectric properties of Ge-doped Mg2Si0.35Sn0.65 were measured in vacuum (10-4 Pa)

at different temperatures by means of TFA device.

Figure IV.18 presents the temperature dependence of electrical conductivity for Ge-doped

Mg2Si0.35Sn0.65. The positive evolution of electrical conductivity for each film with temperature

happens due to an increase of the carrier concentration by intrinsic conduction which overcome

a decrease of the carrier mobility by electron-phonon scattering (figures IV.16 and 17). This

confirms that the films electrical conductivity vs. temperature is more affected by charge carrier

concentration than carrier mobility. The sample with 4 at. % Ge displays the highest electrical

conductivity in vacuum (6.5×103 S m-1 at 200 °C).

Figure IV. 18: Electrical conductivity vs. temperature of Ge-doped Mg2Si0.35Sn0.65 thin films measured

by TFA device in vacuum.

Figure IV.19 reveals the variation of Seebeck coefficient vs. temperature for each sample. It’s

right to assume all films as a p-type semiconductor since the Seebeck coefficient is positive

throughout the temperature range. The undoped film exposes the lowest Seebeck coefficient

and addition of Ge leads to an improvement of the Seebeck coefficient.

The Seebeck coefficient and carrier concentration are inversely proportional. This can be

explained based on the following equation:


𝑆 ∝ ±𝑘𝐵 (𝑟 − ln 𝑛)/𝑒 (IV.1)

Where 𝑘𝐵 is Boltzmann’s constant (1.38×10-23 J K-1), e the elementary charge (1.6×10-19 As),

r is the scattering factor, and n the carrier concentration (m-3). The scattering factor r signifies

the exponent of the relaxation time vs. energy and is supposed to be constant. Therefore, as the

carrier concentration rises with temperature for each film, the Seebeck coefficient decreases

[Gao et al., 2011]. The film Seebeck coefficient increases about four times only with addition

of 1 at. % Ge and the highest Seebeck coefficient is about 248 µV K-1 at 30 °C for the film with

7 at. % Ge. For the films doped with 7 and 4 at. % Ge, the Seebeck coefficient decreases slightly

while for the film with 1 at. % Ge, it drops drastically with the temperature rising.

Figure IV. 19: Seebeck coefficient vs. temperature of Ge-doped Mg2Si0.35Sn0.65 thin films measured by

TFA device in vacuum.

Figure IV.20 illustrates the thermal conductivity for Ge-doped Mg2Si0.35Sn0.65 as a function of

the temperature. The thermal conductivity raises with temperature for the undoped film and

sample with 4 at. % Ge with neutral impurity scattering mechanism. The highest thermal

conductivity value (0.76 W m-1 K-1 at 200 °C) is obtained for the film with 4 at. % Ge. For the

samples with 1 and 7 at. % Ge, the thermal conductivity increases till 140 °C and then drops.

In the case of film with 1 at. % Ge, the low thermal conductivity is expected as this sample

shows the lowest electrical conductivity. For the films with 4 and 7 at. % Ge, both show a high

electrical conductivity. The difference in their thermal conductivity can be related to their

different carrier scattering mechanism. It is obvious that acoustical phonon scattering shows

stronger effect on the reduction of thermal conductivity via decreasing the thermal lattice

conductivity in the case of sample doped with 7 at. % Ge [Gao et al., 2011].


Figure IV. 20: Thermal conductivity of Ge-doped Mg2Si0.35Sn0.65 thin films measured by TFA device

in vacuum vs. temperature

Figure IV.21 a shows the evolution of the figure of merit (ZT) for Ge-doped Mg2Si0.35Sn0.65 vs.

temperature. ZT value is clearly enhanced for all Ge-doped samples, no matter of the Ge

concentration. ZT raises with temperature for all Ge-doped films, while for undoped films, it

remains almost constant for temperature higher than 140 °C (figure IV.21 b). Film with 7 at. %

Ge shows the strongest ZT temperature dependence compared with film with 4 at. % Ge. The

film with 4 at. % Ge displays the higher ZT values till 180 °C compared to the film with 7 at.

% Ge. The maximum ZT ≈ 0.21 is obtained at 200 °C for the films with 4 and 7 at. % Ge, which

is at least 50 times larger than undoped film at the same temperature (ZT ≈ 4×10-3 at 200 °C).

Figure IV. 21 : Figure of merit (ZT) vs. temperature of Ge-doped Mg2Si0.35Sn0.65 thin films measured

by TFA device in vacuum (a) and zoom of ZT variation vs. temperature (b)

IV.3.4. Thermal stability of the Ge-doped Mg2Si0.35Sn0.65 thin films

Ge-doped Mg2Si0.35Sn0.65 thin films deposited on glass substrate were annealed in vacuum (10-

4 Pa) at different temperatures (from 50 °C to 600 °C with an incremental step of 50 °C) with a

dwell time of 2 hours. Such treatments were performed to determine the stability of doped

Mg2Si0.35Sn0.65 and to determine the structural decomposition temperature limit for each

sample.


As shown in figure IV.22, until 550 °C, the face centered cubic structure (jcpds: 01-089-4254)

remains stable without any secondary phase for doped films with 1 at. % and 4 at. % of Ge

while for doped film with 7 at. % of Ge (figure IV.22) and for undoped film of Mg2Si0.35Sn0.65

at 550 °C, the fcc structure decomposition starts (see figure IV.12 b). At 600 °C, the cubic

Mg2Si0.4Sn0.6 structure vanishes for all samples and decomposition of Ge doped Mg2Si0.35Sn0.65

phase occurs which s leads to Mg, Si, Sn and Ge formation. The (200) diffracted signal related

to Sn (bct) phase (jcpds: 03-065-0296) coexists with (110) diffracted peak of Mg related to

(bcc) phase (jcpds: 03-065-0296) and (002) diffracted signal related to Si (based-centered

orthorhombic) phase (jcpds: 01-089-9054). The (220) diffracted peak related to Ge (fcc) phase

(jcpds: 03-065-9209) is also observed.

Figure IV. 22: X-ray diffraction patterns of the Ge-doped Mg2Si0.35Sn0.65 thin films deposited on glass

substrate and post annealed in vacuum (10-4 Pa) for 2 h at different temperatures. Doped with: a) 1 at.

% Ge, b) 4 at. % Ge, and c) 7 at. % Ge

IV.4. Mg2Ge1-xSnx thin films

Mg2Ge1-xSnx (x= 0, 0.5, 0.7) thin films were deposited by magnetron co-sputtering of Mg, Ge

and Sn targets in an argon atmosphere and the results are compared with Mg2Sn sample. The

power was fixed at 42 W for Mg target, 20 W for Sn target and was systematically changed on

Ge target from 6 to 17 W to tune the coating composition. The Mg and Sn targets were powered

by pulsed direct current (DC) power supplies (Pinnacle, Advanced Energy), while the Ge target

was powered by (DC) power supply (MDX 500, Advanced Energy). The main sputtering

parameters are summarized in Table IV.6.


Table IV. 6 : Sputtering parameters used during deposition of Mg2Ge1-xSnx coatings.

Ar flow rate (sccm) 50 Target Mg Sn Ge

Working pressure (Pa) 0.41 Discharge power (W) 50 20 6→17

Draw distance (DT-S) (mm) 60 Frequency (kHz) 50 50 0

Run duration (min) 25 𝑻𝒐𝒇𝒇 (µs) 4 4 0

Table IV.7 shows the chemical composition and thickness of coatings measured by EDS

analyses and profilometer, respectively. Three different zones of each coating deposited on

quartz were selected for EDS measurements and the average concentration was calculated. It

can be noted that EDS analyses show relatively homogeneous composition on the entire surface

of deposited thin films.

Table IV. 7 : Composition and thickness of Mg2Ge1-xSnx thin films

Sample no. Mg content

(at. %)

Ge content

(at. %)

Sn content

(at. %)

Nominal

composition

Thickness(µm)

(±20 nm)

Sample # 1 67 ± 1 33 ± 0.5 0 Mg2Ge 0.42

Sample # 2 67 ± 1 16 ± 0.5 17 ± 0.5 Mg2Ge0.5Sn0.5 0.60

Sample # 3 67 ± 1 11 ± 0.5 22 ± 0.5 Mg2Ge0.3Sn0.7 0.77

Sample # 4* 67 ± 1 0 33 ± 0.5 Mg2Sn 1.0

* The results of Sample # 4 is repeated from chapter III, in the aim of a better comprehension of the

effect of Ge substitution in Mg2Ge1-xSnx solid solutions.

For the antifluorite structure of Mg2Sn and Mg2Ge, the band gap energy is about 0.35 eV and

0.74 eV, respectively. The bandgap energy highly depends on the composition in Mg2Ge1-xSnx

solid solution. Based on the first principal calculation and experimental results, the bandgap of

Mg2Ge1-xSnx decreases by increasing the x value [Jiang et al, 2013; Yuan et al., 2019]. The

optical bandgap energy for Mg2Ge1-xSnx was measured by the Kubelka-Munk method. The

bandgap of Mg2Ge is 0.85 eV, while Mg2Ge is not crystallized and exhibits an amorphous

structure. For the Mg2Ge0.3Sn0.7 film, the bandgap is 0.84 eV, which is higher than reported

value in the litritures. For Mg2Ge0.5Sn0.5 thin film, the bandgap is about 0.67 eV, which is in

good agreement with literature [Ryu et al., 2019].

IV.4.1 Structural characterization and thermal stability of the Mg2Ge1-xSnx thin films

Mg2Ge1-xSnx thin films deposited on glass substrate were annealed in vacuum (10-4 Pa) at

different temperatures (from 50 °C to 600 °C with an incremental step of 50 °C) with a dwell

time of 2 hours (figure IV.23 (a-d)). Such treatments were performed to determine the stability

and structural decomposition limit for each sample.

X-ray diffraction patterns of as-deposited Mg2Ge on glass substrate and annealed Mg2Ge in

vacuum (10-4 Pa) at different temperatures is presented in figure IV.23 (a). As deposited Mg2Ge

film is amorphous and such annealing treatments were performed to determine at which

temperature the Mg2Ge starts to crystallize and until which temperature it remains stable. Until

100 °C, the Mg2Ge has an amorphous state. The film crystallizes at 150 °C and diffracted peaks

are observed indicating the formation of the fcc Mg2Ge compound (jcpds: 01-086-1028). From

150 °C to 350 °C, the FWHM and peak intensity increases for Mg2Ge film with raising the

annealing temperature which indicates improvement of crystallinity. For this range of


temperatures, a strong preferred orientation along (111) crystal plane can be observed. For

temperatures in-between 400-550 °C, the (200) diffraction signal appears but the (111) ones

always remains as a preferential orientated plane. At 600 °C, the preferential orientation is

changed from (111) to (200) crystal plane. It is worth to note that the Mg2Ge film with an

antifluorite structure (space group: 𝐹𝑚3𝑚) and face-centered cubic (fcc) lattice has usually a

preferred orientation along (200) plane [Chuang et al., 2012]. Figure IV.23 (b-c) illustrate te X-

ray diffraction patterns of the Mg2Ge0.5Sn0.5 and Mg2Ge0.3Sn0.7 thin films deposited on glass

substrate and post annealed in vacuum (10-4 Pa) for 2 h at different temperatures. Until 250 °C,

only the main peaks for Mg2Ge1-xSnx solid solutions are observed. For the temperature in-

between 300-500 °C, the main peaks of Mg2Ge1-xSnx solid solutions coexist with (200) and

(101) diffracted peaks related to Sn (bct) phase (jcpds: 03-065-0296). After annealing at 550

°C, Mg2Ge1-xSnx structure vanishes and decomposition phase occurs which leads to Mg, Sn and

Ge formation. The (200) diffracted signal related to Sn phase coexists with (110) diffracted

peak of Mg phase (jcpds: 03-065-0296), and (111) diffracted peak of Ge (jcpds: 03-065-9209).

Figure IV.23 (d) shows the XRD patterns of the Mg2Sn after annealing treatments up to 600 °C

in vacuum. Until 500 °C, the fcc structure (jcpds 03-065-2997) remains. For temperatures

higher than 500 °C, the cubic Mg2Sn structure vanishes and decomposition of Mg2Sn phase

occurs, which leads to Mg and Sn formation. The (200) diffracted signal related to Sn phase

(jcpds 03-065-0296) coexists with (100) and (110) diffracted peaks of Mg phase, respectively.

Figure IV. 23: X-ray diffraction patterns of as deposited Mg2Ge1-xSnx on glass substrate and post

annealed in vacuum (10-4 Pa) for 2 h at different temperatures. a) Mg2Ge, b) Mg2Ge0.5Sn0.5, c)

Mg2Ge0.3Sn0.7, and d) Mg2Sn.


Figure IV.24 illustrates X-ray diffraction patterns of as-deposited Mg2Ge1-xSnx, which indicates

that the main peaks of all coatings correspond to the cubic antifluorite structure (space group:

𝐹𝑚3𝑚), CaF2-type. Since for both Mg2Ge0.5Sn0.5 and Mg2Ge0.3Sn0.7 solid solutions are formed

because the main peaks of Mg2Ge1-xSnx are situated between peaks of Mg2Ge and Mg2Sn.

Figure IV. 24 : X-ray diffraction patterns for thin films of Mg2Ge1-xSnx.

IV.4.2 Morphological characterization of Mg2Ge1-xSnx thin films

Figure IV.25 reveals top surface morphology and brittle fracture cross section observations of

thin films deposited on glass substrates by SEM. The granular morphology with some porosities

and open spaces can be seen for Mg2Sn. By increasing the Ge content, the morphology becomes

more compact. The smooth surface with granular features is observed for the Mg2Ge0.3Sn0.7

film. Mg2Ge0.5Sn0.5 reveals the smooth surface with cone-like features. For Mg2Ge the smooth

surface with granular features is viewed. The morphology becomes more compact for this

sample.

Brittle fracture cross-section observations show a relatively columnar morphology with some

open spaces for Mg2Sn. For Mg2Ge0.3Sn0.7, the morphology becomes more compact with a

dense feature. Mg2Ge0.5Sn0.5 film exhibits a dense and slightly columnar structure. Mg2Ge

reveals a glassy like morphology and the film becomes denser and more compact. By increasing

the Ge content in the films, the thickness of the film decreases. All samples perfectly cover the

surface of the substrate and no cracks and delamination were detected on the top surface of the

films. A good adhesion between films and substrate is also observed. The film thickness

measured by SEM is relatively homogeneous for all samples.


Figure IV. 25: SEM micrographs of films deposited on glass substrate (a-d) and SEM cross section

micrographs (e-h) of Mg2Ge1-xSnx with different compositions.

IV.4.3. Measurement of electronic transport properties of Mg2Ge1-xSnx thin films

The electronic transport properties of Mg2Ge1-xSnx thin films vs. temperature were measured in

air by Hall effect. The electronic properties of the Mg2Ge film were measured for as deposited

(amorphous film) and after 2 hours annealing in vacuum at 400 °C (crystallized film), in order

to compare the results of amorphous and crystallized films. As the improved crystallinity in the

film leads to a reduction of crystal defects (like dislocations), so such a change in defect could

strongly affect the electronic transport properties of the films [Chuang et al., 2012]. Figure

IV.26 shows the temperature dependency of DC electrical conductivity for Mg2Ge1-xSnx thin

films. For all samples the electrical conductivity is enhanced by temperature indicating typical

behavior of semiconductors [Liu et al., 2013]. Amorphous Mg2Ge exhibits the lowest electrical

conductivity throughout the investigated temperature range, while after annealing at 400 °C the

electrical conductivity is improved for this sample. The electrical conductivity for crystallized

Mg2Ge is about 2.5 times higher than amorphous Mg2Ge at 200 °C. It is right to note that, slope

change happened for amorphous Mg2Ge electrical conductivity curve vs. temperature at about

120 °C. It can be related to the beginning of the film crystallization as reported in figure IV.23

(a). The highest electrical conductivity throughout the investigated temperature range was


obtained for Mg2Ge0.3Sn0.7 with maximum value of about 1.76×104 Sm-1 at 200 °C.

Mg2Ge0.5Sn0.5 shows higher electrical conductivity at temperature below 130 °C compare to

Mg2Sn. For a temperature higher than 130°C, both samples exhibit relatively the same electrical

conductivity.

Figure IV. 26: DC electrical conductivity of Mg2Ge1-xSnx thin films vs. temperature

Figure IV.27 presents the variation of carrier concentration vs. temperature for the Mg2Ge1-xSnx

films. The carrier concentration increases with a sharp slope as the temperature rises for

amorphous Mg2Ge. This sample shows the lowest carrier concentration for the temperature

below 120 °C because of its amorphous state but at higher than 120 °C, the film crystallization

process started, and the carrier concentration can reach the same order of magnitude to that of

the crystallized Mg2Ge film. The carrier concentration raises linearly with the temperature for

all crystallized films. It is important to highlight that Mg2Sn thin film presents higher carrier

concentration than Mg2Ge while in solid solution films carrier concentration increases with Ge

content. Mg2Ge0.5Sn0.5 thin film shows the highest carrier concentration throughout the

measured temperature range. The value reaches 3.2×1026 m-3 at 200 °C for this sample.

Figure IV. 27: Carrier concentration of Mg2Ge1-xSnx thin films vs. temperature

The variation of carrier mobility vs. temperature for the Mg2Ge1-xSnx films is shown in figure

IV.28. For all samples except as deposited Mg2Ge, the Hall mobility almost follows the form

µ~𝑇0, corresponding to a neutral impurity scattering mechanism. For as deposited Mg2Ge, the


Hall mobility obeys the form µ~𝑇−3/2, indicating acoustical phonon is the dominating

scattering mechanism for this sample because of its amorphous state [Bashir et al., 2014; Chen

et al., 2015; Mao et al., 2018]. The well-crystallized Mg2Ge shows higher carrier mobility

compare with amorphous layer, which is in good agreement with literature [Chuang et al.,

2012]. The Hall coefficient is positive for both as deposited and well-crystallized Mg2Ge, which

indicte p-type conduction.The Mg2Sn exhibits the highest carrier mobility throughout the

measured temperature. The film carrier mobility decrease, while the Ge content in the film raise

for Mg2Ge1-xSnx solid solution compounds. The Mg2Ge1-xSnx films present higher carrier

mobility compare to the Mg2Si1-xSnx thin films (see section IV.2.2; figure IV.6). It is also worth

to note that the Mg2Ge1-xSnx films show lower carrier mobility compare to the Ge-doped

Mg2Si0.35Sn0.65 thin films (see section IV.3.2; figure IV.17).

Figure IV. 28: Carrier mobility vs. temperature of Mg2Ge1-xSnx thin films.

IV.4.4. Measurement of thermoelectric properties of Mg2Ge1-xSnx thin films


temperatures using the TFA device on Linseis chips covered by Mg2Ge1-xSnx thin films. As

previously noted in section II.4.6.6, after inserting the chip in TFA device, the correct

installation of the chip and resistance homogeneity of deposited film on chip are tested in order

to obtain accurate results after measurements. The chip covered by Mg2Ge was failed in both

tests because of high film resistivity with its amorphous state, and the Mg2Ge crystallized film

on Linseis chip was broken during annealing treatment because of the stress relaxation during

annealing process.

Figures IV.29 illustrates the evolution of the electrical conductivity for Mg2Ge1-xSnx vs.

temperature in vacuum. The positive evolution of electrical conductivity with temperature is

observed for all films. Mg2Sn exhibits the lowest electrical conductivity over the whole

investigated temperature range. The electrical conductivity is improved by formation of

Mg2Ge1-xSnx solid solutions. The highest electrical conductivity of about 2.4×104 S m-1 at 200

°C was obtained for Mg2Ge0.3Sn0.7 thin film.


Figure IV. 29: Electrical resistivity vs. temperature of Mg2Ge1-xSnx thin films measured by TFA device

under vacuum.

Figure IV.30 shows the Seebeck coefficient for Mg2Ge1-xSnx thin films as a function of the

temperature. All samples exhibit a p-type semiconducting behavior since the Seebeck

coefficient is positive throughout the temperature range. Mg2Sn has the highest Seebeck

coefficient value about 174 µV K-1 at 30 °C. The Seebeck coefficient decreases with

temperature and reaches 122 µV K-1at 200 °C. For Mg2Ge0.5Sn0.5 and Mg2Ge0.3Sn0.7 films, the

Seebeck coefficient is enhanced with the temperature, and reaches 180 and 148 µV K-1 at 200

°C, respectively.

Figure IV. 30 : Seebeck coefficient vs. temperature of Mg2Ge1-xSnx thin films measured by TFA

device in vacuum.

Figure IV.31 reveals the variation of thermal conductivity vs. temperature for Mg2Ge1-xSnx thin

films measured by TFA device. Thermal conductivity decreases drastically by formation of

Mg2Ge1-xSnx solid solutions due to effect of alloying on their lattice thermal conductivity. The

mass difference scattering is the main mechanism for decreasing the lattice thermal

conductivity. Therefore, the mass difference between Ge (72.6 a.m.u) and Sn (118.71 a.m.u)

leads to the reduction of thermal conductivity [Bashir et al., 2014]. Compare with Mg2Si1-xSnx

(figure IV.10) and Ge-doped Mg2Si0.35Sn0.65 (figure IV.20), the thermal conductivity is higher

for Mg2Ge1-xSnx films. The mass difference between Si and Sn is huger in Mg2Si1-xSnx, and in

the case of Ge-doped Mg2Si0.35Sn0.65, the phonon scattering is enhanced by various precipitates


[Bashir et al., 2014; Yuan et al., 2019]. The thermal conductivity increases with the temperature

for the Mg2Sn. The Mg2Sn exhibits the highest thermal conductivity of about 1.7 W m-1 K-1 at

200 °C. The thermal conductivity first increases till 140 °C and reaches a maximum value of

1.08 W m-1 K-1 for Mg2Ge0.3Sn0.7, and then decreases. The thermal conductivity remains quite

constant by the temperature for Mg2Ge0.5Sn0.5. This sample shows the lowest thermal

conductivity throughout the investigated temperature range and does not go over 0.73 Wm-1 K-

1.

Figure IV. 31 : Thermal conductivity vs. temperature of Mg2Ge1-xSnx thin films measured by TFA

device in vacuum.

The variation of figure of merit ZT for Mg2Ge1-xSnx vs. temperature is shown in figure IV.32.

The ZT is improved by the formation of Mg2Ge1-xSnx solid solutions. The evolution of ZT vs.

temperature is positive for all samples. The highest ZT~ 0.26 at 200 °C is obtained for the

Mg2Ge0.3Sn0.7, which is at least 6 times higher than ZT obtained for Mg2Sn at the same

temperature.

Figure IV. 32: Figure of merit (ZT) vs. temperature of Mg2Ge1-xSnx thin films measured by TFA

device in vacuum.


IV.5. Conclusion

In the first part, Mg2Si1-xSnx solid solutions were deposited by magnetron co-sputtering of Mg,

Si and Sn targets in an argon atmosphere. All films adopted the stable face-centered cubic

structure. The influence of chemical composition on the electronic transport properties of

Mg2Si1-xSnx thin films was studied in the range of temperatures: 30-200 °C. Hall effect

measurements led to conclude that electrical conductivity is ruled by the carrier concentration

rather than carrier mobility in these samples. The thermoelectric properties of Mg2Si1-xSnx were

investigated in the range of temperatures: 30-200 °C. The Mg2Si0.3Sn0.7 and Mg2Si0.35Sn0.6 are

p-type semiconductors as the Seebeck coefficient is positive all over the measured temperature

range, while Mg2Si0.7Sn0.3 shows an n-type conduction. Thermal conductivity decreases

drastically due to the formation of Mg2Si1-xSnx solid solutions. This is assigned to the effect of

alloying on their lattice thermal conductivity. For Mg2Si0.7Sn0.3 thin film, thermal conductivity

is enhanced till 130 °C and then decreased drastically. This sample has the lowest thermal

conductivity of about 0.37 W m-1 K-1 at 30 °C, and it reaches 0.57 W m-1 K-1 at 200 °C. The

highest ZT ~ 3.6 × 10-2 at 200 °C is obtained for n-type Mg2Si0.7Sn0.3 compound. For the p-type

Mg2Si0.35Sn0.65, ZT = 4×10-3 at 200 °C. Films deposited on glass substrate were annealed in

vacuum (10-4 Pa) at different temperatures to determine their thermal stability. Till 500 °C, the

face centered cubic structure (jcpds 01-089-4254) remains stable. At 600 °C, the cubic

Mg2Si0.4Sn0.6 structure vanishes and decomposition of Mg2Si1-xSnx phase occurs, which leads

to Mg, Si and Sn formation.

In the second part, the p-type Mg2Si0.35Sn0.65 is selected for doping with Ge, to enhance

thermoelectric properties of the films. Ge-doped (0, 1, 4, and 7 at. %) Mg2Si0.35Sn0.65 thin films

were deposited. The stable face-centered cubic structure was observed for all films. The

influence of Ge-doping on the thermoelectric properties of Mg2Si0.35Sn0.65 was studied in the

range of temperatures: 30-200 °C. By Ge-doping electrical conductivity and Seebeck

coefficient were both enhanced, which led to an improvement of thermoelectric performances

of thin films. The influence of carrier scattering mechanism on lattice thermal conductivity was

discussed. The results showed that a lower thermal conductivity was expected while the

acoustical phonon scattering mechanism prevails for the sample doped with 7 at. % Ge. The

film with 4 at. % Ge displayed the highest ZT values till 180 °C compared to other films and

finally the maximum ZT ~ 0.21 was reached at 200 °C for the films doped with 4 and 7 at. %

Ge. Ge-doped Mg2Si0.35Sn0.65 thin films deposited on glass substrate were annealed in vacuum

to determine the thermal stability of Mg2Si0.35Sn0.65 after Ge-doping. Until 550 °C, the face-

centered cubic structure (jcpds: 01-089-4254) is kept and at 600 °C, the cubic Mg2Si0.4Sn0.6

structure vanishes. Structure decomposition occurs, which leads to Mg, Si, Sn and Ge

formation. This group shows the highest thermal stability among the other studied samples in

this work.

In the last part, Mg2Ge1-xSnx (x= 0, 0.5, 0.7) thin films were deposited by magnetron co-

sputtering of Mg, Ge and Sn targets in an argon atmosphere. The results were compared with

Mg2Sn sample. Mg2Ge1-xSnx films adopts the cubic antifluorite (space group: 𝐹𝑚3𝑚), CaF2-

type. Mg2Ge0.5Sn0.5 and Mg2Ge0.3Sn0.7 solid solutions are situated between Mg2Ge and Mg2Sn.


The thermal stability of the Mg2Ge1-xSnx was examined after annealing in vacuum at different

temperatures. Until 250 °C, only the main peaks for Mg2Ge1-xSnx solid solutions are observed.

For the temperature in-between 300-500 °C, the main peaks of Mg2Ge1-xSnx solid solutions

coexist with body-centered tetragonal Sn phase. From 550 °C, Mg2Ge1-xSnx structure vanishes

and decomposition phase occurs, which leads to Mg, Sn and Ge formation. Mg2Ge as deposited

was amorphous. Therefore, Mg2Ge on glass substrate was annealed in vacuum at different

temperatures to determine at which temperature the Mg2Ge starts to crystallize. The film

crystallization started at higher than 100 °C with formation of face-centered cubic Mg2Ge phase

(jcpds: 01-086-1028). The diffraction intensity increased with raising the annealing

temperature, which indicates improving crystallinity and texturing of the film. The influence of

chemical composition and structure on the films electronic transport was discussed. For all

samples except non-crystallized Mg2Ge, the Hall mobility almost follows the form µ~𝑇0,

corresponding to a neutral impurity scattering mechanism. For amorphous Mg2Ge, the Hall

mobility obeys the form µ~𝑇−3/2 , indicating acoustical phonon scattering mechanism for this

sample. The thermoelectric properties were investigated only for Mg2Ge1-xSnx thin films as

Mg2Ge, was failed in pre-measurement tests of TFA device. The results were compared with

Mg2Sn thin film. Mg2Ge1-xSnx is a p-type semiconductor due to the positive sign of Seebeck

coefficient. Thermal conductivity decreases drastically by formation of Mg2Ge1-xSnx solid

solutions compare to Mg2Sn due to the effect of alloying on their lattice thermal conductivity.

The highest ZT~ 0.26 at 200 °C was obtained for the Mg2Ge0.3Sn0.7, which was at least 6 times

higher than ZT obtained for Mg2Sn films at the same temperature.


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p-type thermoelectric properties in an Mg2Sn system. Journal of Korean Physical Society, 60,

1717-1723.

Bashir, M. B. A., Mohd Said, S., Sabri, M. F. M., Shnawah, D. A., & Elsheikh, M. H. (2014).

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Chen, S. Zhang, X., Fan, W., Yi, T., Quach, D. V., Bux, S., Meng, Q., Kauzlarich, S. M., &

Munir, Z. A. (2015). One-step low temperature reactive consolidation of high purity

nanocrystalline Mg2Si. Journal of Alloys and Compounds, 625, 251-257.

Chuang, L., Wang, D. Y., Tan, T. T., Assadi, M. H. N., & Li, S. (2012). Processing dependence

of structural and physical properties of Mg2Ge thin films prepared by pulsed laser deposition.

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Gao, H., Zhu, T., Liu, X., Chen, L., & Zhao, X. (2011). Flux synthesis and thermoelectric

properties of eco-friendly Sb doped Mg2Si0.5Sn0.5 solid solutions for energy harvesting. Journal

of Materials Chemistry, 21, 5933-5937.

Jiang, G., Chen, L., He, J., Gao, H., Du, Z., Zhao, X., Tritt, T. M., & Zhu, T. (2013). Improving

p-type thermoelectric performance of Mg2(Ge, Sn) compounds via solid solution and Ag

doping. Intermetallics, 32, 312-317.

Kamila, H., Sankhla, A., Yasseri, M., Hoang, N. P., Farahi, N., Mueller, E., & de Boor, J.

(2019). Synthesis of p-type Mg2Si1-xSnx with x= 0-1 and optimization of the synthesis

parameters. Materials Today: Proceeding, 8, 546-555.

Kanatzidis, M. G. (2010). Nanostructured thermoelectrics: The new paradigm?. Chemistry of

Materials, 22, 648-659.

Khan, A. U., Vlachos, N., & Kyratsi, T. (2013). High thermoelectric figure of merit of Mg2Si

0.55Sn0.4Ge0.05 materials doped with Bi and Sb. Scripta Materialia, 69, 606-609.

Le-Quoc, H., Lacoste, A., Béchu, S., Bès, A., Bourgault, D., & Fruchart, D. (2012). Deposition

of thin films of Mg2Si1-xSnx solid solution by plasma-assisted co-sputtering. Journal of Alloys

and Compounds, 538, 73-78.

Liu, W., Tan, X., Yin, K., Liu, H., Tang, X., Shi, J., Zhang, Q., & Uher, C. (2012). Convergence

of conduction bands as a means of enhancing thermoelectric performance of n-type Mg2Si1-

xSnx solid solutions. Physical Review Letters, 108, 166601-166606.

Liu, W., Yin, K., Su, X., Li, H., Yan, Y., Tang, X., & Uher, C. (2013). Enhanced hole

concentration through Ga doping and excess of Mg and thermoelectric properties of p-type

Mg2(1+z)(Si0.3Sn0.7)1-yGay” Intermetallics, 32, 352-361.


Mao, J., Liu, Z., Zhou, J., Zhu, H., Zhang, Q., Chen, G., & Ren, Z. (2018). Advances in

thermoelectrics. Advances in Physics, 67, 69-147.

Ryu, B., Park, S., Choi, E. A., Boor, J. D., Ziolkowski, P., Chung, J., & Park, S. D. (2019).

Hybrid-functional and quasi-particle calculation of band structures of Mg2Si, Mg2Ge, and

Mg2Sn. Korean Physical Society, 75, 144-152.

Santos, R., Aminorroaya Yamini, S., & Dou, S. X. (2018). Recent progress in magnesium-

based thermoelectric materials. Journal of Materials Chemistry A, 6, 3328-3341.

Satyala, N., & Vashaee, D. (2012). The effect of crystallite size on the thermoelectric properties

of bulk nanostructured magnesium silicide (Mg2Si) compounds. Applied Physics Letters, 100,

073107-1-073107-4.

Vineis, C. J., Shakouri, A., Majumdar, A., & Kanatzidis, M. G. (2010). Nanostructured

thermoelectrics: Big efficiency gains from small features. Advanced Materials, 22, 3970-3980.

Yuan, G., Han, S., Lei, X., Hu, J., Liu, W., Wang, Q., Chen, C., Zhang, Q., Zhang, Q., & Gu,

M. (2019). The enhancement of thermoelectric performance of p-type Li doped Mg2Ge0.4Sn0.6

by si addition. Scripta Materialia, 166, 122-127.

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Conclusion and Perspectives

The main purpose of this thesis was focusing on developing and improving thermoelectric

performances of p-type Mg-based materials. Different strategies such as thin films, magnesium

deficiency, doping, and solid solutions were selected to study their impacts on thermoelectric

performances of Mg-based compounds.

On this basis, the thesis was organized into the following two main parts. In the first part, Mg2Sn

was selected as a potential p-type candidate among Mg2X (X= Si, Sn, Ge) compounds. Mg-Sn

thin films (21 ≤ at. % Sn ≤ 42.5) were deposited by magnetron co-sputtering in an argon

atmosphere. The aim of this part was investigating the effect of magnesium deficiency on

thermoelectric performances of thin films. XRD results showed that the film structure was

strongly affected by the Sn atomic concentration. Thin films containing 21≤ at. % Sn ≤ 25

exhibited the fcc Mg2Sn structure with a secondary phase of Mg. The latter vanishes and fcc

Mg2Sn structure remained stable in the range of 30 ˂ at. % Sn < 33.5. Thin films with 35 ≤ at.

% Sn ≤ 37.4 exhibited a mixture of cubic and orthorhombic Mg2Sn phases. Films with 37.6 up

to 38 at. % Sn adopted to orthorhombic Mg2Sn structure and finally for coatings containing

39.5≤ at. % Sn ≤ 42.5, orthorhombic Mg2Sn structure with secondary phase of Sn co-existed.

Hall measurements revealed that films with Mg deficiency, the charge carrier concentration

increased as result of formation of Mg vacancies acting as acceptors. Furthermore, the

formation of metastable orthorhombic Mg2Sn, carrier mobility increased as well. The positive

sign of the Seebeck coefficient indicated the p-type conduction for all samples. Due to the

formation of the orthorhombic Mg2Sn structure, ZT value was enhanced compared to that of

the film with cubic Mg2Sn structure. ZT values increased with temperature for orthorhombic

Mg2Sn coatings. The highest values of ZT ~ 0.26 was obtained at 200 °C while cubic and

orthorhombic Mg2Sn phases (36 at. % Sn) coexisted. Thermal stability of the Mg-Sn films with

different crystal structures was studied in vacuum. Such treatments were performed to

determine the stability and structural decomposition temperature limit for each sample. In this

group, the film with 33.5 at. % Sn (fcc) showed the highest thermal stability. For this sample

and till 500 °C, the fcc structure was kept. For temperatures higher than 500 °C, the cubic

Mg2Sn structure vanished and decomposition of Mg2Sn phase occurred, which led to Mg and

Sn formation. For the film with 36 at. % Sn and until 300°C (fcc + orthorhombic), the mixed

structure remained stable. The orthorhombic phase transformed to cubic while annealing

temperature increased from 350 °C to 500 °C and the secondary phase of Sn began to form.

Finally, at temperatures higher than 500 °C, Mg2Sn thin film completely decomposed into Mg

and Sn. For the sample with 38 at. % Sn till 150 °C (orthorhombic), the orthorhombic Mg2Sn

structure was maintained. As this sample has a non-stoichiometric composition (Sn-rich

content) in the temperature above 200 °C, the excess of Sn began to release as Sn secondary

phase. For temperatures in-between 300-400 °C, the cubic Mg2Sn structure coexisted with the

Conclusions and Perspectives 139

metastable orthorhombic Mg2Sn phase and Sn secondary phase, respectively. For temperatures

450-500 °C, the cubic Mg2Sn structure coexisted with the metastable orthorhombic Mg2Sn

phase and body centered tetragonal Sn phase. For temperatures higher than 550 °C, the cubic

and orthorhombic Mg2Sn structures vanished and decomposition of Mg2Sn phase led to Mg

and Sn formation.

In order to investigate the effect of Mg-deficiency and Cu-doping on thermoelectric properties

of Mg-Sn, two groups of Mg-Sn thin films were deposited by magnetron co-sputtering of Mg,

Sn and Cu targets in an argon atmosphere. Group I with ⌈𝑀𝑔⌉

[𝑆𝑛]= 2 and group II with

⌈𝑀𝑔⌉

[𝑆𝑛]= 1.75

were doped by different Cu concentrations (0, 0.5 and 1.5 at. %). Only the film of group I with

0 at. % Cu showed a stable fcc structure. For other samples of both groups, a mixture of fcc and

metastable orthorhombic phases coexisted. Thermoelectric properties of both groups were

measured in the temperature range 30-200 °C to investigate the influence of Cu-doping. It was

shown that the Cu introduction in stoichiometric Mg2Sn compound improved the electronic

properties, but also the thermal conductivity. On the other hand, Cu-doping reduced the Seebeck

coefficient leading to improved thermoelectric properties in a restraint range. The highest ZT ~

0.07 was obtained for films of group I at 200 °C with 0.5 at. % of Cu. Films of group II with a

Mg-deficiency showed a different behavior. They exhibited a higher electrical conductivity due

to a better carrier mobility, with a thermal conductivity and Seebeck coefficient of the same

order of magnitude than in stoichiometric films. As a result, enhanced thermoelectric properties,

almost 4 times higher (ZT = 0.27 at 200 °C with 0.5 at. % of Cu) were produced by means of

Mg-deficiency and Cu-doping of Mg2Sn thin films sputter-deposited. It is believed that the

mixture of cubic and orthorhombic phases contributed to the achievement of a higher carrier

mobility and better thermoelectric properties. These results proved the Mg-deficiency is more

effective strategy to improve thermoelectric performances rather than Cu-doping.

In the next part, the influence of the structural modification of Mg2X (X= Si, Sn, Ge) by solid

solutions formation was studied The solid solution features make changes in the crystal lattice

(i.e., disorder) which produces strong phonon scattering centers and reduce thermal

conductivity. Mg2Si1-xSnx solid solutions were deposited by magnetron co-sputtering of Mg, Si

and Sn targets in an argon atmosphere. All films adopted the stable fcc structure. The influence

of chemical composition on the electronic transport properties of Mg2Si1-xSnx thin films was

explored. Hall effect measurements led to conclude that electrical conductivity is ruled by

carrier concentration rather than carrier mobility in these samples. The thermoelectric

properties of Mg2Si1-xSnx were investigated by means of TFA. The Mg2Si0.3Sn0.7 and

Mg2Si0.35Sn0.65 exhibited a p-type behavior with a positive Seebeck coefficient throughout the

measured temperature range, while Mg2Si0.7Sn0.3 showed n-type conduction. Thermal

conductivity decreased drastically by formation of Mg2Si1-xSnx solid solutions due to effect of

alloying on their lattice thermal conductivity. The highest ZT ~ 3.6 × 10-2 at 200 °C was obtained

for n-type Mg2Si0.7Sn0.3 compound. For the p-type Mg2Si0.35Sn0.65, ZT reached 4 × 10-3 at 200

°C. Films were annealed in vacuum (10-4 Pa) at different temperatures to determine their

stability and structural decomposition temperature limit. Till 500 °C, the fcc structure remained


stable. At 600 °C, the cubic Mg2Si0.4Sn0.6 structure vanished and decomposition of Mg2Si1-xSnx

phase occurred, which led to Mg, Si and Sn formation.

Ge-doped (0, 1, 4, and 7 at. %) Mg2Si0.35Sn0.65 thin films were deposited by magnetron co-

sputtering of Mg, Si, Sn and Ge targets in an argon atmosphere. The stable fcc structure was

observed for all films. The influence of Ge-doping on the thermoelectric properties of

Mg2Si0.35Sn0.65 was studied. By Ge-doping electrical conductivity and Seebeck coefficient were

both enhanced, which led to an improvement of thermoelectric performances of the films. The

influence of carrier scattering mechanism on lattice thermal conductivity was discussed. The

results showed that a lower thermal conductivity was expected while the acoustical phonon

scattering mechanism dominated for the sample doped with 7 at. % Ge. The film with 4 at. %

Ge displayed the highest ZT values till 180 °C compared to other films and finally the maximum

ZT ~ 0.21 was reached at 200 °C for the films doped with 4 and 7 at. % Ge. Ge-doped

Mg2Si0.35Sn0.65 thin films deposited on glass substrate were annealed in vacuum to determine

the stability Mg2Si0.35Sn0.65 after Ge-doping. Until 550 °C, the fcc structure remained and at

600 °C, the cubic Mg2Si0.4Sn0.6 structure vanished and structure decomposition occurred, which

led to Mg, Si, Sn and Ge formation. This group showed the highest thermal stability among the

other studied samples in this work. Mg2Ge1-xSnx (x= 0, 0.5, 0.7) thin films were deposited by

magnetron co-sputtering of Mg, Ge and Sn targets in an argon atmosphere and the results were

compared with Mg2Sn sample. The structure of Mg2Ge1-xSnx films is a cubic antifluorite (space

group: 𝐹𝑚3𝑚), CaF2-type. Since Mg2Ge0.5Sn0.5 and Mg2Ge0.3Sn0.7 solid solutions mains peaks

are between Mg2Ge and Mg2Sn. The thermal stability of the Mg2Ge1-xSnx was examined after

annealing in vacuum at different temperatures. Until 250 °C, only the main peaks related to

Mg2Ge1-xSnx solid solutions were observed. For temperatures in-between 300-500 °C, the main

peaks of Mg2Ge1-xSnx solid solutions coexisted with Sn secondary phase. From 550 °C,

Mg2Ge1-xSnx structure vanished and decomposition phase occurred, which led to Mg, Sn and

Ge formation. As-deposited Mg2Ge was amorphous. Therefore, Mg2Ge on glass substrate was

annealed in vacuum at different temperatures and the film crystallization started at temperatures

higher than 100 °C with the formation of fcc Mg2Ge. The diffraction intensity increased with

raising the annealing temperature, which indicates an improvement of crystallinity and

texturing of the film. The influence of chemical composition and structure on the films

electronic transport was discussed. The thermoelectric properties were investigated only for

Mg2Ge1-xSnx thin films as Mg2Ge, was failed in pre-measurement tests of TFA device and the

results were compared with Mg2Sn thin film. Mg2Ge1-xSnx exhibited a p-type behavior due to

the positive sign of Seebeck coefficient. Thermal conductivity decreased drastically related to

the formation of Mg2Ge1-xSnx solid solutions compare to Mg2Sn due to effect of alloying on

their lattice thermal conductivity. The highest ZT~ 0.26 at 200 °C was obtained for the

Mg2Ge0.3Sn0.7 which was at least 6 times higher than obtained ZT for Mg2Sn at the same

temperature.

In this work, the results of different strategies for enhancing thermoelectric performance of Mg-

based compounds were discussed. The Mg-deficiency in Mg-Sn system and Ge-doping Mg2Si1-

xSnx solid solutions proved to be the most effective strategy.


About the further studies, exploring new p-type dopants such as Ni, Cu, Ag, Zn, or introducing

nano particles as dopant. It is also possible to imagine deposition of Mg2Ge at higher

temperatures by magnetron sputtering, in order to favor crystallized films for measuring

thermoelectric properties by means of TFA. It is also possible to enhance thermoelectric

properties by nanostructuring i.e. Glancing Angle Deposition, or nano multilayer deposition.

https://www.scia-systems.com/products/e-beam-evaporation/scia-eva-200.html



Scientific production

Publications:

Thermoelectric performance of Ge-doped Mg2Si0.35Sn0.65 thin films

Safavi, M., Martin, N., Aubry, E., Linseis, V., Billiard, A., & Arab Pour Yazdi, M. (2021).

Journal of Materials Engineering and Performance, accepted.

Impacts of Cu-doping and Mg-deficiency on Mg2Sn thin films thermoelectric

properties

Safavi, M., Martin, N., Aubry, E., Linseis, V., Billiard, A., & Arab Pour Yazdi, M. (2021).

Journal of Electronic Materials, 50, 2738-2749.

Thermoelectric properties improvement in Mg2Sn thin films by structural

modification

Safavi, M., Martin, N., Linseis, V., Palmino, F., Cherioux, F., Billiard, A., & Arab Pour

Yazdi, M. (2019). Journal of Alloys and Compounds, 797, 1078-1085.

Oral presentation:

Impacts of Cu-doping and Mg-deficiency on Mg2Sn thin films thermoelectric properties

M. Safavi, N. Martin, V. Linseis, A. Billard, M. Arab Pour Yazdi, JNTE2019 (La Journée

thématique de thermoélectrique, 20-22 Janvier 2020, Metz-France

Posters:

Impact of Cu doping and Mg-deficient in Mg2Sn thin films thermoelectric properties

M. Safavi, N. Martin, V. Linseis, A. Billard, M. Arab Pour Yazdi, l’école thématique

Thermoélectricité, organisée par le GIS Thermoélectricité, 6 - 11 octobre 2019, La Bresse-

France.

Revêtements de Mg2Sn par pulvérisation cathodique magnétron : de la synthèse aux

propriétés thermoélectriques

M. Safavi, M. Arab Pour Yazdi, N. Martin, V. Linseis, F. Palmino, F. Cherioux, A. Billard

Matériaux 2014, 24-28 novembre 2018, Strasbourg-France.

Mg2Sn thin films prepared by magnetron sputtering: from synthesis to thermoelectric

properties

M. Safavi, N. Martin, V. Linseis, A. Billard, M. Arab Pour Yazdi, FEMTO-ST annual

conference, 26 juin 2018, Besançon-France

https://www.springer.com/journal/11665/?gclid=CjwKCAiA7939BRBMEiwA-hX5J_mi7yJ9eX1yA3MFBt5XYjbg0CHnX4P7fzgC9nkKNBK4FiFslxw6xBoCqQ0QAvD_BwE

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