Nanostructural and electronic properties of polytypes in InN nanocolumnsJ. Kioseoglou, T. Koukoula, Ph. Komninou, A. Georgakilas, M. Androulidaki, and Th. Kehagias Citation: Journal of Applied Physics 114, 074312 (2013); doi: 10.1063/1.4818517 View online: http://dx.doi.org/10.1063/1.4818517 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/114/7?ver=pdfcov Published by the AIP Publishing

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Nanostructural and electronic properties of polytypes in InN nanocolumns

J. Kioseoglou,1 T. Koukoula,1 Ph. Komninou,1 A. Georgakilas,2 M. Androulidaki,2

and Th. Kehagias1,a)

1Physics Department, Aristotle University of Thessaloniki, GR-54124 Thessaloniki, Greece2Microelectronics Research Group, IESL, FORTH, P.O. Box 1385, GR-71110 Heraklion,Crete and Department of Physics, University of Crete, P.O. Box 2208, GR-71003 Heraklion, Crete, Greece

(Received 18 June 2013; accepted 31 July 2013; published online 21 August 2013)

Transmission electron microscopy techniques and density functional theory calculations were

employed to investigate the nanostructural and electronic properties of InN polytypes observed in

InN nanocolumns, grown on Si(111) by molecular beam epitaxy. Moir�e fringes and alternating

hexagonal and cubic lattice stacking sequences along the c-axis, observed among the wurtzite

layers, implied the presence of different structures embedded in the basic 2H structure of the

nanocolumns. Quantitative electron diffraction analysis and high-resolution image simulations

verified the coexistence of the wurtzite structure with the 4H, 6H, and the 3C zinc-blende structural

polytypes. Total energies calculations established the 2H wurtzite structure as the most stable

polytype. The band gap of all polytypes was found direct with the energies and the band gaps of

the 4H (Eg¼ 0.64 eV) and 6H (Eg¼ 0.60 eV) structures calculated between the corresponding

values of the 2H (Eg¼ 0.75 eV) and 3C (Eg¼ 0.49 eV) basic structures. Theoretical and

experimental analysis showed that at the initial stages of growth InN nanocolumns were under

tensile strain along both the basal plane and growth direction. Structural polytypes were then

introduced in the form of embedded inclusions to accommodate the excess tensile strain along the

growth direction, allowing the entire process of polymorphism to be the dominant strain relaxation

mechanism of InN nanocolumns. Moreover, the lattice and energetic properties and band gap

values of InN polytypes showed a linear dependence on hexagonality, while the presence of

polytypes led to a characteristic broadening of the photoluminescence emission peak toward lower

emission energies. VC 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4818517]

I. INTRODUCTION

One-dimensional III-nitride nanostructures, such as nano-

columns (NCs), have shown high potential not only for the

fabrication of nanodevices but also for the overgrowth of

stress-free films, given that the small lateral dimension of NCs

allows InN heteroepitaxial growth free of threading defects.

The ability to grow high quality InN-based nanostructures

will maximize the high prospectives of InN and its ternary

(InGaN and InAlN) and quaternary (InAlGaN) alloys, which

constitute a unique semiconductor material system covering

from near infrared to the ultraviolet region of the electromag-

netic spectrum, with significant applications in LEDs, LDs,

solar cells, and chemical sensors.1 Understanding of the nano-

scale structural properties of these structures is important for

the optimization of their growth process and control over their

electronic and optical properties.

The main structural defects observed in this type of

nanostructures are stacking faults (SFs),2 which are closely

related to polytypism. Currently, polytypism in semiconduc-

tor groups IV-IV and III–V has attracted much attention

from the scientific community and therefore, becomes a mat-

ter of intense research activity. In particular, SiC exhibits

pronounced polytypism with more than a hundred different

crystalline modifications, namely, polytypes.3–5 The struc-

tural and electronic properties of semiconducting materials

containing multiple polytypes seem to arise as a combination

of the corresponding properties of the basic structures, i.e.,

the cubic/zinc-blende (3C) and the hexagonal/wurtzite (2H)

polytypes of these materials. Polytype inclusions are easier

to form in nanowires, since the small nanowire diameter

allows interlayers of different stacking sequences to form

from sidewall to sidewall and thus, there is no need of

bounding partial dislocations, resulting in more stable struc-

tures.2,6 Current reports in III–V nanowires showed that by

controlling polytypism, new potentials of crystal phase engi-

neering in “heterocrystalline homostructures” are opening.7

However, it was not until recently that polytypism in

III-Nitrides was observed, due to growth on SiC sub-

strates.8,9 In particular, the growth of high quality nonpolar

4H-polytype AlN and AlN/AlGaN multiple-quantum-well

structures on (1�100) or (11�20) 4H-SiC substrates, with low

threading dislocation and SF densities, has been reported

along with theoretical studies.10,11 In addition, polytype

domains in InGaN thick layers and 4H-InN in Mg doped InN

layer were experimentally observed by transmission electron

microscopy (TEM).12,13 Therefore, polytypism in InN but

also in combination with Ga- and Al-based nitrides can bring

about new prospects for band gap tuning and lead to new

complex structures with tailored electronic and optical prop-

erties. Consequently, theoretical understanding and experi-

mental control over quantum size growth of nitride

polytypes will play an important role in semiconductors

technology.a)E-mail: kehagias@auth.gr

0021-8979/2013/114(7)/074312/9/$30.00 VC 2013 AIP Publishing LLC114, 074312-1

JOURNAL OF APPLIED PHYSICS 114, 074312 (2013)

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To explore this possibility, a thorough experimental

and theoretical analysis was carried out to enlighten poly-

typism in InN NCs. TEM-based techniques and density

functional theory (DFT) calculations were employed to

investigate the structural and the electronic properties of

InN polytypes. The study was originally triggered by the

experimental identification of structural polytypes in InN

NCs grown on Si(111) by plasma assisted molecular beam

epitaxy (PAMBE). High-resolution TEM (HRTEM) obser-

vations, image simulations as well as quantitative analysis

of the selected area electron diffraction (SAED) patterns,

based on DFT calculations, revealed the presence of various

polymorphisms along with the ground state wurtzite (2H)structure. Photoluminescence (PL) experiments combined

with band structure DFT calculations were utilized to ana-

lyze the band gap characteristics of the InN structural poly-

types and their influence on the emission spectrum of

wurtzite InN.

II. EXPERIMENTAL AND THEORETICAL METHODS

The InN NCs were grown by PAMBE on boron-doped

p-type Si(111) substrates under intense nitrogen rich condi-

tions. Initially, an ex-situ chemical cleaning method was

applied on the substrate’s surface, followed by in-situ ther-

mal cleaning, which resulted in 7� 7 surface reconstruction

observed by reflection high energy electron diffraction

(RHEED). InN NCs were grown, without prior nitridation of

the Si surface, at Tsub¼ 500 �C for 1 h using a III/N flux ratio

of 0.16 with the In-flux set at 120 nm/h. Details of the growth

process of similar nanostructures have been given

elsewhere.14,15

Specimens for TEM and HRTEM observations were

prepared in cross-sectional geometry (XTEM) by mechanical

grinding, followed by low-voltage Arþ high-precision ion-

milling (Gatan PIPS) to achieve electron transparency. The

TEM and HRTEM experiments were performed using a

200 kV Jeol 2011 microscope with a point resolution of

0.194 nm and Cs¼ 0.5 mm.

DFT calculations under the ABINIT code,16 and the

local density approximation (LDA) were used to resolve

the energies of the polytypes with respect to the wurtzite

structure and the band gap of each different structures

implementing modified pseudopotentials, which accurately

reproduce the band gap of InN (MPP-LDA approach).17 In

particular, the plane waves were expanded up to a cutoff

energy of 140 Ry and 8� 8� 12 for 2H, 8� 8� 8 for 3C,

8� 8� 6 for 4H, and 8� 8� 4 for 6H. Monkhorst-Pack

k-point meshes were used for the 1� 1� 1 unit cell.

Simulated HRTEM images as well as simulated SAED pat-

terns of the complex crystal structures were calculated

using the EMS software.18

The 20 K PL spectrum reported in this work was

obtained using a He–Cd continuous-wave laser at 325 nm

(35 mW) and a monochromator with 600 grooves/mm gra-

ting blazed at 2 lm. The measurements were taken with a

special liquid nitrogen (LN2) cooled InGaAs PIN photodiode

detector with a maximum responsivity at 1.92 lm and a

lock-in amplifier.

III. MORPHOLOGY AND NANOSTRUCTURE OF InNNCs

The overall morphology of the InN NCs is shown in the

XTEM micrograph of Fig. 1(a), viewed along the [11�20]InN//

[1�10]Si zone axis (z.a.). The NCs areal density was �8� 108

cm�2, while their average height was estimated at 330

6 20 nm. Their diameter ranged from 50 nm to 250 nm with

the majority of them in the middle and the high end of the

range. However, the diameter of InN NCs remains rather

constant along the growth axis and thus, a negligible tapering

effect was accounted. Moreover, faceted tip morphology of

the NCs was observed. While their sidewalls are the

m-planes, their tips are formed by 6-fold crystal facets

inclined by �23�–26� relative to the basal plane, and there-

fore, they were characterized as the {10�14} planes. As seen

in the HRTEM image of Fig. 1(b), the high N-flux resulted

in unintentional nitridation of the Si surface and formation of

a thin amorphous layer at the InN/Si interface, which is usu-

ally observed in III/N heteroepitaxy on Si and is character-

ized as SixNy.2 Furthermore, in the NC of Fig. 1(b), besides

the (0001) basal planes of the wurtzite structure, numerous

areas exhibiting Moir�e patterns are evident. This clearly

implies the presence of overlapping crystals tilted or twisted

by a few degrees, even from the early stages of growth.

Different lattice stacking sequences were identified

along the growth direction (Fig. 2(a)). In the HRTEM image

of Fig. 2(a), regions of an integer multiplicity of the 2Hstacking mediated by atomic layers of cubic stacking, as

FIG. 1. (a) XTEM micrograph near the [11�20]InN//[1�10]Si z.a., showing the

faceted tip morphology of InN NCs. (b) HRTEM image of a NC along the

[11�20]InN//[1�10]Si z.a., illustrating the growth of NCs on a SixNy amorphous

layer formed at the InN/Si interface by unintentional nitridation of the Si

surface. Moir�e fringes suggest the superposition of slightly tilted/twisted

crystal lattices in the NC.

074312-2 Kioseoglou et al. J. Appl. Phys. 114, 074312 (2013)

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well as regions exclusively of cubic stacking embedded in

the dominant wurtzite lattice are observed. This obviously

suggests the occurrence of InN structural polytypes in the

NCs. The 4H, 6H, and 3C polytypes could be identified from

several HRTEM images of numerous NCs. These polytypes

appear in the form of inclusions within the basic wurtzite

structure. In Fig. 2(b), Fast-Fourier Transform (FFT) diffrac-

tograms of the marked areas depicted in the HRTEM image

of Fig. 2(a) are shown, revealing the presence of additional

frequencies and thus, verifying the occurrence of structural

polytypes of the 2H structure in conjunction with the [11�20]

oriented 2H and the [1�10] oriented 3C basic structures,

respectively. When polytype inclusions are not localized in

the vicinity of the free lateral sidewalls, they are usually

delimited by partial dislocations resembling to the SF forma-

tion. This issue will be addressed later.

At the interfacial area, i.e., at the early stages of InN

growth, a permutation between narrow (<50 nm in diameter)

and wider NCs was observed. While in narrow NCs phase

transitions from the 2H structure to other InN polytypes were

observed to occur very close to the Si surface (Figs. 1(b) and

2(c)), in wider NCs the wurtzite structure is dominant, and

polytypes were seen to form at later stages of growth,

namely, after several monolayers of 2H InN growth

(Fig. 2(d)). This could be explained in terms of lattice con-

stant differences in smaller and large radius initial InN

nuclei, forming presumably narrow and wider NCs, respec-

tively. For a given surface tension, the Laplace pressure is

inversely proportional to the nuclei radius, thus small nuclei

should exhibit high values of Laplace pressure, in the range

of several GPa,19 which may trigger polymorphic transitions

from the initial stages of NC growth. For larger radii

(>100 nm), Laplace pressure inside InN nuclei drops rapidly,

hence the basic 2H structure is prevailing. Moreover, the ani-

sotropy of surface energy was established as an even stron-

ger driving force for the formation of NCs,19 which leads to

an effective pressure and, consequently, induces a deviation

on the lattice constants in small nuclei.

The unintentional nitridation of the Si surface resulted

in a non-uniform amorphous SixNy layer exhibiting thick-

ness fluctuations (1.5–3.5 nm) and thus, a noticeable rough-

ness (Figs. 2(c) and 2(d)). However, as shown in the

HRTEM images of Figs. 2(c) and 2(d) by black arrows,

crystalline Si islands apparently remained intact at the Si

surface, although it was subjected to the unintentional nitri-

dation at the early stages of InN growth. Indeed the Si sur-

face seems to be rapidly covered by InN nuclei that evolve

into InN NCs and complete amorphization at the InN/Si

interface is prevented. Si islands were observed in almost

every NC/substrate interface and can potentially act as seeds

promoting epitaxial growth of InN-on-Si. Nevertheless,

since the area covered by Si islands is restrained, InN

growth is practically accomplished on the amorphous SixNy

material and thus, the epitaxial strain imposed by the lattice

mismatch should be considered minimal. As a consequence

of the interfacial amorphous layer thickness fluctuations,

deviations from the exact epitaxial relationship between the

two lattices were observed (Fig. 2(d)), i.e., the [0001]

growth axis of the NCs is not parallel to the normal of the

substrate’s surface.

FIG. 2. (a) HRTEM image taken along

the [11�20]InN z.a., showing regions of

successive atomic layers with different

stacking sequences (2H, 4H, 6H, and

3C) along the growth axis. (b)

Corresponding FFT diffractograms of

the four marked domains revealing the

presence of additional spatial frequen-

cies in the [11�20] oriented 2H InN

belonging to the 4H and 6H polytypes

(white arrows), as well as the [1�10]

oriented 3C polytype. (c) HRTEM

image along the [11�20]InN//[1�10]Si

z.a., depicting the InN/Si interface of a

narrow NC. Crystalline Si islands resi-

dues of the unintentional nitridation of

the Si surface are observed (black

arrows). (d) Corresponding HRTEM

image from a wider NC, where the

roughness of the SixNy layer led to

misalignment of the growth axis of the

NC relative to the Si surface normal.

074312-3 Kioseoglou et al. J. Appl. Phys. 114, 074312 (2013)

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IV. CRYSTALLOGRAPHY AND ATOMISTIC MODELINGOF InN STRUCTURAL POLYTYPES

InN commonly adopts the wurtzite structure (2H, space

group (S.G.)P63mc), which comprises four atoms per unit

cell and can be visualized as two interpenetrating hexagonal

substructures; one of In and one of N atoms displaced by the

distance u along the c-axis. The primitive basis vectors of

the unit cell are a1¼ (12;�

ffiffi3p

2; 0)a, a2¼ (1

2;ffiffi3p

2; 0)a, and

a3¼ (0,0,c/a)a in Cartesian coordinates, while the positions

of the atoms, in units of a1, a2, and a3, are (13; 2

3; 0) and

(23; 1

3; 1

2) for atoms of the one species, and (1

3; 2

3; u) and

(23; 1

3; uþ 1

2) for atoms of the other species. In the ideal wurt-

zite structure u¼ 3/8 and c=a ¼ffiffiffiffiffiffiffiffi8=3

p, otherwise in order to

describe small deviations from the ideal u displacement

between the sublattices of the two species, a dimensionless

internal structural parameter e1 should be introduced (then

u ¼ 3=8þ e1).20 The relation between e1 and the strain-free

c=a ratio for the 2H structure can be deduced from the con-

servation law of the bond length as e1 ¼ 18

83

ca

� ��2 � 1� �

.20

The stacking sequence along [0001] is ���ABABAB���, while

each layer parallel to the basal plane is composed of two sub-

layers of distinct atomic species. Now, we define as hexago-

nal layer h each layer which is adjacent to two identical

layers, such as B in ���ABABAB���. This leads to 2H wurtzite

being symbolized as ���hhhhhh���. In Table I, the correspond-

ing crystallographic definitions and symbols for the 3C, 4H,and 6H crystal structures are given.

Based on the above crystallographic analysis, atomistic

models of all relevant polytypes were constructed as shown

in Fig. 3.

V. QUANTITATIVE ELECTRON DIFFRACTIONANALYSIS

The variety of structures resulting from the observed dif-

ferent stacking sequences that match the structural polytypes

of InN were studied by quantitative SAED analysis in con-

junction with DFT calculations. Consequently, SAED pat-

terns taken exactly on the [11�20]InN z.a. were digitized at

4000 dpi using a Nikon SUPER COOLSCAN 9000 and the

spacing of the wurtzite reflections along the [0001] direction

were then measured using line profiles and peak finding tech-

niques.21 In order to identify the exact position of each

reflection, the “center of mass” of each spot corresponding to

a reflection was calculated, where the term “mass” stands for

the intensity of each pixel. In addition, simulated SAED pat-

terns, based on DFT calculations, were calculated, and the

positions of the experimental reflections were compared with

the simulated ones. Figure 4(a) is a SAED pattern of a wider

TABLE I. Crystallographic data of the 3C, 4H, and 6H InN structural polytypes; i.e., space group, primitive basic vectors of the unit cell, atomic positions of

the two species in units of primitive vectors, and the dimensionless internal structural parameters (e1, e2, e3, d1, d2) describing deviations from the ideal crystal

structures. The stacking sequences along [0001] direction and the structure symbols are also depicted.

3C, S.G. F�43m 4H, S.G. P63mc 6H, S.G. P63mc

Primitive vectors a1 ¼ (12; 1

2; 0)a a1 ¼ (1

2;ffiffi3p

2; 0)a a1 ¼ (1

2;ffiffi3p

2; 0)a

a2 ¼ (12; 0; 1

2)a a2 ¼ (1

2;ffiffi3p

2; 0)a a2 ¼ (1

2;ffiffi3p

2; 0)a

a3 ¼ (0; 12; 1

2)a a3 ¼ (0,0,c/a)a a3 ¼ (0,0,c/a)a

Atomic positions in units of a1, a2, a3 1st species 2nd species 1st species 2nd species 1st species 2nd species

(0; 0; 0) (0; 0; 18þe1)

(0; 0; 0) ð13; 2

3; 7

16þ e2Þ (0; 0; 1

2) (0; 0; 5

8þe1)

ð0; 0; 12Þ (0; 0; 3

16þ e1) (1

3þd2;

23þd1;

16þd1) (1

3; 2

3; 7

24þe2)

ð0; 0; 0Þ (14; 1

4; 1

4) (1

3; 2

3; 1

4þ d1) (0; 0; 11

16þ e1) (1

3þd2;

23þd1;

56þd2) (1

3; 2

3; 23

24þe3)

(23; 1

3; 3

4þ d1) (2

3; 1

3; 15

16þ e2) (2

3þd1;

13þd2;

13þd2) (2

3; 1

3; 11

24þe3)

(23þd1;

13þd2;

23þd1) (2

3; 1

3; 19

24þe2)

Stacking sequence along [0001] …ABCABC… …ABCBABCBA… …ABCACBABCACBA…

Structure symbols ���cccccc��� ���hchchc��� ���hcchcchcc���

FIG. 3. Atomistic models of the polytypes identified in the InN NCs. The

various lattice stacking sequences are given on the structural models, while

the atomic stacking is denoted by a green line. The clat is the lattice constant

of each individual structure, in terms of a hexagonal lattice, while c is the

equivalent distance in each polytype corresponding to the d-spacing of the

(0001) planes of the 2H structure. Large/blue and small/red spheres corre-

spond to the In and N atomic species of the InN structure, respectively.

074312-4 Kioseoglou et al. J. Appl. Phys. 114, 074312 (2013)

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NC, oriented along the [11�20] z.a., showing reflections from

the dominant 2H-InN structure along with satellite spots.

Most of the satellite spots belong to hexagonal-like struc-

tures aligned along the [11�20] z.a. of wurtzite. The assess-

ment of numerous SAED patterns taken from various NCs

by the preceding quantitative analysis, in combination with

simulated SAED patterns, resulted in crystallographic identi-

fication of the satellite reflections belonging to InN polytypes

and the d-spacing of their basal planes were determined. The

structural polytypes were characterized as 4H, 6H, and 3Cand their corresponding reflections are denoted in Fig. 4(a).

In addition, HRTEM image simulations based on the

calculated polytypes were used in order to validate the

results of the SAED analysis. In Fig. 4(b), the marked areas

of the HRTEM image of Fig. 2(a), as well as the simulated

HRTEM images of the various identified polytypes are illus-

trated. The unambiguous matching between them verified

the presence of multiple structural polytype inclusions in

wurtzite InN.

In Table II, the results of the quantitative analysis on the

experimental SAED patterns are depicted. Besides the clat

lattice constant values, the c values, which are the distances

in each polytype equivalent to the d0001-spacing of the 2Hstructure, are also given. These values were calculated for

each sC or sH structure (s¼ 3,4,6 for 3C, 4H, and 6H,

respectively) by the following formulas: clat ¼ sacubic=ffiffiffi3p

,

c ¼ 2acubic=ffiffiffi3p

, and ahex ¼ acubic=ffiffiffi2p

for the cubic structure,

and c ¼ clat=ðs=2Þ for the wurtzite structures. For the calcu-

lations, we have postulated that NCs as integral entities are

strain-free, due to their free lateral and top surfaces and

hence, the clat constant of the 2H structure was taken from

Ref. 22 (clat¼ 5.702 A). In Table II, the calculated by DFT

relaxed lattice constants (alat, clat), as well as the correspond-

ing c values and the c/a ratio of all structures, are depicted.

For the various polytypes, the values of the c spacing are

directly comparable. A notable conformity of the experimen-

tal values and the results of theoretical calculations is

observed.

Furthermore, in Table III, the calculated by DFT internal

structural parameters describing the relaxation of the atomic

positions within the unit cells of the hexagonal 2H, 4H, and

6H structures, namely, the deviations from the ideal configu-

rations, are given. Taking into account, the c=a ratios given

in Table II, the conservation law of the bond length resulted

in e1 ¼ 42:7� 10�4, for the 2H structure, which is close to

the corresponding calculated value given in Table III. This

finding is opposed to the disagreement between the bond

length conservation and the DFT calculated values found in

FIG. 4. (a) Experimental SAED pattern taken from a wider NC showing the

wurtzite InN reflections (black indexes) coexist with numerous satellite

spots of the 4H (blue indexes), 6H (white indexes), and 3C (red indexes)

InN structural polytypes. (b) HRTEM image simulations (thick-

ness¼ 10.7 nm defocus¼�63 nm, second maximum of contrast, white spots

correspond to atomic columns) of 2H, 4H, 6H, and 3C structures and the

corresponding experimental images (marked areas of Fig. 2(a)).

TABLE II. The clat lattice constants and the c values of the various InN structural polytypes as measured experimentally by quantitative SAED analysis. The

calculated by DFT strain-free alat, clat lattice constants, c values and c/a ratio are also presented.

Experimental values by SAED analysis Calculated values by DFT

Polytype clat (A) (60:007) c (A) (60:007) alat (A) clat (A) c (A) c/a

2H 5.702 5.702 3.5600 5.7167 5.7167 1.6058

4H 11.468 5.734 3.5501 11.5090 5.7545 1.6210

6H 17.251 5.750 3.5473 17.2962 5.7654 1.6253

3C 8.704

acubic¼ 5.025

ahex¼ 3.553

5.803 acubic¼ 5.0393

ahex¼ 3.563

8.7282 5.8188 1.6330

TABLE III. The dimensionless internal structural parameters calculated by

DFT describing the deviations of the atomic positions (relaxed atomic posi-

tions) from the ideal 2H, 4H, and 6H structures.

Polytype e1 � 10�4 e2 � 10�4 e3 � 10�4 d1 � 10�4 d2 � 10�4

2H 36

4H 7.2 4.9 �4.0

6H 1.6 1.4 4.7 �5.0 �1.8

074312-5 Kioseoglou et al. J. Appl. Phys. 114, 074312 (2013)

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group III–V polytypes.23 To the best of our knowledge, there

are no previous theoretical results for the internal structural

parameters for InN polytypes.

In addition, the strain state of the NCs at the interface

with Si was investigated. Quantitative analysis was imple-

mented on a series of SAED patterns taken on the interfacial

InN/Si area. Using the d-spacing of the (111) Si planes

as reference (3.134 A), the (10�10) as well as the (0002)

d-spacing of InN was measured and both lattice constants of

InN were found expanded with respect to the strain-free val-

ues of InN.22 In particular, the a lattice constant was found

larger by 1.6%, while the c by 1.8%, respectively. Following

elasticity theory, this leads to the conclusion that InN NCs

were grown on SixNy exhibiting tensile strain, probably due

to the particular bonding environment between the InN and

the amorphous layer, as well as due to the growth conditions.

We will come back to this later.

VI. ELECTRONIC PROPERTIES OF InN POLYTYPES

Band structure calculations of the various polytypes, at

the optimized lattice constant values, were performed fol-

lowing specific paths along symmetry directions in the

Brillouin zone of each structure. In Fig. 5, the band struc-

tures of the observed polytypes are depicted, while their

band gaps were found direct and were estimated at 0.75 eV,

0.64 eV, 0.60 eV, and 0.49 eV for the 2H, 4H, 6H, and 3Cstructures, respectively. The calculated 2H InN lattice con-

stants as well as the band gap of 0.75 eV are compliant with

Ref. 17. It should be noticed, however, that in recent experi-

mental studies, even lower band gap energies have been

reported (e.g., Ref. 24, Eg¼ 0.65 eV), which may lead to

lower band gaps for the polytypes.

It is known that the differing potytypes can be described

by the concept hexagonality,20,25 which is defined as the

percentage of the h layers in a crystal, i.e., H ¼ Nh

ðNhþNcÞ,where Nh refers to the total number of hexagonal layers and

Nc refers to the total number of cubic layers, thus,

H2H¼ 100% and H3C¼ 0%, while H4H¼ 50% and

H6H¼ 33%.

In Fig. 6, the calculated c and c/a constants and the total

energies as a function of hexagonality of the structures are

plotted. It is evident that the preceding structural parameters

have a linear dependence on hexagonality. Both c and c/astructural constants are decreasing with increasing hexagon-

ality, while the values of the c spacing consolidate the ex-

perimental evidence that the observed polytypes are

connected with tensile strain along the [0001] direction of

the wurtzite 2H structure. The total energies calculations

confirmed the 2H wurtzite structure as the most stable poly-

type, whereas the energies of the 4H and 6H polytypes were

found to lie among the corresponding values of the 3C and

2H structures.

In order to evaluate the fundamental band gap of the

NCs and the influence of structural polytypes on the emis-

sion properties of InN, we have analyzed the dependence of

their calculated band gap values as a function of hexagonal-

ity, and directly compared the results with the experimental

values derived from the PL spectrum of InN NCs at 20 K

(Fig. 7). Initially, it was determined that the fundamental

band gap of the polytypes has also a linear dependence on

hexagonality, where the corresponding energy values

decrease with increasing hexagonality. Subsequently, the PL

spectrum of the NCs at 20 K exhibited a peak at 0.78 eV,

whereas the full width at half maximum (FWHM) was esti-

mated at 100 meV. The latter rather high value allows us to

deduce that the characteristic broadening of the PL spectrum

can be attributed to the presence of structural polytypes. We

would expect that another consequence of the occurrence of

polymorphic structures within 2H InN, having lower

FIG. 5. DFT calculated band structures

of the various polytypes at the opti-

mized lattice constants. The fundamen-

tal band gaps of the observed

polytypes shown at the C point of the

Brillouin zone were found direct.

074312-6 Kioseoglou et al. J. Appl. Phys. 114, 074312 (2013)

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fundamental band gap than wurtzite, would be the red-shift

of the overall PL peak at energies well below that of the 2H.

Here, in contrast, the 0.78 eV value of the PL peak was even

higher than the fundamental band gap of pure InN. The free

carrier concentration at 20 K in InN films grown in the same

system was n � 1.0� 1019 cm�3,26 indicating a degenerate

semiconductor behavior of InN NCs. It is well established

that due to the Burstein-Moss effect, at high free carrier con-

centrations, the absorption edge and the luminescence peak

are blue-shifted in relation to the fundamental band gap of

InN by a value equal to the Fermi energy.27 The Fermi

energy is calculated for an effective mass of m� ¼ 0:1 m0 by

the equation: EF¼ 3:58 m0

m�

� �nn0

� �2=3 meV,28 where m0 is the

rest mass and n0¼ 1.0� 1018 cm�3 is the electron equilib-

rium carrier concentration. Consequently, taking into

account the Burstein-Moss effect the band gap of NCs

should be, in our case, shifted toward lower energy by

166 meV relative to the experimental 20 K PL peak. This

results in an estimation of Eg¼ 0.61 eV of the fundamental

band gap of the InN NCs at 20 K, significantly lower than

the band gap of wurtzite InN at 300 K

(0.65–0.75 eV),1,17,24,27 which should be attributed to the

presence of the 4H, 6H, and 3C inclusions in the NCs.

Consequently, it is concluded that the introduction of struc-

tural polytypes could explain the lower emission energies

(after correction for the Burstein-Moss shift) from the InN

NCs, while the lowest band gap that could be reached is that

of the cubic InN. It should be noticed that confinement and

recombination of carriers is expected to occur in the low

band gap polytype inclusions in the wurtzite structure.

VII. DISCUSSION

As depicted in Table II and shown in Fig. 6(a), the ex-

perimental values of the c lattice constants of 3C, 4H, and

6H polytypes were expanded with respect to the strain-free

2H structure, in compliance with DFT calculations. In partic-

ular, the 3C polytype was strained by 1.77% with respect to

the 2H structure, while the 6H and the 4H, by 0.84% and

0.56%, respectively. Furthermore, the DFT calculated values

of the corresponding relaxed structures predicted an expan-

sion of 1.79%, 0.85%, and 0.66% for the 3C, 6H, and 4H,

respectively. This means that the observed polytype inclu-

sions in the InN NCs are nearly strain-free. Hence, the way

that multiple polytype structures with slightly different lat-

tice parameters interrelate in a NC becomes of high interest.

Figure 8(a) is a structural model of a 4H domain embedded

in the wurtzite matrix. Both structures are modeled in their

DFT relaxed lattice constants (c4H > c2H, a2H > a4H, Table

I), and they are initially aligned (bottom surface). The unrec-

onstructed boundaries between the overlapped structural

models are along the dashed lines and they comprise partial

dislocations. However, it is clear that those boundaries could

be formed also along inclined planes. The larger c4H lattice

constant with respect with the c2H can lead to corrugated lat-

tice fringes of the (0002) planes between the adjacent

FIG. 6. The structural parameters of the polytypes as a function of the hexa-

gonality of the polytypes are depicted. (a) The DFT calculated c lattice con-

stant (black squares) and the corresponding experimental values (green dots)

present a linear dependence on hexagonality. (b) and (c) The c/a ratio and

the total energies calculated by DFT, respectively, follow the same rule.

FIG. 7. The DFT calculated band gap of the various InN polytypes as a

function of hexagonality along with the PL spectrum of the InN NPs at 20 K.

The experimental luminescence peak of NCs is 0.78 eV, while their funda-

mental band gap, due to the Burstein-Moss effect, was estimated at 0.61 eV.

074312-7 Kioseoglou et al. J. Appl. Phys. 114, 074312 (2013)

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domains, as shown in the top surface of the structural model.

The model is directly comparable to HRTEM experimental

observations. A HRTEM image of the InN NCs is shown in

Fig. 8(b), where multiple polytype inclusions are denoted

with their corresponding stacking sequence. In the center

part, the 2H matrix is depicted, while from both sides 4H as

well as 6H polytypes are identified. The boundaries along

inclined planes between the different structures consist of

partial dislocations (denoted by arrows), whereas the corru-

gated form of the (0002) lattice fringes is also evidenced.

Our finding that the relaxed InN polytypes exhibited

larger c values with respect to the wurtzite structure, along

with the fact that the observed polytypes were introduced in

the form of embedded inclusions delimited by partial disloca-

tions, may lead to the formation mechanism of structural pol-

ytypes in InN NCs. Experimental evidence has shown that at

the onset of growth, the InN NCs grew under tensile strain

along both the basal plane and the growth direction. This sug-

gests the existence of volume elastic strain at the initial stages

of growth, under the following constraint: formation of the

initial stable nuclei of wurtzite InN on the amorphous SixNy

should be governed solely by surface stress, which is highly

probable since the epitaxial strain between InN and the Si

substrate is feeble. A similar case was also evidenced by

Consonni et al.,19 where the nucleation mechanism of self-

induced GaN nanowires grown on amorphous interlayer was

investigated. Soon after, structural polytypes are introduced

in order to accommodate the excess tensile strain along the

growth direction. In addition, the in-plane component of par-

tial dislocations that bound the polytype inclusions relief par-

tially the strain along the basal plane, while the rest is

relieved at the free lateral surfaces of the NCs. In other

words, partial dislocations act as misfit dislocations between

the tensile strained wurtzite InN and its relaxed structural

polytypes. This means that the introduction of polytypes in

the form of embedded inclusions inside 2H InN, is the key

mechanism for the relaxation of NCs.

In order to validate the preceding assumption, we have

constructed the ezz-exx strain diagram of InN polytypes.

Following the biaxial formulation in wurtzite structure, the

strain components are defined by the expressions: exx ¼ a0�aa ,

ezz ¼ c0�cc and ezz ¼ �2 C13

C33exx, where a, c are the strain-free

bulk lattice constants, a0 and c0 the corresponding strained

values and Cij are the elastic constants of InN. In addition,

the volume per In-N pair is defined by the equilibrium a and

c lattice constants from Veq ¼ffiffi3p

4a2c.20 Consequently, in a

ezz-exx strain diagram, we can determine the elastic structural

transitions following the biaxial formulation, as well as the

constant volume transition, where both the a0 and c0 lattice

constants can vary without affecting the equilibrium volume

Veq. In Fig. 9, the corresponding strain diagram of the 2HInN structure is presented, where both the biaxial and vol-

ume elastic transitions are illustrated. In addition, the isovo-

lume expansion and contraction lines with respect to the

equilibrium volume are also marked.

From the diagram of Fig. 9, we deduce that the 4H and

6H polytypes follow an isovolume expansion of �0.12%

with respect to the 2H structure. Moreover, the volume of

the 3C structure is also found expanded by �2%. It is clear

that InN polytypes are not related with biaxial strain.

Therefore, InN polytypes should be scarcely observed in

FIG. 9. The ezz-exx strain diagram of InN polytypes. The ezz and exx strains

are given with respect to the 2H wurtzite structure. The calculated structural

transitions of the polytypes are denoted. The red (solid) line depicts biaxial

strain, while the dashed lines denote various isovolume elastic strains, using

the 2H structure as reference.

FIG. 8. (a) Structural model of a 4H domain in a wurtzite (2H) matrix.

Vertical dashed lines illustrate the unreconstructed boundaries between the

two structures comprising partial dislocations. Both structures are initially

aligned, at the bottom surface, and along the [0001] growth direction the

hexagonal (h) and cubic (c) layers are denoted, following the crystallo-

graphic notation given in the text. Large [blue (2H) or green (4H)] and small

[red (2H) or yellow (4H)] spheres symbolize In and N atoms, respectively.

(b) Experimental HRTEM image, taken along the [11�20]InN z.a., where

structural polytype inclusions with their corresponding stacking sequence

are denoted. The corrugated form of the overlapping basal planes between

polytypes is evident. The location of partial dislocations, marked by arrows,

indicate that boundaries between polytypes are along inclined planes.

074312-8 Kioseoglou et al. J. Appl. Phys. 114, 074312 (2013)

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epitaxially grown films, where the dominant strain state is

the biaxial one. In contrast, the present study establishes that

InN structural polytypes are clearly associated with volume

elastic strain, which seems to be the driving force of struc-

tural polytypes introduction in InN NCs.

VIII. CONCLUSIONS

In summary, HRTEM and SAED analysis of InN NCs

revealed multiple inclusions with different lattice stacking

sequences within the ground state 2H wurtzite structure of

InN, generating satellite reflections in the SAED patterns.

HRTEM imaging and SAED simulations based on DFT cal-

culations identified these inclusions as the 4H, 6H, as well as

the 3C structural InN polytypes, embedded in the wurtzite

matrix of NCs in the form of inclusions delimited by partial

dislocations. Total energy calculations establish the 2Hstructure as the most stable polytype, while the band gap of

the 4H and 6H, and 3C polytypes was estimated at 0.64 eV,

0.60 eV, and 0.49 eV, respectively, compared to the

Eg¼ 0.75 eV of the 2H structure. We demonstrated that the

structural and electronic properties of InN polytypes have a

linear dependence on hexagonality. Based on quantitative

SAED patterns analysis in conjunction with DFT calcula-

tions and the corresponding strain analysis, we deduce that

introduction of the observed structural polytypes is linked

with volume elastic strain and constitutes the main relaxation

mechanism of the NCs. Finally, the presence of 3C, 4H, and

6H polytypes, led to red-shift of the estimated fundamental

band gap (Eg¼ 0.61 eV) of the InN NCs, suggesting that

manipulation of polytypism in III-Nitrides may initiate chal-

lenging opportunities on band gap tuning of functional nano-

structures. Therefore, handling the growth conditions of

structural polytypes in III-Nitrides in a manner that the rela-

tive ratio among them can be regulated, will allow a precise

control of the emission energy and subsequently, novel char-

acteristics for optoelectronic devices.

ACKNOWLEDGMENTS

This research has been co-financed by the European

Union (European Social Fund–ESF) and Greek national

funds through the Operational Program “Education and

Lifelong Learning” of the National Strategic Reference

Framework (NSRF)-Research Funding Program: THALES.

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