Synthesis, structural, electrical, magnetic and dielectric spectroscopic

characterization of C-Er2Si2O7

Shahid Ameer, Ahmad Faraz*, Asghari Maqsood, Nasir M. Ahmad

Thermal Transport Laboratory, School of Chemical and Materials Engineering (SCME), National

University of Sciences and Technology (NUST), H-12, Islamabad, Pakistan.

Cell: +92-333-9319316, Email: faraz.nust83@gmail.com

Keywords: electronic materials, X-ray diffraction, dielectric properties, electrical properties, magnetic parameters, saturation magnetization (Ms), remanance (Mr)

Abstract

The polymorphic Er2Si2O7 is synthesized by solid state double sintering method. Structural

and morphological characterizations have been performed using X-ray diffraction (XRD) and

scanning electron microscopy (SEM). The electrical characterization has been performed by two

probe method as a function of temperature. The dielectric spectroscopic measurements of

polymorphic Er2Si2O7 are performed in the temperature range 300-555 K and frequency range 3

kHz to 1 MHz. The dc electrical transport data are analyzed according to Mott’s variable-range

hopping. The ac conductivity σac(ω) is obtained through the dielectric spectroscopic measurements.

The ac conductivity obeys power law which can be expressed as σac (ω) = B ωs, where s is slope

and it determines the ac electrical transport phenomenon. The ac electrical transport data and its

variation with temperature in this rare earth formulation are well discussed. The magnetic behavior

of synthesized material is analyzed and confirmed that material have non-magnetic behavior with

coercivity (Hc) 842 Oe. While the values of magnetic saturation (MS) and remanace (Mr) were

found in range 3.90emu/g and 1.07emu/g.

1. Introduction

The compound containing rare earth materials specially their silicates are promising

materials for future microelectronics because of their high dielectric constant and low losses as a

replacement for traditional SiON/poly-Si electrodes. Modern solid state technology has recently

made use of rare earth compounds in microwave devices, semiconductors, ferromagnetic,

ferroelectric, laser and phosphors. Dielectric phenomenon in rare earth containing materials has

been recently extensively studied [1]. Currently the dielectric spectroscopic measurements have

been performed and charge transport mechanisms are analyzed by many authors [2, 3] for various

rare earth formulations.

Journal of Nano Research Vol. 17 (2012) pp 85-98Online available since 2012/Feb/03 at www.scientific.net© (2012) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/JNanoR.17.85

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Worldwide, the researchers are analyzing various rare earth formulations specially their oxides and

silicates for transistor scaling as being high dielectric materials for 22nm node and beyond [4]. The

unique properties of this group of compounds, which also include rare-earth silicates/disilicates, are

due to their special 4fn electronic states and the general shielding of these orbitals by higher orbitals

in the rare earth ions [5].

The compound Er2Si2O7 exists in three polymorphs, the low temperature polymorph (type B),

monoclinic (type C) and the high temperature monoclinic modification (type D). The preparation of

this material in the form of both poly- and single crystals has been reported by Maqsood et al [6].

The material was characterized by X-ray diffraction. The lattice constants and possible space groups

were determined by the same authors [7-9]. This paper describes the synthesis, electrical, magnetic

and dielectric characterization of C-Er2Si2O7. The ac electrical parameters are also calculated from

the data of dielectric parameters as a function of both frequency and temperature. The dc electrical

conductivity in the temperature range 410-540 K and ac electrical conductivity as a function of

frequency and temperature in the range 300-555 K and magnetic parameters (Hc, Mr, Ms) are

reported.

2. Experimental procedure

The material was prepared by solid state reaction method. Precursors taken were 99.9 %

Er2O3, BDH silica gel of 60-120 mesh. The SiO2, containing 12 wt % of H2O was calcined at 1000º

C and then kept in a desiccators. The composition calculated from the formula was well mixed and

heated at 1450º C for 24 hours and then kept at this temperature for 24 hours. After that the furnace

was switched off. On cooling, the material was remixed thoroughly and the same process was

repeated. Structural and morphological investigations are achieved by X-ray powder diffraction

(XRD) and Scanning electron microscopy (SEM).

For resistivity measurement, the powder was compacted into pellets of approximately 13

mm in diameter and of thickness of 4.5 mm. Because of very high resistivity of C-Er2Si2O7 at room

temperature, a two probe method was used to measure the dc electrical resistivity. For dielectric

measurements, Wayne Kerr 6500B Impedance analyzer was used to check the response of C-

Er2Si2O7 in the frequency domain. All the measurements were done in a temperature controlled

furnace, and the temperature accuracy is within 2K. The ac electrical conductivity (σac) was

calculated from the dielectric parameters as a function of frequency at different temperatures.

Magnetic parameters Hc, Ms and Mr are analyzed using VSM (BHV-50, Riken Denshi Co. Ltd.

Japan).

86 Journal of Nano Research Vol. 17

3. Results and discussion

3.1 Structural investigation

The x-ray diffraction for C-Er2Si2O7 in powder identifies that the bulk sample be the

polycrystalline nature. Results are analyzed with card No. ASTM 82-0733 and it proves that the

resulted structure is the C-phase of Er2Si2O7 with lattice constants in agreement with previous

reports [6] as shown in Fig. 1. The high temperature polymorph forms a monoclinic structure with

lattice constants, a = 6.849 Å, b= 8.939 Å and c = 4.722 Å, β = 101.8. Scanning electron

microscopy shows the morphology of particle as shown in Fig. 2 (a) .Fig. 2 (b) shows the EDX

compositional analysis which confirms that the resulting Er : Si ratio was 7 : 1 in agreement with

the composition.

20 40 60 800

1000

2000

3000

4000

5000

Intensity (a.u.)

2 θ θ θ θ values

(021)

(201)

(130)(220)(131)

(221)

(222)(132)(200)

(111)

(331)(133) (530)

Fig. 1: X-ray diffraction pattern of C-Er2Si2O7.

Journal of Nano Research Vol. 17 87

Fig. 2(a): SEM Micrograph of C-Er2Si2O7.

Fig. 2(b): EDX analysis of C-Er2Si2O7.

3.2 DC electrical properties

The dc electrical conductivity of C-Er2Si2O7 is measured as a function of temperature in the

range 410-540 K. The dc electrical conductivity of C-Er2Si2O7 follows a semiconductor like

behavior, expressed by the relation [10]:

88 Journal of Nano Research Vol. 17

σdc=σ0exp (-∆E/kBT). (1)

Where σ0 is the pre-exponential factor, kB is the Boltzmann constant and ∆E is the activation energy

for the conduction process. In order to calculate the activation energy, ln σdc vs 1/kBT was plotted

and corresponding slope provided the activation energy as shown in Fig. 3. The electrical

conductivity measured at room temperature is 1.7 × 10-5 S/m and also the activation energy for

conduction process comes out to be 0.367 ± 0.02 eV.

The parameter σ0 as indicated in Eq. 1 is an indication of conduction path that whether the

conduction is caused by the extended states or localized states [11]. For extended state path of

conduction, σ0 should be within the range 103-104 S/cm [12] and σ0 should have a smaller value for

conduction through localized states. In case of C-Er2Si2O7, the value of pre-exponential factor σ0 is

10-3 S/cm, which is fairly small. This small value of σ0 is a confirmation of fact that the hopping of

charge carriers between localized states is responsible for conduction. Another confirmation

towards the hopping of charge carrier can be obtained by the small value of activation energy [13],

which in this case is 0.367 eV for C-Er2Si2O7.

It is further assumed that Mott’s Variable Range Hopping (VRH) mechanism is the criteria for the

conduction, which can be expressed as [14, 15]:

σ = σoexp{- (To/T) 1/4} (2)

where To being the degree of disorder, given by To= λα3/ {kBN(EF)}, N(EF) is the density of states

at fermi level, λ is a dimensionless constant of about 16 [15,16] and α has a value of 107cm-1. Fig. 4

is the graphical form of Mott VRH plot as expressed by Eq. 2. The hopping distance (R) and

average hopping energy (Wdc) are calculated using the relations below as a function of temperature

[15], and are shown in Table 1.

R={9/(8παkBTN(EF)}0.25. (3)

Wdc=3/(4πR3N(EF)). (4)

There are two necessary conditions for applying Mott’s VRH mechanism, which can be

expressed as [14]

(i) average hopping energy must be greater than thermal energy (i.e. Wdc > kBT ) and

(ii) αR > 1

Here both the conditions are satisfied. Values of R and Wdc are shown in Table 1.

Journal of Nano Research Vol. 17 89

Table 1: Parameters of Mott’s VRH mechanism at 410-540 K. To = 8.2×108 K and

N (EF) = 2.2x1017 eV-1cm-3.

Temperature (K) R dc(nm) W dc(meV)

413 14.5 344

433 14.3 357

453 14.1 369

473 14.0 381

493 13.8 393

513 13.7 405

533 13.6 417

Fig. 3: Arrhenius plot for C-Er2Si2O7.

90 Journal of Nano Research Vol. 17

Fig. 4: Mott’s VRH plot.

3.3 Dielectric properties

Fig. 5 shows the variation of dielectric constant (ε′) with the frequency in the temperature

range 300-555 K. The range of frequency used was 3 kHz – 1 MHz. This decreasing trend of

dielectric constant with the frequency is because of the fact that the dielectric constant is explained

by a contribution to polarzibility from various factors like deformational (electronic and ionic) as

well as relaxation (orientation and interfacial modes) polarization. Upon increasing frequency,

orientation mode of polarization decreases as it requires more time than ionic and electronic mode

of polarization. This causes the dielectric constant to decreases with increasing frequency and

reaching a almost constant value at higher frequency because of only interfacial polarization. The

value of dielectric constant increases with increase in temperature showing that the relaxation

frequency of the dispersion increases with rising temperature. Also orientation mode of polarization

is associated with the motion of molecules initiated by thermal energy, so the diploes are unable to

orient themselves at sufficiently low temperature [17]. When the temperature increases, it provides

enough thermal energy for facilitation of orientation polarization and consequently dielectric

constant increases.

Journal of Nano Research Vol. 17 91

Variation of dielectric loss with frequency follows a power law expressed by relation below:

ε′′ = Aωm (5)

where A being a constant. Inset in Fig. 5 shows the graphical representation of power law

expressed by Eq. 5. This plot provides us the value of frequency coefficient of dielectric loss ‘ m’

by the slope of plot. The m values variation with temperature are also shown as inset in Fig. 7. The

m values can also be expressed by famous Guintini relation [18] as:

m=4kBT/wM (6)

where wM being the maximum barrier height and other variables have their usual meanings. The

maximum barrier height height wM calculated for C-Er2Si2O7 comes out to be 0.068 eV.

The increase of dielectric loss with temperature has been explained by Stevels [19] who categorized

the relaxation into three types, conduction losses, dipole losses and viberational losses. At lower

temperature, conduction losses are minimum because they are proportional to {σac(ω) /ω)}. As the

temperature increases, the ac conductivity {σac(ω)} increases and so the conduction losses also

increases, which is the reason of increasing dielectric loss with increasing temperature.

The ac electrical conductivity dependence on frequency can be expressed as:

σtotal(ω)=σdc+σac(ω). (7)

Where σ total(ω) represents the total electrical conductivity at any particular angular frequency (ω)

and at any certain temperature, σdc is the dc conductivity. The dependence of ac electrical

conductivity upon frequency of applied signal can be expressed by a power law expressed below:

σac(ω)=Bωs. (8)

where B is as pre exponential factor and s is the frequency exponent [15, 20-22] which is generally

less than or equal to unity and it defines the degree of interaction between mobile ions and its

surrounding lattices .The pre-factor B is the measure of strength of polarization [23]. It is also

important to mention that the magnitude of ac conductivity (BωS) is slightly greater than the dc

conductivity. Fig. 6 shows the frequency dependence of ac electrical conductivity in the

temperature range 300-555 K. It is evident from Fig. 6 that ac electrical conductivity, σac (ω), almost

increases linearly with the increase in temperature. The increase of σac (ω) with increasing

frequency suggests that hopping of charge carriers is responsible for conduction and that the

increasing of the frequency of applied field enhances the jumping of charge carriers between the

different localized states and reduces the activation energy of doing so.

92 Journal of Nano Research Vol. 17

It is also a well known fact that, the relation σ = σ0 exp (-∆E/ kB T) is indicative of the fact that the

mobile charge carriers are thermally activated by ∆E. The activation energies of conduction,

calculated at various frequencies are listed in Table 2. The values of ac activation energies are much

less than that of the dc activation energies in the entire temperature range. The difference is due to

fact that the charge carriers in dc conduction always chooses the easiest path available which may

sometime include some large jumps, while this is not much important in ac conduction process [24].

It is clear from the Table 2 that ∆E decreases with increasing frequency as found for other materials

[25]. It is because the increase of frequency facilitates the electronic jumping between different

localized states, consequently activation energy decreases with increasing frequency.

Table 2: The ac electronic parameters of C-Er2Si2O7 at different frequencies.

Parameters

∆E (eV)

100 kHz

0.213

200 kHz

0.183

400 kHz

0.154

600 kHz

0.009

800 kHz

0.006

σ 300 (10-7

S/m) 1.38 2.14 38 4.8 63

Table 3: Different parameters of CBH model at 50 KHz; calculated value of U is 0.17eV along with W Loss

Temperature (K) R min (nm) N (eV-1

- cm-3

) W Loss (mwatt)

300 1.42 1.04 x 1019 1.49

450 1.30 2.91 x 1019 7.38

480 1.28 3.62 x1019 1.05

530 1.21 5.16 x1019 1.62

555 1.12 7.85 x 1019 2.55

The temperature dependence of s is shown in Fig. 7. The values of s decreases with the

increase in temperature. It is well known that the power law (BωS) is generally obeyed with the

values s ≈ 0.7 at room temperature, and the classically accepted range of s lies between 0.6 < s < 1

is likely to be associated with the presence of hopping conduction [26, 27]. In nutshell, firstly the

discrepancy between the values of ac and dc activation energies secondly the smaller values of

activation energy lastly the increase of ac conductivity {σac (ω)} with increase of frequency

confirms the presence of hopping conduction be the responsible for conduction.

In order to explain the temperature and frequency variation of ac electrical conductivity,

there are models for conduction, whose identification is achieved by the frequency coefficient s and

its temperature dependence [28-30]. There are two main types of models named the quantum

mechanical tunneling model [31, 32] and classical hopping model [33, 34]. The classical hopping

over a barrier (HOB) model [32] suggests the values of s equal to unity which does not agree with

Journal of Nano Research Vol. 17 93

our experimental results (s ≈ 0.75). So we propose the correlated barrier hopping (CBH) model to

explain experimental observed conductivity behavior. In this model, conduction occurs by means of

hopping of electrons over a coulomb barrier separating two equilibrium states. A coulomb

correlation can be made between these states, which results in correlation between relaxation

variable, U, of coulomb barrier and distance between states, R. This model, first developed by Pike

[35] for single electron hopping, has been modified by Elliot [27] for simultaneous two electron

hopping. According to CBH model, value of s should be from 0.7 to 1 at room temperature and

should decrease with increasing temperature. This agrees well with our results (s ≈ 0.75) and

thermal variation as shown in Table 3.

In the CBH model, electrons in charged defect centers jump over coulomb barrier of height

U expressed by:

U = wM- (8e2/ε′R). (9)

where wM is the maximum barrier height and others have usual meaning. From Eq. 9, U comes out

to be equal to wM as other factors are negligibly small. The ac conductivity is expressed as [31]:

σac(ω) = π�

�� N2ε′εo R

6 (10)

where N is density of a pair of sites and R is expressed as:

R = e2/ [π ε′εo{wM-kBTln (1/ωτ0 )}] (11)

The lower bound (cut off) to R is given by:

Rmin = e2/ π ε′εowM (12)

The temperature dependence of frequency exponent in this model is evaluated to be:

s = (1-6kBT) / [wM-kBTln (1/ωτ0)] (13)

A first approximation to Eq. 13 gives:

s = (1-6kBT) / wM (14)

In ac fields the energy loss per unit volume per unit time may be expressed as :

WLoss = (ωεoE2

ε′′) / (8 π) (15)

Where ω is the angular frequency and E is the ac field [36]. The values of energy loss calculated at

different temperatures are tabulated in Table 3.

94 Journal of Nano Research Vol. 17

Fig.5: Dielectric constant (ε′) dependence on both temperature and frequency. Inset shows graphical

representation of power law ε′′ = A ωm

Fig. 6: lnσac(ω) as a function of frequency at various temperatures.

Journal of Nano Research Vol. 17 95

Fig. 7: Variation of parameters‘s’ and ‘m’ with temperature.

3.3. Magnetic Studies

The magnetic studies are performed using vibrating samples magnetometer (VSM).The magnetic

nature of synthesized sample is revealed from magnetic hysteresis loop. Fig 7 represents hysteresis

loops of synthesized material confirmed non-magnetic nature of synthesized material. Magnetic

saturation (MS) and remanance (Mr) are calculated from hysteresis loop with values found in range

3.90emu/g and 1.07emu/g.The higher coercive force value 842 Oe further confirmed the non-

magnetic behavior of fabricated material. The value of squerence ratio (Mr/Ms) is found in range

0.27.

96 Journal of Nano Research Vol. 17

Fig. 8: Magnetic hysteresis loop for C-Er2Si2O7.

4. Conclusion

The C-type Er2Si2O7 material is prepared by solid state reaction method. Structural

investigation proves that resulted structure is C-type Er2Si2O7. SEM and EDX results show the

morphology and compositional analysis. The dc electrical resistivity/conductivity is measured by

two probe method and dc conduction mechanism operative within material has been discussed. The

dielectric spectroscopic and ac conductivity measurements are performed as a function of both

frequency and temperature. In-depth study of ac conduction mechanism and variation of dielectric

parameters with temperature are made. The magnetic behavior and parameters are analyzed at room

temperature reveals the non-magnetic behavior of fabricated material.

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