Low temperature electrical impedance spectroscopy characterization of n type CuInSe2 semiconductor compound

Physica B: Condensed Matter 565 (2019) 14–17

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Low temperature electrical impedance spectroscopy characterization of n type CuInSe2 semiconductor compound

T

R. Bouferraa, G. Marínb,c, S. Amhila, S.M. Wasimd, L. Essaleha,∗ a

Laboratory of Condensed Matter and Nanostructures (LMCN), Cadi-Ayyad University, Faculty of Sciences and Technology, Marrakech, Morocco Department of Physics, Faculty of Science, University of Santiago Chile, Avenida Ecuador 3493, Estación Central, 9170124, Santiago, Chile c Millennium Institute for Research in Optics (MIRO), Av. Esteban Iturra S/N, Concepción, 4030000, Concepción, Chile d Centro de Estudios de Semiconductores, Facultad de Ciencias, Universidad de Los Andes, Mérida, 5101, Venezuela b

A R T I C LE I N FO

A B S T R A C T

Keywords: Semiconductor compounds Electrical conductivity OLPT model

In this report, the ternary chalcopyrite semiconductor n-CulnSe2 (n-CIS112) was studied using impedance spectroscopy (IS) over a wide range of temperatures [80 K, 300 K] and frequencies [20 Hz, 1 MHz]. The ingot was grown by vertical Bridgman technique. The experimental data are analyzed to estimate the activation and relaxation energies. The activation energies agree with those reported from Hall effect measurements. The predominance of both “bulk” and “grain-boundary” contributions to the electrical conduction is confirmed by using impedance and modulus formalism. AC electrical conductivity data σac(ω,T) for n-CulnSe2 are discussed using the theoretical Overlapping Large Polaron Tunneling process.

1. Introduction

2. Experimental results and discussion

CulnSe2 is a semiconductor with a fundamental absorption edge close to 1 eV and an absorption coefficient exceeding 105 cm−1 [1–4]. Measurements of thermal conductivity, optical absorption, Raman spectra and magnetoresistance measured on both single and polycrystalline samples have been widely reported [1–6]. There is experimental evidence from electrical and optical measurements that several defect states exist in CuInSe2 [5–9]. For this material, various studies were published by us specialy near liquid helium temperature when the electrical conduction occurs in impurity bands by the variable range hopping mechanisms [10–12]. However, no research work has been reported in the literature on the AC electrical conduction in this material when an alternating current is applied to the sample. Hence, we report in this paper results on the AC conductivity in the temperature [80 K, 300 K] and frequency [20 Hz, 1 MHz] ranges for nCuInSe2 that was grown by vertical Bridgman method. These measurements also provide useful information about the conduction mechanism in this material. AC electrical conductivity data σac(ω,T) at different frequencies up to 1 MHz is analyzed and compared with the theoretical model of Overlapping Large Polaron Tunneling process (OLPT).

2.1. Complex impedance analysis

∗

In disordered semiconducting materials, if the applied electric field → → E changes with time, the polarization P (t) follows and relaxes towards a new equilibrium. In a semiconductor, the relaxation time is a measure of how long it takes to become neutralized by conduction process. Thus, the activation energy for the relaxation process is related to the motion of charge carriers through the medium. The importance of impedance spectroscopy lies in the ability to distinguish the dielectric and electric properties of individual contributions to electrical conduction like the bulk and grain boundaries. In the classical model of Debye [13], the complex impedance Z* is given by a simple RC circuit in parallel as

Z ∗ = Z´ + jZ″, where Z´ =

R ωτ and Z″ = −R ( ) 1 + (ωτ )2 1 + (ωτ )2

(1)

Z′ and Z” are the real and imaginary parts of Z*, ω is the angular frequency and τ = RC is the time constant which satisfies the condition ωo τ = 1, where ωo is the relaxation angular frequency at which the semicircle (- Z”) versus Z′ passes through a maximum. Otherwise, the real (M′) and imaginary (M”) parts of complex modulus M* are expressed as

Corresponding author. E-mail addresses: [email protected], [email protected] (L. Essaleh).

https://doi.org/10.1016/j.physb.2019.04.028 Received 30 March 2019; Received in revised form 25 April 2019; Accepted 26 April 2019 Available online 28 April 2019 0921-4526/ © 2019 Elsevier B.V. All rights reserved.

Physica B: Condensed Matter 565 (2019) 14–17

R. Bouferra, et al.

10000

Z'( )

8000 6000

Ln(

)from max Z''

max

Linear FIT

)

max

4750

85K 105K 126K 148K 171K 203K 229K 297K FIT

-12

5700

-13 -14

3800

-Z''( )

12000

85K 105K 126K 148K 171K 203K 229K 297K FIT

a)

Ln(

14000

-15 E =(33 relax

2850

1.6)meV

-16 5,0x10

1900

-3

1,0x10

-2

-1

1/T(K )

4000

950 2000

b)

0 0

2

10

3

4

10

5

10

6

10

10

10

1

10

2

10

3

10

4

10

5

10

6

Frequency(Hz)

Frequency(Hz)

Fig. 1. Frequency dependence of the real (a) and imaginary (b) parts of complex impedance at different temperatures. Inset shows the variation of relaxation time obtained from maximum of Z″ as a function of (1/T). The calculated curves are also represented. 3

8x10

-Z''( )

3

7x10

3

6x10

1200

3

-Z''( )

respectively [14]. However, by using both impedance and modulus spectroscopy, the contribution of largest resistance can be observed with Z” whereas those of the smallest capacitance can be identified in M” spectra. Frequency dependence of Z′ and (-Z″) for different temperatures is given in Fig. 1a, b. The relaxation peaks were observed and, with increase in temperature, it moves to higher frequencies. From the position of the peak of (-Z”) which corresponds to the frequency fmax, the activation energy for the relaxation process Erelax is obtained from the ex−E ) [15,16], where fo is the pre-exponential pression fmax = fo exp( k relax BT factor, kB is the Boltzmann constant and T is the absolute temperature. 1 The corresponding relaxation time τ is deduced from fmax as τ = 2πf .

1800

85K 148K FIT

600

5x10

00

3

4x10

3

3x10

3

2x10

3

1x10

0 0,0

3

3

3

400 800 1200 1600 Z'( ) 85K 105K 126K 148K 171K 203K 229K 297K FIT 4

4

3,0x10 6,0x10 9,0x10 1,2x10 1,5x10 1,8x10

max

As expected, the observed linear behavior is shown in the inset of Fig. 1b where Ln τ is plotted against 1/T. The activation energy for the relaxation process is thus estimated to be(34 ± 2) meV . The variation of (-Z″) with Z’ for various temperatures is shown in Fig. 2. The semicircles are seen to be depressed suggesting a distribution of relaxation time [17,18]. Hence, in our case, the electrical equivalent circuit (R1+R2//CPE2), where the impedance of the con1 stant phase element CPE2 is given by ZCPE2 = Q (jω)n2 [16], is used to fit 2 the data. The parameters R1, R2, Q2 and n2 are considered as adjustable parameters and their values are summarized in Table 1. The pseudo

4

Z'( ) Fig. 2. Nyquist plot of n-CIS112 at various temperatures. The calculated curves with the electrical equivalent circuit (see inset) are also shown.

M ∗ = jωCo Z ∗, where M´ =

Co (ωτ )2 C ωτ ( ) and M″ = o ( ) C 1 + (ωτ )2 C 1 + (ωτ )2

1

capacity C2 of the material calculated fromC2 = (R21 − n2 Q2) n2 also appears in the same table. Its value of the order of 10−10 F indicates that (R2//CPE2) represents the “grain-boundary” contribution. The resistances Ri (i = 1, 2) obey Arrhenius law defined as E Ri (T ) = Rio exp ( k iT ) , where Rio is pre-exponential factor and Ei is the B energy required to activate the mobile charge carriers. The values of Ei are then deduced from the slopes of Ln(R1) and Ln(R2) versus 1/T (Fig. 3). We obtained E1 = (8 ± 1) meV and E2 = (30 ± 2) meV that are in agreement with those obtained previously from Hall effect

(2)

Co is the capacitance of the empty cell. From eqn. (1), we can observe that the complex impedance plots of (-Z″) versus Z′ is useful in determining the dominant resistance of a sample. Similarly, from eqn. (2), complex modulus plot is useful in determining the smallest capacitance. For the (-Z″) and M” versus frequency plots, the peak heights are proportional to R and to C−1,

Table 1 Values of the equivalent circuit parameters calculated for n-CIS112 compound at different temperatures. T (K) 85 105 126 148 171 203 229

R1 (Ω) 202.2 162.5 137.3 129.9 120.5 106.2 102.6

R2 (Ω) 13546 7160 4011 2722 1908 1292 910.2

Q2 (F)

n2 −9

1.73 × 10 1.575 × 10−9 1.42 × 10−9 1.167 × 10−9 9.815 × 10−10 7.82 × 10−10 5.96 × 10−10

15

0.843 0.855 0.867 0.884 0.899 0.917 0.939

τmax (s)

C2(F) −6

3.217 × 10 1.633 × 10−6 8.933 × 10−7 6.032 × 10−7 4.255 × 10−7 2.897 × 10−7 2.124 × 10−7

2.375 × 10−10 2.281 × 10−10 2.227 × 10−10 2.216 × 10−10 2.230 × 10−10 2.242 × 10−10 2.334 × 10−10

Physica B: Condensed Matter 565 (2019) 14–17

R. Bouferra, et al.

10

R1 R2

9

85K 105K 126K 148K 171K 203K 229K 297K FIT

2)meV

Linear FIT

8

10

-3

-1

cm )

Grain boundaries

7

(

6

tot

Ln(R1,R2)( )

E2=(30

E1=(8 1)meV

5

Grain

4

10

-4

3 -3

4.0x10

-3

6.0x10

-3

8.0x10

-2

10

-2

1.0x10

1.2x10

2

10

3

10

4

10

10

7

3

9

4x10

85K

Z'' (85K) M''(85K) 9

3x10 3

- Z''( )

M''

4x10

9

2x10

3

3x10

3

2x10

9

1x10

3

1x10

0

0 3

10

4

10

10

8

higher frequency at about 300 kHz. The observed single peak of (-Z″) plot corresponds then to the grain-boundary component with an average capacitance equals to 0.23 nF (see Table 1) while the observed single peak of M” corresponds to the bulk contribution with a smallest capacitance (usually of the order of 10−12 – 10−13 F [20]). Although the measured temperature range is between 80 and 300 K, it can be observed that in the plot of (-Z″) versus frequency curve of Fig. 1b, the peak practically disappears above 229 K and thus the corresponding (-Z″) versus Z′ impedance diagram can not be correctly analyzed by using the equivalent circuit. This is the reason of why the corresponding value of R1 and R2 does not appear in Table 1 and Fig. 3.

measurements [5,10–12,19]. Since Ei (i = 1, 2) are very small compared to the band gap energy of n-CIS112 (Eg = 1.0 eV), these two impurity levels found here corresponds to shallow levels. In reference 5, Wasim found several donor and acceptor levels in n- and p-type samples of CuInSe2. However, only two of them, at 8 and 80 meV, correspond to shallow donor levels. However, an acceptor level at 28 meV was found in Reference 5 for p-type CIS112. This level could also be present in ntype CuInSe2 because these samples are usually compensated. For this reason, the level at about 30 meV could be due to an acceptor impurity. Combined imaginary parts (-Z″) and M″ plots at a given representative temperature of 85 K are represented in Fig. 4. (-Z″) shows a single peak at about 50 kHz while M″ shows also a single peak but at

5x10

6

Fig. 5. Experimental and theoretical fit for AC conductivity as a function of frequency in a log-log scale in the temperature range of 85–297 K.

Fig. 3. Variation of Ln(R1) and Ln(R2) with inverse of temperature. The continuous straight lines represent the agreement with the Arrhenius law.

3

10

(rd/s)

-1

1/T(K )

6x10

5

5

10 Frequency(Hz)

6

10

Fig. 4. Comparison of imaginary part of Modulus (M″) and impedance (Z″) against frequency at a representative temperature of 85 K. 16

Physica B: Condensed Matter 565 (2019) 14–17

R. Bouferra, et al.

13,68

14,25

Ln( rd/s)) 14,82

associated with charge transfer between the overlapping sites. In Eqn. (4), the reduced quantities Rω′ = 2αR ω and rp′ = 2αrp are used. α−1 is the spatial extension of the polaron. Thus, from eqns (4) and (5), OLPT model predicts that s depends on both temperature and frequency. For small values of rp′ , s exhibits a minimum at a certain temperature while for large values of rp′ , it continues to decrease with increasing temperature [16,22]. So, the observation of the minimum in s(T) in Fig. 6 indicates that the value of rp′ is small in n-CIS112. The predominance of OLPT mechanism in nCuInSe2 in the studied low temperature range up to 80 K, not reported before, has also been observed recently in p-CuIn3Se5 [22,23], which is an ordered defect compound of Cu-In-Se family of CuInSe2.

15,39

1,32

1,14

1,21

123K 1,10

s

s

1,08

1,02

480KHz 0,96

0,99

50

100

150 T(K)

200

250

3. Conclusion Low-temperature electrical conduction of n-CuInSe2 was investigated using impedance spectroscopy method. A constant phase element CPE is used to fit the complex impedance plots. By using both impedance and modulus formalisms, the electrical process in n-CuInSe2 suggests the predominance of both “bulk” and “grain-boundary” contributions. The activation energies of shallow donors obtained from AC conductivity agree very well with those reported from Hall effect measurements. Large polaron mechanism is suggested to be the dominant conduction mechanism.

300

Fig. 6. Variation of universal exponent s as a function of frequency (for a representative temperature of 123 K) and temperature (for a representative frequency of 480 KHz).

2.2. Electrical conduction mechanism Several theoretical models to explain AC conductivity in disordered semiconducting materials were proposed in the literature [16]. Among these models, the power law behavior [16,21] and the Overlapping Large Polaron Tunneling [16] which is considered when the spatial extent of the polaron is large compared with the interatomic distance. Due to large Coulomb interaction, overlap of the potential wells of the neighboring sites is then possible. In these models, the total electrical conductivity σtot is given by

References [1] A.N. Tiwari, D.K. Pandya, K.L. Chopra, Sol. Cell. 22 (1987) 263. [2] I. Khatri, H. Fukai, H. Yamaguchi, M. Sugiyama, T. Nakada, Sol. Energy Mater. Sol. Cells 155 (2016) 280. [3] Ashwini B. Rohoma, Priyanka U. Londhe, Jeong In Han, Nandu B. Chaure, Appl. Surf. Sci. 466 (2019) 358. [4] H.T. Shaban, M. Mobarak, M.M. Nassary, Physica B 389 (2007) 351. [5] S.M. Wasim, Sol. Cell. 16 (1986) 289. [6] C. Rincón, F.J. Ramírez, J. Appl. Phys. 72 (1992) 4321. [7] H. Neumann, N.V. Nam, H.J. Hobler, G. Kuhn, Solid State Commun. 25 (1978) 899. [8] T. Irie, S. Endo, S. Kimpura, Jpn. J. Appl. Phys. 18 (1979) 1303. [9] H. Neumann, E. Nowak, G. Kuhn, Cryst. Res. Technol. 16 (1981) 1369. [10] L. Essaleh, J. Galibert, S.M. Wasim, E. Hernandez, J. Léotin, Phys. Rev. B 52 (1995) 7798. [11] L. Essaleh, J. Galibert, S.M. Wasim, E. Hernandez, J. Léotin, Phys. Rev. B 50 (1994) 18040. [12] L. Essaleh, S.M. Wasim, Mater. Lett. 61 (2007) 2491. [13] E. Barsoukov, J.R. Macdonald, Impedance Spectroscopy: Theory, Experiment, and Applications, Wiley, New York, 2005. [14] D.C. Sinclair, A.R. West, J. Appl. Phys. 66 (1989) 3850. [15] S. Nasri, M. Megdiche, M. Gargouri, Ceram. Int. 42 (2016) 943. [16] S.R. Elliot, Adv. Phys. 36 (1987) 135. [17] M.A.L. Nobre, S. Lanfredi, J. Appl. Phys. 93 (2003) 5557–5562. [18] S. Sen, R.N. P Choudary, P. Pramanik, Physica B 387 (2007) 56–62. [19] C. Rincon, S.M. Wasim, E. Ernandez, M.A. Arsene, F. Voillot, J.P. Peyrade, G. Bacquet, A. Albacete, J. Phys. Chem. Solids 59 (1998) 245. [20] J.T.S. Irvine, D.C. Sinclair, A.R. West, Adv. Mater. 2 (1990) 132. [21] A.K. Jonscher, Dielectric Relaxation in Solids, Chelsea Dielectrics Press, London, 1983. [22] L. Essaleh, S. Amhil, S.M. Wasim, G. Marín, E. Choukri, L. Hajji, Phys. E Low-dimens. Syst. Nanostruct. 99 (2018) 37. [23] S. Amhil, L. Essaleh, S.M. Wasim, S. Ben Moumen, G. Marín, A. Alimoussa, Mater. Res. Express 5 (2018) 085903.

(3)

σtot (ω, T ) = σdc (T ) + σac (ω, T )

where σdc is the low frequency conductivity and σac (ω, T ) is proportionnel toω s (ω, T ) . The frequency exponent s is determined from ∂ ln(σac (ω, T )) s = s (ω, T ) = ( ∂ ln( ) in Fig. 5 where ln(σ ) is represented as a T tot ω) function of ln(ω) for various temperatures between 80 and 300 K. In Fig. 6, we can see that s decreases with ω and exhibits a minimum at certain temperature in agreement with the OLPT theoretical process [16] because in this model, the frequency exponent s and the hopping tunneling distance Rω are given as [16].

4+ s (ω, T ) = 1 − Rω′ (1 +

R ω (ω, T ) =

6 Who r p′ kB T (Rω′ )2 Who r p′ kB T (Rω′ )2

)2

(4)

8 α rp Who 1 1 1 W 1 W {(ln( ) − ho ) + [(ln( ) − ho )2 + ]2 } 4α ωτ0 kB T ωτ0 kB T kB T (5)

where rp is the polaron radius and Who denotes the activation energy

17