Dielectric spectroscopy of n type Cu5In9Se16 semiconductor compound
Introduction
Cu5In9Se16 (CIS) is an ordered defect compound with n = 8 in the formula Cun-3Inn+1Se2n that falls on the In-rich side of the binary phase diagram of (Cu2Se3)x - (In2Se3)1-x with x < 0.5 [1]. This material, which is a member of the Cu–In–Se family is a chalcopyrite semiconductor with an absorption coefficient of the order of 105 cm−1 and an energy gap close to 1 eV that have received considerable attention for its applications in solar energy technologies [[2], [3], [4], [5], [6], [7]]. Some measurements of optical absorption, thermal and electrical conductivity show that several intrinsic defect states exist in this compound [1].
To understand the mechanisms of charge transport and dielectric losses in any disordered compond, electrical impedance spectroscopy (EIS) with an alternating current is applied to the material. By varying the frequency, different contributions of the "grains", "grain boundaries" and "electrodes" can be identified [[8], [9], [10], [11]]. Also, the values of some characteristic parameters related to the dominant conduction mechanisms can be estimated and their frequency and temperature dependence can be analyzed [12,13].
In the literature, there are many recent studies on the temperature and frequency dependence of the dielectric properties and electric modulus for different nature of materials [[14], [15], [16], [17], [18], [19]] but, to our knowledge, no detailed dielectric studies of CIS have been published, especially at low temperatures up to liquid nitrogen temperature (≈−200 °C). Few results of dielectric behavior are reported for some copper ternary semiconductor materials but only at higher temperature up to +440 °C [20]. In an our previous work, we reported on the analysis of ac electrical conductivity (σac) on CIS in frequency up to 1 MHz [11] where we identified two activated conduction regimes: one below −130 °C and the other above of −77 °C and by using the universal Jonscher's law, it was shown that the data are in agreement with the theoretical model of polaron tunnelling [13,21,22].
Hence, continuing our previous work of reference 11 the main aim of this study is to use the impedance spectroscopy method in order to determine the effect of temperature and frequency on the real and imaginary parts of the complex dielectric constant (), tangent-loss () and complex electric modulus (M* = M' + jM") of Cu5In9Se16. For this subject, dielectric measurements were performed by using the HP-4284A spectrometer in a wide range of frequency [20 Hz - 1 MHz] with an applied voltage of 50 mV in temperatures between −175 and −10 °C. In this range of low temperatures, electrical conduction occur in impurity bands in the forbidden energy gap by hopping process. The temperature and frequency dependence of is analyzed in terms of theoretical models of correlated barrier hopping (CBH) and non-overlapping small-polaron tunneling (NSPT) [13,21,22]. Reported here also are the values of some parameters related to the dominant conduction mechanism like the maximum barrier height (Wm) at infinite intersite separation and the binding energy (Wh) for small polaron.
Section snippets
Experimental details
Ingots of CIS were obtained by using the Bridgmann technique [1,11]. For this, elements of Cu, In and Se of at least 5 N purity were used. Details related to the growth and structural properties of this material are already reported in previous works [1,11]. For the dielectric measurements, a silver paste is employed at the end parts of the sample, which were prepared in the form of cylindrical pellets. For the permittivity measurements, an HP-4284A spectrometer with frequency varying between
Dielectric properties
The dielectric properties (loss tangent, real (ε ׳) and imaginary (ε ״) parts of complex dielectric permittivity of Cu5In9Se16 have been studied within the frequency range from 20 Hz to 1 MHz in temperature range from −175 to −10 °C. The values of and are determined from the experimental data of capacitance C and dielectric loss D using the following expressionswhere S is the area of the electrode, d is the thickness of the sample and is the permittivity of free
Conclusion
Some physical properties of n type Cu5In9Se16 material has been studied in the present work. Complex permittivity, electrical modulus and complex impedance formalisms are considered to interpret experimental data. The experimental data of conductivity agrees with the Jonscher's law where the frequency exponent n(f,T), calculated as , shows a frequency and temperature dependence. Conduction process of Correlated Barrier Hopping and intermediate frequencies
Author contributions
All authors have participated in (a) conception and design, or analysis and interpretation of the data; (b) drafting the article or revising it critically for important intellectual content; and (c) approval of the final version: A. Bouchehma and L. Essaleh has realized the impedance spectroscopy measurements with contributions from S. Amhil, R. Bouferra and A. Bourezza. L. Essaleh wrote the manuscript with contributions from S. Amhil, R. Bouferra, M. Essaleh and S. Belhouideg. G. Marín and
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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