Impedance spectroscopy of Cu2SnS3 material for photovoltaic applications

Accepted Manuscript Impedance spectroscopy of Cu2SnS3 material for photovoltaic applications L. Essaleh, H. Chehouani, M. Belaqziz, K. Djessas, J.L. Gauffier PII: DOI: Reference:

S0749-6036(15)30080-X http://dx.doi.org/10.1016/j.spmi.2015.07.007 YSPMI 3866

To appear in:

Superlattices and Microstructures

Received Date: Revised Date: Accepted Date:

27 June 2015 30 June 2015 1 July 2015

Please cite this article as: L. Essaleh, H. Chehouani, M. Belaqziz, K. Djessas, J.L. Gauffier, Impedance spectroscopy of Cu2SnS3 material for photovoltaic applications, Superlattices and Microstructures (2015), doi: http://dx.doi.org/ 10.1016/j.spmi.2015.07.007

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Impedance spectroscopy of Cu2SnS3 material for photovoltaic applications

L. Essaleh a*, H. Chehouani b, M. Belaqziz b, K. Djessas c, J.L. Gauffier d

a

Laboratory of Condensed Matter and Nanostructures (LMCN), Cadi-Ayyad University. Faculty of Sciences

and Technology, Departement of Applied Physics, Marrakech, Morocco. b

Laboratoire Procédés, Métrologie, Matériaux pour l’Energie et Environnement (LP2M2E), Cadi-Ayyad

University, Faculty of Sciences and Techniques, Departement of Applied Physics, Marrakech Morocco. c

Laboratoire Procédés, Matériaux et Énergie Solaire (PROMES-CNRS), Université de Perpignan, Rambla

de la thermodynamique, Tecnosud, 66100 Perpignan Cedex, France. d

Département de Génie Physique, INSA de Toulouse, 135 Avenue de Rangueil, 31077 Toulouse cedex 4,

France.

Abstract The complex impedance spectroscopy in the frequency range 100Hz–1MHz and temperature range 300K–475K is used to study the electrical properties of the bulk ternary semiconductor compound Cu2SnS3. The dynamic electrical conductivity study shows that correlated barrier hopping model may be appropriate to describe the transport mechanism in our material. The dependences of dielectric parameters by fitting data with Cole–Cole equations on temperature have been discussed in detail. Relaxation time was found to decrease with increasing temperature and to obey the Arrhenius relationship. The values of calculated resistances for bulk were found to be smaller compared with that of grain boundary contributions.

Keywords: Electrical Conductivity; Copper Ternary compounds; Impedance Spectroscopy.

* Corresponding author: Pr. L. Essaleh Phone: (+212) 6 68 05 13 56, Fax: Fax:(+212) 5 24 43 31 70, E-mail: [email protected], [email protected]

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1. Introduction Ternary semiconductors such as copper tin sulfides Cu-Sn-S have attracted a great deal of attention as excellent absorber materials because of their high absorption coefficient (>104 cm−1) for photovoltaic cells, and are suitable candidates for nonlinear optical materials [13]. A semiconducting phase Cu2SnS3 (CTS) with a direct band gap between 0.93 and 1.35 eV that can be used in solar cells have been reported [4-6]. The polymorphic state of a grown Cu2SnS3 is dependent on the growth temperature, where the cubic Cu 2SnS3 is known to format at high temperatures (>775 °C) and the monoclinic and triclinic as well as the tetragonal phases are low temperature phases (<775 °C) [7-8]. The copper tin sulfides compounds are also very useful in understanding and extending the basic physical concepts of the electrical conduction mechanisms involved in elemental and binary compound semiconductors. Moreover, continuing our earlier works on bulk [9-10] and also on thin films [11-12] ternary compounds, we investigated the electrical properties of the CTS compound by means of impedance spectroscopy using an alternating signal with voltage amplitude of 20 mV. Impedance spectroscopy (IS) is a non-destructive method that can correlate the structural and electrical characteristics of polycrystalline solids in a wide range of frequencies as a function of temperature [13]. It also describes the electrical processes occurring in a system by applying an a.c. signal as input perturbation, which helps to separate the contributions of electro-active regions (such as grain boundary and bulk (or grain) effects). Complex impedance spectroscopy consists of measuring the real and imaginary part (Z’ and Z″) of the impedance (Z*) of a material at various temperatures and for different frequencies. The impedance plots of a polycrystalline sample allow the presence of grain and grain boundary properties to be resolved in the form of succession of semicircles associated with the bulk resistance (R1) and grain boundary resistance (R2) of the sample, providing that their time constants differ sufficiently [13]. These properties are explained by complex parameters like complex impedance (Z* = Z’ – j Z’’) expressed as:

(1) Where the indices i refers to all contributions to the impedance Z* and i = RiCi is the relaxation time for the circuit ( Ri, Ci). A pure capacity (C) can be replaced by a constant phase element (CPE) if there is distribution of relaxation time due to defects and inhomogeneity of the material. In the present work, we discuss the electrical conduction 2

mechanisms in CTS material and analyze the experimental data using the existing theoretical models.

2. Experimental details The CTS nanoparticles were prepared using the hydrothermal synthesis with high purity water as the solvent. Precursors (CuCl2.2H2O: Sigma Aldrich 99%), (SnCl2 : sigma Aldrich, 98%) and Na2S (Na2S.9H2O: Sigma Aldrich 98%) were used as source materials. The reagents were loaded into a 23 ml autoclave with Teflon-liner. The molar ratio of Cu, Sn, and S was fixed at 2:1:3. The reaction temperature of the autoclave was controlled up to 230 °C for time up to 24 h. The prepared products were washed with high purity water and dispersed in ethanol. The finely crushed mixture was dried at 100 °C during 4 h. The formation of the single phase compound was confirmed by X-ray powder diffraction (XRD) technique. The fine homogenous obtained powder grains were linked with organic binder polyvinyl alcohol which burned at low temperature to provide the strength and flow ability of granules and to reduce the brittleness of the sample. Powders of these compounds were initially compacted with a pressure of 2 tons/cm2 to obtain the cylindrical pellet sample having approximately 10 mm of diameter and 1 mm of thickness. Finally, the obtained pellet was sintered during 1 h at 450 °C [14]. Impedance measurements were carried using the HP 4284A spectrometer in the frequency range of 10–106 Hz. A source of 20 mV was applied to the electroded pellet samples. The temperature variation was performed using a programmable Thermolyne heater with a temperature stability of ±0.1°C. Silver electrodes were deposited on the two circular faces of the sample to get the capacitor shaped samples. 3. Results and discussion 3.1 Temperature and frequency dependence of electrical conductivity Figure 1 shows the variation of ac resistivity (ac) with the inverse of temperature at some representative frequencies. The curves was fitted with Arrhenius equation and the values of the activation energy (Econd) for ac conduction at different frequencies were calculated from the slope of the curves. We obtained a gradual decrease in this activation energy from 360 to 213meV when increasing frequency from 100Hz to 1MHz, respectively. A similar kind of behavior has also been reported in the literature [13, 3

15]. Such a decrease can be attributed to the fact that the increase of the applied field enhances the charge carrier’s jumps between the localized states [16]. Generally, smallest values of the ac activation energy and its decrease with frequency are related the hopping conduction mechanism between localized states [16-18]. The angular dependence in the frequency of the alternating current conductivity at different temperatures is shown in Fig.2. It is generally analyzed using the Jonscher’s equation [19] where

,

is the conductivity at low frequencies, A is temperature-dependent parameters

and s is the power exponent in range 0 < s < 1, which can be determined from the measured results. The conductivity increases with increasing angular frequency, as, the conductivity increases with increasing temperature at a certain fixed angular frequency. The frequency exponent, s, is obtained from the best fit of the experimental data of Fig.2 with the Jonscher’s equation. The exponent s is found to decrease linearly from 0.492 to 0.427 with increasing temperature from 35 °C to 170 °C. This behavior was associated with a correlated barrier hopping (CBH) model for ac conductivity [20-22]. 3.2 Temperature and frequency dependence of impedance The temperature dependence of the complex impedance (Nyquist plot) is shown in Fig. 3(a) from 35°C to 100 °C and Fig.3(b) from 100°C to 170 °C. From these curves, we see that the experimental points are located on arcs. The evolution curves Z’’ = f(Z’) at different temperatures from 35 °C to 170 °C shows the thermal behavior of the material strength. An increase of temperature is accompanied by a decrease in resistance. To explain the electrical behavior of such materials, equivalent electrical circuits are proposed. The shape and the width of the arc indicate the type of relaxation mechanism for the system. In the present case depressed semicircles were observed indicating a distribution of the relaxation time. This suggest that the arc cannot be fit using an ideal capacitor C, and should be replaced by a constant phase element (CPE) Q defined as

[19] where, n is

the empirical exponent and its value varies from 0 to 1; for an ideal capacitor n = 1 and for an ideal resistor it is 0. From the best fitting of the diagrams of impedance, frequency and the complex plane of impedances, an equivalent circuit for our material is made by a series combination of (R1//C1) and (R2//CPE2), where R, C and CPE are respectively resistance, capacity and constant phase element, which represents the electric behavior of material and permits to determine data of resistance and capacitance for the interfaces of the sample. Then, the Cole–Cole diagrams are interpreted in this way: the semicircle close to the origin 4

(high frequency domain which corresponds to low relaxation time) gives the intra-grain resistance R1 and capacitance C1, and the semicircle of high real part Z’ of total impedance Z* (low frequency domain which corresponds to high relaxation time) is related with the inter-grain (grain boundary) coupling with resistance R2 and constant phase element CPE2. The real and imaginary components of the whole impedance of this circuit were calculated according to the following expressions:

(2)

(3)

Both Eqs. (2) and (3) are in the form of two terms corresponding to two relaxations process. The first response consists of parallel combination of resistance R1 and capacitance C1 attributed to the grains, the second of parallel combination of resistance R 2 and a constant phase element Q attributed to the grains boundary. Nyquist plots reported in Fig. 3 shows a good agreement between the calculated curves and the experimental data. The continuous line curves are calculated from the corresponding equations defined for equivalent circuit. Moreover, experimental and calculated curves of real (Z’) and imaginary (Z’’) parts vs. frequency at some representative temperatures are superposed in Fig. 4 for Z’ and in Fig.5 for Z’’. The continuous line curves are calculated from the corresponding equations (2) and (3) defined for equivalent circuit. The good conformity between experimental and calculated curves indicates that the proposed equivalent circuits describe well the behavior of our material. The relaxation times of these two different contributions are calculated from the values of the parameters R1, C1, R2, Q et n given in Table 1. These parameters are obtained from the best fits of the imaginary part Z’’ versus Z’ curves (ColeCole diagrams). The expressions that we used to calculate relaxation times are 1 = R1C1 for the (R1//C1) contribution and 2 = ( R2 Q )1/n for (R2//CPE2) contribution. For example, at 400K, 1 = 8.99 10-7 s and 2 = 2.68 10-5 s. We obtained, as we can see in Fig. 6, that at each temperature, 1 < 2 indicating clearly that: a) 1 is attributed to the bulk (or grain) contribution. Then, the resistance related to bulk contribution is R1. b) 2 is attributed to the grain boundary contribution. Then, the resistance related to grain boundary contribution is R2. 5

The values of calculated resistances for bulk (R1) were found to be smaller compared with that of grain boundary (R2) contributions. The logarithmic variations of R1 and R2 as a function of the inverse of temperature (1/T) are presented in Fig.7 and for a comparison we include in this figure the variations of electrical resistivity ρDC estimated from Fig.2 in the low frequency domain. It also shows that bulk resistance decreases with increase in temperature, manifesting the semiconducting behavior of the compound. A linear behavior is obtained with an activation energy of the order of

. The relaxation times,

represented in Fig.6, of different contributions are calculated from the values of the parameters given in Table 1. That is g =1 = R1C1 for the bulk (grain) and gb=2=(R2 Q)1/n for the grain boundary contribution. It is evident that g < gb and both decreases when the temperature increases. For a thermally activated relaxation process, the relaxation time () generally follows the Arrhenius law: (4) where τo is the relaxation time at infinite temperature, T is the absolute temperature, E relax is the activation energy for relaxation, and kB is the Boltzmann constant. The relaxation parameters Erelax and τo were determined by plotting ln() as a function of the inverse of temperature and fitting using Eq. (4) (Fig. 6). The values of activation energy for relaxation for bulk and grain boundary were found to be ( 204 ± 2 ) meV and ( 315 ± 1 ) meV, respectively. Further, a low difference between these activation energies (111 meV) suggests a small potential barrier between the grain and grain boundary. By comparison with the activation energy for the conduction process obtained from the analysis of electrical conductivity in the high temperature range (

), we

conclude that Erelax < E cond. The activation energy for conduction (E cond) is the sum of both the creation of charge carriers and hopping free energy of charge carriers over long distances while the activation energy for relaxation is equal to the migration free energy of charge carriers and their hopping between the adjacent lattice sites. The difference between the conduction and relaxation activation energies may be attributed to the creation of free energy [23]. 4. Conclusion The ac conductivity measurements of the bulk Cu2SnS3 compound are found to be temperature and frequency dependent and obey to the universal power law. The complete

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impedance spectroscopy is analyzed. Nyquist plots show both grain and grain boundary contributions to impedance. It also shows that bulk resistance decreases with increase in temperature, manifesting the semiconducting behavior of the compound. Relaxation time was found to decrease with increasing temperature which follows the Arrhenius relationship. The electrical relaxation process occurring in the material has been found to be temperature dependent.

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References [1] Emin S, Singh SP, Han L, Satoh N, Islam A, Sol. Energy 85(2011)1264. [2] Blöb S, Jansen M, Z. Natur for sch 58b(2002)1075. [3] Liang X, Cai Q, Xiang W, Chen Z, Zhong J, Wang Y, Shao M, Li Z, J. Mater. Sci.Technol. 29(2013)231. [4] Fernandes PA, Salome PMP, da Cunha AF, J. Phys. D: Appl. Phys. 43(2010)215403. [5] Bouaziz M, Amlouk M, Belgacem S, Thin Solid Films 517(2009)2527. [6] Dominik M. Berg, Rabie Djemour, Levent Gütay, Guillaume Zoppi, Susanne Siebentritt, Phillip J. Dale, Thin Solid Films 520(2012)6291. [7] Onoda M, Chen X-A, Sato A, Wada H, Mater. Res. Bull 35(2000)1563. [8] Berg DM, Djemour R, Gütay L, Siebentritt S, Dale PJ, Fontane X, Izquierdo-Roca V, PerezRodriguez A, Appl. Phys. Lett. 100(2012)192103. [9] Marín G, Wasim SM, Rincón C, Essaleh L, Materials Letters 157(2015)70. [10] Essaleh L, Galibert J, Wasim SM, Hernandez E, J. Leotin, Phs. Rev. B, 52(1995)7798. [11]Abounachit O, Chehouani H, Djessas K, Thin Solid Films, 540( 2013) 58. [12] Abounachit O, Chehouani H, Djessas K, Thin Solid Films, 520( 2012) 4841 [13] Kaushala A., Olhero S.M., Budhendra Singh, Duncan P. Fagg, Igor Bdikin, Ferreira J.M.F., Ceramics International 40(2014)10593. [14] Yu Wang, Yanhua Huang, Alex YS Lee, Chiou Fu Wang, Hao Gong, Journal of Alloys and Compounds 539(2012)237. [15] Singh BK, Kumar B, Cryst.Res.Tech. 45(2010)1003. [16] Bekheet A.E., Physica B 403(2008)4342. [17] Austin I.G., Mott N.F., Adv. Phys. 18(1969)41. [18] Hegab N.A., Afifi M.A., Atyia H.E., Farid A.S., J. Alloys Compd. 477(2009)925. [19] A.K. Jonscher, Dielectric Relaxation in Solids, Chelsea Dielectrics press, London, 1983. [20] Elliott S.R., Adv Phys., 36(1987)135. [21] Elliott S.R., Phil. Mag.,36(1977)291. [22] El-Nahass M.M., Farag A.M.M., Abu-Samaha F.S.H., Eman Elesh, Vacuum 99 (2014)153. [23] Ridha Bellouz, SamiKallel, KamelKhirouni, OctavioPena, MohamedOumezzin, Ceramics International41(2015)1929.

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Table captions Table 1: Temperature dependence of fitted circuit parameters.

Figure captions Figure1: AC electrical resistivity as a function of 1/T at some representative frequencies. The straight lines represent the best fits. Figure2: Frequency dependence of ac conductivity, at some representative temperatures of CTS. Figure 3(a): Le diagramme Cole-Cole lorsque la température varie de 35 à 100 °C. The calculated curves are represented by continuos lines. Figure 3(b): Le diagramme Cole-Cole lorsque la température varie de 100 à 170 °C. The

calculated curves are represented by continuos lines. Figure 4: Variation of (Z’) as a function of the frequency at some representative

temperatures. Figure 5: Variation of (Z’’) as a function of the frequency at some representative

temperatures. Figure 6: Variation of a relaxation time for a bulk (g) and grain boundary (gb) with inverse of temperature. The straight continuos lines represents the agreement with the Arrhenius law. Figure 7: Variations of R1 et R2 with temperature.

9

T (° C)

R1(Ω)

C1(F)

R2(Ω)

Q(F)

35

8271

3,85E- 10

292740

2,6708E-8

0,66538

45

7202

4,676E- 10

195200

2,9257E-8

0,66219

55

5647

6,312E- 10

138740

4,7637E-8

0,62714

65

3597

5,394E- 10

105360

4,5463E-8

0,63751

70

3123

4,866E- 10

79578

4,1913E-8

0,64746

80

5243

2,466E- 10

58573

4,8381E-8

0,67065

90

3361

5,065E- 10

52675

1,178E-7

0,59189

100

1953

5,789E- 10

34052

7,7501E-8

0,62382

110

1512

7,035E- 10

24792

1,1675E-7

0,59801

120

1219

6,622E- 10

17102

9,2739E-8

0,61944

130

1031

8,726E- 10

13177

1,5898E-7

0,58622

140

922,5

5,45E- 10

10161

1,2275E-7

0,6161

150

773,2

6,963E- 10

8231

2,1945E-7

0,58195

160

735,3

6,402E- 10

6886

2,0885E-7

0,59327

170

459,1

8,115E- 10

5357

2,4028E-7

0,58892

Table 1

10

15

0 Hz 3 kHz

14 ln [ac ( Cm ) ]

8 kHz 30 kHz

13

50 kHz 200 kHz

12

1 MHz

11

10 2.5x10

-3

3.0x10 1/T (K

Figure 1

11

-1

)

-3

3.5x10

-3

170 °C -5

ac (  - 1 cm - 1)

6,0x10

150 °C -5

4,0x10

130 °C 110 °C 80 K

-5

2,0x10

70 °C 55 °C 35 °C

0,0 3

10

4

10

5

6

10

10

 ( rd / s ) Figure 2

12

7

10

8

10

Figure 3(a)

13

6,0x10

3

100 °C 110 °C

Calculated curves

4,0x10

120 °C

3

Z'' ()

130 °C

2,0x10

3

140 °C

150 °C

0,0 0,0

160 °C

170 °C

2,0x10

3

4,0x10

3

6,0x10

Z' (  )

Figure 3(b)

14

3

8,0x10

3

1,0x10

4

5

Z ' ()

1,5x10

35 ° C

Calculated curves

5

1,0x10

55 ° C 70 ° C

4

5,0x10

100° C

0,0 1 10

2

10

3

4

10

10



Figure 4

15

( Hz )

5

10

6

10

5

1,0x10

4

35 ° C

Z '' ()

8,0x10

Calculated curves

4

6,0x10

4

4,0x10

55 ° C

4

2,0x10

0,0 1 10

70 ° C 100° C 2

10

3

4

10

10



( Hz )

Figure 5

16

5

10

6

10

-5

-1

10

10 Erelax.g= ( 204 ± 2 ) meV

-2

10

o.g= ( 1,47 ± 0,08 ) ns

-3

10

-6

10

Grains

-6

10 Erelax.bg= ( 315 ± 1 ) meV o.bg= ( 3,11 ± 0,09 ) ns

-8

10

-7

10

-8

10

-9

-9

10

0,0

o.bg = 3,11 ns

o.g = 1,47 ns -3

1,0x10

10

-3

2,0x10

1/T ( K

-1

)

Figure 6

17

-10

-3

3,0x10

10

(s)

(s)



grains

10

-5

10

grains Bound.

Grains Boundary

-7



-4

10

ln ( R, R2 , dc )

dc 14

R2

12

10

R1 8

6 2,0x10

-3

2,5x10

-3

3,0x10

1/T (K-1)

Figure 7

18

-3

3,5x10

-3

Highlights

   

We analyse the variation of the impedance on Cu2SnS3 with temperatura and frequency. The activation energy and its dependence on frequency is studied. The data are analyzed with the correlated barrier hopping model. Tne Cole-Cole model is considered for this study.

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