Energy spectrum of near-edge holes and conduction mechanisms in Cu2ZnSiSe4 single crystals

Journal of Alloys and Compounds 580 (2013) 481–486

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Energy spectrum of near-edge holes and conduction mechanisms in Cu2ZnSiSe4 single crystals K.G. Lisunov a,b, M. Guc a,⇑, S. Levcenko a,c, D. Dumcenco d, Y.S. Huang d, G. Gurieva c, S. Schorr c,e, E. Arushanov a a

Institute of Applied Physics, Academy of Sciences of Moldova, Academiei Str. 5, MD 2028 Chisßina˘u, Republic of Moldova Lappeenranta University of Technology, PO Box 20, FIN-53852 Lappeenranta, Finland Helmholtz Zentrum Berlin für Materialien und Energie, Hahn-Meitner-Platz 1, D-14109 Berlin, Germany d Department of Electronic Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan e Free University Berlin, Institute of Geological Sciences, Malteserstr., 74-100 Berlin, Germany b c

a r t i c l e

i n f o

Article history: Received 28 May 2013 Received in revised form 24 June 2013 Accepted 26 June 2013 Available online 4 July 2013 Keywords: Optical materials Semiconductors Electrical transport Electronic properties

a b s t r a c t A model of the energy spectrum of holes near the edge of the valence band of Cu2ZnSiSe4 is proposed from investigations of the resistivity, q(T), in Cu2ZnSiSe4 single crystals. The Mott variable-range hopping (VRH) conductivity mechanism is established in the temperature interval of 100–200 K, whereas between 200 and 300 K, the conductivity is determined by thermal excitations of holes to the mobility edge of the joint energy spectrum of the overlapped acceptor and valence bands. Parameters of the localized holes and details of the density of states near the edge of the valence band are determined, including the relative acceptor concentration, N/Nc  0.41–0.49 (where Nc  7  1018 cm3 is the critical concentration of the metal–insulator transition), the relative localization radius a/aB  1.7–2.1 (where aB  13.1 Å is the Bohr radius), the semi-width of the acceptor band, W  95–106 meV, centered at the energy E0  59 meV above the top of the valence band, the average density of the localized states (DOS), gav  (1.4–1.8)  1016 meV1 cm3 and the DOS at the Fermi level, g(l)  (4.1–5.4)  1015 meV1 cm3. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction The family of I2-II-IV-VI4 quaternary chalcogenide semiconductors attracts considerable attention due to their nonlinear optical properties [1,2] and a potential application as absorber layer in thin film solar cells [3], for which recently an efficiency above 11% was reported [4]. Moreover, these compounds can be used as photocatalysts for solar water splitting [5,6] and as high-temperature thermoelectric materials [7,8]. Cu2ZnSiSe4 belongs to the compound family described above. It crystallizes in the wurtz-stannite type crystal structure (space group Pmn21) [9–12] within the orthorhombic crystal system. The crystal structure is characterized by a well-defined framework of tetrahedral bonds: each selenium anion is tetrahedrally surround by four cations (two Cu, one Zn and one Si), whereas each cation is tetrahedrally coordinated by four anions. The wurtz-stannite type structure can be derived from the MnSiN2 type structure (space group Pna21) by replacing Mn by Cu, half of the Si by Zn and N by Se, respectively. It should be noted that the mineral laforetite (high-temperature modification of AgInS2) crystallizes in this ⇑ Corresponding author. Tel.: +373 22 738170; fax: +373 22 738149. E-mail address: [email protected] (M. Guc). 0925-8388/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2013.06.156

structure. The wurtz-stannite type structure belongs to the hexagonal branch of the structural family tree of the Adamantine compounds, which is based on the Lonsdaleite type structure (hexagonal diamond, space group P63/mmc). Cu2ZnSiSe4 crystals can be grown by chemical vapor transport (CVT) using iodine as a transport agent [10,11,13–16], as well as applying horizontal gradient freezing [17] and sinter-annealing [9] methods. The melting point [17,18], the lattice constants [9– 13,17,18], the room temperature optical gap [10,11,17,18], the resistivity values [10,11] as well as the Raman spectra measured on samples prepared by the sintering method [19] have been reported. Properties of Cu2ZnSiSe4 were investigated paying major attention to optical methods [14–16,20]. Polarization-dependent absorption and electrolyte electro-reflectance measurements were carried out using oriented Cu2ZnSiSe4 single crystals and plausible band structures have been proposed [14,15]. Photoluminescence and Raman scattering investigations were also used to characterize Cu2ZnSiSe4 single crystals [16]. The complex pseudo-dielectric function in the photon energy range 1.2–4.6 eV was determined by spectroscopic ellypsometry (at room temperature) and analyzed applying the Adachi model of interband transitions using Cu2ZnSiSe4 crystals grown by modified Bridgman method [20].

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First-principle calculations were performed to establish the electronic structure of Cu2ZnSiSe4 [21–23]. To investigate phase stabilities, the enthalpies of formation of the kesterite (KS), the stannite (ST), and the wurtz-stannite phases (WST) of Cu2Zn(Sn, Ge, Si)Se4 were calculated [21]. The effective electron and hole masses of the kesterite and stannite modifications of Cu2Zn-IVVI4 (IV = Sn, Ge, Si and VI = S, Se) were evaluated using the firstprinciple calculations [23]. The electron effective masses were found to be almost isotropic, while the hole effective masses exhibited a strong anisotropy. Namely, the values of the transversal effective mass (in units of the free electron mass, m0), m\ = 0.58 and 0.27, and of the longitudinal effective mass, m|| = 0.21 and 0.52, for KS and ST structures, respectively, were obtained for holes of the Cu2ZnSiSe4 topmost valence band [23]. The theoretically calculated energy band gaps (Eg) of KS, ST and WST-type Cu2ZnSiSe4 are found to be equal to 1.48 eV [21] (1.92 eV [23]), 1.07 eV [21] (1.53 eV [23]) and 1.17 eV [21]. These Eg values are lower than those determined from optical measurements, 2.33 eV [10] and 2.08–2.14 eV [14], respectively. Taking into account the band gap value, Cu2ZnSiSe4 could be used in particular as possible top-cell absorber in a tandem solar cell. The solid solution series Cu2ZnSn1xSixSe4 with energy band gaps ranging between 2.3 and 1.0 eV, covering a large part of the solar spectrum, are potentially useful for solar energy conversion. Concerning the transport properties of Cu2ZnSiSe4, only the room temperature resistivity data were reported so far [10,11]. However, the expected high degree of a microscopic lattice disorder, including the cation disorder within the Cu–Zn planes of Cu2Zn-IV-VI4 structure [22], favors a hopping charge transfer, making important the investigations of conductivity of the material at lower temperatures, as well. Such situation takes place, e.g., in Cu2ZnSnS4, which belongs to the I2-II-IV-VI4 quaternary chalcogenide semiconductors, too, where the Mott variable-range hopping (VRH) conduction has been observed within a broad temperature interval between 30 and 150 K [24]. Here, we present the resistivity measurements of the p-type Cu2ZnSiSe4 single crystals at T  10–300 K and their analysis. The purpose of the work is to investigate the conductivity mechanisms of the compound and to obtain details of the energy spectrum and microscopic properties of the localized carriers. 2. Experimental details Cu2ZnSiSe4 single crystals were grown by chemical vapor transport using iodine as a transport agent. The growth process was done in sealed evacuated silica ampoules. The source material was obtained by melting a stoichiometric mixture of Cu, Zn, Si and Se, where the elements of high purity were used. The source temperature was kept at 850° C, the grown temperature was 800° C, and the iodine concentration used was 5 mg/cm3. Energy dispersive X-ray microanalysis (EDX) was applied to analyze the chemical composition of the obtained crystals. EDX measurements yield a slight Si rich composition, the composition ratios being in the range of Cu/(Zn + Si) = 0.894– 0.995, Zn/Si = 0.825–0.981 and Se/metals = 0.944–1.028. The crystal structure of the samples was checked by single crystal X-ray diffraction. The orthorhombic wurtz-stannite type structure was confirmed. The resistivity, q(T), was measured using the van der Pauw method in a temperature interval of 10–300 K. The contacts were made by a silver paste. It was assured that the results of these measurements do not depend on a surface treatment. The dependence of q(T) is given in Fig. 1.

3. Results and discussion 3.1. Conductivity mechanisms and characteristic macroscopic parameters As can be seen in Fig. 1, the dependence q(T) exhibits an activated character, following in the high-temperature interval, DTa, the law

Fig. 1. Temperature dependence of the resistivity in the investigated Cu2ZnSiSe4 samples. Inset: Plots of ln q vs. 1/T in the high-temperature interval (two plots are shifted along the vertical axis by the values given in parenthesis). The straight lines are linear fits.

q ðTÞ ¼ qa exp½Ea =ðkTÞ;

ð1Þ

see inset to Fig. 1. The values of DTa, the prefactor, qa, and the activation energy, Ea, obtained with linear fits of the plots ln(q) vs. 1/T, are collected in Table 1 for all studied samples. Such a dependence can be connected to one of the following mechanisms: to an activation of the holes to the valence band (VB), to excitations on the mobility edge of the acceptor band (AB), or to a nearest-neighbor hopping (NNH) charge transfer [25,26]. This issue will be clarified in Section 3.3 with a more detailed analysis. On the other hand, as follows from Fig. 2, the resistivity in the interval DTM, lying below DTa, satisfies the expression

qðTÞ ¼ AT 1=4 exp½ðT 0 =TÞ1=4 ;

ð2Þ

characterizing the Mott VRH conductivity [25,26]. The values of DTM, the prefactor constant, A, and the characteristic temperature, T0, determined with linear fits of the plots in Fig. 2, are displayed in Table 1 as well. 3.2. Theoretical background To analyze the macroscopic parameters in Table 1, characterizing the conductivity mechanisms given by Eqs. (1) and (2), the expression [26] was used:

T 0 ¼ b=½k a3 gðlÞ;

ð3Þ

where b  21 is a numerical constant, g(l) is the density of the localized states (DOS) at the Fermi level, l, and

a ¼ a0 ð1  N=Nc Þm

ð4Þ

is the localization radius of the holes [27]. In Eq. (4), m  1 is the critical exponent of the correlation length, N is the acceptor concentration, Nc is the critical concentration of the metal–insulator transition (MIT) [27], and a0 is the localization radius of acceptor states far from the MIT. It is important to mention at this point the expressions:

a0 ¼ hð2 mE0 Þ1=2

and aB ¼ h

2

1

j0 ðme2 Þ ;

ð5Þ

where the Bohr radius, aB, of a hydrogenic impurity practically coincides with a0 [26]. In Eq. (5), m is the hole effective mass, E0 is the energy of the DOS peak of the acceptor band (AB) as shown in Fig. 3 [25], and j0 is the dielectric permittivity far from the MIT. The

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Table 1 The prefactor, qa, and the activation energy, Ea, of the resistivity in the interval DTa; the prefactor constant, A, and the characteristic temperature, T0, in the Mott-VRH interval, DTM, in the investigated Cu2ZnSiSe4 samples. Sample no.

qa X (cm)

Ea (meV)

DTa (K)

A (105X cm K1/4)

DTM (K)

T0 (106 K)

1 2 3 4 5

3.03 1.38 1.44 0.85 1.90

42 60 62 75 56

210–240 200–260 210–260 250–300 230–300

21.2 8.08 3.88 13.1 7.57

70–210 115–200 90–190 80–185 90–210

2.60 4.03 5.27 5.43 4.12

parameters Nc and a0 are interrelated with the Mott universal criterion [25],

N1=3 c a0  0:25:

Fig. 2. Plots of ln(qT1/4) vs. T1/4 for the samples #1–5 (from down to up). For convenience, some of the plots are shifted along the vertical axis by the values given in parenthesis. The straight lines are linear fits.

ð6Þ

We consider first an Anderson-type symmetric AB with a semiwidth W [25], which is connected to broadening of an isolated acceptor level with the energy E0 due to microscopic disorder and contains both the localized and the delocalized states, separated by the mobility edges Ec and Ec [25]. The DOS of the AB is shown schematically in Fig. 3a and the symmetry above also means that the AB is well separated from the VB with the edge Ev, given by the dashed line in Fig. 3a, where the localized states are hatched and all energies are measured from the energy of the DOS peak. In such a case, the conductivity is activated when l lies in one of the regions of the localized states, (W, Ec) or (Ec, W), respectively. It turns to be metallic or activationless when l falls on the interval (Ec, Ec). The MIT above takes place when l crosses Ec or Ec [25,26] at N = Nc and a tends to infinity, as follows from Eq. (4). On the other hand, as can be seen from Fig. 3a, this can be described identically (and more straightforward) with the equation [25–27]

a ¼ aB ð1  Ec =lÞm :

ð7Þ

The mobility edge satisfies the expression:

Ec  W 

V 20 ; 4ðz  1ÞJ

ð8Þ

where z  6 is the number of the nearest neighbors in the acceptor system, V0 represents a scale of scattering of the hole energy due to the cation disorder [25], and J = J0 exp (R/aB) is the overlap integral [25]. Here, R  (4pN/3)1/3 is the half of the mean distance between the acceptors and the prefactor J0 satisfies the equation [24,25]

"    2 # e2 3 R 1 R : þ J0  1þ aB 6 aB j0 aB 2

ð9Þ

As can be seen in Fig. 3a, the completely symmetric AB and its separation from the VB mentioned above means satisfaction of the condition E0 > W. However, for a broad enough AB connected to a high degree of the microscopic disorder, it can be partially overlapped with the states of the VB, bringing an asymmetry and yielding the inequality E0 < W, which may lead to a disappearance of Ec if it falls on the overlap energy interval as shown in Fig. 3b [25]. In such a case, the activated conduction can take place if only l lies between W and Ec, as displayed in Fig. 3b. Generally, at E0 < W, the AB and the VB form a unified energy spectrum, as shown in Fig. 3b with a solid line [25]. Finally, W can be obtained with the expression [24]:

Fig. 3. (a) The DOS of the AB (solid line) and the VB (dashed line) in the case of E0 > W. The localized states of the AB are hatched (schematically). (b) Joint spectrum of the DOS near the edge of the VB in the case of E0 < W (solid line). The localized states are hatched. The dashed and the dotted lines represent the imaginative nearedge intervals of the VB and the AB, respectively, addressed to the absence of their overlap (schematically).

W  0:5 kðT 3v T 0 Þ

1=4

;

ð10Þ

where Tv is the high-temperature border of the Mott VRH conductivity, provided that l lies close to W or W. This takes place for K  1 and 1 K  1, respectively, where K = ND/N is the degree of the compensation and ND is the donor concentration.

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3.3. Analysis of the macroscopic parameters It can be seen that a broad temperature interval DTM  100 K (Table 1) of the Mott VRH conduction, persisting up to temperatures as high as 200 K (Fig. 2), suggests a position of l close to one of the edges of AB. Indeed, near the edges of the AB all the states are localized and the DOS values are small (Fig. 3). This means a small probability for a carrier to find an appropriate energy level among the nearest neighboring sites, stimulating hopping beyond them which leads to domination of the VRH conductivity over the NNH conduction up to high temperatures. In addition, below it will be shown that the conductivity in the interval DTa, which lies above DTM, is not connected to the NNH mechanism, supporting close proximity of l to the band edge, as well. This permits us to obtain W with Eq. (10) using the data of Table 1, where Tv is the high-temperature border of DTM. The values of W are collected in Table 2. Our quantitative analysis below consists of two steps. On the first step, we approximate the DOS of the AB with a rectangular shape, g(l)  gav N/(2W). Then, one finds with Eqs. (3), (4), (6), and (10) the equation



T0 Tv

1=4

 4b1=3

 1=3  m Nc N 1 ; Nc N

ð11Þ

which yields at m = 1 and with the data of T0 and Tv from Table 1 the values of a/a0 and N/Nc, collected in Table 2. The ratio of a/aB can be evaluated with Eqs. (7)–(9) putting V0  2W, taking into account the second of Eq. (5) and using the 1=3

DTa, where Eq. (1) is satisfied (see the inset to Fig. 1), yielding Ea = |lEc| [25] as shown in Fig. 3b. The values of Ea, obtained with this expression (EðcalcÞ in Table 2), are close to those of Ea in Table 1, a supporting the conductivity mechanism above in the interval DTa, but exceeding them systematically. A possible reason of such a disagreement is the utilization of the average DOS value, gav = N/(2W), instead of g(l) in the calculations above. Indeed, the relation g(l)  gav or the approximation of the DOS in the AB with a rectangular shape is rather crude, if l lies close to the DOS edges. Therefore, on the second step, this drawback is improved by putting g(l) = agav, where a < 1. This leads to substitution of b ? b/a in Eq. (11). Consequently, two parameters, j0 and a, should be found now by fitting a/a0 with a/aB and EðcalcÞ with a Ea by minimizing both SD (a) given above and  h i2 1=2 P 5 ðcalcÞ SDðEÞ ¼ 15 i¼1 ðEa Þi  ðEa Þi simultaneously. The best fit yields SD(a) = 0.068 and SD(E)  5.5 as well as the values of

j0  9.4 and a  0.3, whereas the parameters a0  aB  13.1 Å, E0  59 meV, and Nc  7  1018 cm3 are obtained in the same way as in the previous calculations. As can be seen in Table 3, the values of N/Nc, a/a0, and a/aB are increased with respect to Table 2 and the agreement between those of a/a0 and a/aB becomes much better. In addition, the agreement between Ea in Table 1 and EðcalcÞ in Taa ble 3 is evidently improved with respect to Table 2 for the majority of the samples, excluding only #4. However, the latter is not surprising because above we have assumed a to be the same in all the samples. On the other hand, in a real situation, a should fluctuate from sample to sample, where the scale of such fluctuations

mean value of the hole effective mass, m  ðm2? mk Þ [26]. With the data of m\ and m|| in Cu2ZnSiSe4 [23] (see Introduction) one finds m = 0.38 ± 0.04, varying insignificantly for the kesterite and the stannite modifications of Cu2ZnSiSe4. Another parameter, which is important for the calculations of a/aB, is j0. On the other hand, because a0  aB for a shallow hydrogenic impurity [26], the value of j0 can be picked up to fit the ratio of a/aB to the data of a/a0 in Table 2 by minimizing the standard deviation, n P  2 o1=2 , where i is the sample numSDðaÞ ¼ 15 5i¼1 ða=a0 Þi  ða=aB Þi

can be estimated by the relative difference of Ea and EðcalcÞ . As can a be seen from Table 3, the values of Ec are increased with respect to those in Table 2, as well, which is in agreement with the corresponding increase in N/Nc, a/a0 and a/aB, making the system closer to the MIT than it has been obtained previously. The values of gav in Table 3 are modified with respect to Table 2, whereas those of g(l), collected in Table 3, being 3 times smaller gav are obtained within a more consistent approach and therefore are more accurate.

ber. As follows from Table 2, we obtain a reasonable agreement between a/a0 and a/aB, evaluated with two different methods based on Eqs. (4) and (7), respectively, yielding SD (a)  0.127 at j0  8.9. Then, the values of a0  aB  12.4 Å and E0  65 meV are found with Eq. (5) and Nc  8.1  1018 cm3 with Eq. (6). In Table 2 are also collected the values of Ec and g(l), evaluated with Eqs. (8) and (3), respectively. In the calculations above, we did not specify the position of l, using only the assumption that it should be close to one of the AB edges by putting simply l  W. However, the obtained value of E0 is evidently smaller than those of W (Table 2), permitting us to choose the variant of the hole spectrum shown in Fig. 3b in conditions of a strong degree of compensation (1 K  1, see Section 3.2), with the position of the Fermi level close to W, as exhibited in Fig. 3b. In such conditions, the mechanism of the conductivity, connected to the thermal excitations of the holes, on the mobility edge Ec should be important in the interval

3.4. Discussion The microscopic parameters collected in Table 3 give a reasonable overview of the properties of the localized holes in Cu2ZnSiSe4 single crystals. The value of j0  9.4 looks reasonable being close to the data determined from the capacitance spectra of the Cu2ZnSnS4 thin films (j0  8) [28] or evaluated with first-principle calculations (j0 = 9.1–9.7) in Cu2ZnSnS4, belonging to the same family of compounds [29]. A similar set of parameters has been obtained recently by investigations of the Mott VRH conduction in Cu2ZnSnS4 [24]. Therefore, it is interesting to compare the results obtained in [24] and in our work. So, the interval DTM in Cu2ZnSnS4 lying between 30–70 K and 130–150 K is shifted to lower temperatures, whereas the values of gav (1–3)  1017 meV1 cm3 [24] exceed those of Cu2ZnSiSe4 by an order of the magnitude. On the other hand, the values of Nc  (8 ± 1)  1018 cm3 and those of N  (5–7)  1018 cm3 found in Cu2ZnSnS4 [24] are comparable

Table 2 The relative acceptor concentration, N/Nc, the localization radius in units of that far from the MIT, a/a0, and in units of the Bohr radius, a/aB, the semi-width of the acceptor band, W, the mobility threshold, Ec, the average DOS, gav, and the calculated values of the activation energy, EðcalcÞ , at a = 1 (approximation of the DOS with the rectangular shape) in the a investigated Cu2ZnSiSe4 samples. Sample no.

N/Nc

a/a0

a/aB

W (meV)

Ec (meV)

gav (1016 mev1 cm3)

(meV) EðcalcÞ a

1 2 3 4 5

0.34 0.29 0.26 0.25 0.29

1.51 1.41 1.35 1.34 1.41

1.72 1.41 1.22 1.21 1.38

95 102 106 106 106

40 29 19 18 29

1.43 1.14 0.98 0.97 1.12

55 73 86 88 77

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Table 3 The relative acceptor concentration, N/Nc, the localization radius in units of that far from the MIT, a/a0, and in units of the Bohr radius, a/aB, the mobility threshold, Ec, the average DOS, gav, the DOS at the Fermi level, g(l), and the calculated values of the activation energy, EðcalcÞ , at a = 0.3 in the investigated Cu2ZnSiSe4 samples. a Sample no.

N/Nc

a/a0

a/aB

Ec meV

gav (1016 meV1 cm3)

g(l) (1015 meV1 cm3)

(meV) EðcalcÞ a

1 2 3 4 5

0.49 0.45 0.42 0.41 0.45

1.98 1.81 1.71 1.70 1.83

2.10 1.82 1.67 1.65 1.77

50 46 42 42 46

1.81 1.53 1.37 1.36 1.49

5.42 4.58 4.11 4.07 4.46

46 57 64 60 60

with the corresponding values of Nc  7  1018 cm3 and N  (2.9– 3.4)  1018 cm3 obtained in the investigated Cu2ZnSiSe4 samples. Finally, the values of j0  10.8 ± 0.5, aB  12.2 ± 0.6 Å, and E0  55 ± 6 meV in Cu2ZnSnS4 [24] are quite close to those of j0  9.4, aB  13.1 Å and E0  59 meV obtained in this work. Eventually, important information has been obtained recently in Cu2ZnSnS4 polycrystalline films [30], which can be compared with our data as well. Namely, the Mott VRH conduction has been observed within the interval 100–180 K [30], which is close to that of DTM in Table 1. The values of T0 = 3.5  106 K, a = 35 Å and g(l) = 1.5  1015 meV1 cm3 in Cu2ZnSnS4 films [30] are similar with the corresponding data of T0 = (2.60–5.43)  106 K in Table 1, those of a  22–28 Å (following from Table 3 at aB  a0 = 13.1 Å) and g(l) = (4.07–5.42)  1015 meV1cm3 in Table 3. The similarity of the parameters above is noticeable, reflecting similar €intrinsic properties of both compounds in general. This is not surprising, provided that the cation disorder within the Cu–Zn planes of Cu2Zn-IV-VI4 structure [22] plays an important role in formation of the electronic properties of both materials belonging to the same family. Moreover, the closeness of the microscopic data above is established on a background of the strong difference of their macroscopic behavior, including the difference of the resistivity up to four orders of the magnitude and two opposite limits of K (K  1 in Cu2ZnSnS4 [24] and 1K  1 in Cu2ZnSiSe4 single crystals and Cu2ZnSnS4 polycrystalline films [30]). Finally, deviations from the Mott VRH conductivity of Eq. (2) with lowering the temperature (Fig. 2) are attributable to an enhanced influence of the Coulomb interaction between the holes, which are neglected in the Mott model [25], but are taken into account in the VRH conductivity mechanism proposed by Shklovskii and Efros (SE) [26]. This leads to another VRH conduction law, similar to Eq. (2), but differing by changing of the exponent 1/4 to 1/2 both in the argument of the exponential function and in the prefactor of Eq. (2) [26]. Although a transition from the Mott to the SE VRH conduction is often observed in doped crystalline semiconductors with lowering T [27,31], we found no significant temperature interval below DTM where the plots of ln [q(T) T1/2] vs. T1/2 could be linearized with sufficient accuracy. Therefore, the onset of the purely SE VRH conduction regime at T 0v is expected in our material to lie below 10 K, whereas at higher temperatures and up to DTM, only a crossover of the two VRH regimes can be observed. Namely, estimation of the onset temperature, 2 T 0v  4D2 =ðk T 00 Þ [26], where D  [g(l)]1/2 (e6/j3)1/2 is the semiwidth of the Coulomb gap [26], T 00 ¼ 2:8e2 =ðk j aÞ [26] is the characteristic temperature of the SE VRH conduction and j  j0(a/a0)2 [27], yields T 0v  1 K, which is in agreement with the conjecture above. In addition, the values of T 00  500  700 K are much smaller than those of T0  (3–5)  106 K (Table 1). Therefore, the dependence of q(T) is weakened with lowering T, resembling saturation as takes place, e.g., in FeSi2 doped with different impurities [32]. It is worth mentioning that the situation with the SE VRH conduction in the Cu2ZnSnS4 single crystals is quite similar, where the value of T 0v  1  2 K has been found [24]. At this point, the onset of the SE VRH mechanism at temperature as high as T  100 K, reported in Cu2ZnSnS4 polycrystalline films [30], looks quite overes-

timated. On the other hand, observation of the law ln q  T1/2, established in Ref. [30], may not be related to the SE VRH conduction mechanism, but is attributable rather to the inter-grain tunneling [33], which is expectable in polycrystalline materials with grain size 100 nm as determined in Ref. [30]. 4. Conclusions We have investigated the resistivity of Cu2ZnSiSe4, exhibiting an activated character in a broad temperature range between T  10–300 K. The Mott type of the VRH conductivity followed by the conduction, associated with the temperature excitations of holes on the mobility edge of the joint energy spectrum of the acceptor and the valence band, is observed in conditions of a strong degree of the compensation. The macroscopic (Ea and T0) and the microscopic parameters, characterizing the concentration, energy spectrum and properties of the localized carriers, are obtained. Our results suggest a high degree of the cation disorder in the investigated Cu2ZnSiSe4 single crystals, as has been established in the Cu2ZnSnS4 single crystals [24] and thin polycrystalline films [30] belonging to the same family of compounds. Acknowledgments Financial supports from IRSES PVICOKEST 269167, BMBF MDA11002 and FRCFB 13.820.05.11/BF projects are acknowledged. S. Levcenco would like to thank Humboldt foundation for support. Authors also appreciate assistance of Dr. Hab. V. Ursaki in sample characterization. References [1] J.W. Lekse, M.A. Moreau, K.L. McNerny, J. Yeon, P.S. Halasyamani, J.A. Aitken, Inorg. Chem. 48 (2009) 7516–7518. [2] J.W. Lekse, B.M. Leverett, C.H. Lake, J.A. Aitken, J. Solid State Chem. 181 (2008) 3217–3222. [3] Q. Guo, G.M. Ford, W.C. Yang, C.J. Hages, H.W. Hillhouse, R. Agrawal, Sol. Energy Mater. Sol. Cells 105 (2012) 132–136. [4] T.K. Todorov, J. Tang, S. Bag, O. Gunawan, T. Gokmen, Y. Zhu, D.B. Mitzi, Adv. Energy Mater. 3 (2013) 34–38. [5] I. Tsuji, Y. Shimodaira, H. Kato, H. Kobayashi, A. Kudo, Chem. Mater. 22 (2010) 1402–1409. [6] D. Yokoyama, T. Minegishi, K. Jimbo, T. Hisatomi, G. Ma, M. Katayama, J. Kubota, H. Katagiri, K. Domen, Appl. Phys. Express 3 (2010) 101202–101203. [7] M.L. Liu, F.Q. Huang, L.D. Chen, I.W. Chen, Appl. Phys. Lett. 94 (2009) 202103 (3pp). [8] C. Sevik, T. Cagin, Phys. Rev. B 82 (2010) 045202 (7pp). [9] W. Schafer, R. Nitsche, Mater. Res. Bull. 9 (1974) 645–654. [10] D.M. Schleich, A. Wold, Mater. Res. Bull. 12 (1977) 111–114. [11] G.Q. Yao, H.S. Shen, E.D. Honig, R. Kershaw, K. Dwight, A. Wold, Solid State Ionics 24 (1987) 249–252. [12] G. Gurieva, V. Kravstov, E. Arushanov, S. Schorr, J. Alloys Comp. (to be submitted). [13] R. Nitsche, D.F. Sargent, P. Wild, J. Cryst. Growth 1 (1967) 52–53. [14] S. Levcenco, D. Dumcenco, Y.S. Huang, E. Arushanov, V. Tezlevan, K.K. Tiong, C.H. Du, J. Alloys Comp. 509 (2011) 4924–4928. [15] S. Levcenco, D. Dumcenco, Y.S. Huang, E. Arushanov, V. Tezlevan, K.K. Tiong, C.H. Du, J. Alloys Comp. 509 (2011) 7105–7108. [16] S. Levcenco, D.O. Dumcenco, Y.P. Wang, J.D. Wu, Y.S. Huang, E. Arushanov, V. Tezlevan, K.K. Tiong, Opt. Mater. 34 (2012) 1072–1076. [17] H. Matsusita, T. Ichikawa, A. Katsui, J. Mater. Sci. 40 (2005) 2003–2005. [18] H. Matsushita, A. Katsui, J. Phys. Chem. Solids 66 (2005) 1933–1936. [19] M. Himmrich, H. Haeuseler, Spectrochim. Acta 47A (1991) 933–942.

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