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Electrical conduction in ordered defect compounds
Journal of Physics and Chemistry of Solids 64 (2003) 1627–1632 www.elsevier.com/locate/jpcs
Electrical conduction in ordered defect compounds S.M. Wasim*, C. Rinco´n, G. Marı´n, R. Ma´rquez Departamento de Fı´sica, Facultad de Ciencias, Centro de Estudios de Semiconductores, Universidad de Los Andes, Me´rida, Venezuela
Abstract A comparative study of the temperature dependence of electrical resistivity, carrier concentration and carrier mobility of the Ordered Defect Compounds (ODCs) CuIn3Se5, CuIn3Te5, and CuIn5Te8 with their corresponding normal 1:1:2 phase is reported. Relatively lower carrier concentration and higher activation energy observed in ODCs is explained on the basis that shallow acceptor or donor levels observed in 1:1:2 phase are partially annihilated in these compounds due to attractive þ2 interaction between V21 Cu and InCu defect pair. In the activation regime, the mobility is explained by taking into account a scattering mechanism of the charge carriers with donor – acceptor defect pairs. The electrical data at lower temperatures is explained with the existing theoretical expression for the nearest neighbor hopping conduction mechanism. q 2003 Elsevier Ltd. All rights reserved. Keywords: A. Semiconductors; A. Electronic materials; D. Electrical properties; D. Transport properties; D. Defects
1. Introduction It has been shown [1,2] from first-principle calculations that the formation energy of interacting donor – þ2 acceptor defect pairs (DADPs), like (2V21 Cu þ InCu ), is very small in the ternary compound semiconductor CuInSe2. This concept is used to explain the existence of CuIn5Se8, CuIn3Se5, Cu2In4Se7, and Cu3In5Se9, as a þ2 repeat of a single unit of (2V21 Cu þ InCu ) in each n ¼ 4; 5; 7 and 9 units, respectively, of CuInSe2 [2]. They can also be obtained from the formula Cun 2 3Inn þ 1Se2n where n ¼ 4; 5; 7; and 9, respectively. Because of the presence of DADPs, they are referred to in the literature as Ordered Defect Compounds (ODCs). Similarly, the existence of CuGa5Se8, CuGa3Se5, CuIn5Te8, CuIn3Te5, CuGa5Te8 and CuGa3Te5 has also been established and their crystal structure and optical properties reported [2 –8]. Some of these compounds are promising materials in the fabrication of opto-electronic devices. They are also of academic interest in exploring new physical concepts that cannot be developed with normal 1:1:2 chalcopyrites or the binary compounds. For example, it is suggested that þ2 the attractive interaction between V21 Cu and InCu leads to * Corresponding author. Fax: þ 58-7440-1286. E-mail address: [email protected] (S.M. Wasim).
annihilation of their corresponding acceptor and donor levels [1,2]. Thus, one should expect the DADPs to be electrically inactive and therefore, these ODCs should have relatively lower concentration as compared to their normal 1:1:2 phase. Furthermore, it is important to understand as to how the mobility of the charge carriers is affected by the presence of the ordered arrays of DADPs. To study this effect, in the present work, we report on a comparative study of the temperature dependence of electrical resistivity, carrier concentration and carrier mobility of bulk samples of n- and p-CuIn3Se5, and ptype CuIn3Te5 and CuIn5Te8 with their corresponding normal 1:1:2 phase. Relatively lower carrier concentration and higher activation energy are observed in the ODCs. This is explained on the basis that shallow donor or acceptor levels observed in normal 1:1:2 phase are partially annihilated in ODCs due to attractive interaction þ2 between V21 Cu and InCu defect pair. In the activation regime, the mobility is explained by taking into account an additional scattering mechanism of the charge carriers by DADPs. The electrical data in the impurity band is explained on the basis of the existing theoretical expression for the nearest neighbor hopping conduction mechanism.
0022-3697/03/$ - see front matter q 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0022-3697(03)00099-4
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2. Experimental details The samples of these ODCs were cut from ingots that were prepared by Bridgman technique. They crystallize in a chalcopyrite-related structure [4], and had their chemical composition, as determined by energy dispersive X-ray spectroscopy, very close to the ideal value 1:3:5 or 1:5:8. The electrical resistivity r and the majority carrier concentration n or p in a magnetic field of 1 T were measured between liquid nitrogen and room temperature on rectangular samples of representative dimensions of 1 £ 2 £ 8 mm3. The representative n- and p-type CuIn3Se5 samples mentioned in the present study are denoted as S1 and S2, whereas p-type CuIn3Te5 and CuIn5Te8 as S3 and S4, respectively.
3. Experimental results and discussion 3.1. Electrical resistivity and carrier concentration in the activation regime The electrical resistivity r of samples S1 – S4 on a logarithmic scale is plotted in Fig. 1 as a function of the inverse of the temperature T: At temperatures below about 125 K, three possible mechanisms, i.e. nearest neighbor hopping with ln r / 1=T; variable range hopping of Mott type with ln r / 1=T 1=4 ; and Efros– Shklovskii type where
Fig. 1. Plot of the electrical resistivity of (X) n-type and (A) p-type CuIn3Se5, (B) p-type CuIn3Te5, and (P) p-type CuIn5Te8 on the logarithmic scale versus reciprocal temperature. The nearly linear behavior represented by ln r versus 1=T observed in these samples in the temperature range from about 80 to 110 K is shown by the continuous lines.
ln r / 1=T 1=2 are expected to dominate in different temperature ranges [9], but not necessarily each of them in the same sample. From the analysis of the data, not shown here, and whose general details are published elsewhere [10], the exponent s in ln r / 1=T s was found to be very close to unity. Hence, the data below 110 K in Fig. 1 are fitted to a straight line showing that the conduction is due to the nearest neighbor hopping of the charge carrier in the impurity band. The variation of the majority charge carrier concentration n (or p) on logarithmic scale with 103 =T between 80 and 300 K for samples S1 – S4 is plotted in Fig. 2. In the same figure, we plot for comparison, the change of n (or p) with 103 =T of samples of the corresponding 1:1:2 phase that have, as mentioned in Table 1, the lowest reported carrier concentration. Their values at 300 K are also shown in Table 1 together with the present data. A trend is observed, where the carrier concentration in the tellurides of these ODCs is smaller by at least two orders of magnitude, whereas in n-type CuIn3Se5 by one order. However, in the case of p-CuIn3Se5, its magnitude is similar to that reported for the corresponding p-type 1:1:2 phase. This is indicative of the electrically inactive nature of the DADPs and that they do not contribute to the total free charge carriers. The temperature dependent behavior of n in S1 and p in S2, S3, and S4 in Fig. 2 indicates that above around 125 K, the electrical conduction is mainly due to activation in the conduction (valence) band and below 100 K, as mentioned earlier from the analysis of the resistivity data, due to charge carriers in the impurity band. To estimate the activation energy ED of the donor level and the effective mass mpe of
Fig. 2. Plot of the temperature dependence of electron concentrations n for (X) CuIn3Se5 and (W) CuInSe2 (left scale); and hole concentration p for (A) CuIn3Se5, (B) CuIn3Te5, (P) CuIn5Te8, and (K) CuInTe2 (right scale). The n versus T data for CuInSe2 are taken from Ref. [13] whereas those of p-type CuInTe2 from Ref. [23].
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Table 1 Values of the electron and hole concentration n or p and charge mobility m at 300 K, activation energy of shallow donor or acceptor levels ED or EA ; effective mass mpe and mpp of carriers in units of the free electron mass, deformation potential Eac of the conduction or valence band, static dielectric constant 10 and formation energy H of ordered arrays of defect pairs in n- and p-CuIn3Se5, p-CuIn3Te, and p-CuIn5Te8 obtained in the present work. The range of values of these parameters for n-CuInSe2, p-CuInSe2, and p-CuInTe2 reported in the literature is also shown Compound
n or p (cm23)
m (cm2/V s)
ED or EA (meV)
mpe or mpp
Eac (eV)
10
H (meV)
n-CuIn3Se5 p-CuIn3Se5 n-CuInSe2 p-CuInSe2 p-CuIn3Te5 p-CuIn5Te8 p-CuInTe2
(3–7 £ 106) £ 109a,b 1.0 £ 1017a (3.5–200) £ 1016c,d (2–20) £ 1016c 2 £ 1014a 1.0 £ 1013a (3–5200) £ 1016g,h
3–200b 50a 150–1500c 50–100c 3a 1.5a 27–135 g,h
36 ^ 2a,f 28 ^ 2a,f 6–12c 24–32c 30 ^ 2a 88 ^ 8a 9–22i
0.13 ^ 0.01a,f 1.06 ^ 0.10a,f 0.09c 0.78c 0.80 ^ 0.11a 1.02 ^ 0.12a 0.78 h
13.7 ^ 2.7a,f 3.5 ^ 0.5a,f 13 –20c 6– 8c 6.2 ^ 1.5a 5.0 ^ 1.2a 5.35 h
11 ^ 2a 11 ^ 2a 9.5–13.6c 9.5–13.6c 12 ^ 2a 12 ^ 2a 9.7 h
27 ^ 4a,f 80 ^ 10a,f ,10e ,10e 32 ^ 4a 140 ^ 9a –
a b c d e f g h i
Present work. Ref. [21]. Ref. [13]. Ref. [22]. Ref. [2]. Ref. [10]. Ref. [23]. Ref. [24]. Ref. [25].
ð1Þ
It can be noted that the activation energy of 36 meV of the donor level is consistent with ED < 38 meV estimated from the calculation based on the effective mass theory [12]. The relatively low electron concentration of n-CuIn3Se5 sample,
In this expression, nc is the concentration of electrons and Nc the effective density of states in the conduction band. ND and NA are the donor and acceptor concentrations, and g the degeneracy factor of the donor ground state. For the analysis of the data in the high temperature region, it is assumed that the contribution of the impurity band to the total electron concentration n is negligible. Thus, by replacing nc with the measured value n; a linear plot of ln½nðn þ NA Þ=T 3=2 ðND 2 NA 2 nÞ is obtained against 103 =T with the adjustable parameters ND < 7:9 £ 1017 cm23 and NA < 7:4 £ 1017 cm23. This is shown in Fig. 3. From the slope, ED is estimated to be 36 meV. Also, assuming g ¼ 2 which is the value of the degeneracy factor of the conduction band, from the intercept of the straight line at 103 =T ! 0; mpe in CuIn3Se5 is estimated to be 0:13me : In the case of the p-type sample S2, similar analysis is made where ED ; nc ; and Nc ; are replaced in Eq. (1) by the acceptor activation energy EA ; the concentration of holes in the valence band pv ; and the effective density of states in the valence band Nv ; respectively. Under this approach, EA ; NA ; and ND estimated from the fit were 28 meV, 8 £ 1019 cm23, and 6 £ 1016 cm23, respectively. Also, from the intercept of the straight lines at 103 =T ! 0; using g ¼ 2; which is the value for the degeneracy factor of the defect ground state when the top of the valence band are nondegenerate [11], mph is found to be 1:06me :
Fig. 3. (X) Plot of ½nðn þ NA Þ=T 3=2 ðND 2 NA 2 nÞ for CuIn3Se5 (left scale) and ½pðp þ ND Þ=T 3=2 ðNA 2 ND 2 pÞ for (A) CuIn3Se5, (B) CuIn3Te5 and (P) CuIn5Te8 (right scale) against 1000=T: The fit to the data above about 100 K is shown by the continuous lines.
the electron for n-type sample S1 from the high temperature data, we use the well-known expression for non-degenerate statistics in the conduction band given by Ref. [11] nc ðnc þ NA Þ=ðND 2 NA 2 nc Þ ¼ ðNc =gÞexpð2ED =KTÞ:
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as compared to n-CuInSe2, can be explained as due to the fact that the shallow donor level observed in CuInSe2 between 5 and 15 meV, which is responsible for the electrical properties of n-type CuInSe2, is partially annihilated due to the 21 attractive interaction between Inþ2 Cu and VCu defects that form the electrically inactive DADPs. On the contrary, the acceptor level with EA < 28 meV observed in p-CuIn3Se5 is in good agreement with the activation energy of the most shallow acceptor level reported in p-CuInSe2 (Table 1) from electrical measurements [13]. The origin of this level, consistent with EDX analysis indicates that this sample is Cu-rich. This can be attributed to copper atoms on indium sites (CuIn). This defect state is not expected to be annihilated due to the formation of the DADPs. This could explain the fact that the hole concentration in CuIn3Se5 is of the same order of magnitude as in CuInSe2 and provide additional evidence that this ODC is formed due to the presence of þ2 ordered arrays of (2V21 Cu þ InCu ) DADPs in CuInSe2. In p addition, values of me and mph of CuIn3Se5 are in good agreement with 0.16 and 1:1me estimated from optical data [14]. For comparison, it is worth mentioning that the electron effective mass in CuInSe2 obtained from Shubnikov– de Hass oscillations in the magnetoresistance is mpe ¼ 0:085me [15] whereas, mph < 0:78me for the hole is estimated from both electrical and optical data [16]. In the case of CuIn3Te5 and CuIn5Te8 samples, using the same analysis as for S2, we get from the fits in Fig. 3, NA < 7:0 £ 1017 cm23, ND < 6:99 £ 1017 cm23, and EA < 30 meV for S3, and NA < 5:0 £ 1015 cm23, ND < 4:9 £ 1015 cm23, and EA < 88 meV for S4. On the other hand, with g ¼ 2; the degeneracy factor for degenerate valence bands as reported in the case of 1:1:2 phase, the effective mass mpp < 0:80me and 1:02me of the hole in S3 and S4, respectively, are estimated. These values together with those of CuInSe2 and CuInTe2 reported in the literature are given in Table 1. It is observed that ED and EA are slightly higher than the values of the shallow levels of the corresponding 1:1:2 phases. This again confirms that the shallow acceptor levels observed in p-type 1:1:2 chalcopyrite phase are partially annihilated in ODCs due to the attractive þ2 interaction between V21 Cu and InCu pair. 3.2. Carrier mobility in the activation regime The variation of the charge carrier (electrons or holes) mobility m with T for all the samples is shown in Fig. 4. It can be seen from the Table 1 that with the exception of p-CuInSe2 and p-CuIn3Se5, its value at 300 K is between one or two orders of magnitude smaller in comparison to the corresponding 1:1:2 phase. Attempt to fit the data corresponding to the activation regime (not shown here) using Mathiessen rule given by [13] 21 21 21 21 m21 c ¼ mI þ mAC þ mPO þ mNPO ;
ð2Þ
Fig. 4. Variation of electron mobility with temperature on logarithmic scales for (X) n-CuIn3Se5, (A) p-CuIn3Se5, (B) CuIn3Te5, and (P) CuIn5Te8. The continuous curves represent a theoretical fit to the data in the activation regime by considering the combined effect of the scattering of the charge carriers by DADPs, ionized impurities, acoustic, polar optical (s-like in n-type S1) and non-polar optical (p-like in p-type S2, S3 and S4) phonons. For nCuIn3Se5 and p-CuIn3Te5 the data in the impurity band regime were fitted with Eq. (4).
where mI ; mAC ; mPO ; and mNPO represent the mobilities of charge carriers due to the scattering by ionized impurities, acoustic-lattice modes, polar optical modes, and non-polar optical modes, respectively, was unsuccessful. This is indicative of the presence of additional scattering of the charge carriers in the ODCs by a mechanism that is not found in n- and p-type samples of binary and ternary compounds of the 1:1:2 phase. Thus, to explain the temperature dependence of the mobility, an additional term that involved the scattering of the charge carriers by DADPs was introduced in Eq. (2). This can be expressed as [17]
mDP ¼ m0 exp½ðEDðAÞ þ HÞ=KB T;
ð3Þ
where m0 is a nearly constant parameter, and H the formation energy of the arrays of defect pairs. The temperature dependence of m of samples S1 – S4 in Fig. 4 above 100 K, in the activation regime, was fitted by taking into account the combined effect of the scattering of the charge carriers by DADP, ionized impurities, acoustic, polar optical (s-like in n-type S1) and non-polar optical (p-like in p-type S2 – S4) phonons. For this, Eqs. (2) and (3) and the respective expressions for the mobility were used. These expressions are given in Ref. [13]. In the fit, the static dielectric constant 10 ; optical 1a ; the deformation potential Eac of the conduction (n-type), valence (p-type) bands, H; and m0 were considered as
S.M. Wasim et al. / Journal of Physics and Chemistry of Solids 64 (2003) 1627–1632
adjustable parameters. Others, like the ionized impurity concentration NI ¼ ND þ NA ; mpe ; mpp ; ED and EA were those obtained from the analysis of the carrier concentration data. The longitudinal sound velocity u < 2 – 3 £ 105 cm/s, was estimated from the Debye temperature uD of the corresponding 1:1:2 phase [18], and 10 =1a was taken as 1.7, which is the average obtained for Cu-ternaries [13]. An excellent fit above 110 K, as shown in Fig. 4 by continuous lines, is obtained with the values of 10 ; Eac ; and H given in Table 1.
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which does not form part of the DADPs, gives further þ2 evidence that the defect pairs (2V21 Cu þ InCu ) are electrically inactive. The temperature dependence of the relatively low mobility in the high temperature region is explained by taking into account the scattering mechanism of the charge carriers by DADPs, ionized impurities, acoustic and polar optical phonons. At low temperatures, where the conduction in the impurity band is due to the thermally activated hopping between localized states, the theoretical model proposed by Cutler and Mott successfully explains the mobility data.
3.3. Carrier mobility in the impurity band At temperatures lower than about 100 K where the electrical conduction, as mentioned earlier, is mainly by nearest neighbor hopping mechanism in the impurity band ðln r / 1=TÞ; the electron and hole mobility is analyzed by considering the thermally activated hopping of the charge carriers between localized states in such a band. In this case, the mobility is given by the expression [19]
Acknowledgements
mi ¼ ðD=KB TÞexpð2W=KB TÞ;
References
ð4Þ
where D is a constant and W the hopping activation energy. The experimental data of m below 100 K was fitted to Eq. (4). A good fit, shown by continuous curves in Fig. 4 for S1 and S3 samples was obtained with the adjustable parameters W < 32 and 50 meV, and D < 4 and 6 eV cm2/V s, respectively. It is worth mentioning that attempt to fit the mobility data below 100 K with the expression used earlier [20] for variable range hopping conduction mechanisms, not shown here, was far from satisfactory. This further confirms the nearest neighbor hopping conduction in the low temperature regime.
4. Conclusions In summary, a comparative study of the electrical properties of n- and p-type CuIn3Se5, and p-type CuIn3Te5 and CuIn5Te8 ODCs is made. It is found that above around 110 K, the electrical conduction is due to the thermal activation of donor and/or acceptor levels with activation energies of 36, 28, 30, and 88 meV, respectively. The density of states effective mass of the charge carriers in these compounds are estimated to be mpe < 0:13me for n-type CuIn3Se5 and mph < 1:07; 0.80, 1:02me for p-type CuIn3Se5, CuIn3Te5, and CuIn5Te8, respectively. Below this temperature, the electrical conduction is found to be due to nearest neighbor hopping mechanism in the impurity band. The relatively low electron concentration in n-CuIn3Se5 is explained as due to the partial annihilation of the shallow donor level originating from the indium on copper site defect state that forms the þ2 electrically inactive (2V21 Cu þ InCu ) DADP. The absence of low concentration in p-type CuIn3Se5 where the dominant acceptor level is attributed to the antisite defect CuIn,
This work was supported by grants from FONACIT (Contract No. G-97000670), and CDCHT-ULA (Contract Nos. C-917-98-05-A and C-918-98-05-E).
[1] S.B. Zhang, S.H. Wei, A. Zunger, Phys. Rev. Lett. 78 (1997) 4059. [2] S.B. Zhang, S.H Wei, A. Zunger, H. Katayama Yoshida, Phys. Rev. B 57 (1998) 9642. [3] A.J. Nelson, G.S. Horner, J.K. Sinha, M.H. Bode, Appl. Phys. Lett. 64 (1994) 3600. [4] S.M. Wasim, C. Rinco´n, G. Marı´n, J.M. Delgado, Appl. Phys. Lett. 77 (2000) 94. [5] S.H. Wei, S.B. Zhang, A. Zunger, Appl. Phys. Lett. 72 (1998) 3199. [6] C. Rinco´n, S.M. Wasim, G. Marı´n, J.M. Delgado, J.R. Huntzinger, A. Zwick, J. Gailbert, Appl. Phys. Lett. 73 (1998) 441. [7] C. Rinco´n, S.M. Wasim, G. Marı´n, E. Herna´ndez, G. Sa´nchez Pe´rez, J. Galibert, J. Appl. Phys. 87 (2000) 2293. [8] C. Rinco´n, S.M. Wasim, G. Marı´n, E. Herna´ndez, J.M. Delgado, J. Galibert, J. Appl. Phys. 88 (2000) 3439. [9] B.I. Shklovskii, A.L. Efros, Electronic Properties of Doped Semiconductors, Springer, Berlin, 1984. [10] S.M. Wasim, C. Rinco´n, G. Marı´n, Phys. Status Solidi A 194 (2002) 244. [11] J.S. Blakemore, Semiconductor Statistics, Pergamon Press, New York, 1962. [12] R. Ma´rquez, C. Rinco´n, Sol. Energy Mater. Sol. Cells 71 (2000) 19. [13] S.M. Wasim, Sol. Cells 16 (1986) 286. [14] G. Marı´n, S.M. Wasim, C. Rinco´n, G. Sa´nchez Pe´rez, Ch. Power, A.E. Mora, J. Appl. Phys. 83 (1998) 3364. [15] E. Arushanov, L. Essaleh, J. Galibert, J. Leotin, M. Arsene, J.P. Peyrade, S. Askenazy, Appl. Phys. Lett. 61 (1992) 958. [16] H. Weinert, H. Neumann, H.J. Ho¨bler, G. Ku¨hn, N. Van Nam, Phys. Status Solidi B 81 (1977) K59. [17] C. Rinco´n, S.M. Wasim, G. Marı´n, Appl. Phys. Lett. 80 (2002) 998. [18] K. Bohmhammel, P. Deus, G. Ku¨hn, W. Mo¨ller, Phys. Status Solidi A 71 (1982) 505. [19] M. Cutler, N.F. Mott, Phys. Rev. 181 (1969) 1336.
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[20] L. Essaleh, S.M. Wasim, J. Galibert, J. Appl. Phys. 90 (2001) 3993. [21] H.P. Wang, W.W. Lam, I. Shi, J. Cryst. Growth 200 (1999) 137. [22] L. Essaleh, J. Galibert, S.M. Wasim, J. Leotin, Phys. Status Solidi B 177 (1993) 449.
[23] W. Ho¨rig, G. Ku¨hn, W. Mo¨ller, A. Mu¨ller, H. Neumamm, E. Reccius, Krist. Res. Tech. 14 (1979) 229. [24] S.M. Wasim, J.G. Albornoz, Phys. Status Solidi A 110 (1988) 575. [25] G. Marı´n, S.M. Wasim, G. Sa´nchez Pe´rez, P. Bocaranda, A.E. Mora, J. Electr. Mater. 27 (1998) 1351.
Electrical conduction in ordered defect compounds S.M. Wasim*, C. Rinco´n, G. Marı´n, R. Ma´rquez Departamento de Fı´sica, Facultad de Ciencias, Centro de Estudios de Semiconductores, Universidad de Los Andes, Me´rida, Venezuela
Abstract A comparative study of the temperature dependence of electrical resistivity, carrier concentration and carrier mobility of the Ordered Defect Compounds (ODCs) CuIn3Se5, CuIn3Te5, and CuIn5Te8 with their corresponding normal 1:1:2 phase is reported. Relatively lower carrier concentration and higher activation energy observed in ODCs is explained on the basis that shallow acceptor or donor levels observed in 1:1:2 phase are partially annihilated in these compounds due to attractive þ2 interaction between V21 Cu and InCu defect pair. In the activation regime, the mobility is explained by taking into account a scattering mechanism of the charge carriers with donor – acceptor defect pairs. The electrical data at lower temperatures is explained with the existing theoretical expression for the nearest neighbor hopping conduction mechanism. q 2003 Elsevier Ltd. All rights reserved. Keywords: A. Semiconductors; A. Electronic materials; D. Electrical properties; D. Transport properties; D. Defects
1. Introduction It has been shown [1,2] from first-principle calculations that the formation energy of interacting donor – þ2 acceptor defect pairs (DADPs), like (2V21 Cu þ InCu ), is very small in the ternary compound semiconductor CuInSe2. This concept is used to explain the existence of CuIn5Se8, CuIn3Se5, Cu2In4Se7, and Cu3In5Se9, as a þ2 repeat of a single unit of (2V21 Cu þ InCu ) in each n ¼ 4; 5; 7 and 9 units, respectively, of CuInSe2 [2]. They can also be obtained from the formula Cun 2 3Inn þ 1Se2n where n ¼ 4; 5; 7; and 9, respectively. Because of the presence of DADPs, they are referred to in the literature as Ordered Defect Compounds (ODCs). Similarly, the existence of CuGa5Se8, CuGa3Se5, CuIn5Te8, CuIn3Te5, CuGa5Te8 and CuGa3Te5 has also been established and their crystal structure and optical properties reported [2 –8]. Some of these compounds are promising materials in the fabrication of opto-electronic devices. They are also of academic interest in exploring new physical concepts that cannot be developed with normal 1:1:2 chalcopyrites or the binary compounds. For example, it is suggested that þ2 the attractive interaction between V21 Cu and InCu leads to * Corresponding author. Fax: þ 58-7440-1286. E-mail address: [email protected] (S.M. Wasim).
annihilation of their corresponding acceptor and donor levels [1,2]. Thus, one should expect the DADPs to be electrically inactive and therefore, these ODCs should have relatively lower concentration as compared to their normal 1:1:2 phase. Furthermore, it is important to understand as to how the mobility of the charge carriers is affected by the presence of the ordered arrays of DADPs. To study this effect, in the present work, we report on a comparative study of the temperature dependence of electrical resistivity, carrier concentration and carrier mobility of bulk samples of n- and p-CuIn3Se5, and ptype CuIn3Te5 and CuIn5Te8 with their corresponding normal 1:1:2 phase. Relatively lower carrier concentration and higher activation energy are observed in the ODCs. This is explained on the basis that shallow donor or acceptor levels observed in normal 1:1:2 phase are partially annihilated in ODCs due to attractive interaction þ2 between V21 Cu and InCu defect pair. In the activation regime, the mobility is explained by taking into account an additional scattering mechanism of the charge carriers by DADPs. The electrical data in the impurity band is explained on the basis of the existing theoretical expression for the nearest neighbor hopping conduction mechanism.
0022-3697/03/$ - see front matter q 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0022-3697(03)00099-4
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2. Experimental details The samples of these ODCs were cut from ingots that were prepared by Bridgman technique. They crystallize in a chalcopyrite-related structure [4], and had their chemical composition, as determined by energy dispersive X-ray spectroscopy, very close to the ideal value 1:3:5 or 1:5:8. The electrical resistivity r and the majority carrier concentration n or p in a magnetic field of 1 T were measured between liquid nitrogen and room temperature on rectangular samples of representative dimensions of 1 £ 2 £ 8 mm3. The representative n- and p-type CuIn3Se5 samples mentioned in the present study are denoted as S1 and S2, whereas p-type CuIn3Te5 and CuIn5Te8 as S3 and S4, respectively.
3. Experimental results and discussion 3.1. Electrical resistivity and carrier concentration in the activation regime The electrical resistivity r of samples S1 – S4 on a logarithmic scale is plotted in Fig. 1 as a function of the inverse of the temperature T: At temperatures below about 125 K, three possible mechanisms, i.e. nearest neighbor hopping with ln r / 1=T; variable range hopping of Mott type with ln r / 1=T 1=4 ; and Efros– Shklovskii type where
Fig. 1. Plot of the electrical resistivity of (X) n-type and (A) p-type CuIn3Se5, (B) p-type CuIn3Te5, and (P) p-type CuIn5Te8 on the logarithmic scale versus reciprocal temperature. The nearly linear behavior represented by ln r versus 1=T observed in these samples in the temperature range from about 80 to 110 K is shown by the continuous lines.
ln r / 1=T 1=2 are expected to dominate in different temperature ranges [9], but not necessarily each of them in the same sample. From the analysis of the data, not shown here, and whose general details are published elsewhere [10], the exponent s in ln r / 1=T s was found to be very close to unity. Hence, the data below 110 K in Fig. 1 are fitted to a straight line showing that the conduction is due to the nearest neighbor hopping of the charge carrier in the impurity band. The variation of the majority charge carrier concentration n (or p) on logarithmic scale with 103 =T between 80 and 300 K for samples S1 – S4 is plotted in Fig. 2. In the same figure, we plot for comparison, the change of n (or p) with 103 =T of samples of the corresponding 1:1:2 phase that have, as mentioned in Table 1, the lowest reported carrier concentration. Their values at 300 K are also shown in Table 1 together with the present data. A trend is observed, where the carrier concentration in the tellurides of these ODCs is smaller by at least two orders of magnitude, whereas in n-type CuIn3Se5 by one order. However, in the case of p-CuIn3Se5, its magnitude is similar to that reported for the corresponding p-type 1:1:2 phase. This is indicative of the electrically inactive nature of the DADPs and that they do not contribute to the total free charge carriers. The temperature dependent behavior of n in S1 and p in S2, S3, and S4 in Fig. 2 indicates that above around 125 K, the electrical conduction is mainly due to activation in the conduction (valence) band and below 100 K, as mentioned earlier from the analysis of the resistivity data, due to charge carriers in the impurity band. To estimate the activation energy ED of the donor level and the effective mass mpe of
Fig. 2. Plot of the temperature dependence of electron concentrations n for (X) CuIn3Se5 and (W) CuInSe2 (left scale); and hole concentration p for (A) CuIn3Se5, (B) CuIn3Te5, (P) CuIn5Te8, and (K) CuInTe2 (right scale). The n versus T data for CuInSe2 are taken from Ref. [13] whereas those of p-type CuInTe2 from Ref. [23].
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Table 1 Values of the electron and hole concentration n or p and charge mobility m at 300 K, activation energy of shallow donor or acceptor levels ED or EA ; effective mass mpe and mpp of carriers in units of the free electron mass, deformation potential Eac of the conduction or valence band, static dielectric constant 10 and formation energy H of ordered arrays of defect pairs in n- and p-CuIn3Se5, p-CuIn3Te, and p-CuIn5Te8 obtained in the present work. The range of values of these parameters for n-CuInSe2, p-CuInSe2, and p-CuInTe2 reported in the literature is also shown Compound
n or p (cm23)
m (cm2/V s)
ED or EA (meV)
mpe or mpp
Eac (eV)
10
H (meV)
n-CuIn3Se5 p-CuIn3Se5 n-CuInSe2 p-CuInSe2 p-CuIn3Te5 p-CuIn5Te8 p-CuInTe2
(3–7 £ 106) £ 109a,b 1.0 £ 1017a (3.5–200) £ 1016c,d (2–20) £ 1016c 2 £ 1014a 1.0 £ 1013a (3–5200) £ 1016g,h
3–200b 50a 150–1500c 50–100c 3a 1.5a 27–135 g,h
36 ^ 2a,f 28 ^ 2a,f 6–12c 24–32c 30 ^ 2a 88 ^ 8a 9–22i
0.13 ^ 0.01a,f 1.06 ^ 0.10a,f 0.09c 0.78c 0.80 ^ 0.11a 1.02 ^ 0.12a 0.78 h
13.7 ^ 2.7a,f 3.5 ^ 0.5a,f 13 –20c 6– 8c 6.2 ^ 1.5a 5.0 ^ 1.2a 5.35 h
11 ^ 2a 11 ^ 2a 9.5–13.6c 9.5–13.6c 12 ^ 2a 12 ^ 2a 9.7 h
27 ^ 4a,f 80 ^ 10a,f ,10e ,10e 32 ^ 4a 140 ^ 9a –
a b c d e f g h i
Present work. Ref. [21]. Ref. [13]. Ref. [22]. Ref. [2]. Ref. [10]. Ref. [23]. Ref. [24]. Ref. [25].
ð1Þ
It can be noted that the activation energy of 36 meV of the donor level is consistent with ED < 38 meV estimated from the calculation based on the effective mass theory [12]. The relatively low electron concentration of n-CuIn3Se5 sample,
In this expression, nc is the concentration of electrons and Nc the effective density of states in the conduction band. ND and NA are the donor and acceptor concentrations, and g the degeneracy factor of the donor ground state. For the analysis of the data in the high temperature region, it is assumed that the contribution of the impurity band to the total electron concentration n is negligible. Thus, by replacing nc with the measured value n; a linear plot of ln½nðn þ NA Þ=T 3=2 ðND 2 NA 2 nÞ is obtained against 103 =T with the adjustable parameters ND < 7:9 £ 1017 cm23 and NA < 7:4 £ 1017 cm23. This is shown in Fig. 3. From the slope, ED is estimated to be 36 meV. Also, assuming g ¼ 2 which is the value of the degeneracy factor of the conduction band, from the intercept of the straight line at 103 =T ! 0; mpe in CuIn3Se5 is estimated to be 0:13me : In the case of the p-type sample S2, similar analysis is made where ED ; nc ; and Nc ; are replaced in Eq. (1) by the acceptor activation energy EA ; the concentration of holes in the valence band pv ; and the effective density of states in the valence band Nv ; respectively. Under this approach, EA ; NA ; and ND estimated from the fit were 28 meV, 8 £ 1019 cm23, and 6 £ 1016 cm23, respectively. Also, from the intercept of the straight lines at 103 =T ! 0; using g ¼ 2; which is the value for the degeneracy factor of the defect ground state when the top of the valence band are nondegenerate [11], mph is found to be 1:06me :
Fig. 3. (X) Plot of ½nðn þ NA Þ=T 3=2 ðND 2 NA 2 nÞ for CuIn3Se5 (left scale) and ½pðp þ ND Þ=T 3=2 ðNA 2 ND 2 pÞ for (A) CuIn3Se5, (B) CuIn3Te5 and (P) CuIn5Te8 (right scale) against 1000=T: The fit to the data above about 100 K is shown by the continuous lines.
the electron for n-type sample S1 from the high temperature data, we use the well-known expression for non-degenerate statistics in the conduction band given by Ref. [11] nc ðnc þ NA Þ=ðND 2 NA 2 nc Þ ¼ ðNc =gÞexpð2ED =KTÞ:
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as compared to n-CuInSe2, can be explained as due to the fact that the shallow donor level observed in CuInSe2 between 5 and 15 meV, which is responsible for the electrical properties of n-type CuInSe2, is partially annihilated due to the 21 attractive interaction between Inþ2 Cu and VCu defects that form the electrically inactive DADPs. On the contrary, the acceptor level with EA < 28 meV observed in p-CuIn3Se5 is in good agreement with the activation energy of the most shallow acceptor level reported in p-CuInSe2 (Table 1) from electrical measurements [13]. The origin of this level, consistent with EDX analysis indicates that this sample is Cu-rich. This can be attributed to copper atoms on indium sites (CuIn). This defect state is not expected to be annihilated due to the formation of the DADPs. This could explain the fact that the hole concentration in CuIn3Se5 is of the same order of magnitude as in CuInSe2 and provide additional evidence that this ODC is formed due to the presence of þ2 ordered arrays of (2V21 Cu þ InCu ) DADPs in CuInSe2. In p addition, values of me and mph of CuIn3Se5 are in good agreement with 0.16 and 1:1me estimated from optical data [14]. For comparison, it is worth mentioning that the electron effective mass in CuInSe2 obtained from Shubnikov– de Hass oscillations in the magnetoresistance is mpe ¼ 0:085me [15] whereas, mph < 0:78me for the hole is estimated from both electrical and optical data [16]. In the case of CuIn3Te5 and CuIn5Te8 samples, using the same analysis as for S2, we get from the fits in Fig. 3, NA < 7:0 £ 1017 cm23, ND < 6:99 £ 1017 cm23, and EA < 30 meV for S3, and NA < 5:0 £ 1015 cm23, ND < 4:9 £ 1015 cm23, and EA < 88 meV for S4. On the other hand, with g ¼ 2; the degeneracy factor for degenerate valence bands as reported in the case of 1:1:2 phase, the effective mass mpp < 0:80me and 1:02me of the hole in S3 and S4, respectively, are estimated. These values together with those of CuInSe2 and CuInTe2 reported in the literature are given in Table 1. It is observed that ED and EA are slightly higher than the values of the shallow levels of the corresponding 1:1:2 phases. This again confirms that the shallow acceptor levels observed in p-type 1:1:2 chalcopyrite phase are partially annihilated in ODCs due to the attractive þ2 interaction between V21 Cu and InCu pair. 3.2. Carrier mobility in the activation regime The variation of the charge carrier (electrons or holes) mobility m with T for all the samples is shown in Fig. 4. It can be seen from the Table 1 that with the exception of p-CuInSe2 and p-CuIn3Se5, its value at 300 K is between one or two orders of magnitude smaller in comparison to the corresponding 1:1:2 phase. Attempt to fit the data corresponding to the activation regime (not shown here) using Mathiessen rule given by [13] 21 21 21 21 m21 c ¼ mI þ mAC þ mPO þ mNPO ;
ð2Þ
Fig. 4. Variation of electron mobility with temperature on logarithmic scales for (X) n-CuIn3Se5, (A) p-CuIn3Se5, (B) CuIn3Te5, and (P) CuIn5Te8. The continuous curves represent a theoretical fit to the data in the activation regime by considering the combined effect of the scattering of the charge carriers by DADPs, ionized impurities, acoustic, polar optical (s-like in n-type S1) and non-polar optical (p-like in p-type S2, S3 and S4) phonons. For nCuIn3Se5 and p-CuIn3Te5 the data in the impurity band regime were fitted with Eq. (4).
where mI ; mAC ; mPO ; and mNPO represent the mobilities of charge carriers due to the scattering by ionized impurities, acoustic-lattice modes, polar optical modes, and non-polar optical modes, respectively, was unsuccessful. This is indicative of the presence of additional scattering of the charge carriers in the ODCs by a mechanism that is not found in n- and p-type samples of binary and ternary compounds of the 1:1:2 phase. Thus, to explain the temperature dependence of the mobility, an additional term that involved the scattering of the charge carriers by DADPs was introduced in Eq. (2). This can be expressed as [17]
mDP ¼ m0 exp½ðEDðAÞ þ HÞ=KB T;
ð3Þ
where m0 is a nearly constant parameter, and H the formation energy of the arrays of defect pairs. The temperature dependence of m of samples S1 – S4 in Fig. 4 above 100 K, in the activation regime, was fitted by taking into account the combined effect of the scattering of the charge carriers by DADP, ionized impurities, acoustic, polar optical (s-like in n-type S1) and non-polar optical (p-like in p-type S2 – S4) phonons. For this, Eqs. (2) and (3) and the respective expressions for the mobility were used. These expressions are given in Ref. [13]. In the fit, the static dielectric constant 10 ; optical 1a ; the deformation potential Eac of the conduction (n-type), valence (p-type) bands, H; and m0 were considered as
S.M. Wasim et al. / Journal of Physics and Chemistry of Solids 64 (2003) 1627–1632
adjustable parameters. Others, like the ionized impurity concentration NI ¼ ND þ NA ; mpe ; mpp ; ED and EA were those obtained from the analysis of the carrier concentration data. The longitudinal sound velocity u < 2 – 3 £ 105 cm/s, was estimated from the Debye temperature uD of the corresponding 1:1:2 phase [18], and 10 =1a was taken as 1.7, which is the average obtained for Cu-ternaries [13]. An excellent fit above 110 K, as shown in Fig. 4 by continuous lines, is obtained with the values of 10 ; Eac ; and H given in Table 1.
1631
which does not form part of the DADPs, gives further þ2 evidence that the defect pairs (2V21 Cu þ InCu ) are electrically inactive. The temperature dependence of the relatively low mobility in the high temperature region is explained by taking into account the scattering mechanism of the charge carriers by DADPs, ionized impurities, acoustic and polar optical phonons. At low temperatures, where the conduction in the impurity band is due to the thermally activated hopping between localized states, the theoretical model proposed by Cutler and Mott successfully explains the mobility data.
3.3. Carrier mobility in the impurity band At temperatures lower than about 100 K where the electrical conduction, as mentioned earlier, is mainly by nearest neighbor hopping mechanism in the impurity band ðln r / 1=TÞ; the electron and hole mobility is analyzed by considering the thermally activated hopping of the charge carriers between localized states in such a band. In this case, the mobility is given by the expression [19]
Acknowledgements
mi ¼ ðD=KB TÞexpð2W=KB TÞ;
References
ð4Þ
where D is a constant and W the hopping activation energy. The experimental data of m below 100 K was fitted to Eq. (4). A good fit, shown by continuous curves in Fig. 4 for S1 and S3 samples was obtained with the adjustable parameters W < 32 and 50 meV, and D < 4 and 6 eV cm2/V s, respectively. It is worth mentioning that attempt to fit the mobility data below 100 K with the expression used earlier [20] for variable range hopping conduction mechanisms, not shown here, was far from satisfactory. This further confirms the nearest neighbor hopping conduction in the low temperature regime.
4. Conclusions In summary, a comparative study of the electrical properties of n- and p-type CuIn3Se5, and p-type CuIn3Te5 and CuIn5Te8 ODCs is made. It is found that above around 110 K, the electrical conduction is due to the thermal activation of donor and/or acceptor levels with activation energies of 36, 28, 30, and 88 meV, respectively. The density of states effective mass of the charge carriers in these compounds are estimated to be mpe < 0:13me for n-type CuIn3Se5 and mph < 1:07; 0.80, 1:02me for p-type CuIn3Se5, CuIn3Te5, and CuIn5Te8, respectively. Below this temperature, the electrical conduction is found to be due to nearest neighbor hopping mechanism in the impurity band. The relatively low electron concentration in n-CuIn3Se5 is explained as due to the partial annihilation of the shallow donor level originating from the indium on copper site defect state that forms the þ2 electrically inactive (2V21 Cu þ InCu ) DADP. The absence of low concentration in p-type CuIn3Se5 where the dominant acceptor level is attributed to the antisite defect CuIn,
This work was supported by grants from FONACIT (Contract No. G-97000670), and CDCHT-ULA (Contract Nos. C-917-98-05-A and C-918-98-05-E).
[1] S.B. Zhang, S.H. Wei, A. Zunger, Phys. Rev. Lett. 78 (1997) 4059. [2] S.B. Zhang, S.H Wei, A. Zunger, H. Katayama Yoshida, Phys. Rev. B 57 (1998) 9642. [3] A.J. Nelson, G.S. Horner, J.K. Sinha, M.H. Bode, Appl. Phys. Lett. 64 (1994) 3600. [4] S.M. Wasim, C. Rinco´n, G. Marı´n, J.M. Delgado, Appl. Phys. Lett. 77 (2000) 94. [5] S.H. Wei, S.B. Zhang, A. Zunger, Appl. Phys. Lett. 72 (1998) 3199. [6] C. Rinco´n, S.M. Wasim, G. Marı´n, J.M. Delgado, J.R. Huntzinger, A. Zwick, J. Gailbert, Appl. Phys. Lett. 73 (1998) 441. [7] C. Rinco´n, S.M. Wasim, G. Marı´n, E. Herna´ndez, G. Sa´nchez Pe´rez, J. Galibert, J. Appl. Phys. 87 (2000) 2293. [8] C. Rinco´n, S.M. Wasim, G. Marı´n, E. Herna´ndez, J.M. Delgado, J. Galibert, J. Appl. Phys. 88 (2000) 3439. [9] B.I. Shklovskii, A.L. Efros, Electronic Properties of Doped Semiconductors, Springer, Berlin, 1984. [10] S.M. Wasim, C. Rinco´n, G. Marı´n, Phys. Status Solidi A 194 (2002) 244. [11] J.S. Blakemore, Semiconductor Statistics, Pergamon Press, New York, 1962. [12] R. Ma´rquez, C. Rinco´n, Sol. Energy Mater. Sol. Cells 71 (2000) 19. [13] S.M. Wasim, Sol. Cells 16 (1986) 286. [14] G. Marı´n, S.M. Wasim, C. Rinco´n, G. Sa´nchez Pe´rez, Ch. Power, A.E. Mora, J. Appl. Phys. 83 (1998) 3364. [15] E. Arushanov, L. Essaleh, J. Galibert, J. Leotin, M. Arsene, J.P. Peyrade, S. Askenazy, Appl. Phys. Lett. 61 (1992) 958. [16] H. Weinert, H. Neumann, H.J. Ho¨bler, G. Ku¨hn, N. Van Nam, Phys. Status Solidi B 81 (1977) K59. [17] C. Rinco´n, S.M. Wasim, G. Marı´n, Appl. Phys. Lett. 80 (2002) 998. [18] K. Bohmhammel, P. Deus, G. Ku¨hn, W. Mo¨ller, Phys. Status Solidi A 71 (1982) 505. [19] M. Cutler, N.F. Mott, Phys. Rev. 181 (1969) 1336.
1632
S.M. Wasim et al. / Journal of Physics and Chemistry of Solids 64 (2003) 1627–1632
[20] L. Essaleh, S.M. Wasim, J. Galibert, J. Appl. Phys. 90 (2001) 3993. [21] H.P. Wang, W.W. Lam, I. Shi, J. Cryst. Growth 200 (1999) 137. [22] L. Essaleh, J. Galibert, S.M. Wasim, J. Leotin, Phys. Status Solidi B 177 (1993) 449.
[23] W. Ho¨rig, G. Ku¨hn, W. Mo¨ller, A. Mu¨ller, H. Neumamm, E. Reccius, Krist. Res. Tech. 14 (1979) 229. [24] S.M. Wasim, J.G. Albornoz, Phys. Status Solidi A 110 (1988) 575. [25] G. Marı´n, S.M. Wasim, G. Sa´nchez Pe´rez, P. Bocaranda, A.E. Mora, J. Electr. Mater. 27 (1998) 1351.