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Electronic band gap of Zn2x(CuIn)1−xX2 solid solution series (X = S, Se, Te)
Journal of Alloys and Compounds 414 (2006) 26–30
Electronic band gap of Zn2x(CuIn)1−xX2 solid solution series (X = S, Se, Te) S. Schorr a,∗ , V. Riede b , D. Spemann b , Th. Doering c a
Institute of Mineralogy, Crystallography and Materials Science, Scharnhorststr. 20, D-04275 Leipzig, Germany b Institute of Experimental Physics II, University Leipzig, Leipzig, Germany c Institute of Non-Classical Chemistry, Leipzig, Germany Received 14 June 2005; received in revised form 8 July 2005; accepted 12 July 2005 Available online 29 August 2005
Abstract The Zn2x (CuIn)1−x X2 solid solution series with X = S, Se and Te have been investigated concerning variation of the band gap Eg with the chemical composition, especially, with regard to the two-phase field (miscibility gap) occuring in all three systems. The band gap Eg was determined by diffuse reflection on powder samples of the quaternary alloys. A highly non-linear dependence of Eg on the chemical composition was found, which may be caused by the repulsive interactions of Cu3d and anion 3p states. Moreover, the Eg value of the ternary end member of the solid solution series is even reached in a composition range x ∼ 0.45 (X = S), x ∼ 0.4 (X = Se) and x ∼ 0.3 (X = Te). This is due to a nearly constant band gap within the small single-phase tetragonal region (0 ≤ x < 0.1) and almost no variation within the broad two-phase field. © 2005 Elsevier B.V. All rights reserved. Keywords: Electronic band gap; Solid solution; ZnS/CuInS2 alloys; ZnSe/CuInSe2 alloys; ZnTe/CuInTe2 alloys; Diffuse reflection
1. Introduction Solid solutions of DII XVI and AI BIII XVI 2 compounds were studied intensively due to possible photovoltaic applications. Both end members are semiconductors with a direct band gap. Alloys of 2(ZnX)–CuInX2 offer the advantage to vary the band gap at room temperature from the large value of the binary wide band gap semiconductor ZnX to the band gap of the ternary chalcopyrite end member CuInX2 (see Table 1), as already reported by Refs. [1–3]. II–VI and I–III–VI2 compounds crystallize in the spha¯ lerite (cubic, SG F 43m) and chalcopyrite type (tetragonal, ¯ SG I 42d) structures, respectively. Both structures are closely related to each other, the latter can be derived from the first by doubling the unit cell in c-direction. For long time, it was assumed that by alloying the non-isotype II–VI and I–III–VI2 compounds, a complete or nearly complete solid solution ∗
Corresponding author. Tel.: +49 341 9736271; fax: +49 341 9736299. E-mail address: [email protected] (S. Schorr).
0925-8388/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2005.07.014
series [10–12] is formed. Our latest investigation revealed for all three systems a broad region, where both a tetragonal and a cubic phase coexist (two-phase field) [13–16]. The aim of this paper is to present a new investigation of the band gap energy in the solid solution series Zn2x (CuIn)1−x X2 , especially, with respect to the two-phase field.
2. Experimental Zn2x (CuIn)1−x S2 , Zn2x (CuIn)1−x Se2 and Zn2x (CuIn)1−x Te2 powder samples, the latter within 0 ≤ x ≤ 0.25, were synthesized by solid state reaction of the elements (purity > 99.999%) in sealed evacuated silica tubes at T = 950, 850 and 700 ◦ C, respectively. For all three systems, this procedure was repeated three times homogenizing the samples in between by grinding in an agate mortar. Finally, the samples were cooled down to room temperature with 10 K/h. Zn2x (CuIn)1−x Te2 powder samples within
S. Schorr et al. / Journal of Alloys and Compounds 414 (2006) 26–30
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Table 1 Band gap of the binary and ternary end members of the solid solution series Zn2x (CuIn)1−x X2 Eg (ZnX) (eV)
Eg (CuInX2 ) (eV)
X=S 3.7–3.8 [4] 3.66 [4] 3.68 [5]
1.53 [6]
X = Se 2.73 [4] 2.71 [5]
1.02 [6]
X = Te 2.23 [6], [7] 2.29 [9]
0.96 [8] 0.97 [3] 1.06 [6]
0.3 ≤ x ≤ 1 were prepared by the directional freezing method as described in Ref. [3]. These samples were homogenized by a further annealing of pellets in evacuated silica tubes at T = 700 ◦ C. More details about the sample synthesis can be found in Refs. [13–16]. The average composition of the samples was determined by 2 MeV H+ -proton induced X-ray emission (PIXE) with a beam diameter of 0.4 mm and by electron microprobe measurements (CAMECA SX100, 15 kV/20 nA, standards: synthetic roquesite CuInS2 , sphalerite ZnS, CuInSe2 and ZnSe, respectively). The electronic band gap was determined from spectra of the diffuse reflection Rdiff . The measurements have been performed with a Perkin-Elmer spectrometer LAMBDA19 in the wavelength range from 300 to 2000 nm (4.1–0.62 eV) at room temperature with a spectralon sample as reflectance standard. Using Kubelka–Munk function f (Rdiff ) =
(1 − Rdiff )2 α = 2Rdiff s
where α is the absorption and s is the scattering coefficient. The band gap energy was determined from the linear slope of the function (f (Rdiff ) energy)2 assuming a direct band gap for all compounds (see Fig. 1).
3. Results and discussion The obtained band gap energies for CuInX2 and ZnX agree very well with the known literature data. The values for the Zn2x (CuIn)1−x X2 alloys are presented in Tables 2–4 and Figs. 2–4 as well. The band gap energies Eg in the Zn2x (CuIn)1−x S2 series exhibit a highly non-linear dependence on the composition. Even an amount of about 1 mol% Cu0.5 In0.5 S in ZnS lower the band gap energy by nearly 1 eV. Although these is above the doping level, an analogy from the impurity physics may be used as an explanation. It has been known [18] that substituting impurity atoms with one less valence electron on the cation site, as doping ZnS with Cu, leads
Fig. 1. Plot of (1 − Rdiff )2 /2Rdiff vs. energy for Zn2x (CuIn)1−x Te2 alloys.
to deep acceptors about 1.4 eV above the valence band maximum. It results from a small εpd (Cu d to anion p) energy separation which repels the antibonding state upwards. This antibonding state is the acceptor level of Cu Table 2 Band gap energy of: (a) experimentally determined energy of Zn2x (CuIn)1−x S2 powder samples and (b) Zn2x (CuIn)1−x S2 single crystals Molfraction ZnS in Cu0.5 In0.5 S
Band gap (eV)
Part (a) 1.00 1.00 0.990P 0.978m 0.945 0.934m 0.902 0.866m 0.871m 0.697 0.614m 0.590m 0.469m 0.398 0.309m 0.251m 0.247m 0.191m 0.172m 0.156m 0.090P 0.055P 0
3.60* 3.57 2.72 2.74 2.74* 2.42 2.47 2.38 2.35 2.12* 1.94 1.94 1.78 1.63* 1.57 1.63 1.53 1.50 1.61 1.51 1.47 1.60 1.48
Part (b) 0.98 0.91 0.862 0.805
2.80 (10) 2.42 (10) 2.21 (10) 2.18 (10)
The error was estimated with ±0.10. Values marked by a star are taken from Ref. [17], values for single crystals are taken from Ref. [19]. The chemical composition was determined by PIXE (P) and by electron microprobe (m), respectively.
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S. Schorr et al. / Journal of Alloys and Compounds 414 (2006) 26–30
Table 3 Band gap energy of Zn2x (CuIn)1−x Se2 powder samples determined experimentally Molfraction ZnSe in Cu0.5 In0.5 Se
Band gap (eV)
1.0 0.99P 0.98P 0.97P 0.945m 0.879m 0.829m 0.797P 0.698P 0.545P 0.491P 0.466P 0.424P 0.390 0.329P 0.239P 0.246P 0.146P 0.096P 0.048P 0
2.57 (13) 2.53 (13) 2.49 (12) 2.37 (12) 2.14 (11) 2.08 (11) 1.91 (9) 1.79 (9) 1.60 (8) 1.51 (8) 1.44 (7) 1.33 (7) 1.32 (7) 1.08 (6)* 1.09 (7) 1.02 (5) 1.07 (5) 1.00 (5) 1.03 (5) 1.10 (6) 1.00 (5)
Values marked by a star are taken from Ref. [20]. The chemical composition was determined by PIXE (P) and by electron microprobe (m), respectively.
in II–VI compounds and decreases with εpd , i.e. in the sequence ZnS → ZnSe → ZnTe, the anion binding energy decreases and the acceptor energy decreases from 1.4 to 0.7 and 0.14 eV, respectively [21]. Thus, the lowering of Eg within a small composition range 1 ≥ x ≥ 0.9 is strongest in Zn2x (CuIn)1−x S2 alloys and decreases in the sequence Zn2x (CuIn)1−x S2 → Zn2x (CuIn)1−x Se2 → Zn2x (CuIn)1−x Te2 (see Fig. 5). Also from band structure calculations [22], it was found that even for very low compositions of Cu0.5 In0.5 S in ZnS, the upper valence band of the quaternary compound
Fig. 2. Band gap energy of Zn2x (CuIn)1−x S2 alloys in dependence on chemical composition. The dash-dotted lines mark the two-phase field, the solid and the dotted lines correspond to different fits as described in the text. Open circles refer to literature.
is dominated by Cu3d states. The presence of this state causes the valence band maximum to move toward the conduction band due to repulsive interactions between the Cu3d and S3p states. In the composition range 0 < x ≤ 0.4 for X = S, Se and 0 < x < 0.3 for X = Te, the experimentally determined band gap energies do not differ (within the experimental errors) from the value of the ternary end member CuInX2 . This composition range includes the two-phase field, where a cubic phase with x = 0.42 (X = S), x = 0.36 (X = Se) and x = 0.3 (X = Te) and a tetragonal phase with x = 0.1 (X = S, Se, Te) coexists [14–16]. Because of the small difference between the band gap energies of the CuInX2 -rich end of the cubic
Table 4 Experimentally determined band gap energy of Zn2x (CuIn)1−x Te2 powder samples Molfraction ZnTe in Cu0.5 In0.5 Te
Band gap (eV)
1.0 0.892 0.837 0.784 0.697 0.58 0.572 0.496 0.248 0.199 0.177 0.146 0.135 0.100 0.089 0.056 0.050 0
2.27 (10) 1.84 (10) 1.73 (9) 1.65 (8) 1.55 (8) 1.38 (6) 1.44 (8) 1.31 (6) 1.20 (5) 1.10 (5) 1.12 (5) 1.15 (5) 1.15 (5) 1.15 (5) 1.08 (5) 1.10 (5) 1.00 (5) 1.00 (5)
The average sample composition was determined by PIXE.
Fig. 3. Band gap energy of Zn2x (CuIn)1−x Se2 alloys in dependence on chemical composition. The dash-dotted lines mark the two-phase field, the solid and the dotted lines correspond to different fits as described in the text. Open circles refer to literature.
S. Schorr et al. / Journal of Alloys and Compounds 414 (2006) 26–30
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expression bx (1 − x) with the bowing parameter b > 0 characterizing the degree of deviation from the linear dependence of Eg for the average composition Eg (0.5). In analogy, the expression Eg (x) = Eg (ZnX)x + (1 − x)Eg (CuInX2 ) − bx (1 − x) (1) was used to describe the non-linear behaviour of the Zn2x (CuIn)1−x X2 alloys band gap energy. Because of the strong decrease of Eg in the ZnS-rich region in Zn2x (CuIn)1−x S2 as described above, the dependence of the band gap energy on chemical composition cannot be expressed by Eq. (1). To reach a satisfactory agreement in the region 0 ≤ x ≤ 0.95, a polynom of second order was used Eg (x) = a1 + a2 x + bx2 Fig. 4. Band gap energy of Zn2x (CuIn)1−x Te2 alloys in dependence on chemical composition. The dash-dotted lines mark the two-phase field, the solid and the dotted lines correspond to different fits as described in the text. Open circles refer to literature.
single-phase region and the ZnX-rich end of the tetragonal single-phase region, the band gap energy is nearly constant within the two-phase field and moreover, also in the tetragonal single-phase region. Thus, it can be explained that the Eg value of the ternary end member of the solid solution series is even reached in a composition range x ∼ 0.45 (X = S), x ∼ 0.4 (X = Se) and x ∼ 0.3 (X = Te). The optical bowing in semiconductor alloys [23] is used to describe the non-linear dependence of the band gap energy Eg on the chemical composition x. It is known that the lowest band gaps of binary semiconductor alloys are usually smaller than the concentration (x) weighted average of the band gaps of the constituent binary semiconductors. This alloy band gap reduction is often expressed phenomenologically by the
(2)
where a1 = Eg (CuInX2 ) and a2 = Eg (ZnX) − Eg (CuInX2 ) − b, here, b and a2 were taken as a free parameter to get a better coincidence. With Eg (CuInS2 ) = 1.48 eV and the parameters a2 = 1.485 eV and b = 1.88 eV, a good agreement between calculated values and experimental data can be reached in this region. In the case of Zn2x (CuIn)1−x Se2 , the non-linearity of Eg can be expressed by Eq. (1) and a bowing parameter b = 1.88 eV. Using Eq. (2) with the parameters a2 = 1.46 eV and b = 1.60 eV, a slightly better agreement, with the exception that the value of Eg (ZnSe) is not reached, can be found. Also the non-linear behaviour of Eg for Zn2x (CuIn)1−x Te2 alloys can be better expressed with Eq. (2) using Eg (CuInTe2 ) = 1.0 eV and the parameters a2 = 1.09 eV and b = 0.78 eV as a result of the fit. In the sequence Zn2x (CuIn)1−x S2 → Zn2x (CuIn)1−x Se2 → Zn2x (CuIn)1−x Te2 , the bowing parameter b decreases but remains greater than zero indicating a decreasing bowing, i.e. decreasing non-linearity for S → Se → Te. 4. Conclusions The band gap energy Eg (x) in the Zn2x (CuIn)1−x X2 solid solution series (X = S, Se, Te) was determined experimentally by diffuse reflection measurements. A highly non-linear dependence of Eg on the chemical composition was detected, which may be caused by the repulsive interactions of Cu3d and S3p, Se3p and Te3p states, respectively. The non-linearity decreases in the sequence Zn2x (CuIn)1−x S2 → Zn2x (CuIn)1−x Se2 → Zn2x (CuIn)1−x Te2 . For Zn2x (CuIn)1−x S2 , the composition-dependent behaviour of the band gap Eg cannot be described by means of the expression bx (1 − x) with the bowing parameter b, for the other two systems, a rather good agreement can be achieved. Acknowledgements
Fig. 5. Lowering of the band gap energy Eg in the ZnX-rich region of Zn2x (CuIn)1−x X2 alloys. The values given in the figure are the energy of the Cu acceptor levels in ZnX.
The author thank especially Mrs. Geyer and Mrs. Teschner for the measurements of the diffuse reflection spectra and Dr.
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I. Victorov (Institute of Physics of Solids and Semiconductors, National Academy of Sciences, Minsk, Belarus) for the preparation of the Zn2x (CuIn)1−x Te2 samples in the range 0.3 ≤ x ≤ 1. References [1] I. Luck, W. Henrion, R. Scheer, Th. Doering, K. Bente, H.-J. Lewerenz, Cryst. Res. Technol. 31 (1996) 841–844. [2] I.V. Bodnar, V.F. Gremenok, Inorg. Mater. 39 (2003) 1122–1126. [3] I.V. Bodnar, A. Eiffler, Th. Doering, W. Schmitz, K. Bente, I.V. Gremenok, I.A. Victorov, V. Riede, Cryst. Res. Technol. 35 (2000) 1135–1140. [4] S.V. Svechnikov, in: A. Hermann (Ed.), Proceedings of the Third International School, Cietniewo, Poland, 1981, p. 141. [5] M. Boustani, K. Elassili, T. Bekkay, A. Khiara, Sol. Energy Mater. Sol. Cells 45 (1997) 369. [6] H. Neumann, in: A. Hermann (Ed.), Proceedings of the Third International School, Cetniewo, Poland, 1981, p. 171. [7] J.H. Haanstzra, C. Haas, Phys. Lett. 2 (1961) 21. [8] B.R. Pamplin, T. Kiyosawa, K. Masumoto, Prog. Cryst. Growth Charact. 1 (1979) 331.
[9] W.H. Srehlow, E.L. Cook, J. Phys. Rev. Data 2 (1973) 163. [10] (a) K. Bente, Th. Doering, Chem. Erde 51 (1991) 291; (b) O.V. Parasyuk, S.V. Voronyuk, L.D. Gulay, G.Ye. Davidyuk, V.O. Halko, J. Alloys Compd. 348 (2003) 57–64. [11] J.N. Gan, J. Tauc, V.J. Lamprecht Jr., M. Robbins, Phys. Rev. B 12 (1975) 5797. [12] L. Garbato, F. Ledda, J. Solid State Chem. 30 (1979) 189– 195. [13] S. Schorr, G. Wagner, J. Alloys Compd. 396 (2005) 202–207. [14] G. Wagner, F. Fleischer, S. Schorr, J. Cryst. Growth, in press. [15] G. Wagner, S. Lehmann, S. Schorr, J. Solid State Chem., submitted for publication. [16] L. Roussak, G. Wagner, S. Schorr, J. Solid State Chem., submitted for publication. [17] F. Fleischer, Diploma Thesis, University Leipzig, 2003. [18] Y.S. Park, B.K. Shin, in: J.I. Pankove (Ed.), Electroluminescence, Springer, Berlin, 1977, p. 133. [19] L. Schubert, Diploma Thesis, University Leipzig, 2001. [20] S. Lehmann, Diploma Thesis, University Leipzig, 2003. [21] J.E. Jaffe, A. Zunger, Phys. Rev. B 29 (1984) 1882–1906. [22] I. Luck, V. Eyert, M. Fieber-Erdmann, E. Holub-Krappe, R. Scheer, Jpn. J. Appl. Phys. 39-1 (2000) 164–165. [23] J.E. Jaffe, A. Zunger, Phys. Rev. Lett. 51 (1983) 662.
Electronic band gap of Zn2x(CuIn)1−xX2 solid solution series (X = S, Se, Te) S. Schorr a,∗ , V. Riede b , D. Spemann b , Th. Doering c a
Institute of Mineralogy, Crystallography and Materials Science, Scharnhorststr. 20, D-04275 Leipzig, Germany b Institute of Experimental Physics II, University Leipzig, Leipzig, Germany c Institute of Non-Classical Chemistry, Leipzig, Germany Received 14 June 2005; received in revised form 8 July 2005; accepted 12 July 2005 Available online 29 August 2005
Abstract The Zn2x (CuIn)1−x X2 solid solution series with X = S, Se and Te have been investigated concerning variation of the band gap Eg with the chemical composition, especially, with regard to the two-phase field (miscibility gap) occuring in all three systems. The band gap Eg was determined by diffuse reflection on powder samples of the quaternary alloys. A highly non-linear dependence of Eg on the chemical composition was found, which may be caused by the repulsive interactions of Cu3d and anion 3p states. Moreover, the Eg value of the ternary end member of the solid solution series is even reached in a composition range x ∼ 0.45 (X = S), x ∼ 0.4 (X = Se) and x ∼ 0.3 (X = Te). This is due to a nearly constant band gap within the small single-phase tetragonal region (0 ≤ x < 0.1) and almost no variation within the broad two-phase field. © 2005 Elsevier B.V. All rights reserved. Keywords: Electronic band gap; Solid solution; ZnS/CuInS2 alloys; ZnSe/CuInSe2 alloys; ZnTe/CuInTe2 alloys; Diffuse reflection
1. Introduction Solid solutions of DII XVI and AI BIII XVI 2 compounds were studied intensively due to possible photovoltaic applications. Both end members are semiconductors with a direct band gap. Alloys of 2(ZnX)–CuInX2 offer the advantage to vary the band gap at room temperature from the large value of the binary wide band gap semiconductor ZnX to the band gap of the ternary chalcopyrite end member CuInX2 (see Table 1), as already reported by Refs. [1–3]. II–VI and I–III–VI2 compounds crystallize in the spha¯ lerite (cubic, SG F 43m) and chalcopyrite type (tetragonal, ¯ SG I 42d) structures, respectively. Both structures are closely related to each other, the latter can be derived from the first by doubling the unit cell in c-direction. For long time, it was assumed that by alloying the non-isotype II–VI and I–III–VI2 compounds, a complete or nearly complete solid solution ∗
Corresponding author. Tel.: +49 341 9736271; fax: +49 341 9736299. E-mail address: [email protected] (S. Schorr).
0925-8388/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2005.07.014
series [10–12] is formed. Our latest investigation revealed for all three systems a broad region, where both a tetragonal and a cubic phase coexist (two-phase field) [13–16]. The aim of this paper is to present a new investigation of the band gap energy in the solid solution series Zn2x (CuIn)1−x X2 , especially, with respect to the two-phase field.
2. Experimental Zn2x (CuIn)1−x S2 , Zn2x (CuIn)1−x Se2 and Zn2x (CuIn)1−x Te2 powder samples, the latter within 0 ≤ x ≤ 0.25, were synthesized by solid state reaction of the elements (purity > 99.999%) in sealed evacuated silica tubes at T = 950, 850 and 700 ◦ C, respectively. For all three systems, this procedure was repeated three times homogenizing the samples in between by grinding in an agate mortar. Finally, the samples were cooled down to room temperature with 10 K/h. Zn2x (CuIn)1−x Te2 powder samples within
S. Schorr et al. / Journal of Alloys and Compounds 414 (2006) 26–30
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Table 1 Band gap of the binary and ternary end members of the solid solution series Zn2x (CuIn)1−x X2 Eg (ZnX) (eV)
Eg (CuInX2 ) (eV)
X=S 3.7–3.8 [4] 3.66 [4] 3.68 [5]
1.53 [6]
X = Se 2.73 [4] 2.71 [5]
1.02 [6]
X = Te 2.23 [6], [7] 2.29 [9]
0.96 [8] 0.97 [3] 1.06 [6]
0.3 ≤ x ≤ 1 were prepared by the directional freezing method as described in Ref. [3]. These samples were homogenized by a further annealing of pellets in evacuated silica tubes at T = 700 ◦ C. More details about the sample synthesis can be found in Refs. [13–16]. The average composition of the samples was determined by 2 MeV H+ -proton induced X-ray emission (PIXE) with a beam diameter of 0.4 mm and by electron microprobe measurements (CAMECA SX100, 15 kV/20 nA, standards: synthetic roquesite CuInS2 , sphalerite ZnS, CuInSe2 and ZnSe, respectively). The electronic band gap was determined from spectra of the diffuse reflection Rdiff . The measurements have been performed with a Perkin-Elmer spectrometer LAMBDA19 in the wavelength range from 300 to 2000 nm (4.1–0.62 eV) at room temperature with a spectralon sample as reflectance standard. Using Kubelka–Munk function f (Rdiff ) =
(1 − Rdiff )2 α = 2Rdiff s
where α is the absorption and s is the scattering coefficient. The band gap energy was determined from the linear slope of the function (f (Rdiff ) energy)2 assuming a direct band gap for all compounds (see Fig. 1).
3. Results and discussion The obtained band gap energies for CuInX2 and ZnX agree very well with the known literature data. The values for the Zn2x (CuIn)1−x X2 alloys are presented in Tables 2–4 and Figs. 2–4 as well. The band gap energies Eg in the Zn2x (CuIn)1−x S2 series exhibit a highly non-linear dependence on the composition. Even an amount of about 1 mol% Cu0.5 In0.5 S in ZnS lower the band gap energy by nearly 1 eV. Although these is above the doping level, an analogy from the impurity physics may be used as an explanation. It has been known [18] that substituting impurity atoms with one less valence electron on the cation site, as doping ZnS with Cu, leads
Fig. 1. Plot of (1 − Rdiff )2 /2Rdiff vs. energy for Zn2x (CuIn)1−x Te2 alloys.
to deep acceptors about 1.4 eV above the valence band maximum. It results from a small εpd (Cu d to anion p) energy separation which repels the antibonding state upwards. This antibonding state is the acceptor level of Cu Table 2 Band gap energy of: (a) experimentally determined energy of Zn2x (CuIn)1−x S2 powder samples and (b) Zn2x (CuIn)1−x S2 single crystals Molfraction ZnS in Cu0.5 In0.5 S
Band gap (eV)
Part (a) 1.00 1.00 0.990P 0.978m 0.945 0.934m 0.902 0.866m 0.871m 0.697 0.614m 0.590m 0.469m 0.398 0.309m 0.251m 0.247m 0.191m 0.172m 0.156m 0.090P 0.055P 0
3.60* 3.57 2.72 2.74 2.74* 2.42 2.47 2.38 2.35 2.12* 1.94 1.94 1.78 1.63* 1.57 1.63 1.53 1.50 1.61 1.51 1.47 1.60 1.48
Part (b) 0.98 0.91 0.862 0.805
2.80 (10) 2.42 (10) 2.21 (10) 2.18 (10)
The error was estimated with ±0.10. Values marked by a star are taken from Ref. [17], values for single crystals are taken from Ref. [19]. The chemical composition was determined by PIXE (P) and by electron microprobe (m), respectively.
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S. Schorr et al. / Journal of Alloys and Compounds 414 (2006) 26–30
Table 3 Band gap energy of Zn2x (CuIn)1−x Se2 powder samples determined experimentally Molfraction ZnSe in Cu0.5 In0.5 Se
Band gap (eV)
1.0 0.99P 0.98P 0.97P 0.945m 0.879m 0.829m 0.797P 0.698P 0.545P 0.491P 0.466P 0.424P 0.390 0.329P 0.239P 0.246P 0.146P 0.096P 0.048P 0
2.57 (13) 2.53 (13) 2.49 (12) 2.37 (12) 2.14 (11) 2.08 (11) 1.91 (9) 1.79 (9) 1.60 (8) 1.51 (8) 1.44 (7) 1.33 (7) 1.32 (7) 1.08 (6)* 1.09 (7) 1.02 (5) 1.07 (5) 1.00 (5) 1.03 (5) 1.10 (6) 1.00 (5)
Values marked by a star are taken from Ref. [20]. The chemical composition was determined by PIXE (P) and by electron microprobe (m), respectively.
in II–VI compounds and decreases with εpd , i.e. in the sequence ZnS → ZnSe → ZnTe, the anion binding energy decreases and the acceptor energy decreases from 1.4 to 0.7 and 0.14 eV, respectively [21]. Thus, the lowering of Eg within a small composition range 1 ≥ x ≥ 0.9 is strongest in Zn2x (CuIn)1−x S2 alloys and decreases in the sequence Zn2x (CuIn)1−x S2 → Zn2x (CuIn)1−x Se2 → Zn2x (CuIn)1−x Te2 (see Fig. 5). Also from band structure calculations [22], it was found that even for very low compositions of Cu0.5 In0.5 S in ZnS, the upper valence band of the quaternary compound
Fig. 2. Band gap energy of Zn2x (CuIn)1−x S2 alloys in dependence on chemical composition. The dash-dotted lines mark the two-phase field, the solid and the dotted lines correspond to different fits as described in the text. Open circles refer to literature.
is dominated by Cu3d states. The presence of this state causes the valence band maximum to move toward the conduction band due to repulsive interactions between the Cu3d and S3p states. In the composition range 0 < x ≤ 0.4 for X = S, Se and 0 < x < 0.3 for X = Te, the experimentally determined band gap energies do not differ (within the experimental errors) from the value of the ternary end member CuInX2 . This composition range includes the two-phase field, where a cubic phase with x = 0.42 (X = S), x = 0.36 (X = Se) and x = 0.3 (X = Te) and a tetragonal phase with x = 0.1 (X = S, Se, Te) coexists [14–16]. Because of the small difference between the band gap energies of the CuInX2 -rich end of the cubic
Table 4 Experimentally determined band gap energy of Zn2x (CuIn)1−x Te2 powder samples Molfraction ZnTe in Cu0.5 In0.5 Te
Band gap (eV)
1.0 0.892 0.837 0.784 0.697 0.58 0.572 0.496 0.248 0.199 0.177 0.146 0.135 0.100 0.089 0.056 0.050 0
2.27 (10) 1.84 (10) 1.73 (9) 1.65 (8) 1.55 (8) 1.38 (6) 1.44 (8) 1.31 (6) 1.20 (5) 1.10 (5) 1.12 (5) 1.15 (5) 1.15 (5) 1.15 (5) 1.08 (5) 1.10 (5) 1.00 (5) 1.00 (5)
The average sample composition was determined by PIXE.
Fig. 3. Band gap energy of Zn2x (CuIn)1−x Se2 alloys in dependence on chemical composition. The dash-dotted lines mark the two-phase field, the solid and the dotted lines correspond to different fits as described in the text. Open circles refer to literature.
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29
expression bx (1 − x) with the bowing parameter b > 0 characterizing the degree of deviation from the linear dependence of Eg for the average composition Eg (0.5). In analogy, the expression Eg (x) = Eg (ZnX)x + (1 − x)Eg (CuInX2 ) − bx (1 − x) (1) was used to describe the non-linear behaviour of the Zn2x (CuIn)1−x X2 alloys band gap energy. Because of the strong decrease of Eg in the ZnS-rich region in Zn2x (CuIn)1−x S2 as described above, the dependence of the band gap energy on chemical composition cannot be expressed by Eq. (1). To reach a satisfactory agreement in the region 0 ≤ x ≤ 0.95, a polynom of second order was used Eg (x) = a1 + a2 x + bx2 Fig. 4. Band gap energy of Zn2x (CuIn)1−x Te2 alloys in dependence on chemical composition. The dash-dotted lines mark the two-phase field, the solid and the dotted lines correspond to different fits as described in the text. Open circles refer to literature.
single-phase region and the ZnX-rich end of the tetragonal single-phase region, the band gap energy is nearly constant within the two-phase field and moreover, also in the tetragonal single-phase region. Thus, it can be explained that the Eg value of the ternary end member of the solid solution series is even reached in a composition range x ∼ 0.45 (X = S), x ∼ 0.4 (X = Se) and x ∼ 0.3 (X = Te). The optical bowing in semiconductor alloys [23] is used to describe the non-linear dependence of the band gap energy Eg on the chemical composition x. It is known that the lowest band gaps of binary semiconductor alloys are usually smaller than the concentration (x) weighted average of the band gaps of the constituent binary semiconductors. This alloy band gap reduction is often expressed phenomenologically by the
(2)
where a1 = Eg (CuInX2 ) and a2 = Eg (ZnX) − Eg (CuInX2 ) − b, here, b and a2 were taken as a free parameter to get a better coincidence. With Eg (CuInS2 ) = 1.48 eV and the parameters a2 = 1.485 eV and b = 1.88 eV, a good agreement between calculated values and experimental data can be reached in this region. In the case of Zn2x (CuIn)1−x Se2 , the non-linearity of Eg can be expressed by Eq. (1) and a bowing parameter b = 1.88 eV. Using Eq. (2) with the parameters a2 = 1.46 eV and b = 1.60 eV, a slightly better agreement, with the exception that the value of Eg (ZnSe) is not reached, can be found. Also the non-linear behaviour of Eg for Zn2x (CuIn)1−x Te2 alloys can be better expressed with Eq. (2) using Eg (CuInTe2 ) = 1.0 eV and the parameters a2 = 1.09 eV and b = 0.78 eV as a result of the fit. In the sequence Zn2x (CuIn)1−x S2 → Zn2x (CuIn)1−x Se2 → Zn2x (CuIn)1−x Te2 , the bowing parameter b decreases but remains greater than zero indicating a decreasing bowing, i.e. decreasing non-linearity for S → Se → Te. 4. Conclusions The band gap energy Eg (x) in the Zn2x (CuIn)1−x X2 solid solution series (X = S, Se, Te) was determined experimentally by diffuse reflection measurements. A highly non-linear dependence of Eg on the chemical composition was detected, which may be caused by the repulsive interactions of Cu3d and S3p, Se3p and Te3p states, respectively. The non-linearity decreases in the sequence Zn2x (CuIn)1−x S2 → Zn2x (CuIn)1−x Se2 → Zn2x (CuIn)1−x Te2 . For Zn2x (CuIn)1−x S2 , the composition-dependent behaviour of the band gap Eg cannot be described by means of the expression bx (1 − x) with the bowing parameter b, for the other two systems, a rather good agreement can be achieved. Acknowledgements
Fig. 5. Lowering of the band gap energy Eg in the ZnX-rich region of Zn2x (CuIn)1−x X2 alloys. The values given in the figure are the energy of the Cu acceptor levels in ZnX.
The author thank especially Mrs. Geyer and Mrs. Teschner for the measurements of the diffuse reflection spectra and Dr.
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