Pentanary chalcopyrite compounds without tetragonal deformation in the heptanary system Cu(Al,Ga,In)(S,Se,Te)2

ARTICLE IN PRESS Solar Energy Materials & Solar Cells 91 (2007) 44–46 www.elsevier.com/locate/solmat Pentanary chalcopyrite compounds without tetragonal deformation in the heptanary system Cu(Al,Ga,In)(S,Se,Te)2 F. Hergerta,, R. Hocka, S. Schorrb a Chair for Crystallography and Structural Physics, University of Erlangen-Nürnberg, StaudtstraX e 3, D–91058 Erlangen, Germany b Hahn-Meitner Institut, Division Solar Energy, Glienicker Street 100, D-14109 Berlin, Germany Received 9 May 2006; accepted 9 July 2006 Available online 22 August 2006 Abstract The c/a ratios of the nine ternary Cu–III–VI2 compounds in the system Cu(Al,Ga,In)(S,Se,Te)2 range from 1.939 for CuAlSe2 to 2.014 (CuInS2) at room temperature. The validity of Vegard’s law was presumed to determine the tetragonal deformation 1–c/(2a) for all pentanary mixed crystal compounds Cu–(III,III)–(VI–VI)2. For six of these nine compounds it is possible to achieve zero tetragonal deformation by adjusting the correct cation and anion substitution. The calculations are performed for room temperature as well as for 500 1C, which is a typical temperature for the synthesis of thin films of these semiconductor compounds. r 2006 Elsevier B.V. All rights reserved. Keywords: Semiconductors; Chalcopyrite compounds; Alloys 1. Introduction Chalcopyrite compounds based on CuInSe2 are applied as thin film semiconductor materials for photovoltaic applications. The band gap can be adjusted continuously by the chemical composition of mixed crystal compounds assuming that all ternary chalcopyrite compounds are completely miscible. 2. Crystallographic data of the compounds All nine ternary Cu–III–VI2 compounds under investigation crystallise in the chalcopyrite structure in space group I-4 2d and form mixed crystals with each other. Good examples are the quasibinary systems CuAlSe2– CuAlTe2 [1] and CuInSe2–CuGaSe2 [2]. Table 1 contains accurate lattice parameters of the ternary chalcopyrite compounds within the system Cu(Al,Ga,In)(S,Se,Te)2. The room temperature data are taken from various references given in Table 1. The values for 500 1C are determined by Rietveld refinement of synchrotron X-ray powder data measured in situ at elevated temperatures [3–5]. We define Corresponding author. Tel.: +49 9131 8525195; fax: 49 9131 8525182. E-mail address: frank.hergert@krist.uni-erlangen.de (F. Hergert). 0927-0248/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.solmat.2006.07.001 the tetragonal deformation as D ¼ 1
c/(2a) (Table 1). The divisor ‘‘2’’ is a normalisation by the number of distorted cubic subcells. Although the tetragonal deformation amounts to only some 10
3 it can be well determined by X-ray diffraction. It influences the electronic properties by introducing a crystal field splitting of the valence band [6]. Furthermore, it was shown that most chalcopyrite compounds remain stable up to their melting temperature, if D40.023 [7]. Else, a structural transition into the cubic high temperature modification occurs, which is the case for the ternary chalcopyrite compounds CuInS2, CuGaSe2, CuInSe2, CuAlTe2, CuGaTe2 and CuInTe2 [3,5,8]. The compounds CuAlS2 and CuGaS2 do not undergo a phase transition [8], although Do0.023 (Table 1). This is caused by the fact that the criterion D40.023 was derived from lattice parameters measured at room temperature [7]. However, since the tetragonal deformation D varies with temperature in-situ studies at higher temperatures are essential to tackle this problem [7]. For example, when using the D values determined from lattice parameters measured at 5001C (Table 1), the criterion D40.023 is fulfilled for CuAlS2, CuGaS2 and CuAlSe2. Moreover, it was verified experimentally [8] that only these three compounds of the nine Cu-III-VI2 chalcopyrites show no high-temperature phase transition. ARTICLE IN PRESS F. Hergert et al. / Solar Energy Materials & Solar Cells 91 (2007) 44–46 45 Table 1 Crystallographic data of all chalcogenide compounds at room temperature (RT) and at 500 1C Compound a [pm] (RT) c [pm] (RT) D [  10+3] (RT) Ref. a [pm] (500 1C) c [pm] (500 1C) D [  10+3] (500 1C) CuAlS2 a CuGaS2 b CuInS2 c CuAlSe2 d CuGaSe2 e CuInSe2 f CuAlTe2 g CuGaTe2 h CuInTe2 i 5.3336 (5) 5.3449 (5) 5.522 (1) 5.5966 (3) 5.5963 (1) 5.7818 (
) 6.0308 (2) 6.02348 (7) 6.19288 (6) 10.444 (2) 10.468 (1) 11.136 (2) 10.9198 (7) 11.0036 (2) 11.6173 (
) 11.9218 (6) 11.93979 (2) 12.4232 (2) +20.9240 +20.7488
8.33032 +24.4255 +16.8862
4.64388 +11.5905 +8.89602
3.02283 [9] 5.380 (5) 5.387 (2) 5.5555 (
) 5.639 (2) 5.649 (2) 5.8300 (
) 6.0718 (
) 6.067 (4) 6.2288 (
) 10.467 (2) 10.4923 (5) 11.1900 (
) 10.93 (2) 11.0334 (7) 11.6999 (
) 11.9569 (
) 11.994 (2) 12.4792 (
) +27.2305 +26.1463
7.11007 +30.8565 +23.4201
3.42196 +15.3744 +11.5378
1.73388 [10] [11] [12] [13] [14] RT values without reference are provided in this work for the first time. The data for 500 1C are published here for the first time, except for CuInSe2 (see [3]). a RT refers to 27 1C; values for 500 1C averaged from 450, 523 and 621 1C. b RT refers to 32 1C; values for 500 1C averaged from 25, 161 and 962 1C. c RT refers to ‘‘room temperature’’; values for 500 1C averaged from 25 and 865 1C. d RT refers to 30 1C; values for 500 1C averaged from 336, 408, 483 and 556 1C. e RT refers to ‘‘room temperature’’; values for 500 1C averaged from 207, 388 and 573 1C. f RT refers to ‘‘room temperature’’; values for 500 1C averaged from 25 and 471 1C. g RT refers to 39 1C; values for 500 averaged from 463 and 610 1C. h RT refers to 26 1C; values for 500 1C averaged from 326, 473 and 684 1C. i RT refers to 27 1C; values for 500 1C averaged from 25 and 622 1C. 3. Method of calculation Vegards’s law [15] states that the lattice parameter of a mixed crystal depends linearly on the concentration of the substituting element. This has been experimentally confirmed for the solid solutions CuInSe2–CuGaSe2 [2] and CuInSe2–CuInS2 [16]. The tetragonal deformation D is calculated from the lattice parameters for the nine edge compounds. Since three of the tetragonal deformations of the nine ternary chalcopyrite compounds are negative whereas the others are positive it is possible to find six pentanary mixed crystal compounds with D ¼ 0. Their chemical compositions are calculated as follows exemplified here on the compound Cu(In1
yGay)(Se1
xSx)2. The four edge compounds CuInSe2, CuGaSe2, CuInS2 and CuGaS2 are defined by their gallium and sulphur concentration as (x, y) ¼ (0, 0), (0, 1), (1, 0) and (1, 1). The tetragonal deformation D(x, y) was calculated by the multiple linear regression method. This algorithm determines the best plane fitted through the four points D(x, y) given. It allows an error for the tetragonal deformation D, only, but does not shift the points in their concentration (x, y). The intersection of the plane D(x, y) with the plane D ¼ 0 results in a straight line y(x) giving the optimal gallium content dependent on the sulphur concentration. In all cases the cation substitution is very low (yE0.18), whereas the anion concentration allows for the full range of replacements. This fact was considered by weighing the initial values D of the four edge compounds by the calculated gallium substitution y followed by a redetermination of the best-fit plane and the computation of the function y(x) for D ¼ 0. The whole procedure converges after a few cycles. For Cu(In1
yGay)(Se1
xSx)2, the sulphur-dependent gallium substitution is refined to y ¼ 0.062x+0.215. The final weights w for D(x, y) are w(0, 0) ¼ 1
y(0) for CuInSe2, w(0, 1) ¼ y(0) for CuGaSe2, w(1, 0) ¼ 1
y(1) for CuInS2 and w(1, 1) ¼ y(1) for CuGaS2. All calculations were performed for the room temperature and 500 1C data of Table 1. 4. Results The six pentanary compounds for which the tetragonal deformation can be eliminated are listed in Table 2. The cation substitution y is provided as a function of the anion substitution x as y(x) with the coefficient of determination R2 given. Taking the compound Cu(In1
yGay)(Se1
xSx)2 as example the tetragonal approaches zero deformation at room temperature for a cation substitution of indium by gallium of y ¼ 0.22 in the quaternary compound Cu(In0.78Ga0.22)Se2. The gallium fraction can be increased further, if sulphur is introduced as additional resulting in a pentanary chalcopyrite compound. The sulphur substitution can vary over the whole range 0pxp1. Setting x ¼ 0.5 the resulting sum formula is Cu(In0.75Ga0.25)(Se0.5S0.5)2, for x ¼ 1 the quaternary end member Cu(In0.71Ga0.29)S2 is obtained. The chemical composition required for zero tetragonal deformation depends on the temperature. In this work a complete set of lattice parameters at 500 1C was calculated from experimental high-temperature data. For Cu(In1
yGay)Se2, the minimal defect concentration and the highest efficiency of a solar cell device are achieved for the gallium concentration of y ¼ 0.28 [17]. This value is significantly higher than our calculated value for nondeformed unit cells of y ¼ 0.22 (RT) or y ¼ 0.13 (500 1C). Thus, we assume that the reason for the efficiency drop of Cu(In1
yGay)Se2 solar cells with y40.30 is not due to the deformation of the crystal structure. Recently, the ARTICLE IN PRESS 46 F. Hergert et al. / Solar Energy Materials & Solar Cells 91 (2007) 44–46 Table 2 Chemical composition of the six pentanary chalcopyrites without tetragonal deformation (D ¼ 0) Chalcopyrite compound D ¼ 0 (RT) R2 (RT) D ¼ 0 (500 1C) R2 (500 1C) Cu(In1
yGay)(Se1
xSx)2 Cu(In1
yAly)(Se1
xSx)2 Cu(In1
yGay)(Te1
xSx)2 Cu(In1
yAly)(Te1
xSx)2 Cu(In1
yGay)(Te1
xSex)2 Cu(In1
yAly)(Te1
xSex)2 y ¼ 0.22+0.07x y ¼ 0.16+0.13x y ¼ 0.25+0.03x y ¼ 0.21+0.08x y ¼ 0.25–0.04x y ¼ 0.21–0.05x 0.979 1.000 0.855 0.907 0.922 0.897 y ¼ 0.13+0.09x y ¼ 0.10+0.11x y ¼ 0.13+0.08x y ¼ 0.11+0.10x y ¼ 0.13–0.00x y ¼ 0.10–0.00x 0.990 1.000 0.869 0.921 0.897 0.899 detrimental effect of greater gallium contents (y40.30) on the electronic properties of a Cu(In,Ga)Se2-based solar cell device has been proven by band structure calculations [18]. 5. Conclusion and outlook In the heptanary system Cu(Al,Ga,In)(S,Se,Te)2 the tetragonal deformation of the chalcopyrite crystal structures can be eliminated by adjusting the elemental composition. Six undistorted pentanary compounds could be identified. The respective cation and anion concentrations are given for room temperature and 500 1C. In this article only the tetragonal deformation, sometimes called external distortion has been discussed. There is, however, another parameter called internal distortion describing the x-coordinate of the anion position. The ideal value (referred to a face centred cubic structure) is u ¼ 14. Since the nine ternary chalcopyrites used for the calculations have partly uo14 as well as u414 one can in analogy derive the cation and anion substitution for all pentanary chalcopyrite compounds with u ¼ 14. It was shown that most ABX2 compounds which undergo the tetragonal to cubic phase transition have an internal distortion parameter uo0.264 [7]. The advantage of this criterion compared to D40.023 [7] is that the internal distortion is temperature independent [3,19]. However, unfortunately the internal distortion is determined less accurate than the external which lowers the coefficient of its determination significantly. Moreover, it is not clarified if the assumption of a linear dependence such as Vegard’s law is justified in this case, too. Therefore, we refrain from providing these values here. In general, the internal and external distortion will approach their ‘‘ideal’’ values (D ¼ 0 and u ¼ 14) independent of each other, which means that they cannot be achieved at the same chemical composition of the pentanary mixed crystal chalcopyrite compound. Acknowledgements The authors thank Mrs. A. Franz for assistance in the synchrotron experiments. Moreover, funding of Bundesministerium für Umwelt, Naturschutz und Reaktorsicherheit – Fachbereich Erneuerbare Energien is greatly acknowledged. References [1] B.V. Korzun, A.A. Fadzeyeva, K. Bente, W. Kommichau, Phys. Stat. Solidi (b) 242 (2005) 1581. [2] B. Grzeta-Plenkovic, S. Popovic, B. Celustka, B. Santic, J. Appl. Crystallogr. 13 (1980) 311. [3] S. Schorr, G. Geandier, Crystallogr. Res. Technol. 41 (2006) 450. [4] S. Schorr, M. Tovar, D. Sheptyakov, L. Keller, G. Geandier, J. Phys. Chem. Sol. 66 (11) (2005) 1961. [5] S. Schorr, G. Geandier, B.V. Korzun, Phys. Stat. Solidi c (2006), in press. [6] J.L. Shay, J.H. Wernick, Ternary Chalcopyrite Semiconductors: Growth, Electronic Properties, and Applications, Pergamon Press, Oxford, UK, 1975. [7] L. Garbato, F. Ledda, A. Rucci, Progr.Crystal Growth Characterization 15 (1) (1987) 1. [8] S. Schorr, A. Franz, B.V. Korzun, European Synchrotron Radiation Facility: Users’ Reports, Experiment HS-2661 (May 9–15, 2005) 31176 A. [9] G. Brandt, A. Räuber, J. Schneider, Solid State Commun. 12 (1973) 481. [10] S. Schorr, G. Wagner, J. Alloys Comp. 396 (2005) 202. [11] S.C. Abrahams, J.L. Bernstein, J. Chem. Phys. 61 (1974) 1140. [12] L.I. Gladkikh, E.I. Rogacheva, T.V. Tavrina, L.P. Fomina, Neorganicheskie Materialy 36 (11) (2000) 1309; Inorganic Mater. (USSR), 36(11) (2000) 1098. [13] M. Leon, J.M. Merino, J.L.M. de Vidales, J. Mater. Sci. 27 (1992) 4495. [14] A.M. Moustafa, E.A. El-Sayad, G.B. Sakr, Crystallogr. Res. Technol. 39 (3) (2004) 266. [15] L. Vegard, Z. Phys. 5 (1921) 17. [16] K. Zeaiter, Y. Llinares, C. Llinares, Sol. Energy Mat. Sol. Cells 61 (3) (2000) 313. [17] G. Hanna, A. Jasenek, U. Rau, H.W. Schock, Thin Solid Films 387 (2001) 71. [18] C. Persson, A. Zunger, Appl. Phys. Lett. 87 (2005) 211904. [19] H. Neumann, Cryst. Res. Technol. 22 (5) (1987) 723.