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Electronic structure and structural phase stability of CuAlX2 (X=S, Se, Te) under pressure
Journal of Physics and Chemistry of Solids 67 (2006) 669–674 www.elsevier.com/locate/jpcs
Electronic structure and structural phase stability of CuAlX2 (XZS, Se, Te) under pressure Venkatachalam Jayalakshmi, Subramanian Davapriya, Ramaswamy Murugan, Balan Palanivel * Department of Physics, Pondicherry Engineering College, Pondicherry 605 014, India Received 17 March 2005; received in revised form 10 August 2005; accepted 10 August 2005
Abstract The electronic and structural properties of chalcopyrite compounds CuAlX2 (XZS, Se, Te) have been studied using the first principle selfconsistent Tight Binding Linear Muffin-Tin Orbital (TBLMTO) method within the local density approximation. The present study deals with the ground state properties, structural phase transition, equations of state and pressure dependence of band gap of CuAlX2 (S, Se, Te) compounds. Electronic structure and hence total energies of these compounds have been computed as a function of reduced volume. The calculated lattice parameters are in good agreement with the available experimental results. At high pressures, structural phase transition from bct structure (chalcopyrite) to cubic structure (rock salt) is observed. The pressure induced structural phase transitions for CuAlS2, CuAlSe2, and CuAlTe2 are observed at 18.01, 14.4 and 8.29 GPa, respectively. Band structures at normal as well as for high-pressure phases have been calculated. The energy band gaps for the above compounds have been calculated as a function of pressure, which indicates the metallic character of these compounds at high-pressure fcc phase. There is a large downshift in band gaps due to hybridatization of the noble-metal d levels with p levels of the other atoms. q 2005 Elsevier Ltd. All rights reserved. Keywords: A. Semiconductors; C. High pressure; D. Electronic structure; D. Phase transitions; D. Equation-of-state
1. Introduction I–III–IV2 chalcopyrite semiconductors have attracted the attention of the physicists due to their wide technological applications. These semiconductors are used in photovoltaic optical detectors, solar cells, and light emitting diodes or in nonlinear optics. High-pressure studies of these chalcopyrite semiconductors have attracted considerable attention due to their phase transition and electronic properties. The original volume of the materials is reduced to their fraction of volume under high pressure. The inter-atomic distance decreases due to reduction in volume. Due to decrease in inter-atomic distance, there are significant changes in bonding, structures and properties. Under pressure, the tetrahedral coordination of the compounds undergoes transformation to a denser cubic structure [1] with octahedral coordination. This transition is caused by the necessity of the relatively open tetrahedral structure to become more closely packed under compression. This transition is similar in nature to the corresponding IV–III–V and II–IV families. Several * Corresponding author. E-mail address: [email protected] (B. Palanivel).
0022-3697/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2005.08.092
experimental studies [2–4] have been carried out on the electronic, electrical and optical properties of CuAlS2 and CuAlSe2 at ambient pressure. Single- crystalline samples of CuAlS2 and CuAlSe2 are grown by chemical vapor transport method by Roa et al. [4] and a pressure has been determined using linear ruby scale. However, a very limited number of studies on structural phase transitions under pressure have been performed [5,6] in which the bulk modulus of CuAlS2 have been reported. Grima Gallardo [7] estimated the isothermal bulk modulus of ABC2 semiconductors through semi-empirical models. Roa et al. [8] performed X-ray diffraction studies for CuAlS2 and CuAlSe2 under high pressure and determined the phase transition from chalcopyrite to cubic phase for CuAlSe2. Due to less number of experimental points it was not possible to determine reliable parameters for the high-pressure phase of CuAlS2. Using EDXRD studies Ravhi et al. [9] investigated similar phase transition under high pressure for CuAlS2 and CuAlSe2. Alonso et al. [10] studied the optical properties of CuAlSe2 at room temperature using spectroscopic ellipsometry technique. The energies are assigned to certain electronic interband transition by comparison with the existing band structure calculation. Using Pseudopotential calculation, Lazewski et al. [11] studied the structural, electronic, dynamical and elastic properties of similar chalcopyrite compounds. Using
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spectroscopic ellipsometry, Alonso et al. [12] calculated the complex dielectric tensor components of the similar type chalcopyrites like CuInSe2, CuInS2, CuGaSe2, and CuGaS2 and compared the band structure results with the earlier data. Early electronic structure calculations reveal that these compounds are direct band gap semiconductors. However, electronic behavior of these materials is not known under pressure. In order to understand the electronic behavior of these compounds at ambient as well as at high pressure phases, we carried out full fledged theoretical calculations of these compounds using TB-LMTO method. The present work deals with the electronic and structural properties of CuAlX2 (XZS, Se, Te). The stability of highpressure phases [13] of the above semiconductors has been studied. In the present work the ground state properties and high-pressure behavior of CuAlX2 have been studied by means of self-consistent TBLMTO [14–18] method. The CuAlX2 chalcopyrite semiconductors undergo transformation from bct phase of space group I4_2d to cubic phase of space group Fm3m. The electronic energy band gaps for bct structure of CuAlS2, CuAlSe2 and CuAlTe2 are estimated as a function of pressure calculated using density of states. In the following sections, we described the method of calculations, obtained results with discussion and conclusion. 2. Methodology The energy band structure and electronic properties of the chalcopyrite CuAlX2 are obtained using TB-LMTO method within atomic sphere approximations [14–16]. The calculations are performed within the framework of local density approximation (LDA). The von Barth and Hedin exchange correlation potential [19] is employed in the present calculations. The relativistic mass–velocity variation is taken into account. However, the spin-orbit coupling is neglected. In this work, for all the three compounds 3p, 4s, 4p orbitals of Cu, 3s, 3p, 3d orbitals of Al, 3s, 3p, 3d orbitals of S, 4s, 4p, 4d orbitals of Se and 5s, 5p, 5d orbitals of Te are treated as valence states. In bct structure empty spheres are included to obtain close packing, which is necessary to obtain accurate results. The calculations are performed on a grid of 144 k points in the entire Brillouin Zone of bct. The equilibrium lattice parameters for the bct of CuAlS2, CuAlSe2 and CuAlTe2 are calculated from fitted total energies. In the case of fcc structure, calculations are carried out with 64 k points in the entire Brillouin Zone. The lattice parameter for the fcc structure of the above compounds is calculated from the fitted total energies. The densities of states are calculated by the tetrahedron method. The present study also indicates the metallic character of these compounds at highpressure fcc structure.
Table 1 Calculated equilibrium lattice parameters and bulk modulus for compounds in bct structure with the available values Compounds
˚) a (A
˚) c (A
Bulk modulus (GPa)
CuAlS2
5.313(5.313a, 5.33b, 5.31c) 5.6099 (5.610a, 5.61b, 5.606c) 6.0618 (5.964c)
10.4299(10.430a, 10.536b, 10.42c) 10.9578 (10.958a, 10.90b 10.90c) 11.9733 (11.78c)
82.35 (99a)
CuAlSe2 CuAlTe2 a b c
71.15 (85a, 85b) 52.72
Ref. [8]. Ref. [9]. Experimental values in Ref. [20].
Table 2 Calculated cell volume and bulk modulus for the compounds in high pressure fcc phase Compounds
Cell volume (a.u.)
Bulk modulus (GPa)
CuAlS2 CuAlSe2 CuAlTe2
397.371 461.906 (543.402)a 565.528
109.27 96.04 (50G3)a 73.61
a
Ref. [8].
equal to 0.27 for S, 0.26 for Se and 0.25 for Te [20]. The average Wigner–Seitz radius was scaled so that the total volume of the sphere is equal to the equilibrium volume of the primitive cell. For bct structure two empty spheres are included for close packing. The percentage of overlapping is w8.7– 8.2% for the above mentioned compounds in bct structure. For bct structure, the variation in c/a ratio has been estimated using total energy calculations. At ambient conditions, the calculated c/a ratio for CuAlS2, CuAlSe2 and CuAlTe2 are 2.0, 1.98 and 1.99, respectively. It is well known that (2Kc/a) measures the tetragonal distortion. Present study reveals that the rate of change in c/a with respect to pressure is very low. Hence, experimental c/a ratios for these compounds have been adopted in the present calculation. In the case of fcc structure, the position of Cu is at 0, 0, 0, for Al is at 0.5, 0.5, 0.5 and for X is
3. Results and discussion The present work deals with the electronic structure, phase stability and metallisation of the chalcopyrite CuAlX2 (XZS, Se, Te) compounds. For bct structure, the atomic positions are: CuZ0, 0, 0, AlZ0, 0, 0.5 and for XZu, 0.25, 0.125 where u is
Fig. 1. Total energy curve of CuAlS2.
V. Jayalakshmi et al. / Journal of Physics and Chemistry of Solids 67 (2006) 669–674
Fig. 2. Total energy curve of CuAlSe2.
at 0.25, 0.25, 0.25. The percentage of overlapping for fcc structure is w8.2–8.3%. The total energy is calculated by varying volume from 1.2 to 0.70 V0 where V0ZVexp The calculated total energies as a function of volume are fitted with Birch Murnaghan’s equation of state to obtain the equilibrium lattice parameter, bulk modulus and pressure–volume relation. The calculated lattice parameters and bulk modulus for the bct phase of all the three compounds are compared with the available experimental values [8,20], which are given in Table 1. Calculated lattice parameters for bct structure of CuAlS2 and CuAlSe2 are in good agreement with experimental values. However, in the case of CuAlTe2, calculated lattice parameters are slightly more than the available experimental data. The cell volume for the highpressure fcc structure with its bulk modulus is given in Table 2. Figs. 1–3 represent the graph plotted between the fitted total energy and relative volume for CuAlS2, CuAlSe2 and CuAlTe2. At ambient condition, all the three compounds are stable in the bct structure and undergo transition from bct structure to fcc structure under the application of high pressure. The structural
Fig. 3. Total energy curve of CuAlTe2.
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Fig. 4. Pressure dependence of relative volume for CuAlS2 with experimental data.
transition from bct to fcc structure occurs nearly at 0.8 V/V0 for CuAlS2 and 0.8 V/V0 for CuAlSe2 and 0.85 V/V0 for CuAlTe2. It is found that the calculated lattice parameter for bct and fcc structure increases from CuAlS2 to CuAlTe2. However, the calculated bulk modulus of CuAlX2 shows a linear decrease from CuAlS2 to CuAlTe2, i.e. from the lower to the higher atomic number of X atom. From the values of bulk modulus, it suggests that CuAlTe2 is more easily compressible than the other two compounds. The pressure at which the enthalpies are same for both the structures are taken as calculated transition pressure. Equation of state (EOS) is calculated with the help of fitted total energy values. Fig. 4 shows the EOS for CuAlS2 with experimental data [8], which is having errors of G0.1 cm3/mol in volume and G3 GPa in Bulk modulus. While comparing the calculated EOS with the experimental data at experimental volume V0, it is found that calculated pressure is more than the experimental pressure by 0.9 GPa. In order to compare the results with
Fig. 5. Pressure dependence of relative volume for CuAlSe2 with experimental data.
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Fig. 6. Pressure dependence of relative volume for CuAlTe2.
experimental data with out any numerical uncertainties, the deviation in pressure (i.e. 0.9 GPa) at V0 has been subtracted from the calculated pressure values of BCT phase for all reduced volumes. It can be seen from the Fig. 4 that the calculated slopes at lower pressures are in good agreement with experimental data. The deviations at high pressures may be due to the constant pressure correction of 0.9 GPa. From the equation of states, the volume collapse for these compounds is estimated. The high-pressure phase of CuAlS2 is found to occur at w18 GPa. The volume collapse (KDV/V0) per formula unit has been determined as 17.5%, which agrees with the earlier work [8]. Fig. 5 represents the EOS for CuAlSe2 with experimental data [8], which is having errors of G0.1 cm3/mol in volume and G2 GPa in Bulk modulus. When comparing the calculated EOS with the experimental data, it is found that calculated pressure at V0 deviates from the experimental pressure by 0.18 GPa. For the sake of comparison, the deviation in pressure (i.e. 0.18 GPa) has been subtracted from all the calculated pressure for different reduced volumes for BCT phase. In the
case of CuAlSe2 phase transition occurs at 14.4 GPa with a volume collapse of 13%, which agrees with experimental observations [8]. In the case of CuAlTe2, calculated lattice parameters at ambient pressure are slightly more than the available experimental data. Since, experimental EOS is not available, the EOS for CuAlTe2 is drawn by considering the calculated V0 instead of experimental volume as reference (Fig. 6). For CuAlTe2, the high-pressure structure appears at 8.29 GPa with a volume collapse of about 20%. These values are in need of experimental data for comparison. The band structures for CuAlS2, CuAlSe2 and CuAlTe2 have been computed for the bct phase at equilibrium volume. It is well known that energy band structures of II– IV–V2 compounds are similar to that of III–V compounds. However energy band structure of ternary analogs of II–IV compounds are different from that of I–III–IV2 compounds. This is mainly due to the difference of uppermost valence band in I–III–VI 2 compounds from those of II–VI compounds. The calculated band structures for CuAlX2 compounds in bct structure along the symmetry directions Z–G–X are presented in Fig. 7. The overall band profiles are found to be the same for all the three compounds. The valence band maximum (VBM) occurs at G in the direction of Z–G and the conduction band minimum (CBM) is at G indicating that the chalcopyrite semiconductors CuAlS2, CuAlSe2 and CuAlTe2 possess direct band gap semiconductors. The uppermost valence bands are derived from a combination of the p-orbital of the anion with the d-orbital of the noble metal, while the conduction band is derived from the s-states of the cation. Fig. 8 represents the band structure plot along L–G–X directions for the fcc structure, which shows the metallic nature of the compounds. The density of states for both the bct and fcc structures is calculated by tetrahedron method. The valence bands of the compounds results from a hybridization of the noble-metal d levels with p levels on the other atoms. The calculated density of states shows a well-developed gap at EF for bct structure.
Fig. 7. Band structure profiles for bct phase of CuAlS2, CuASe2 and CuAlTe2.
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Fig. 8. Band structure profiles for fcc phase of CuAlS2, CuAlSe2 and CuAlTe2.
There is a large downshift in the energy gaps relative to the binary analogs. The band gaps are underestimated due to LDA, as it does not clearly predict the excited state of the conduction band. The band gap values for the three compounds with experimental data are given in the Table 3. Domashevskaya et al. [21] had reported that the excluding of Cu 3d electrons as valence states, led to overestimation of the band gaps for similar other semiconductors. Shay et al. [22] had predicted that without dstates for CuInSe2, band structure shows an indirect energy band gap. The indirect energy band gap is a surprising result. This motivated us to perform the calculation for the CuAlX2 compounds without considering 3d orbitals as valence states. However, these states are treated as core electrons, which overestimate the band gap values, which agree with the earlier prediction [21]. The calculated band structure values are larger than that of the experimental values and follow the same trend of decreasing magnitude from CuAlS2 to CuAlTe2. The present study reveals that the d-states of noble metals have to be treated as valence states to get the correct nature of the energy band gaps. The calculated density of states of these compounds in fcc structure confirms the metallic nature. The present investigation predict that application of high pressure on these compounds leads to structural phase transition along with semiconductor to metal transition.
Table 3 Band gap for the ABC2 semiconductors with available experimental values Compounds
Band gap (eV)
Experimental value (eV)
CuAlS2 CuAlSe2 CuAlTe2
2.25 1.63 1.5
3.49a 2.67a 2.06a
a
Experimental values in Ref. [20].
4. Conclusion In the present study, the ground state properties and high-pressure behavior of CuAlX2 (XZS, Se, Te) are studied. The bct structure of these chalcopyrite compounds changes to fcc under pressure. In both the structures, the lattice parameter increases from S to Te. This increase of lattice parameter from S to Te agrees well with the available experimental results. At the same time, the bulk modulus decreases from S to Te in both the structure. The calculated lattice parameter and bulk modulus of fcc structure of CuAlS2 and CuAlTe2 need experimental data for comparison. From the total energy and relative volume curves, it has been found that the fcc structure becomes a stable phase at nearly about 0.8 V/V0 for CuAlS2 and 0.8 V/V0 for CuAlSe2 and 0.85 V/V0 for CuAlTe2. The equation of state for CuAlS2, CuAlSe2 and CuAlTe2 is calculated. Band structures for both the structures of all the three compounds are calculated. In order to study the importance of 3d orbital, the band structures of these compounds in bct structure have been calculated with 3d electrons as valence and also without considering 3d orbitals of the copper as valence states. When 3d orbitals are included, DOS shows large downshifts in the energy gaps relative to the binary analogs. The bct phase of CuAlX2 shows direct band gap. The band gap for all the three compounds are calculated from the density of states, which shows the decreasing trend from CuAlS2 to CuAlTe2. The calculated band structure of these compounds in fcc structure confirms the metallic nature. Acknowledgements The authors are thankful to Professor O.K. Anderson and Professor O. Jepson, Max Planck Institute, Stuttgart, Germany for providing TB-LMTO code.
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References [1] A. Werner, D.H. Hocheimer, A. Jayaraman, Phys. Rev. B 23 (1981) 3836. [2] S. Chichibu, M. Shishikura, J. Ino, S. Matsumoto, J. Appl. Phys. 70 (1991) 3. [3] A.M. Andriesh, H.N. Syrbu, S.M. Iovu, E.V. Tazlavan, Phys. Status Solidi (b) 187 (1995) 83. [4] L. Roa, P. Grima, J. Gonzalez, C.J. Chervin, P.J. Itie, A. Chevy, Cryst. Res. Technol. 31 (1996) 49. [5] L. Roa, C.J. Chervin, A. Chevy, M. Davila, P. Grima, J. Gonzalez, Phys. Status Solidi (b) 198 (1996) 99. [6] M. Bettini, B.W. Holzapfel, Solid State Commun. 16 (1975) 27. [7] P. Grima Gallardo, Phys. Status Solidi (b) 182 (1994) K67. [8] L. Roa, C.J. Chervin, P.J. Itie, A. Polian, M. Gauthier, A. Chevy, Phys. Status Solidi (b) 211 (1999) 455. [9] Ravhi S. Kumar, A. Sekar, N. Victor Jaya, S. Natarajan, S. Chichibu, J. Alloys Compd. 312 (2000) 4–8. [10] M.I. Alonso, J. Pascual, M. Garriga, Y. Kilkuno, N. Yamamoto, K. Wakita, J. Appl. Phys. 88 (2000) 1923.
[11] J. Lazewski, T.P. Jochym, K. Parlinski, J. Chem. Phys. 117 (2002) 2726. [12] M.I. Alonso, K. Wakita, J. Pascual, M. Garriga, N. Yamamoto, Phys. Rev. B 63 (2001) 075203. [13] B. Palanivel, S.R. Rao, K.B. Godwal, K.S. Sikka, J. Phys. Condens. Matter 4 (2000) 8831. [14] O.K. Anderson, O. Jepson, Phys. Rev. Lett. 53 (1984) 2871. [15] O.K. Anderson, Phys. Rev. B 12 (1975) 3060. [16] H.L. Skriver, The LMTo Method, Springer, Berlin, 1984. [17] B. Palanivel, in: Proceedings of the International Conference on High Pressure Science and Technology, NPL, New Delhi, 2001. [18] V. Jayalakshmi, R. Murugan, B. Palanivel, J. Alloys Compd. 388 (2004) 19. [19] U. von Barth, L. Hedin, J. Phys. 5 (1972) 1629. [20] J.E. Jaffe, A. Zunger, Phys. Rev. B 29 (1984) 1882. [21] P.E. Domashevskaya, N.L. Marshakove, A.V. Terekhov, N.A. Lukin, A.Ya. Ugai, I.V. Nefedov, V.Ya. Salyn, Phys. Status Solidi (b) 106 (1981) 429. [22] L.J. Shay, B. Tell, M.H. Kasper, M.L. Schiavone, Phys. Rev. B 7 (1973) 4485.
Electronic structure and structural phase stability of CuAlX2 (XZS, Se, Te) under pressure Venkatachalam Jayalakshmi, Subramanian Davapriya, Ramaswamy Murugan, Balan Palanivel * Department of Physics, Pondicherry Engineering College, Pondicherry 605 014, India Received 17 March 2005; received in revised form 10 August 2005; accepted 10 August 2005
Abstract The electronic and structural properties of chalcopyrite compounds CuAlX2 (XZS, Se, Te) have been studied using the first principle selfconsistent Tight Binding Linear Muffin-Tin Orbital (TBLMTO) method within the local density approximation. The present study deals with the ground state properties, structural phase transition, equations of state and pressure dependence of band gap of CuAlX2 (S, Se, Te) compounds. Electronic structure and hence total energies of these compounds have been computed as a function of reduced volume. The calculated lattice parameters are in good agreement with the available experimental results. At high pressures, structural phase transition from bct structure (chalcopyrite) to cubic structure (rock salt) is observed. The pressure induced structural phase transitions for CuAlS2, CuAlSe2, and CuAlTe2 are observed at 18.01, 14.4 and 8.29 GPa, respectively. Band structures at normal as well as for high-pressure phases have been calculated. The energy band gaps for the above compounds have been calculated as a function of pressure, which indicates the metallic character of these compounds at high-pressure fcc phase. There is a large downshift in band gaps due to hybridatization of the noble-metal d levels with p levels of the other atoms. q 2005 Elsevier Ltd. All rights reserved. Keywords: A. Semiconductors; C. High pressure; D. Electronic structure; D. Phase transitions; D. Equation-of-state
1. Introduction I–III–IV2 chalcopyrite semiconductors have attracted the attention of the physicists due to their wide technological applications. These semiconductors are used in photovoltaic optical detectors, solar cells, and light emitting diodes or in nonlinear optics. High-pressure studies of these chalcopyrite semiconductors have attracted considerable attention due to their phase transition and electronic properties. The original volume of the materials is reduced to their fraction of volume under high pressure. The inter-atomic distance decreases due to reduction in volume. Due to decrease in inter-atomic distance, there are significant changes in bonding, structures and properties. Under pressure, the tetrahedral coordination of the compounds undergoes transformation to a denser cubic structure [1] with octahedral coordination. This transition is caused by the necessity of the relatively open tetrahedral structure to become more closely packed under compression. This transition is similar in nature to the corresponding IV–III–V and II–IV families. Several * Corresponding author. E-mail address: [email protected] (B. Palanivel).
0022-3697/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2005.08.092
experimental studies [2–4] have been carried out on the electronic, electrical and optical properties of CuAlS2 and CuAlSe2 at ambient pressure. Single- crystalline samples of CuAlS2 and CuAlSe2 are grown by chemical vapor transport method by Roa et al. [4] and a pressure has been determined using linear ruby scale. However, a very limited number of studies on structural phase transitions under pressure have been performed [5,6] in which the bulk modulus of CuAlS2 have been reported. Grima Gallardo [7] estimated the isothermal bulk modulus of ABC2 semiconductors through semi-empirical models. Roa et al. [8] performed X-ray diffraction studies for CuAlS2 and CuAlSe2 under high pressure and determined the phase transition from chalcopyrite to cubic phase for CuAlSe2. Due to less number of experimental points it was not possible to determine reliable parameters for the high-pressure phase of CuAlS2. Using EDXRD studies Ravhi et al. [9] investigated similar phase transition under high pressure for CuAlS2 and CuAlSe2. Alonso et al. [10] studied the optical properties of CuAlSe2 at room temperature using spectroscopic ellipsometry technique. The energies are assigned to certain electronic interband transition by comparison with the existing band structure calculation. Using Pseudopotential calculation, Lazewski et al. [11] studied the structural, electronic, dynamical and elastic properties of similar chalcopyrite compounds. Using
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spectroscopic ellipsometry, Alonso et al. [12] calculated the complex dielectric tensor components of the similar type chalcopyrites like CuInSe2, CuInS2, CuGaSe2, and CuGaS2 and compared the band structure results with the earlier data. Early electronic structure calculations reveal that these compounds are direct band gap semiconductors. However, electronic behavior of these materials is not known under pressure. In order to understand the electronic behavior of these compounds at ambient as well as at high pressure phases, we carried out full fledged theoretical calculations of these compounds using TB-LMTO method. The present work deals with the electronic and structural properties of CuAlX2 (XZS, Se, Te). The stability of highpressure phases [13] of the above semiconductors has been studied. In the present work the ground state properties and high-pressure behavior of CuAlX2 have been studied by means of self-consistent TBLMTO [14–18] method. The CuAlX2 chalcopyrite semiconductors undergo transformation from bct phase of space group I4_2d to cubic phase of space group Fm3m. The electronic energy band gaps for bct structure of CuAlS2, CuAlSe2 and CuAlTe2 are estimated as a function of pressure calculated using density of states. In the following sections, we described the method of calculations, obtained results with discussion and conclusion. 2. Methodology The energy band structure and electronic properties of the chalcopyrite CuAlX2 are obtained using TB-LMTO method within atomic sphere approximations [14–16]. The calculations are performed within the framework of local density approximation (LDA). The von Barth and Hedin exchange correlation potential [19] is employed in the present calculations. The relativistic mass–velocity variation is taken into account. However, the spin-orbit coupling is neglected. In this work, for all the three compounds 3p, 4s, 4p orbitals of Cu, 3s, 3p, 3d orbitals of Al, 3s, 3p, 3d orbitals of S, 4s, 4p, 4d orbitals of Se and 5s, 5p, 5d orbitals of Te are treated as valence states. In bct structure empty spheres are included to obtain close packing, which is necessary to obtain accurate results. The calculations are performed on a grid of 144 k points in the entire Brillouin Zone of bct. The equilibrium lattice parameters for the bct of CuAlS2, CuAlSe2 and CuAlTe2 are calculated from fitted total energies. In the case of fcc structure, calculations are carried out with 64 k points in the entire Brillouin Zone. The lattice parameter for the fcc structure of the above compounds is calculated from the fitted total energies. The densities of states are calculated by the tetrahedron method. The present study also indicates the metallic character of these compounds at highpressure fcc structure.
Table 1 Calculated equilibrium lattice parameters and bulk modulus for compounds in bct structure with the available values Compounds
˚) a (A
˚) c (A
Bulk modulus (GPa)
CuAlS2
5.313(5.313a, 5.33b, 5.31c) 5.6099 (5.610a, 5.61b, 5.606c) 6.0618 (5.964c)
10.4299(10.430a, 10.536b, 10.42c) 10.9578 (10.958a, 10.90b 10.90c) 11.9733 (11.78c)
82.35 (99a)
CuAlSe2 CuAlTe2 a b c
71.15 (85a, 85b) 52.72
Ref. [8]. Ref. [9]. Experimental values in Ref. [20].
Table 2 Calculated cell volume and bulk modulus for the compounds in high pressure fcc phase Compounds
Cell volume (a.u.)
Bulk modulus (GPa)
CuAlS2 CuAlSe2 CuAlTe2
397.371 461.906 (543.402)a 565.528
109.27 96.04 (50G3)a 73.61
a
Ref. [8].
equal to 0.27 for S, 0.26 for Se and 0.25 for Te [20]. The average Wigner–Seitz radius was scaled so that the total volume of the sphere is equal to the equilibrium volume of the primitive cell. For bct structure two empty spheres are included for close packing. The percentage of overlapping is w8.7– 8.2% for the above mentioned compounds in bct structure. For bct structure, the variation in c/a ratio has been estimated using total energy calculations. At ambient conditions, the calculated c/a ratio for CuAlS2, CuAlSe2 and CuAlTe2 are 2.0, 1.98 and 1.99, respectively. It is well known that (2Kc/a) measures the tetragonal distortion. Present study reveals that the rate of change in c/a with respect to pressure is very low. Hence, experimental c/a ratios for these compounds have been adopted in the present calculation. In the case of fcc structure, the position of Cu is at 0, 0, 0, for Al is at 0.5, 0.5, 0.5 and for X is
3. Results and discussion The present work deals with the electronic structure, phase stability and metallisation of the chalcopyrite CuAlX2 (XZS, Se, Te) compounds. For bct structure, the atomic positions are: CuZ0, 0, 0, AlZ0, 0, 0.5 and for XZu, 0.25, 0.125 where u is
Fig. 1. Total energy curve of CuAlS2.
V. Jayalakshmi et al. / Journal of Physics and Chemistry of Solids 67 (2006) 669–674
Fig. 2. Total energy curve of CuAlSe2.
at 0.25, 0.25, 0.25. The percentage of overlapping for fcc structure is w8.2–8.3%. The total energy is calculated by varying volume from 1.2 to 0.70 V0 where V0ZVexp The calculated total energies as a function of volume are fitted with Birch Murnaghan’s equation of state to obtain the equilibrium lattice parameter, bulk modulus and pressure–volume relation. The calculated lattice parameters and bulk modulus for the bct phase of all the three compounds are compared with the available experimental values [8,20], which are given in Table 1. Calculated lattice parameters for bct structure of CuAlS2 and CuAlSe2 are in good agreement with experimental values. However, in the case of CuAlTe2, calculated lattice parameters are slightly more than the available experimental data. The cell volume for the highpressure fcc structure with its bulk modulus is given in Table 2. Figs. 1–3 represent the graph plotted between the fitted total energy and relative volume for CuAlS2, CuAlSe2 and CuAlTe2. At ambient condition, all the three compounds are stable in the bct structure and undergo transition from bct structure to fcc structure under the application of high pressure. The structural
Fig. 3. Total energy curve of CuAlTe2.
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Fig. 4. Pressure dependence of relative volume for CuAlS2 with experimental data.
transition from bct to fcc structure occurs nearly at 0.8 V/V0 for CuAlS2 and 0.8 V/V0 for CuAlSe2 and 0.85 V/V0 for CuAlTe2. It is found that the calculated lattice parameter for bct and fcc structure increases from CuAlS2 to CuAlTe2. However, the calculated bulk modulus of CuAlX2 shows a linear decrease from CuAlS2 to CuAlTe2, i.e. from the lower to the higher atomic number of X atom. From the values of bulk modulus, it suggests that CuAlTe2 is more easily compressible than the other two compounds. The pressure at which the enthalpies are same for both the structures are taken as calculated transition pressure. Equation of state (EOS) is calculated with the help of fitted total energy values. Fig. 4 shows the EOS for CuAlS2 with experimental data [8], which is having errors of G0.1 cm3/mol in volume and G3 GPa in Bulk modulus. While comparing the calculated EOS with the experimental data at experimental volume V0, it is found that calculated pressure is more than the experimental pressure by 0.9 GPa. In order to compare the results with
Fig. 5. Pressure dependence of relative volume for CuAlSe2 with experimental data.
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Fig. 6. Pressure dependence of relative volume for CuAlTe2.
experimental data with out any numerical uncertainties, the deviation in pressure (i.e. 0.9 GPa) at V0 has been subtracted from the calculated pressure values of BCT phase for all reduced volumes. It can be seen from the Fig. 4 that the calculated slopes at lower pressures are in good agreement with experimental data. The deviations at high pressures may be due to the constant pressure correction of 0.9 GPa. From the equation of states, the volume collapse for these compounds is estimated. The high-pressure phase of CuAlS2 is found to occur at w18 GPa. The volume collapse (KDV/V0) per formula unit has been determined as 17.5%, which agrees with the earlier work [8]. Fig. 5 represents the EOS for CuAlSe2 with experimental data [8], which is having errors of G0.1 cm3/mol in volume and G2 GPa in Bulk modulus. When comparing the calculated EOS with the experimental data, it is found that calculated pressure at V0 deviates from the experimental pressure by 0.18 GPa. For the sake of comparison, the deviation in pressure (i.e. 0.18 GPa) has been subtracted from all the calculated pressure for different reduced volumes for BCT phase. In the
case of CuAlSe2 phase transition occurs at 14.4 GPa with a volume collapse of 13%, which agrees with experimental observations [8]. In the case of CuAlTe2, calculated lattice parameters at ambient pressure are slightly more than the available experimental data. Since, experimental EOS is not available, the EOS for CuAlTe2 is drawn by considering the calculated V0 instead of experimental volume as reference (Fig. 6). For CuAlTe2, the high-pressure structure appears at 8.29 GPa with a volume collapse of about 20%. These values are in need of experimental data for comparison. The band structures for CuAlS2, CuAlSe2 and CuAlTe2 have been computed for the bct phase at equilibrium volume. It is well known that energy band structures of II– IV–V2 compounds are similar to that of III–V compounds. However energy band structure of ternary analogs of II–IV compounds are different from that of I–III–IV2 compounds. This is mainly due to the difference of uppermost valence band in I–III–VI 2 compounds from those of II–VI compounds. The calculated band structures for CuAlX2 compounds in bct structure along the symmetry directions Z–G–X are presented in Fig. 7. The overall band profiles are found to be the same for all the three compounds. The valence band maximum (VBM) occurs at G in the direction of Z–G and the conduction band minimum (CBM) is at G indicating that the chalcopyrite semiconductors CuAlS2, CuAlSe2 and CuAlTe2 possess direct band gap semiconductors. The uppermost valence bands are derived from a combination of the p-orbital of the anion with the d-orbital of the noble metal, while the conduction band is derived from the s-states of the cation. Fig. 8 represents the band structure plot along L–G–X directions for the fcc structure, which shows the metallic nature of the compounds. The density of states for both the bct and fcc structures is calculated by tetrahedron method. The valence bands of the compounds results from a hybridization of the noble-metal d levels with p levels on the other atoms. The calculated density of states shows a well-developed gap at EF for bct structure.
Fig. 7. Band structure profiles for bct phase of CuAlS2, CuASe2 and CuAlTe2.
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Fig. 8. Band structure profiles for fcc phase of CuAlS2, CuAlSe2 and CuAlTe2.
There is a large downshift in the energy gaps relative to the binary analogs. The band gaps are underestimated due to LDA, as it does not clearly predict the excited state of the conduction band. The band gap values for the three compounds with experimental data are given in the Table 3. Domashevskaya et al. [21] had reported that the excluding of Cu 3d electrons as valence states, led to overestimation of the band gaps for similar other semiconductors. Shay et al. [22] had predicted that without dstates for CuInSe2, band structure shows an indirect energy band gap. The indirect energy band gap is a surprising result. This motivated us to perform the calculation for the CuAlX2 compounds without considering 3d orbitals as valence states. However, these states are treated as core electrons, which overestimate the band gap values, which agree with the earlier prediction [21]. The calculated band structure values are larger than that of the experimental values and follow the same trend of decreasing magnitude from CuAlS2 to CuAlTe2. The present study reveals that the d-states of noble metals have to be treated as valence states to get the correct nature of the energy band gaps. The calculated density of states of these compounds in fcc structure confirms the metallic nature. The present investigation predict that application of high pressure on these compounds leads to structural phase transition along with semiconductor to metal transition.
Table 3 Band gap for the ABC2 semiconductors with available experimental values Compounds
Band gap (eV)
Experimental value (eV)
CuAlS2 CuAlSe2 CuAlTe2
2.25 1.63 1.5
3.49a 2.67a 2.06a
a
Experimental values in Ref. [20].
4. Conclusion In the present study, the ground state properties and high-pressure behavior of CuAlX2 (XZS, Se, Te) are studied. The bct structure of these chalcopyrite compounds changes to fcc under pressure. In both the structures, the lattice parameter increases from S to Te. This increase of lattice parameter from S to Te agrees well with the available experimental results. At the same time, the bulk modulus decreases from S to Te in both the structure. The calculated lattice parameter and bulk modulus of fcc structure of CuAlS2 and CuAlTe2 need experimental data for comparison. From the total energy and relative volume curves, it has been found that the fcc structure becomes a stable phase at nearly about 0.8 V/V0 for CuAlS2 and 0.8 V/V0 for CuAlSe2 and 0.85 V/V0 for CuAlTe2. The equation of state for CuAlS2, CuAlSe2 and CuAlTe2 is calculated. Band structures for both the structures of all the three compounds are calculated. In order to study the importance of 3d orbital, the band structures of these compounds in bct structure have been calculated with 3d electrons as valence and also without considering 3d orbitals of the copper as valence states. When 3d orbitals are included, DOS shows large downshifts in the energy gaps relative to the binary analogs. The bct phase of CuAlX2 shows direct band gap. The band gap for all the three compounds are calculated from the density of states, which shows the decreasing trend from CuAlS2 to CuAlTe2. The calculated band structure of these compounds in fcc structure confirms the metallic nature. Acknowledgements The authors are thankful to Professor O.K. Anderson and Professor O. Jepson, Max Planck Institute, Stuttgart, Germany for providing TB-LMTO code.
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References [1] A. Werner, D.H. Hocheimer, A. Jayaraman, Phys. Rev. B 23 (1981) 3836. [2] S. Chichibu, M. Shishikura, J. Ino, S. Matsumoto, J. Appl. Phys. 70 (1991) 3. [3] A.M. Andriesh, H.N. Syrbu, S.M. Iovu, E.V. Tazlavan, Phys. Status Solidi (b) 187 (1995) 83. [4] L. Roa, P. Grima, J. Gonzalez, C.J. Chervin, P.J. Itie, A. Chevy, Cryst. Res. Technol. 31 (1996) 49. [5] L. Roa, C.J. Chervin, A. Chevy, M. Davila, P. Grima, J. Gonzalez, Phys. Status Solidi (b) 198 (1996) 99. [6] M. Bettini, B.W. Holzapfel, Solid State Commun. 16 (1975) 27. [7] P. Grima Gallardo, Phys. Status Solidi (b) 182 (1994) K67. [8] L. Roa, C.J. Chervin, P.J. Itie, A. Polian, M. Gauthier, A. Chevy, Phys. Status Solidi (b) 211 (1999) 455. [9] Ravhi S. Kumar, A. Sekar, N. Victor Jaya, S. Natarajan, S. Chichibu, J. Alloys Compd. 312 (2000) 4–8. [10] M.I. Alonso, J. Pascual, M. Garriga, Y. Kilkuno, N. Yamamoto, K. Wakita, J. Appl. Phys. 88 (2000) 1923.
[11] J. Lazewski, T.P. Jochym, K. Parlinski, J. Chem. Phys. 117 (2002) 2726. [12] M.I. Alonso, K. Wakita, J. Pascual, M. Garriga, N. Yamamoto, Phys. Rev. B 63 (2001) 075203. [13] B. Palanivel, S.R. Rao, K.B. Godwal, K.S. Sikka, J. Phys. Condens. Matter 4 (2000) 8831. [14] O.K. Anderson, O. Jepson, Phys. Rev. Lett. 53 (1984) 2871. [15] O.K. Anderson, Phys. Rev. B 12 (1975) 3060. [16] H.L. Skriver, The LMTo Method, Springer, Berlin, 1984. [17] B. Palanivel, in: Proceedings of the International Conference on High Pressure Science and Technology, NPL, New Delhi, 2001. [18] V. Jayalakshmi, R. Murugan, B. Palanivel, J. Alloys Compd. 388 (2004) 19. [19] U. von Barth, L. Hedin, J. Phys. 5 (1972) 1629. [20] J.E. Jaffe, A. Zunger, Phys. Rev. B 29 (1984) 1882. [21] P.E. Domashevskaya, N.L. Marshakove, A.V. Terekhov, N.A. Lukin, A.Ya. Ugai, I.V. Nefedov, V.Ya. Salyn, Phys. Status Solidi (b) 106 (1981) 429. [22] L.J. Shay, B. Tell, M.H. Kasper, M.L. Schiavone, Phys. Rev. B 7 (1973) 4485.