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disordering and electronic structures of II1III2VI4 compounds
Journal of Crystal Growth 214/215 (2000) 452}456
Vacancy ordering/disordering and electronic structures of II III VI compounds M. Ishikawa, T. Nakayama* Department of Physics, Faculty of Science, Chiba University, 1-33 Yayoi, Inage, Chiba 263-8522, Japan
Abstract Electronic structures of II III VI compounds are calculated by the "rst-principles method, for four di!erent vacancy-ordering structures; defect chalcopyrite, defect stannite, pseudocubic and its family. It is shown that the valence-band top is made of dangling bonds of anion atoms around vacancies and its energy position hardly depends on the vacancy ordering. On the other hand, since the lowest conduction band is made the anti-bonding states of cation atoms and the cation-site vacancy acts as a potential barrier for electrons, the band-gap energy remarkably depends on the vacancy ordering. 2000 Elsevier Science B.V. All rights reserved. PACS: 71.20.Nr; 71.55.Ht; 73.20.Dx Keywords: Vacancy ordering; Disorder; Chalcopyrite; Stannite; Electronic structure; Bowing
1. Introduction The ternary chalcopyrite semiconductors and their families are of technological interest as they possess peculiar optical properties such as high photosensitivity and can be used as optoelectronic and solar cell materials [1]. For these reasons, II}IV}V and I}III}VI compounds have been intensively studied so far. Even when the lattice vacancy is incorporated in these materials, such fascinating properties do not disappear and mater-
* Corresponding author. Tel.: #81-43-290-2762; fax:#8143-290-2874. E-mail addresses: masato}[email protected] (M. Ishikawa), [email protected] (T. Nakayama). Present address: Device Design Center, Yokogawa Electronics Corporation, 2-9-31 Nakamachi, Musasino, Tokyo 1808750, Japan.
ials stabilize with a composition such as 䊐 II III VI , where 䊐 is a vacancy [2]. On the other hand, when II}VI compound is epitaxialized on the III}V substrate, 䊐 II III VI compound is often grown as the interface layers having the vacancy-ordered/disordered cation sites [3,4]. This is because the mismatch of valence-electron number between II}VI and III}V, i.e. the heterovalency, can be relaxed by using the freedom of vacancy. In this sense, 䊐 II III VI becomes one of the key mater ials for the heterovalent epitaxy. If we categorize the vacancy, 䊐, into cation atoms, there are three kinds of cations in 䊐 II III VI . When the coordination is limited to the tetrahedral one, according to the cation arrangement, especially according to the vacancy ordering, there are four possible crystal structures [1]. These are called defect chalcopyrite (DC), defect stannite (DS), pseudocubic (PS) and the other
0022-0248/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 0 0 ) 0 0 1 2 8 - 7
M. Ishikawa, T. Nakayama / Journal of Crystal Growth 214/215 (2000) 452}456
(we call this PS ). 䊐CdGa Se , b-䊐HgCu I , and 䊐CdIn Se are, respectively, the representatives of the former three structures. Physical properties of individual materials have been studied and more than two structures sometimes coexist in one crystal depending on growth condition. However, there have been no systematic studies for the fundamental electronic properties, especially the di!erence that exists among the four structures. In this work, we investigate electronic structures of 䊐 II III VI compounds having four di!erent vacancy orderings, by using the "rst-principles pseudopotential method in a local density theory, and clarify the e!ect of vacancy ordering/disordering on the electronic structures.
2. Calculational method Electronic structures are calculated by using the "rst-principles pseudopotential method in a local density approximation (LDA), where d electrons of Cd and Zn atoms and the spin}orbit interaction are not included. This is a standard method and the details are described elsewhere [3,5]. Four vacancy-ordering structures are considered. They are defect chalcopyrite (DC) and pseudocubic (PS) with (䊐,III), (II,III), and defect stannite (DS) and the other (PS ) with (䊐,II), (III,III), where the atom kinds in two cation layers along the c direction are denoted in parentheses. Figs. 1(a) and (b) show DC and DS structures, respectively. PS and PS are obtained by arranging the vacancies straight along the c direction.
Fig. 1. Schematic pictures of (a) defect chalcopyrite and (b) defect stannite structures.
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Atoms nearest the vacancy sites show substantial relaxation from the four-coordinated ideal positions. However, since we are interested in the vacancy ordering and such a relaxation merely a!ects electronic structures as a perturbation [4,6], in this work we assume no relaxation and use the lattice constants observed in experiments [7].
3. Results and discussion Fig. 2 shows the calculated band-gap energies of various 䊐 II III VI in four di!erent vacancy ordering structures. It is noted that in all compounds studied the band-gap energy is much larger in DC structure than in the other structures. In order to clarify this feature, we analyze the band structures and the state charge density. Since the electronic structures are similar among DS, PS and PS , hereafter, we concentrate on the di!erence between DC and DS structures by using 䊐CdGa Se as an example. Figs. 3(a) and (b) show the calculated band structures of 䊐CdGa Se in DC and DS structures, respectively. To clarify the band character, the charge density of the valence-band top and the conduction-band bottom states at C are shown in Figs. 4(a)}(c). The valence-band top is located at C and the overall features of valence bands are similar in both structures. The only di!erence is the degeneracy of the valence-band top, double for DS and triple for
Fig. 2. LDA-calculated band-gap energies of various 䊐 II III VI compounds in four di!erent structures; DC, PS , DS and PS.
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M. Ishikawa, T. Nakayama / Journal of Crystal Growth 214/215 (2000) 452}456
Fig. 4. Calculated state charge density. (a) The highest valenceband state and (b) the lowest conduction-band state at C point in defect chalcopyrite structure, and (c) the lowest conductionband state at C in defect stannite structure.
Fig. 3. Calculated band structures of 䊐CdGa Se in (a) defect chalcopyrite and (b) defect stannite structures. CA, CA and CC directions correspond to the a, a and c directions in Fig. 1, respectively.
DC, due to the di!erence of crystal symmetry of I4 (DC) and I4 2 m (DS). As seen in Fig. 4(a), the highest valence band is made of dangling bonds of Se atoms localized around vacancies. Thus, as seen in Figs. 3(a) and (b), its energy position hardly depends on the vacancy ordering and it has small dispersion along every direction. On the other hand, a remarkable di!erence exists between the conduction bands of DC and DS structures. It is noted that the lowest conduction band of DC structure has considerably less width, about 1.7 eV, than that of DS structure, about 2.3 eV. Apparently, this di!erence causes the di!erence of band-gap energies. The origin of such di!erence is explained by considering the cation atom ordering as follows. As seen in Figs. 4(b) and (c), the lowest conduction band is mainly made of the anti-bonding states
of s orbitals of Ga and p orbitals of Se. Remembering that the vacancy is located at cation sites, not only Cd atoms but also the vacancy acts as a potential barrier for the conduction band electrons. Figs. 5(a) and (b) show the cation orderings of DC and DS structures, viewed from three di!erent directions. In these "gures, the Ga atoms are surrounded by dashed lines. One can see that Ga atoms produce arrays along a and a directions in DS structure, while they are limited to one-dimensional array along a in DC structure. Namely, re#ecting the vacancy ordering network, the DS structure produces the two-dimensional Ga-atom conductive network for the conduction electrons, while the DC structure o!ers the one-dimensional one. This is why the remarkable di!erence appears between the conduction bands of DC and DS structures. As shown in the above, both DC and DS structures are quasi-low-dimensional systems for electrons. Thus, similar to ordinary semiconductors, we may expect that disorders such as antisites will strongly localize the electrons and increase the optical transition strength across the fundamental
M. Ishikawa, T. Nakayama / Journal of Crystal Growth 214/215 (2000) 452}456
Fig. 5. Schematic pictures of cation atom arrangement viewed from three di!erent directions, a, a and c. (a) Defect chalcopyrite and (b) defect stannite structures.
band gap [3]. In this work, however, we consider another kind of disorder: the vacancy-array disorder. To study this vacancy disordering, we made the super-unit-cell systems of (DC) (DS) with L \L n"0}4 and calculated their electronic structures. It was found that the energy position of the valence-band top hardly changes with varying n while that of the conduction-band bottom gradually changes. In particular, similar to ordinary alloying compounds, the band-gap energy of (DC) (DS) V \V changes as E "1.0#0.5x!bx(1!x) eV with the bowing parameter of b"0.45 eV. This result indicates that the vacancy acts as one kind of atom for the conduction-band electrons. It is instructive to note the di!erence of electronic structures between the present 䊐 II III VI and another type of vacancy-ordering compounds such as 䊐 Ga Se [4,6]. Although the vacancy localizes the valence- and conduction-band states, the band dispersions are larger in 䊐CdGa Se compared to the case of 䊐Ga Se . This is because the vacancy concentration in 䊐 II III VI is smaller, 25%, than in 䊐 Ga Se , 33%. Finally, we comment on the structural stability of 䊐 II III VI . The present calculations do not consider the atom-position relaxation and thus the elastic energy is not fully taken into account. However, the calculated total energies show some chemical trend. For example, 䊐CdGa Se has the
455
lowest energy in DC structure, while 䊐CdIn Se in PS structure, which is consistent with observations [1]. In previous works studying the stability of 䊐 III VI [4,6,8], we had shown the chemical trend of crystal structures; as increasing the ionicity of compounds, i.e. the electronegativity di!erence between cation and anion, the crystal structure changes from mesoscopic structure of 䊐Ga Te to monoclinic one of 䊐 Ga Se , layered one of 䊐 In Se and defect spinel of 䊐 In S . For the present 䊐 II III VI systems, a sum of observed data shows the similar chemical trend of crystal structure change from DS of 䊐CdGa Se to DC of 䊐CdGa Se , PS of 䊐CdIn Se and spinel of 䊐CdIn S [1]. These have good correspondence to 䊐 III VI systems and might be explained by a similar scenario as 䊐 III VI .
4. Conclusions By the "rst-principles electronic-structure calculations of II III VI compounds in defect chalcopyrite, defect stannite and pseudocubic structures, we have clari"ed the e!ect of vacancy ordering/disordering. It has been shown that the valence-band states are localized around vacancies and their energy positions hardly depend on the vacancy ordering. On the other hand, the cationsite vacancy acts as a potential barrier for the conduction-band electrons and the vacancy ordering sensitively changes their energy positions and the band-gap energy of system.
Acknowledgements This work was supported by JSPS Research for the Future Programs in the Area of Atomic Scale Surface and Interface Dynamics, and JSPSRFTF96R16201. Parts of this work were supported by the Ministry of Education, Science, Sports and Culture, Japan, and Graduate School of Science and Technology, Chiba University. We also thank the Supercomputer Center, Institute for Solid State Physics, University of Tokyo for the use of FACOM VPP500.
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M. Ishikawa, T. Nakayama / Journal of Crystal Growth 214/215 (2000) 452}456
References [1] A. Miller, A. MacKinnon, D. Weaire, Solid State Phys. 36 (1981) 119. [2] L.K. Samanta, D.K. Ghosh, P.S. Ghosh, Phys. Rev. B 39 (1989) 10261. [3] T. Nakayama, M. Ishikawa, J. Phys. Soc. Jpn. 66 (1997) 3887. [4] M. Ishikawa, T. Nakayama, Jpn. J. Appl. Phys. 36 (1997) L1576.
[5] M. Murayama, T. Nakayama, Phys. Rev. B 49 (1994) 4710. [6] M. Ishikawa, T. Nakayama, Jpn. J. Appl. Phys. 37 (1998) L1125. [7] O. Madelung, M. Schulz, H. Weiss (Eds.), Semiconductors, Physics of Ternary Compounds, Landolt-BoK rnstein, New series, Group III, Vol. 17, Part. h, Springer, Berlin, 1985. [8] M. Ishikawa, T. Nakayama, J. Phys. Low Dimensional Structures 11 (1997) 95.
Vacancy ordering/disordering and electronic structures of II III VI compounds M. Ishikawa, T. Nakayama* Department of Physics, Faculty of Science, Chiba University, 1-33 Yayoi, Inage, Chiba 263-8522, Japan
Abstract Electronic structures of II III VI compounds are calculated by the "rst-principles method, for four di!erent vacancy-ordering structures; defect chalcopyrite, defect stannite, pseudocubic and its family. It is shown that the valence-band top is made of dangling bonds of anion atoms around vacancies and its energy position hardly depends on the vacancy ordering. On the other hand, since the lowest conduction band is made the anti-bonding states of cation atoms and the cation-site vacancy acts as a potential barrier for electrons, the band-gap energy remarkably depends on the vacancy ordering. 2000 Elsevier Science B.V. All rights reserved. PACS: 71.20.Nr; 71.55.Ht; 73.20.Dx Keywords: Vacancy ordering; Disorder; Chalcopyrite; Stannite; Electronic structure; Bowing
1. Introduction The ternary chalcopyrite semiconductors and their families are of technological interest as they possess peculiar optical properties such as high photosensitivity and can be used as optoelectronic and solar cell materials [1]. For these reasons, II}IV}V and I}III}VI compounds have been intensively studied so far. Even when the lattice vacancy is incorporated in these materials, such fascinating properties do not disappear and mater-
* Corresponding author. Tel.: #81-43-290-2762; fax:#8143-290-2874. E-mail addresses: masato}[email protected] (M. Ishikawa), [email protected] (T. Nakayama). Present address: Device Design Center, Yokogawa Electronics Corporation, 2-9-31 Nakamachi, Musasino, Tokyo 1808750, Japan.
ials stabilize with a composition such as 䊐 II III VI , where 䊐 is a vacancy [2]. On the other hand, when II}VI compound is epitaxialized on the III}V substrate, 䊐 II III VI compound is often grown as the interface layers having the vacancy-ordered/disordered cation sites [3,4]. This is because the mismatch of valence-electron number between II}VI and III}V, i.e. the heterovalency, can be relaxed by using the freedom of vacancy. In this sense, 䊐 II III VI becomes one of the key mater ials for the heterovalent epitaxy. If we categorize the vacancy, 䊐, into cation atoms, there are three kinds of cations in 䊐 II III VI . When the coordination is limited to the tetrahedral one, according to the cation arrangement, especially according to the vacancy ordering, there are four possible crystal structures [1]. These are called defect chalcopyrite (DC), defect stannite (DS), pseudocubic (PS) and the other
0022-0248/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 0 0 ) 0 0 1 2 8 - 7
M. Ishikawa, T. Nakayama / Journal of Crystal Growth 214/215 (2000) 452}456
(we call this PS ). 䊐CdGa Se , b-䊐HgCu I , and 䊐CdIn Se are, respectively, the representatives of the former three structures. Physical properties of individual materials have been studied and more than two structures sometimes coexist in one crystal depending on growth condition. However, there have been no systematic studies for the fundamental electronic properties, especially the di!erence that exists among the four structures. In this work, we investigate electronic structures of 䊐 II III VI compounds having four di!erent vacancy orderings, by using the "rst-principles pseudopotential method in a local density theory, and clarify the e!ect of vacancy ordering/disordering on the electronic structures.
2. Calculational method Electronic structures are calculated by using the "rst-principles pseudopotential method in a local density approximation (LDA), where d electrons of Cd and Zn atoms and the spin}orbit interaction are not included. This is a standard method and the details are described elsewhere [3,5]. Four vacancy-ordering structures are considered. They are defect chalcopyrite (DC) and pseudocubic (PS) with (䊐,III), (II,III), and defect stannite (DS) and the other (PS ) with (䊐,II), (III,III), where the atom kinds in two cation layers along the c direction are denoted in parentheses. Figs. 1(a) and (b) show DC and DS structures, respectively. PS and PS are obtained by arranging the vacancies straight along the c direction.
Fig. 1. Schematic pictures of (a) defect chalcopyrite and (b) defect stannite structures.
453
Atoms nearest the vacancy sites show substantial relaxation from the four-coordinated ideal positions. However, since we are interested in the vacancy ordering and such a relaxation merely a!ects electronic structures as a perturbation [4,6], in this work we assume no relaxation and use the lattice constants observed in experiments [7].
3. Results and discussion Fig. 2 shows the calculated band-gap energies of various 䊐 II III VI in four di!erent vacancy ordering structures. It is noted that in all compounds studied the band-gap energy is much larger in DC structure than in the other structures. In order to clarify this feature, we analyze the band structures and the state charge density. Since the electronic structures are similar among DS, PS and PS , hereafter, we concentrate on the di!erence between DC and DS structures by using 䊐CdGa Se as an example. Figs. 3(a) and (b) show the calculated band structures of 䊐CdGa Se in DC and DS structures, respectively. To clarify the band character, the charge density of the valence-band top and the conduction-band bottom states at C are shown in Figs. 4(a)}(c). The valence-band top is located at C and the overall features of valence bands are similar in both structures. The only di!erence is the degeneracy of the valence-band top, double for DS and triple for
Fig. 2. LDA-calculated band-gap energies of various 䊐 II III VI compounds in four di!erent structures; DC, PS , DS and PS.
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M. Ishikawa, T. Nakayama / Journal of Crystal Growth 214/215 (2000) 452}456
Fig. 4. Calculated state charge density. (a) The highest valenceband state and (b) the lowest conduction-band state at C point in defect chalcopyrite structure, and (c) the lowest conductionband state at C in defect stannite structure.
Fig. 3. Calculated band structures of 䊐CdGa Se in (a) defect chalcopyrite and (b) defect stannite structures. CA, CA and CC directions correspond to the a, a and c directions in Fig. 1, respectively.
DC, due to the di!erence of crystal symmetry of I4 (DC) and I4 2 m (DS). As seen in Fig. 4(a), the highest valence band is made of dangling bonds of Se atoms localized around vacancies. Thus, as seen in Figs. 3(a) and (b), its energy position hardly depends on the vacancy ordering and it has small dispersion along every direction. On the other hand, a remarkable di!erence exists between the conduction bands of DC and DS structures. It is noted that the lowest conduction band of DC structure has considerably less width, about 1.7 eV, than that of DS structure, about 2.3 eV. Apparently, this di!erence causes the di!erence of band-gap energies. The origin of such di!erence is explained by considering the cation atom ordering as follows. As seen in Figs. 4(b) and (c), the lowest conduction band is mainly made of the anti-bonding states
of s orbitals of Ga and p orbitals of Se. Remembering that the vacancy is located at cation sites, not only Cd atoms but also the vacancy acts as a potential barrier for the conduction band electrons. Figs. 5(a) and (b) show the cation orderings of DC and DS structures, viewed from three di!erent directions. In these "gures, the Ga atoms are surrounded by dashed lines. One can see that Ga atoms produce arrays along a and a directions in DS structure, while they are limited to one-dimensional array along a in DC structure. Namely, re#ecting the vacancy ordering network, the DS structure produces the two-dimensional Ga-atom conductive network for the conduction electrons, while the DC structure o!ers the one-dimensional one. This is why the remarkable di!erence appears between the conduction bands of DC and DS structures. As shown in the above, both DC and DS structures are quasi-low-dimensional systems for electrons. Thus, similar to ordinary semiconductors, we may expect that disorders such as antisites will strongly localize the electrons and increase the optical transition strength across the fundamental
M. Ishikawa, T. Nakayama / Journal of Crystal Growth 214/215 (2000) 452}456
Fig. 5. Schematic pictures of cation atom arrangement viewed from three di!erent directions, a, a and c. (a) Defect chalcopyrite and (b) defect stannite structures.
band gap [3]. In this work, however, we consider another kind of disorder: the vacancy-array disorder. To study this vacancy disordering, we made the super-unit-cell systems of (DC) (DS) with L \L n"0}4 and calculated their electronic structures. It was found that the energy position of the valence-band top hardly changes with varying n while that of the conduction-band bottom gradually changes. In particular, similar to ordinary alloying compounds, the band-gap energy of (DC) (DS) V \V changes as E "1.0#0.5x!bx(1!x) eV with the bowing parameter of b"0.45 eV. This result indicates that the vacancy acts as one kind of atom for the conduction-band electrons. It is instructive to note the di!erence of electronic structures between the present 䊐 II III VI and another type of vacancy-ordering compounds such as 䊐 Ga Se [4,6]. Although the vacancy localizes the valence- and conduction-band states, the band dispersions are larger in 䊐CdGa Se compared to the case of 䊐Ga Se . This is because the vacancy concentration in 䊐 II III VI is smaller, 25%, than in 䊐 Ga Se , 33%. Finally, we comment on the structural stability of 䊐 II III VI . The present calculations do not consider the atom-position relaxation and thus the elastic energy is not fully taken into account. However, the calculated total energies show some chemical trend. For example, 䊐CdGa Se has the
455
lowest energy in DC structure, while 䊐CdIn Se in PS structure, which is consistent with observations [1]. In previous works studying the stability of 䊐 III VI [4,6,8], we had shown the chemical trend of crystal structures; as increasing the ionicity of compounds, i.e. the electronegativity di!erence between cation and anion, the crystal structure changes from mesoscopic structure of 䊐Ga Te to monoclinic one of 䊐 Ga Se , layered one of 䊐 In Se and defect spinel of 䊐 In S . For the present 䊐 II III VI systems, a sum of observed data shows the similar chemical trend of crystal structure change from DS of 䊐CdGa Se to DC of 䊐CdGa Se , PS of 䊐CdIn Se and spinel of 䊐CdIn S [1]. These have good correspondence to 䊐 III VI systems and might be explained by a similar scenario as 䊐 III VI .
4. Conclusions By the "rst-principles electronic-structure calculations of II III VI compounds in defect chalcopyrite, defect stannite and pseudocubic structures, we have clari"ed the e!ect of vacancy ordering/disordering. It has been shown that the valence-band states are localized around vacancies and their energy positions hardly depend on the vacancy ordering. On the other hand, the cationsite vacancy acts as a potential barrier for the conduction-band electrons and the vacancy ordering sensitively changes their energy positions and the band-gap energy of system.
Acknowledgements This work was supported by JSPS Research for the Future Programs in the Area of Atomic Scale Surface and Interface Dynamics, and JSPSRFTF96R16201. Parts of this work were supported by the Ministry of Education, Science, Sports and Culture, Japan, and Graduate School of Science and Technology, Chiba University. We also thank the Supercomputer Center, Institute for Solid State Physics, University of Tokyo for the use of FACOM VPP500.
456
M. Ishikawa, T. Nakayama / Journal of Crystal Growth 214/215 (2000) 452}456
References [1] A. Miller, A. MacKinnon, D. Weaire, Solid State Phys. 36 (1981) 119. [2] L.K. Samanta, D.K. Ghosh, P.S. Ghosh, Phys. Rev. B 39 (1989) 10261. [3] T. Nakayama, M. Ishikawa, J. Phys. Soc. Jpn. 66 (1997) 3887. [4] M. Ishikawa, T. Nakayama, Jpn. J. Appl. Phys. 36 (1997) L1576.
[5] M. Murayama, T. Nakayama, Phys. Rev. B 49 (1994) 4710. [6] M. Ishikawa, T. Nakayama, Jpn. J. Appl. Phys. 37 (1998) L1125. [7] O. Madelung, M. Schulz, H. Weiss (Eds.), Semiconductors, Physics of Ternary Compounds, Landolt-BoK rnstein, New series, Group III, Vol. 17, Part. h, Springer, Berlin, 1985. [8] M. Ishikawa, T. Nakayama, J. Phys. Low Dimensional Structures 11 (1997) 95.