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Indium oxide with its wide gap is a multifunctional semiconductor material, which has gained application in many areas. Indium oxide films show high electrical property and high transparency, which have been applied in OLED display, flat-panel display, thin film solar cells, etc. However, the mechanisms of both high electrical and high transparent properties are still not clear up to now. So in this paper, the electronic structures of the In2O3 crystals are studied by GGA, GGA+U, HSE06 and G0W0 corrections. The mechanisms of optical transition and formation of transparent electrode in In2O3 crystals are studied using Hedin's G0W0 approximation and the Bethe-Salpeter equation. The complex refractive index, complex dielectric function and optical absorption spectrum of the In2O3 crystal have been obtained, which are in good agreement with experimental results. By analyzing the quasi-particle band structures, optical transition matrix and optical absorption spectrum, the mechanisms of optical transition and formation of transparent electrode in In2O3 can be interpreted. BSE (Bethe-Salpeter equation) calculation results show that the transition from 8 to 1 is permitted, however, the transition probability is far less than that from 10 to 1. This is because, for 8 to 1 transition, there are three even symmetry bands and two odd symmetry bands, in which only the transition from two odd symmetry bands to the conduction band is permitted. Other causes for this phenomenon are that in the In2O3 primitive cell there exist some overlapping bands, which result in the false transition. Therefore, this work argues that in the In2O3 crystals optical band gap is 4.167 eV, which corresponds to the direct transition from 10 to 1. This result will help understand the mechanisms of optical transition and the transparent electrode in In2O3.
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Keywords:
- G0W0-BSE method /
- quasi-particle band structure /
- optical properties /
- mechanism of absorption
[1] Gordon R G 2000 MRS Bull. 25 52
[2] Hartnagel H L, Dawar A K J, Jagadish C 1995 Semiconducting Transparent Thin Films (Bristol: Institute of Physics Publishing), 110-126
[3] Hung L S, Chen C H 2002 Mater. Sci. Eng.: R: Reports 39 143
[4] Matino F, Persano L, Arima V, Pisignano D, Blyth RIR, Cingolani R, Rinaldi Ross 2005 Phys. Rev. B 72 085437
[5] Zhao H X, Chen X L, Yang X, Du J, Bai L S, Chen Z, Zhao Y, Zhang X D 2014 Acta Phys. Sin. 63 056801(in Chinese) [赵慧旭, 陈新亮, 杨旭, 杜建, 白立沙, 陈泽, 赵颖, 张晓丹 2014 63 056801]
[6] Hashimoto R, Abe Y, Nakada T 2008 App. Phys. Express 1 015002
[7] Gupta R K, Ghosh K, Mishra S R, Kahol P K 2008 Thin Solid Films 516 3204
[8] Granqvist C G, Hultker A 2002 Thin Solid Films 411 1
[9] Murali K R, Elango P, Andavan P, Venkatachalam K 2008 J. Mater. Sci.-Mate. in Electron. 19 289
[10] Kundakci M, Grbulak B, Doğan S, Ate A, Yildirim M 2008 App. Phys. A 90 479
[11] Bouabid K, Ihlal A, Amira Y, Sdaq A, Outzourhit A, Nouet G 2007 The Eur. Phys. J. Appl. Phys. 40 149
[12] Jiang D Y, Shen D Z, Liu K W, Shan C X, Zhao Y M, Yang T, Yao B, Lu Y M, Zhang J Y 2008 Semicond. Sci. Technol. 23 035002
[13] Weiher R L, Ley R P 1966 J. Appl. Phys. 37 299
[14] Saha S, Pal U, Chaudhuri A K, Rao V V, Banerjee H D 1989 Phys. Status Solidi A 114 721
[15] Galdikas A, Mironas A, Senulienc D, etkus A 1998 Thin solid films 323 275
[16] Novkovski N, Tanuevski A 2008 Semicond. Sci. Technol. 23 095012
[17] Walsh A, Silva J L F D, Wei S H, Krber C, Klein A, Piper L F J, Demasi A, Smith K E, Panaccione G, Torelli P 2008 Phys. Rev. Lett. 100 167402
[18] goston P, Erhart P, Klein A, Albe K 2009 J. Phys. Condens. Matter 21 455801
[19] Erhart P, Klein A, Egdell R G, Albe K 2007 Phys. Rev. B 75 153205
[20] King P D C, Veal T D, Fuchs F, Wang C Y, Payne D J, Bourlange A, Zhang H, Bell G R, V. Cimalla, Ambacher O, Egdell R G, Bechstedt F, McConville C F 2009 Phys. Rev. B 79 205211
[21] Luttinger J M, Ward J C 1960 Phys. Rev. 118 1417
[22] Rinke P, Schleife A, Kioupakis E, Janotti A, Rdl C, Bechstedt F, Scheffler M, Van De Walle C G 2012 Phys. Rev. Lett. 108 126404
[23] Gao S P, Zhu T 2012 Acta Phys. Sin. 61 137103(in Chinese) [高尚鹏, 祝桐 2012 61 137103]
[24] Rinke P, Janotti A, Scheffler M, Van De Walle C G 2009 Phys. Rev. Lett. 102 026402
[25] Onida G, Reining L, Rubio A 2002 Rev. Mod. Phys. 74 601
[26] F Fuchs, C Rdl, A Schleife, F Bechstedt 2008 Phys. Rev. B 78 085103
[27] Kresse G, Furthmller J 1996 Phys. Rev. B 54 11169
[28] Kresse G, Furthmller J 1996 Comput. Mater. Sci. 6 15
[29] Mostofi A A, Yates J R, Lee Y S, Souza I, Vanderbilt D, Marzari N 2008 Comput. Phys. Commun. 178 685
[30] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[31] Blchl P E 1994 Phys. Rev. B 50 17953
[32] Kresse G, Jouber Dt 1999 Phys. Rev. B 59 1758
[33] Fuchs F, Bechstedt F 2008 Phys. Rev. B 77 155107
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[1] Gordon R G 2000 MRS Bull. 25 52
[2] Hartnagel H L, Dawar A K J, Jagadish C 1995 Semiconducting Transparent Thin Films (Bristol: Institute of Physics Publishing), 110-126
[3] Hung L S, Chen C H 2002 Mater. Sci. Eng.: R: Reports 39 143
[4] Matino F, Persano L, Arima V, Pisignano D, Blyth RIR, Cingolani R, Rinaldi Ross 2005 Phys. Rev. B 72 085437
[5] Zhao H X, Chen X L, Yang X, Du J, Bai L S, Chen Z, Zhao Y, Zhang X D 2014 Acta Phys. Sin. 63 056801(in Chinese) [赵慧旭, 陈新亮, 杨旭, 杜建, 白立沙, 陈泽, 赵颖, 张晓丹 2014 63 056801]
[6] Hashimoto R, Abe Y, Nakada T 2008 App. Phys. Express 1 015002
[7] Gupta R K, Ghosh K, Mishra S R, Kahol P K 2008 Thin Solid Films 516 3204
[8] Granqvist C G, Hultker A 2002 Thin Solid Films 411 1
[9] Murali K R, Elango P, Andavan P, Venkatachalam K 2008 J. Mater. Sci.-Mate. in Electron. 19 289
[10] Kundakci M, Grbulak B, Doğan S, Ate A, Yildirim M 2008 App. Phys. A 90 479
[11] Bouabid K, Ihlal A, Amira Y, Sdaq A, Outzourhit A, Nouet G 2007 The Eur. Phys. J. Appl. Phys. 40 149
[12] Jiang D Y, Shen D Z, Liu K W, Shan C X, Zhao Y M, Yang T, Yao B, Lu Y M, Zhang J Y 2008 Semicond. Sci. Technol. 23 035002
[13] Weiher R L, Ley R P 1966 J. Appl. Phys. 37 299
[14] Saha S, Pal U, Chaudhuri A K, Rao V V, Banerjee H D 1989 Phys. Status Solidi A 114 721
[15] Galdikas A, Mironas A, Senulienc D, etkus A 1998 Thin solid films 323 275
[16] Novkovski N, Tanuevski A 2008 Semicond. Sci. Technol. 23 095012
[17] Walsh A, Silva J L F D, Wei S H, Krber C, Klein A, Piper L F J, Demasi A, Smith K E, Panaccione G, Torelli P 2008 Phys. Rev. Lett. 100 167402
[18] goston P, Erhart P, Klein A, Albe K 2009 J. Phys. Condens. Matter 21 455801
[19] Erhart P, Klein A, Egdell R G, Albe K 2007 Phys. Rev. B 75 153205
[20] King P D C, Veal T D, Fuchs F, Wang C Y, Payne D J, Bourlange A, Zhang H, Bell G R, V. Cimalla, Ambacher O, Egdell R G, Bechstedt F, McConville C F 2009 Phys. Rev. B 79 205211
[21] Luttinger J M, Ward J C 1960 Phys. Rev. 118 1417
[22] Rinke P, Schleife A, Kioupakis E, Janotti A, Rdl C, Bechstedt F, Scheffler M, Van De Walle C G 2012 Phys. Rev. Lett. 108 126404
[23] Gao S P, Zhu T 2012 Acta Phys. Sin. 61 137103(in Chinese) [高尚鹏, 祝桐 2012 61 137103]
[24] Rinke P, Janotti A, Scheffler M, Van De Walle C G 2009 Phys. Rev. Lett. 102 026402
[25] Onida G, Reining L, Rubio A 2002 Rev. Mod. Phys. 74 601
[26] F Fuchs, C Rdl, A Schleife, F Bechstedt 2008 Phys. Rev. B 78 085103
[27] Kresse G, Furthmller J 1996 Phys. Rev. B 54 11169
[28] Kresse G, Furthmller J 1996 Comput. Mater. Sci. 6 15
[29] Mostofi A A, Yates J R, Lee Y S, Souza I, Vanderbilt D, Marzari N 2008 Comput. Phys. Commun. 178 685
[30] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[31] Blchl P E 1994 Phys. Rev. B 50 17953
[32] Kresse G, Jouber Dt 1999 Phys. Rev. B 59 1758
[33] Fuchs F, Bechstedt F 2008 Phys. Rev. B 77 155107
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