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Firstly, some results about the frequencies of phonons in wurtzite ternary mixed crystals (TMCs) fitted by several methods (modified random-element-isodiplacement model (MREI), virtual crystal approximation, and simplified coherent potential approximation, etc.) are compared. Then, combined with the continuous dielectric model and uniaxial crystal model, a fitting method available to experimental data is adopted to derive the dispersion relations of different kinds of optical phonon modes in TMC InxGa1－xN and AlxGa1－xN quantum wells. Furthermore, the variation of phonon modes dependent on the composition is analyzed. The results show that the fitting by the MREI for phonon frequencies of wurtzite TMCs with one-mode property agrees better with the experimental data. It can be also found that the optical phonon modes in quantum wells vary with the composition. The phonon modes, such as localized modes, interface modes, half-space modes, and propagating modes, exist in certain composition regions and frequency regions due to the anisotropy of phonon dispersion of wurtzite nitrides. Moreover, the shape of the same kind of phonon modes also varies with the composition.
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Keywords:
- wurtzite /
- ternary mixed crystal /
- quantum well /
- optical phonon mode
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[17] Alexson D, Bergman L, Nemanich R J, Dutta M, Stroscio M A, Parker C A, Bedair S M, El-Masry N A, Adar F 2001 J. Appl. Phys. 89 798
[18] Chen Y S, Shockley W, Pearson G L 1966 Phys. Rev. 151 648
[19] Chang I F, Mitra S S 1968 Phys. Rev. 172 924
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[29] Komirenko S M, Kim K W, Stroscio M A, Dutta M 1999 Phys. Rev. B 59 5013
[30] Wendler L 1985 Phys. Status Solidi B 129 513
[31] Loudon R 1964 Adv. Phys. 13 423
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[33] Shi J J 2003 Phys. Rev. B 68 165335
[34] Zheng R S, Matsuura M 1999 Phys. Rev. B 60 4937
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[37] Wang X J, Wang L L, Huang W Q, Tang L M, Zou B S, Chen K Q 2007 Acta Phys. Sin. 56 429(in Chinese) [王新军、 王玲玲、 黄维清、 唐黎明、 邹炳锁、 陈克求 2007 物理学报 56 429]
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[39] Demangeot F, Groenen J, Frandon J, Renucci M A, Briot O, Clur S, Aulombard R L 1998 Appl. Phys. Lett. 72 2674
[40] Vurgaftman I, Meyer J R, Ram-Mohan L R 2001 J. Appl. Phys. 89 5815
[41] Harima H 2002 J. Phys. : Condens. Matter 14 R967
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[43] Behr D, Niebuhr R, Wagner J, Bachem K H, Kaufmann U 1997 Gallium Nitride and Related Materials II (Pittsburgh: Materials Research Society) p213
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[1] Kong Y C, Zheng Y D 2006 Prog. Phys. 26 127 (in Chinese) [孔月婵、郑有炓 2006 物理学进展 26 127]
[2] Reine M B, Hairston A, Lamarre P, Wong K K, Tobin S P, Sood A K, Cooke C, Pophristic M, Guo S, Peres B, Singh R, Eddy Jr C R, Chowdhury U, Wong M M, Dupuis R D, Li T, DenBaars S P 2006 Proc. SPIE 6119 611901
[3] Wu J, Walukiewicz W, Yu K M, Ager III J W, Haller E E, Lu H, Schaff W J, Saito Y, Nanishi Y 2002 Appl. Phys. Lett. 80 3967
[4] Jain S C, Willander M, Narayan J, Overstraeten R V 2000 J. Appl. Phys. 87 965
[5] Lei S Y, Shen B, Zhang G Y 2008 Acta Phys. Sin. 57 2386 (in Chinese)[雷双瑛、 沈 波、 张国义 2008 物理学报 57 2386]
[6] Jiang Y, Luo Y, Xi G Y, Wang L, Li H T, Zhao W, Han Y J 2009 Acta Phys. Sin. 58 7282 (in Chinese) [江 洋、 罗 毅、 席光义、 汪 莱、 李洪涛、 赵 维、 韩彦军2009 物理学报 58 7282]
[7] Rigutti L, Castaldini A, Meneghini M, Cavallini A 2008 Semicond. Sci. Tech. 23 025004
[8] Lochthofen A, Mertin W, Bacher G, Furitsch M, Brüderl G, Strauss U, Hrle V 2008 J. Phys. D: Appl. Phys. 41 135115
[9] Shen G D, Zhang J M, Zou D S, Xu C, Gu X L 2008 Acta Phys. Sin. 57 472 (in Chinese) [沈光地、 张剑铭、 邹德恕、 徐 晨、 顾晓玲2008 物理学报 57 472]
[10] Zhang J M, Zou D S, Xu C, Zhu Y X, Liang T, Da X L, Shen G D 2007 Chin. Phys. 16 1135
[11] Li Z H, Yu T J, Yang Z J, Feng Y C, Zhang G Y, Guo B P, Niu H B 2005 Chin. Phys. 14 830
[12] Hao G D, Ban S L, Jia X M 2007 Chin. Phys. 16 3766
[13] Harima H, Inoue T, Nakashima S, Okumura H, Ishida Y, Yoshida S, Koizumi T, Grille H, Bechstedt F 1999 Appl. Phys. Lett. 74 191
[14] Davydov V Y, Goncharuk I N, Smirnov A N, Nikolaev A E, Lundin W V, Usikov A S, Klochikhin A A, Aderhold J, Graul J, Semchinova O, Harima H 2002 Phys. Rev. B 65 125203
[15] Holtz M, Prokofyeva T, Seon M, Copeland K, Vanbuskirk J, Williams S, Nikishin S A, Tretyakov V, Temkin H 2001 J. Appl. Phys. 89 7977
[16] Tabata A, Leite J R, Lima A P, Silveira E, Lemos V, Frey T, As D J, Schikora D, Lischka K 1999 Appl. Phys. Lett. 75 1095
[17] Alexson D, Bergman L, Nemanich R J, Dutta M, Stroscio M A, Parker C A, Bedair S M, El-Masry N A, Adar F 2001 J. Appl. Phys. 89 798
[18] Chen Y S, Shockley W, Pearson G L 1966 Phys. Rev. 151 648
[19] Chang I F, Mitra S S 1968 Phys. Rev. 172 924
[20] Yu S G, Kim K W, Bergman L, Dutta M, Stroscio M A, Zavada J M 1998 Phys. Rev. B 58 15283
[21] Liang X X, Ban S L 2004 Chin. Phys. 13 71
[22] Martin T P 1975 Phys. Status Solidi B 67 137
[23] Grille H, Schnittler Ch, Bechstedt F 2000 Phys. Rev. B 61 6091
[24] Ban S L, Hasbun J E 1999 Eur. Phys. J. B 8 453
[25] Yu X L, Ban S L 2003 J. Inner Mongolia University (Sci. Ed.) 34 235 (in Chinese) [于晓龙、 班士良 2003 内蒙古大学学报(自然科学版) 34 235]
[26] Liaci F, Bigenwald P, Briot O, Gil B, Briot N, Cloitre T, Aulombard R L 1995 Phys. Rev. B 51 4699
[27] Osamura K, Nakajima K, Murakami Y, Shingu P H, Ohtsuki A 1972 Solid State Commun. 11 617
[28] Lee B C, Kim K W, Stroscio M A, Dutta M 1998 Phys. Rev. B 58 4860
[29] Komirenko S M, Kim K W, Stroscio M A, Dutta M 1999 Phys. Rev. B 59 5013
[30] Wendler L 1985 Phys. Status Solidi B 129 513
[31] Loudon R 1964 Adv. Phys. 13 423
[32] Lü J T, Cao J C 2005 J. Appl. Phys. 97 033502
[33] Shi J J 2003 Phys. Rev. B 68 165335
[34] Zheng R S, Matsuura M 1999 Phys. Rev. B 60 4937
[35] Zheng R S, Taguchi T, Matsuura M 2000 J. Appl. Phys. 87 2526
[36] Wei S Y, Zhang F, Huang W D, Li W, Zhao X 2006 Chinese J. Liq. Cryst. Displays 21 336 (in Chinese) [危书义、 张 芳、 黄文登、 李 伟、赵 旭 2006 液晶与显示 21 336]
[37] Wang X J, Wang L L, Huang W Q, Tang L M, Zou B S, Chen K Q 2007 Acta Phys. Sin. 56 429(in Chinese) [王新军、 王玲玲、 黄维清、 唐黎明、 邹炳锁、 陈克求 2007 物理学报 56 429]
[38] Bungaro C, Rapcewicz K, Bernholc J 2000 Phys. Rev. B 61 6720
[39] Demangeot F, Groenen J, Frandon J, Renucci M A, Briot O, Clur S, Aulombard R L 1998 Appl. Phys. Lett. 72 2674
[40] Vurgaftman I, Meyer J R, Ram-Mohan L R 2001 J. Appl. Phys. 89 5815
[41] Harima H 2002 J. Phys. : Condens. Matter 14 R967
[42] Walukiewicz W, Ager III J W, Yu K M, Liliental-Weber Z, Wu J, Li S X, Jones R E, Denlinger J D 2006 J. Phys. D: Appl. Phys. 39 R83
[43] Behr D, Niebuhr R, Wagner J, Bachem K H, Kaufmann U 1997 Gallium Nitride and Related Materials II (Pittsburgh: Materials Research Society) p213
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