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运用改进的无规元素等位移模型和玻恩-黄近似，结合电磁场的麦克斯韦方程和边界条件，研究了真空/极性二元晶体薄膜/极性三元混晶薄膜/极性二元晶体衬底四层系统的表面和界面声子极化激元. 以AlxGa1-xAs/GaAs和ZnxCd1-xSe/ZnSe为例，获得了表面和界面声子极化激元模的色散关系以及表面模和界面模的频率随混晶组分和薄膜厚度的变化关系. 结果表明，三元混晶四层异质结系统中存在七支表面和界面声子极化激元模，且这七支表面模和界面模的频率随混晶组分和薄膜厚度呈非线性变化，三元混晶的“单模”和“双模”性也在色散曲线中得到了很好的体现.
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关键词:
- 表面和界面声子极化激元 /
- 四层系统 /
- 三元混晶
Surface and interface phonon-polaritons in a four-layer (vacuum/polar binary crystal slab/polar ternary mixed crystal slab/polar binary crystal substrate) system are investigated with the modified random-element-isodisplacement model and the Born-Huang approximation, based on the Maxwell's equations with the usual boundary conditions. The numerical results of the surface and interface phonon-polariton frequencies as functions of the wave-vector, composition x, and thickness of slab in the two four-layer systems, i.e., AlxGa1-xAs/GaAs and ZnxCd1-xSe/ZnSe, are obtained and discussed. It is shown that there are seven branches of surface and interface phonon-polariton modes in the heterostructure systems, and that the frequencies of the surface and interface modes vary non-linearly with the composition and thickness of slab. The “one mode” and “two mode” behaviors of the ternary mixed crystals are also shown in the dispersion curves.[1] Francoeur M, Menguc M P, Vaillon R 2010 J. Appl. Phys. 107 034313
[2] Ocelie N, Hillenbrand R 2004 Nat. Mater. 3 606
[3] Greffet J J, Carminati R, Joulain K, Mulet J P, Mainguy S, Chen Y 2002 Nature 416 61
[4] Taubner T, Keilmann F, Hillenbrand R 2004 Nano Lett. 4 1669
[5] Huber A J, Ocelic N, Hillenbrand R 2008 J. Microscopy 229 389
[6] Evans D J, Ushioda S, McMullen J D 1973 Phys. Rev. Lett. 31 369
[7] Torii K, Koga T, Sota T, Azuhata T, Chichibu S F, Nakamura S 2000 J. Phys.: Condens. Matter 12 7041
[8] Gong Z Q, He M D 2007 Acta Phys. Sin. 56 6607 (in Chinese)[龚志强, 贺梦冬 2007 56 6607]
[9] Ng S S, Yoon T L, Hassan Z, Hassan H A 2009 Appl. Phys. Lett. 94 241912
[10] Ng S S, Lee S C, Ooi P K, Saw K, Abdullah M, Hassan Z, Hassan H A 2013 Ceramics Inter. 39 S529
[11] Zhang L W, Xu J P, He L, Qiao W T 2010 Acta Phys. Sin. 59 7863 (in Chinese)[张利伟, 许静平, 赫丽, 乔文涛 2010 59 7863]
[12] Chang I F, Mitra S S 1971 Adv. Phys. 20 359
[13] Born M, Huang K 1954 Dynamical Theory of Crystal Lattices (New York: Oxford University Press) p82
[14] Mills D L, Maradudin A A 1973 Phys. Rev. Lett. 31 372
[15] Liang X X, Ban S L 2004 Chin. Phys. 13 71
[16] Liang X X, Yang J S 1996 Solid State Commum. 100 629
[17] Adachi S 1985 J. Appl. Phys. 58 R1
[18] Yu S, Kim K W, Bergman L, Dutta M, Stroscio M A, Zavada J M 1998 Phys. Rev. B 58 15283
[19] Strite S, Morkoc H 1992 J. Vac. Sci. Technol. B 10 1237
[20] Ooi P K, Lee S C, Ng S S, Hassan Z, Hassan H A 2011 Thin Solid Films 519 5481
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[1] Francoeur M, Menguc M P, Vaillon R 2010 J. Appl. Phys. 107 034313
[2] Ocelie N, Hillenbrand R 2004 Nat. Mater. 3 606
[3] Greffet J J, Carminati R, Joulain K, Mulet J P, Mainguy S, Chen Y 2002 Nature 416 61
[4] Taubner T, Keilmann F, Hillenbrand R 2004 Nano Lett. 4 1669
[5] Huber A J, Ocelic N, Hillenbrand R 2008 J. Microscopy 229 389
[6] Evans D J, Ushioda S, McMullen J D 1973 Phys. Rev. Lett. 31 369
[7] Torii K, Koga T, Sota T, Azuhata T, Chichibu S F, Nakamura S 2000 J. Phys.: Condens. Matter 12 7041
[8] Gong Z Q, He M D 2007 Acta Phys. Sin. 56 6607 (in Chinese)[龚志强, 贺梦冬 2007 56 6607]
[9] Ng S S, Yoon T L, Hassan Z, Hassan H A 2009 Appl. Phys. Lett. 94 241912
[10] Ng S S, Lee S C, Ooi P K, Saw K, Abdullah M, Hassan Z, Hassan H A 2013 Ceramics Inter. 39 S529
[11] Zhang L W, Xu J P, He L, Qiao W T 2010 Acta Phys. Sin. 59 7863 (in Chinese)[张利伟, 许静平, 赫丽, 乔文涛 2010 59 7863]
[12] Chang I F, Mitra S S 1971 Adv. Phys. 20 359
[13] Born M, Huang K 1954 Dynamical Theory of Crystal Lattices (New York: Oxford University Press) p82
[14] Mills D L, Maradudin A A 1973 Phys. Rev. Lett. 31 372
[15] Liang X X, Ban S L 2004 Chin. Phys. 13 71
[16] Liang X X, Yang J S 1996 Solid State Commum. 100 629
[17] Adachi S 1985 J. Appl. Phys. 58 R1
[18] Yu S, Kim K W, Bergman L, Dutta M, Stroscio M A, Zavada J M 1998 Phys. Rev. B 58 15283
[19] Strite S, Morkoc H 1992 J. Vac. Sci. Technol. B 10 1237
[20] Ooi P K, Lee S C, Ng S S, Hassan Z, Hassan H A 2011 Thin Solid Films 519 5481
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