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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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