三元混晶中的激子极化激元
摘要
三元混晶具有许多二元晶体所没有的独特的物理性质，例如其禁带宽度和光学声子频率可以通过改变组分来人为控制，从而被广泛地应用于许多人造层状材料和低维系统，如：异质结、量子阱、超晶格、量子点等，成为制造许多新型的电子和光电器件的重要材料．多年来，三元混晶中的声子、激子、极化子和声子极化激元等元激发问题得到了广泛的研究．本文主要研究极性三元混晶体材料和半无限大材料表面的激子极化激元的色散性质及其相关问题．
首先在波恩-黄近似下，利用麦克斯韦方程组研究了极性三元混晶体材料中的激子极化激元的色散关系以及两支色散曲线的能量分裂问题．以Ⅲ-Ⅴ和Ⅱ-Ⅵ族三元混晶Al_xGa_(1-x)As，Cd_xZn_(1-x)Se和Al_xGa_(1-x)N为例，数值计算了激子极化激元的能量随波矢和混晶组分的变化规律，以及两支色散曲线的分裂能随组分的变化规律．研究结果表明：当三元混晶的组分趋于极限0或1时，三元混晶中的激子极化激元与相应的二元晶体中的激子极化激元相同；当组分不为0或1时，与二元晶体相比，三元混晶激子极化激元具有新的色散特征，其能量与二元晶体中的激子极化激元有定量的不同，且随着混晶组分的变化呈非线性变化，且其分裂能亦随混晶组分的变化呈非线性变化，并在长波范围存在一极小值．本文对一些三元混晶如Al_xGa_(1-x)As，以及一些二元晶体如GaAs、ZnSe和CdSe等的理论计算，获得了与实验报道结果吻合很好的结果．
在对体材料研究的基础上，我们又采用Fuchs和Kliewer的表面阻抗方法研究了半无限大三元混晶材料表面的激子极化激元．数值计算了Ⅲ-Ⅴ和Ⅱ-Ⅵ族三元混晶材料Al_xGa_(1-x)As，Cd_xZn_(1-x)Se和Al_xGa_(1-x)N中表面激子极化激元随波矢和混晶组分的变化关系．结果表明，与体激子极化激元类似，三元混晶中的表面激子极化激元也具有新的色散特征，其能量与二元晶体中的激子极化激元有定量的不同且随组分的变化呈非线形变化，但其变化的非线形性不如体材料中的极化激元的变化明显．
Ternary mixed crystals (TMCs) are extensively used in artifical layered structures and low-dimensionality systems, e.g.: heterostructure, quantum well, superlattice and quantum dot etc, due to their unique physical properties quite different from binary crystals, such as band-gap energy and the optical phonon frequency, can be controlled directly by the concentration x. Therefore, they are considered to be very important materials for many new electronic and photoelectronic devices. Some important elementary excitations in TMCs, such as phonons, excitons, polarons and phonon-polaritons, have been extensively studied. In this work, we investigate the dispersion properties of exciton-polaritons and related problems in bulk and semi-infinite polar TMC materials.
Firstly, within the Born-Huang approximation, the dispersion relations and corresponding energy splitting of bulk exciton-polaritons in polar TMCs are investigated by using the Maxwell's equations. The numerical results of the polariton frequencies as functions of the wave-vector and the compositions, and the dependences of their energy splitting on functions of the compositions for TMCs Al_xGa_(1-x)As, Cd_xZn_(1-x)Se, and Al_xGa_(1-x)N are obtained and discussed. Theoretical results show that the dispersion curves of TMCs are the same to those of the corresponding binary crystals when x=0 and x=1; when the composition x is neither zero nor one, the new dispersion characteristics for exciton, polaritons in TMC systems are found in comparison with binary crystals. The values of energies are different from quantitatively those of the binary crystals, and change nonlinearly with the variety of the composition x of the TMCs. The dependence of the splitting of two branches of polaritons on the compositions of TMCs is found nonlinear and there exists a minimum of the splitting at the long-wavelength case. The calculated results for some TMC systems, such as Al_xGa_(1-x)As as well as GaAs, ZnSe and CdSe are in agree with the reported experimental results.
Next, we have investigated theoretically the surface exciton-polaritons of TMCs in the surface impedance method by Fuchs and Kliewer. The energies of the surface exciton-polaritons have been calculated. The numerical calculations for severalⅢ-ⅤandⅡ-Ⅵcompound systems are performed and the polariton frequencies as functions of the wave-vector and the compositions for TMCs Al_xGa_(1-x)As, Cd_xZn_(1-x)Se and Al_xGa_(1-x)N as examples are given and discussed. The results show that the dispersion characteristics of surface exciton-polaritons of TMCs are the similar to those of the corresponding bulk exciton-polaritons, their energies are different from those of the binary crystals quantitatively, but the nonlinearly with the composition x of the TMCs are weaker than those of bulk modes.
首先在波恩-黄近似下，利用麦克斯韦方程组研究了极性三元混晶体材料中的激子极化激元的色散关系以及两支色散曲线的能量分裂问题．以Ⅲ-Ⅴ和Ⅱ-Ⅵ族三元混晶Al_xGa_(1-x)As，Cd_xZn_(1-x)Se和Al_xGa_(1-x)N为例，数值计算了激子极化激元的能量随波矢和混晶组分的变化规律，以及两支色散曲线的分裂能随组分的变化规律．研究结果表明：当三元混晶的组分趋于极限0或1时，三元混晶中的激子极化激元与相应的二元晶体中的激子极化激元相同；当组分不为0或1时，与二元晶体相比，三元混晶激子极化激元具有新的色散特征，其能量与二元晶体中的激子极化激元有定量的不同，且随着混晶组分的变化呈非线性变化，且其分裂能亦随混晶组分的变化呈非线性变化，并在长波范围存在一极小值．本文对一些三元混晶如Al_xGa_(1-x)As，以及一些二元晶体如GaAs、ZnSe和CdSe等的理论计算，获得了与实验报道结果吻合很好的结果．
在对体材料研究的基础上，我们又采用Fuchs和Kliewer的表面阻抗方法研究了半无限大三元混晶材料表面的激子极化激元．数值计算了Ⅲ-Ⅴ和Ⅱ-Ⅵ族三元混晶材料Al_xGa_(1-x)As，Cd_xZn_(1-x)Se和Al_xGa_(1-x)N中表面激子极化激元随波矢和混晶组分的变化关系．结果表明，与体激子极化激元类似，三元混晶中的表面激子极化激元也具有新的色散特征，其能量与二元晶体中的激子极化激元有定量的不同且随组分的变化呈非线形变化，但其变化的非线形性不如体材料中的极化激元的变化明显．
Ternary mixed crystals (TMCs) are extensively used in artifical layered structures and low-dimensionality systems, e.g.: heterostructure, quantum well, superlattice and quantum dot etc, due to their unique physical properties quite different from binary crystals, such as band-gap energy and the optical phonon frequency, can be controlled directly by the concentration x. Therefore, they are considered to be very important materials for many new electronic and photoelectronic devices. Some important elementary excitations in TMCs, such as phonons, excitons, polarons and phonon-polaritons, have been extensively studied. In this work, we investigate the dispersion properties of exciton-polaritons and related problems in bulk and semi-infinite polar TMC materials.
Firstly, within the Born-Huang approximation, the dispersion relations and corresponding energy splitting of bulk exciton-polaritons in polar TMCs are investigated by using the Maxwell's equations. The numerical results of the polariton frequencies as functions of the wave-vector and the compositions, and the dependences of their energy splitting on functions of the compositions for TMCs Al_xGa_(1-x)As, Cd_xZn_(1-x)Se, and Al_xGa_(1-x)N are obtained and discussed. Theoretical results show that the dispersion curves of TMCs are the same to those of the corresponding binary crystals when x=0 and x=1; when the composition x is neither zero nor one, the new dispersion characteristics for exciton, polaritons in TMC systems are found in comparison with binary crystals. The values of energies are different from quantitatively those of the binary crystals, and change nonlinearly with the variety of the composition x of the TMCs. The dependence of the splitting of two branches of polaritons on the compositions of TMCs is found nonlinear and there exists a minimum of the splitting at the long-wavelength case. The calculated results for some TMC systems, such as Al_xGa_(1-x)As as well as GaAs, ZnSe and CdSe are in agree with the reported experimental results.
Next, we have investigated theoretically the surface exciton-polaritons of TMCs in the surface impedance method by Fuchs and Kliewer. The energies of the surface exciton-polaritons have been calculated. The numerical calculations for severalⅢ-ⅤandⅡ-Ⅵcompound systems are performed and the polariton frequencies as functions of the wave-vector and the compositions for TMCs Al_xGa_(1-x)As, Cd_xZn_(1-x)Se and Al_xGa_(1-x)N as examples are given and discussed. The results show that the dispersion characteristics of surface exciton-polaritons of TMCs are the similar to those of the corresponding bulk exciton-polaritons, their energies are different from those of the binary crystals quantitatively, but the nonlinearly with the composition x of the TMCs are weaker than those of bulk modes.
引文
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[2] G. M. Minkov, A. V. Germanenko, O. E. Rut, et al., Interference-induced metalliclike behavior of a two-dimensional hole gas in an asymmetric GaAs/In_xGa_(1-x)As/GaAs quantum well, Phys. Rev., 2007, B75(19), 193311 (1-4).
[3] I. A. Yugova, A. Greilich, E. A. Zhukov, et al., Exciton fine structure in InGaAs/GaAs quantum dots revisited by pump-probe Faraday rotation, Phys. Rev., 2007, B75(19), 195325 (1-9).
[4] H. J. Chang, T. W. Chen, J. W. Chen, et al., Current and strain-induced spin polarization in InGaN/GaN superlattices, Phys. Rev. Lett., 2007, 98(13), 136403(1-4).
[5] D. W. Taylor, Optical properties of mixed crystals, edited by R. J. Elliott and I. P. Ipatova (North-Holland, Amsterdam, 1988).
[6] R N. Sen, Exciton doublets in mixed crystals of alkali and cuprous halides: coherent-potential approximation, Phys. Rev. Lett., 1973, 30(12), 553-556.
[7] S. D. Mahanti, Exciton in semiconducting alloy, Phys. Rev., 1974, B10(4), 1384-1390.
[8] G. J. Zhao, X. X. Liang, S. L. Ban, Bingding energies of wannier excitons in polar ternary mixed crystals, Journal of optoelectronics. Laser, 2004, 15(4), 487-491.
[9] R. J. Nelson and N. Holonyak, Jr., Exciton absorption, photoluminescence and band structure of N-free and N-doped In_(1-x)Ga-xP, J. Phys. Chem. Solids, 1976, 37(6), 629-637.
[10] R. J. Nelson, N. Holonyak, Jr., W. O. Groves, Free-exciton transitions in the optical absorption spectra of GaAs_(1-x)P_x, Phys. Rev., 1976, B13(12), 5415-5419.
[11] M. D. Sturge, E. Cohen, R. A. Logan, Dynamics of intrinsic and nitrogen-induced exciton emission in indirect-gap Ga_(1-x)Al_xAs, Phys. Rev., 1983, B27(4), 2362-2373.
[12] C. D. Lee, H. L. Park, C. H. Chung, et al., Free-exciton luminescence from ZnSe_(1-x)Te_x, Phys. Rev., 1992, B45(8), 4491-4493.
[13] C. Uzan, H. Mariette, A. Muranevich, Optical characterization and thermal dissociation of bound excitons in CdSe_xTe_(1-x), Phys. Rev., 1986, B34(12), 8728-8732.
[14] J. A. Kash, A. Ron, E. Cohen, Subnanosecond spectroscopy of disorder-localized excitons in CdS_(0.53)Se_(0.47), Phys. Rev., 1983, B28(10), 6147-6150.
[15] E. F. Schubert and W. T. Tsang, Photoluminescence line shape of excitons in alloy semiconductors, Phys. Rev., 1986, B34(4), 2991-2994.
[16] S. T. Lai and M. V. Klein, Photoluminescence study of excitons localized in indirect-gap GaAs_(1-x)P_x, Phys. Rev., 1984, B29(6), 3217-3224.
[17] J. J. Hopfield, Theory of the contribution of excitons to the complex dielectric constant of crystals, Phys. Rev., 1958, 112(5), 1555-1567.
[18] J. J. Hopfield and D. G. Thomas, Theoretical and experimental effects of spatial dispersion on the optical properties of crystals, Phys. Rev., 1963, 132(2), 563-572.
[19] M. Born and K Huang, Dynamical theory of crystal lattices lattices, (Oxford University Press, New York, 1954).
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