Study of Cyclotron Resonance of Interface Polarons

This paper presents a study of the cyclotron resonance of the interface polarons in a semiinfinite polar crystal. In the resonant magnetic field region the Landau-level corrections due to the resonant coupling of the electron with the bulk longitudinal-optical (LO) phonon and the surface optical (SO) phonon are calculated. At resonance the n-th Landau level (n > 0) splits into a triplet. The cyclotron-resonance mass of the electron is evaluated for an arbitrary magnetic-field strength. For the interface system the magneto-optical anomalies display three branches of the cyclotron-resonance mass spectra. The numerical results show that in the interface system the polaron effect is weakened with respect to the ideal twodimensional system. It is found that in the very weak magnetic fields the polaron effect is contributed mainly by the SO phonons, whereas in the large magnetic fields the LO-phonon contribution to the polaron.effect becomes predominant.     

表面磁极化子的回旋共振性质

在磁场中有不少的极性晶体,电子和体纵光学声子的耦合弱,而与表面光学声子的耦合强。本文讨论电子和体纵光学声子耦合弱,与表面光学声子耦合强时对表面磁极化子的性质的影响。采用改进了的线性组合算符法导出了磁场中表面极化子的回旋共振频率和回旋共振质量,对AgCl晶体进行了数值计算。结果表明,磁场中表面极化子的回旋共振频率和回旋共振质量随磁场的增加而增加。     

Interface polarons in a realistic heterojunction potential

The ground states of interface polarons in a realistic heterojunction potential are investigated by considering the bulk and the interface optical phonon influence. A self-consistent heterojunction potential is used and an LLP-like method is adopted to obtain the polaron effect. The numerical computation has been done for the Zn_1-xCd_xSe/ZnSe system to obtain the polaron ground state energy, self energy and effective mass parallel to the interface. A simplified coherent potential approximation is developed to obtain the parameters of the ternary mixed crystal and the energy band offset of the heterojunction. It is found that at small Cd concentration the bulk longitudinal optical phonons give the main contribution for lower areal electron densities, whereas the interface phonon contribution is dominant for higher areal electron densities. The interface polaron effect is weaker than the effect obtained by the three dimensional bulk phonon and by the two dimensional interface phonon models. Received 17 September 1998     

Interface Polaron Within Parallel Electric and Magnetic Fields

A combinative method of variational wavefunction and harmonic oscillator operator algebra is used to treat the interface polaron in a semi-infinite polar crystal within parallel electric and magnetic fields perpendicular to the interface. Both the bulk longitudinal optical phonon and the interface optical phonon together with the anisotropic mass of the electron are included. The energy level correction up to the second-order perturbation, cyclotron-resonance frequency and cyclotron mass are expressed as functions of the electric and magnetic fields and a parameter characterizing the mean distance of the polaron from the interface. This theory is used to calculate numerically the single heterostructure AlAs/GaAs, when the electron is at the X high-symmetry point of the conduction band of AlAs. The results show that the magnetic field greatly enhances the polaronic correction of the electron energy levels while the electric field only increases the correction of their surface optical phonon part but obviously decreases that of their bulk optical mode part and thus the total energy correction decreases as the electric field increases. The change of red shift due to the electron-phonon interaction with electric and magnetic fields is also obf ained.     

Interface polarons in a heterojunction with triangular bending-band

The interface polaron states in a heterojunction are discussed by considering an energy-band bending near the interface and the influence of an image potential. The ground state energy and the effective mass of a polaron are variationally calculated. The numerical results for the GaAs/ heterojunction are given. It is shown that even though the influences from bulk longitudinal optical (LO) phonons are more important for the heterojunctions with lower Al composition, the contributions from two branches of interface optical (IO) phonons are not negligible. For the heterojunctions with higher Al composition, both the influences from LO phonons and two branches of IO phonons are important. The band-bending plays an important role for the interface localization of polarons, but the influence of the image potential is not essential. Received: 4 November 1997 / Revised and Accepted: 9 March 1998     

磁场中准二维强耦合磁极化子的有效质量

采用改进的线性组合算符和LLP变分法,研究了外磁场对量子阱中电子与界面光学声子强耦合、与体纵光学声子弱耦合磁极化子的有效质量的影响。对AgCl/KI量子阱进行了数值计算,结果表明,磁极化子的有效质量随阱宽的增加而减小,随磁场的增强而增大,但不同支声子与电子和磁场相互作用对磁极化子有效质量的贡献大不相同。     

表面极化子光学声子平均数的磁场和温度依赖性

采用变分法、幺正变换和拉格朗日乘子法,研究了有限温度下纯二维晶体中表面磁极化子的性质.讨论了表面光学声子平均数、磁极化子振动频率λ与磁场B、温度T及Lsgrange乘子u之间的关系.对KCl晶体进行了数值计算,结果表明:磁极化子振动频率、表面光学声子平均数均随磁场B的增强而增加,且随温度T升高而增加.当bgrange乘子u超出慢电子范围时磁极化子振动频率、表面光学声子平均数均随u增加而增大且变化越来越显著.     

Electron self-energy and effective mass in a single heterostructure

In this paper, we investigate the electron self-energy and effective mass in a single heterostructure using Greenfunction method. Numerical calculations of the electron self-energy and effective mass for GaAs/A1As heterostructure are performed. The results show that the self-energy (effective mass) of electrons, which incorporate the energy of electron coupling to interface-optical phonons and half of the three-dimensional longitudinal optical phonons, increase (decrease) monotonically from that of interface polaron to that of the 3D bulk polaron with increasing the distance between the positions of the electron and interface.     

Magnetophonon resonances of the two-dimensional electron gas in GaAs/AlGaAs heterostructures

We have studied magnetophonon resonances of the two-dimensional (2D) electron gas at the GaAs/AlGaAs interface in a single interface heterostructure and a superlattice. In magnetic fields up to 30T, one set of oscillations is observed, corresponding to the coupling of 2D electrons with LO phonons of GaAs. The effective mass obtained directly from the magnetic field position of the fundamental resonance, where the Landau splitting equals the bulk phonon energy, and of the next two harmonics is $\text{m}{}^1\text{= (0.071 ± 0.0015)m}{}_0$. A comparison with cyclotron resonance measurements on the same system and with bulk GaAs data gives an upper limit of about 2% for the mass corrections due to polaron effects and due to the confinement of the electron gas.     

Temperature dependence of the cyclotron mass in ZnCdSe/ZnSe multi-QWs

The temperature dependence of the cyclotron resonance mass (CRM) of the magnetopolaron in ZnCdSe/ZnSe multi-quantum wells with strong magnetic field is investigated theoretically using the Lee-Low-Pines variational method. The contributions to the CRM due to the nonparabolicity of the conduction band and the coupling of electron with both confined longitudinal optical and interface optical phonons are considered. Results of our calculations are compared with the experimental data, and a qualitative agreement is found over a large temperature range. We show that these three contributions complement each other to determine the cyclotron mass as a function of the temperature.     

Influence of Electron-Phonon Interactions on the Physical Properties of an Interface Polaron

Taking into account the interactions of both bulk longitudinal optical (LO) pltonons and surface optical (SO) pltonons and using Haga's perturbatioit method, we derive an effective Hamiltonian for the interface magnetopolaron in polar crystals at zero temperature. We illustrate in details how to solve this effective Hamiltonian analytically and we obtain explicit formulae not on1y for the electron cyclotron mass associated with the Landau levels but also for the self-trapping energy of the magnetopolaron with respect to its first three quantum states in the direction normal to the interface of the system. Numerical results are calculated for some Ⅱ-Ⅵ and Ⅲ-Ⅴ semiconductor compounds,indicting that the bulk LO phonons and SO phonons do have different trends of effects on the electron in different quantum states.     

Effect of Strong Electron-Phonon Interactions on an Interface Polaron

The present work deals with an electron interacting strongly with both bulk longitudinal optical (LO) phonons and interface (IF) optical phonons in which we adopt and generalize the Tokuda's variational method for studying the interface polaron properties in polar crystals at zero temperature, In our approach, we can reduce the Hamiltollian equation of the system to a pair of integro-differential equations in two variational parameters of the electron wavefunction from which we can calculate various physical properties of an interface polaron including the ground state energy, average numbers of interacting phonons, the average distance from the interface and the anisotropic effective masses of the interface polaron. Numerical results are obtained explicitly for LiF crystal interfaced with NaF crystal as well as other similar systems with varying physical constants, which show the typical trends of variations for the effects of strong electron-phonon interactions on different physical properties of an interface polaron.     

磁场中与形变势相互作用的表面极化子的有效质量

近年来 ,磁场中极性晶体表面极化子的性质已引起人们的广泛关注。Ｌａｒｓｅｎ[1 ] 采用四级微扰法计算了磁场中二维极化子的基态能量。Ｗｅｉ等[2 ] 用格林函数方法研究了交界面磁极化子的回旋共振质量和频率。本文作者之一[3] 用线性组合算符讨论了磁场中表面极化子的性质。实际上 ,到目前为止 ,对表面磁极化子的研究 ,只限于考虑表面电子只与表面光学 (ＳＯ)声子和体纵光学 (ＬＯ)声子相互作用 ,而忽略了表面电子与表面声学 (ＳＡ)声子相互作用。对电子通过形变势与晶格声学振动相互作用形成的准粒子 声学形变势 (ＡＤＰ)极化子性质的研…     

极性晶体中表面极化子的温度效应

有不少的极性晶体,电子与体纵光学声子的耦合弱,但与表面光学声予的耦合强.本文讨论电子和体纵光学声子耦合弱,与表面光学声子耦合强时对表面极化子的温度特性的影响,用线性组合算符法研究表面极化子的振动频率、诱生势和有效质量的温度依赖性.对AgBr晶体进行了数值计算,结果表明极化子的振动频率,诱生势和有效质量随温度的升高而减小.     

表面磁极化子的光学声子平均数

采用Tokuda改进的线性组合算符、Lagrange乘子和变分法,讨论了强、弱耦合表面磁极化子的性质。计算了极化子的基态能量和光学声子平均数。以AgCl和ZnS晶体为例进行了数值计算。讨论了表面磁极化子振 动频率、基态能量和光学声子平均数与磁场B和拉格朗日乘子u的关系。     

晶格热振动对准二维强耦合极化子有效质量的影响

采用Tokuda改变的线性组合算符法和改进的LLP变分法，研究了晶格热振动对无限势垒量子阱中电子与界面光学声子强耦合、与体纵光学声子弱耦合系统的影响，推导出作为阱宽和温度函数的极化子有效质量的表达式. 尤其得到了量子阱中极化子的振动频率及其随阱宽和温度变化的规律. 对KI/AgCl/KI量子阱进行了数值计算，结果表明，极化子的振动频率和有效质量随阱宽的增加而减小、随温度的升高而减小，但不同支声子与电子相互作用对极化子的振动频率和有效质量的贡献以及它们随阱宽和温度的变化情况大不相同. 关键词： 量子阱 强耦合极化子 振动频率 有效质量 温度依赖性     

柱形量子线中体纵光学声子平均数

考虑电子与体纵光学声子相互作用时,采用LLP变分方法,研究柱形量子线中极化子性质,导出了柱形量子线中极化子光学声子平均数随量子线截面半径和电子-LO声子耦合强度的变化关系.结果表明柱形量子线中极化子的光学声子平均数随量子线截面半径减小而减小,随电子-LO声子耦合强度增强而增加.     

半无限晶体中慢速运动的表面极化子

本文研究电子与体纵光学声子耦合弱、与表面光学声子耦合强的半无限晶体中的表面极化子的性质.采用改进了的线性组合算符法和微扰法导出了半无限晶体中的慢速运动极化子的有效哈密顿量.在计及电子在反冲效应中发射和吸收的不同波矢的声子之间的相互作用时,讨论了对有效哈密顿量,诱生势和有效质量的影响.对AgBr晶体进行了数值计算,结果表明反冲效应中发射和吸收的不同波矢的声子之间的相互作用对有效质量和诱生势的影响随耦合常数αt的增加而增加,对有效质量的影响随坐标z的增加而减小的更多,对诱生势的影响随z的增加而增加的更多.     

Theory of surface polarons

We investigate the possibility that an electron may be trapped at the surface of an ionic crystal by the electron-surface optical phonon interaction. For a model Hamiltonian used earlier in a discussion of the inelastic scattering of low energy electrons by surface optical phonons, we find that for all values of the polaron coupling constant α, this trapping does occur. We refer to these surface states as surface polaron states. By the use of a variational procedure, we calculate the surface polaron binding energy and effective mass as a function of α. The present treatment does not include the coupling of the electron to bulk LO phonons.     

Electron mobility for a model Al<Subscript>x</Subscript> Ga<Subscript>1-x</Subscript> As/GaAs heterojunction under pressure

A variational method and a memory function approach are adopted to investigate the electron mobility parallel to the interface for a model Al_xGa_1-xAs/GaAs heterojunction and its pressure effect by considering optical phonon modes (including both of the bulk longitudinal optical (LO) in the channel side and interface optical (IO) phonons). The influence of a realistic interface heterojunction potential with a finite barrier and conduction band bending are taken into account. The properties of electron mobility versus Al concentration, electronic density and pressure are given and discussed, respectively. The results show that the electron mobility increases with Al concentration and electronic density, whereas decreases with pressure from 0 to 40 kbar obviously. The Al concentration dependent and the electron density dependent contributions to the electron mobility from the scattering of IO phonons under pressure becomes more obvious. The variation of electron mobility with the Al concentration and electron density are dominated by the properties of IO and LO phonons, respectively. The effect of IO phonon modes can not be neglected especially for higher pressure and electronic density.