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     

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.     

Influence of spin–orbit interactions on the polaron properties in wurtzite semiconductor quantum well

We have study the simultaneous effect of Rashba and Dresselhaus spin–orbit interactions on the polaron properties in wurtzite semiconductor quantum wells. The linear and cubic contributions of the bulk Dresselhaus spin–orbit coupling and the effects of phonon confinement on electron–optical-phonon interaction Hamiltonians are taken into account. We have found analytical solutions for the polaron energies as well as polaron effective mass within the range of validity of perturbation theory. It is shown that the polaron energy and effective mass correction are both significantly enhanced by the spin–orbit coupling. Wave number dependent phonon contribution on the electron energy has minima and varies differently of the spin-up and spin-down states. Polaron self-energy due to interface optical phonon modes has larger values than of the confined optical phonon modes ones. The polaron effective mass exhibits anisotropy and the contribution of the Dresselhaus spin–orbit coupling term on the polaron effective mass is dominated by Rashba one.     

Bound polaron in a wurtzite GaN/AlxGa1 − xN ellipsoidal finite-potential quantum dot

A variational method is used to study the ground state of a bound polaron in a weakly oblate wurtzite GaN/Al_xGa_1 − xN ellipsoidal quantum dot. The binding energy of the bound polaron is calculated by taking the electron couples with both branches of LO-like and TO-like phonons due to the anisotropic effect into account. The interaction between impurity and phonons has also been considered to obtain the binding energy of a bound polaron. The results show that the binding energy of bound polaron reaches a peak value as the quantum dot radius increases and then diminishes for the finite potential well. We found that the binding energy of bound polaron is reduced by the phonons effect on the impurity states, the contribution of LO-like phonon to the binding energy is dominant, the anisotropic angle and ellipticity influence on the binding energy are small.     

多原子半无限晶体中表面极化子的内部激发态

研究多原子半无限晶体中电子与表面光学(SO)声子耦合强,而与体纵光学(LO)声子耦合弱的极化子的激发态性质.采用线性组合算符和幺正变换方法导出与SO声子耦合强而与LO声子耦合弱情形下极化子的基态能量、第一内部激发态能量和激发能量.结果表明,多原子半无限晶体中与SO声子耦合强,而与LO声子耦合弱的极化子的基态能量、第一内部激发态能量不仅包含不同支LO声子和不同支SO声子与电子耦合的能量,而且也包含不同支SO声子之间相互作用贡献的附加能量.激发能量与体纵光学声子无关.     

量子阱中极化子的声子平均数

采用有效质量近似下的变分法,考虑到电子同时与表面光学声子和体纵光学声子相互作用,研究了无限深量子阱中极化子的表面光学声子平均数,体纵光学声子平均数和光学声子平均数。讨论了电子与体纵光学声子耦合强度α,阱宽L和势垒材料Al_xGa_1-xAs中Al的含量x对上述光学声子平均数的影响。以GaAs/Al_xGa_1-xAs量子阱为例进行了数值计算。结果表明:量子阱中表面光学声子平均数随耦合强度α,阱宽L和Al含量x增大而增大。量子阱中体纵光学声子平均数随耦合强度α,阱宽L的增大而增大。光学声子平均数随耦合强度α,阱宽L和Al含量x的增大而增大。     

极性晶体中极化子效应对界面强耦合激子性质的影响

在Huybrechts关于强耦合极化子的模型基础上,采用LLP变分法研究了极性晶体中激子与IO声子强耦合、与LO声子弱耦合体系的基态能量,推导出了激子的自陷能和诱生势的表达式,并以AgCl/AgBr晶体为例进行了数值计算,结果表明,激子的自陷能不仅与激子的坐标z有关,而且电子-空穴间距离ρ对激子自陷能的影响也十分显著;激子的诱生势不仅与电子-空穴间距离ρ有关,而且激子距离晶体界面的位置z对诱生势的影响也十分显著.     

Cyclotron resonance of a polaron in a realistic heterojunction and its pressure effect

The Larsen perturbation method is adopted to study the influence of magnetic fields on polarons in realistic heterojunctions in a quasi-two-dimension approximation. The interaction between an electron and both the bulk longitudinal optical phonons and the two branches of interface optical phonons is taken into account to show the influence of magnetic fields at different ranges on the polaron cyclotron mass due to the coupling of the electron with each branch of phonon modes. The result indicates that not only do the bulk phonons influence the polaron cyclotron mass, but the interface phonons do as well. The pressure effect on the cyclotron mass is also discussed.     

Polaronic effects on the energy levels of a double donor impurity in quantum wells in the presence of a magnetic field

In the presence of a magnetic field the Hamiltonian of the single or double polaron bound to a helium-type donor impurity in semiconductor quantum wells (QWs) are given in the case of positively charged donor center and neutral donor center. The couplings of an electron and the impurity with various phonon modes are considered. The binding energy of the single and double bound polaron in Al_xlGa _1-xlAs/GaAs/Al_xrGa _1-xrAs QWs are calculated. The results show that for a thin well the cumulative effects of the electron-phonon coupling and the impurity-phonon coupling can contribute appreciably to the binding energy in the case of ionized donor. In the case of neutral donor the contribution of polaronic effects are not very important, however the magnetic field significantly modifies the binding energy of the double donor. The comparison between the binding energies in the case of the impurity placed at the quantum well center and at the quantum well edge is also given. Received 16 February 1999     

The phonon effects on the impurity states in cylindrical quantum wire with a finite confining potential

The variational method and the effective mass approximation are applied to calculate the binding energies of the hydrogenic impurity states in a cylindrical quantum wire with finite deep potential well. The phonon effects on the impurity states are considered by taking both the couplings of the electron-phonon and the impurity ion-phonon into account. The numerical results for the GaAs cylindrical quantum wire are given and discussed. It is found that the ion-phonon interaction reduces the impurity binding energy and supplies key contribution to the energy shift, but the electron-phonon coupling enhances the binding energy less. Longitudinal optical (LO) phonons play more important role than interface optical (IO) phonons in the impurity potential screening. The polaron effect caused by LO phonons is more important when the wire is thinner, otherwise the LO phonons are dominant for the thicker wires.     

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.     

Polaron self-energy and effective mass in a freestanding cylindrical quantum wire

The polaron self-energy and correction to the electron effective mass in a freestanding quantum wire is investigated by the perturbation approach.The polaron effect of the electron-confined longitudinal optical (LO) phonon and surface optical (SO) phonon interactions are separately worked out. Numerical calculation on a GaAs quantum wire shows that the confined LO phonon contribution to the polaron self-energy is relatively small for a narrow wire and gradually approach that of the bulk material when the radius of the wire increases. While the contribution of the SO phonon modes is big for small wire radius and then decreases as the radius increases.     

Quantum adiabatic polarons by translationally invariant perturbation theory

The translationally invariant diagrammatic quantum perturbation theory (TPT) is applied to the polaron problem on the 1D lattice, modeled through the Holstein Hamiltonian with the phonon frequency ω₀, the electron hopping t and the electron-phonon coupling constant g. The self-energy diagrams of the fourth-order in g are calculated exactly for an intermittently added electron, in addition to the previously known second-order term. The corresponding quadratic and quartic corrections to the polaron ground state energy become comparable at t/ω₀>1 for g/ω₀∼(t/ω₀) ^1/4 when the electron self-trapping and translation become adiabatic. The corresponding non adiabatic/adiabatic crossover occurs while the polaron width is large, i.e. the lattice coarsening negligible. This result is extended to the range (t/ω₀)^1/2>g/ω₀>(t/ω₀)^1/4>1 by considering the scaling properties of the high-order self-energy diagrams. It is shown that the polaron ground state energy, its width and the effective mass agree with the results found traditionally from the broken symmetry side, kinematic corrections included. The Landau self-trapping of the electron in the classic self-consistent, localized displacement potential, the restoration of the translational symmetry by the classic translational Goldstone mode and the quantization of the polaronic translational coordinate are thus all encompassed by a quantum theory which is translationally invariant from the outset. This represents the first example, open to various generalizations, of the capability of TPT to hold through the adiabatic symmetry breaking crossover. Plausible arguments are also given that TPT can describe the g/ω₀>(t/ω₀)^1/2 regime of the small polaron with adiabatic or non-adiabatic translation, i.e., that TPT can cover the whole g/ω₀, t/ω₀ parameter space of the Holstein Hamiltonian.     

Effect of electron-phonon interaction on surface states in a ternary mixed crystal

A variational theory is proposed to study the surface states of electrons in a semi-infinite ternary mixed crystal, by taking the effect of electron-surface optical (SO) phonon interaction into account. The energy and the wave function of the electronic surface-states are calculated. The numerical results of the energies of the surface states of the polarons and the self-trapping energies are obtained as functions of the composition x and surface potential V₀ for several ternary mixed crystal materials. The results show that the electron-phonon interaction lowers the surface-state levels with the energies from several to scores of meV. It is also found that the self-trapping energy of the surface polaron has a minimum at some middle value of the composition x. It is indicated that the electron-phonon coupling effect can not be neglected. Received 4 January 1999 and Received in final form 7 January 2000     

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…     

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.     

弱耦合多原子半无限晶体中磁极化子的激发能量

近年来国内外对多原子极性晶体中磁极化子性质的研究十分活跃,Zorkani等采用变分法计算了束缚磁极化子的基态能量,Kandemir等采用束缚朗道态讨论了二维大磁极化子的基态和第一激发态能量,国内一些学者采用微扰法和新颖算符法讨论了多原子极性晶体中表面和体磁极化子的性质。采用线性组合算符和幺正变换,研究磁场中多原子半无限极性晶体中电子和光学声子弱耦合相互作用所产生的极化子的第一激发态能量及平均声子数。结果表明:当电子无限接近晶体表面时,磁极化子的基态能量仅为Landau能量;第一激发态能量为Landau基态能量的2倍;平均声子数等于各支与电子耦合的体光学声子数和表面光学声子数之和。而当电子处于晶体深处时,磁极化子的基态能量却为Landau基态能量与各支体光学声子以及表面光学声子分别耦合的能量之和;第一激发态能量仍为Landau基态能量的2倍;平均声子数等于各支与电子耦合的体光学声子数和与所处深度有关的各支体光学声子数之和,而与各支表面光学声子无关。     

抛物量子阱中束缚极化子的极化势和结合能

利用改进的Lee-Low-Pines(LLP)方法,用变分法计算了无限深抛物量子阱中同时考虑与体纵光学声子和界面纵光学声子相互作用的束缚极化子的极化势和结合能.数值计算得出:阱宽较大时极化势很小,阱宽较小时极化势较大,所以对于较窄的抛物阱必须考虑极化势.对于给定阱宽的抛物阱,随着远离阱中心极化势迅速减小,当到达阱的界面附近极化势又开始增大.阱宽较小时,束缚极化子的结合能随着阱宽L的增大而急剧减小;阱宽较大时,结合能减小的非常缓慢,最后接近体材料中的三维值.     

抛物量子点中弱耦合束缚极化子的相互作用能

研究了抛物量子点中弱耦合束缚极化子的性质,采用改进的线性组合算符和幺正变换方法导出了束缚极化子的振动频率、有效质量和相互作用能。讨论了量子点的有效受限长度、电子LO声子耦合强度和库仑场对抛物量子点中弱耦合极化子的振动频率、有效质量和相互作用能的影响。数值计算结果表明:弱耦合束缚极化子的振动频率和相互作用能随有效受限长度的减少而急剧增大,振动频率随库仑势以及电子LO声子耦合强度的增加而增加,而相互作用能随库仑势以及电子LO声子耦合强度的增加而减小。有效质量仅与电子LO声子耦合强度有关。     

Properties of a Bound Polaron under a Perpendicular Magnetic Field

We investigate the influence of a perpendicular magnetic field on a bound polaron near the interface of a polar-polar semiconductor with Rashba effect. The external magnetic field strongly changes the ground state binding energy of the polaron and the Rashba spin-orbit （SO） interaction originating from the inversion asymmetry in the heterostructure splits the ground state binding energy of the bound polaron. In this paper, we have shown how the ground state binding energy will be with the change of the external magnetic field, the location of a single impurity, the wave vector of the electron and the electron areal density, taking into account the SO coupling. Due to the presence of the phonons, whose energy gives negative contribution to the polaron＇s, the spin-splitting states of the bound polaron are more stable, and we find that in the condition of week magnetic field, the Zeeaman effect can be neglected.