无限深量子阱中强耦合极化子的基态结合能

研究了无限深量子阱中极化子的基态性质,采用线性组合算符和变分相结合的方法导出了强耦合极化子的振动频率λ、基态能量E₀和基态结合能E_b,讨论了阱宽L和电子-LO声子耦合强度α对强耦合极化子的振动频率λ、基态能量E₀和基态结合能E_b的影响。通过数值计算,结果表明:强耦合极化子的振动频率和基态结合能随阱宽L的增大而减小,随电子-LO声子耦合强度α的增强而增大;基态能量随阱宽L的增大而减小,其绝对值随电子-LO声子耦合强度α的增强而增大;当量子阱阱宽L趋近于无限大和无限小两种极限情况下,分别与三维和二维极化子的结果相一致。     

The role of spatial dispersion of an electromagnetic wave in its penetration through a quantum well

The theory of light penetration through a quantum well in a strong magnetic field perpendicular to the well plane is developed under the conditions where interband transitions occur in the well. The light wavelength is assumed to be comparable to the well width. The relationships for the reflection, absorption, and transmission are derived with due regard for the spatial dispersion of a monochromatic light wave and the difference between the refractive indices of the quantum well and the barrier. The normal incidence of light with respect to the well plane is considered, and one excited level is taken into account. It is demonstrated that the above two factors most strongly affect the reflection, because the reflection from the well boundaries appears in addition to the reflection caused by interband transitions in the quantum well. The most radical changes in the reflection are observed in the case when the reciprocal radiative lifetime of the excited state in the quantum well is short compared to the reciprocal nonradiative lifetime. In the range of large well widths, the applicability of the theory is limited by the existence condition of quantum well levels.     

Vertical hall effect in GaAs quantum wells

Applying orthogonal in-plane electric and magnetic fields in a 2D system leads to the development of a Hall voltage across the width of the quantum well when the cyclotron orbit is greater than the well width. Tang and Butcher [1] have calculated the developed Hall voltage for a parabolic quantum well where they find that the Hall voltage is dependent on the frequency associated with the harmonic potential in the well. The limitation of this model is that it does not enable one to determine the well width dependence of the Hall Voltage, nor is it a particularly good model for a quantum well. It is also difficult to compare their model with the bulk result which would apply at large well widths. In this work we present a model calculation which considers a square quantum well and hence is able to predict the well width dependence of the Hall Voltage and compare the large well width case to the bulk result. An electro-optic probing method previously used to measure bulk Hall voltages [2] is shown to be capable of measuring the Hall 'voltage across a quantum well, and therefore can be used to confirm the prediction of the model presented here.     

水平井与直井混合注采井网的流场计算——以五点法注采井网为例

基于保角变换和镜像反映原理,建立五点法水平井与直井混合注采井网流场数学模型,导出其势函数和流函数数学表达式,得到五点法混合注采井网内部等势线和流线分布.研究水平井长度、水平井与直井连线夹角、平面各向异性及水平井不同平面位置等因素对混合注采井网内部流场分布的影响.结果表明：混合注采井网水平井跟端和趾端,流线分布相对密集,两端位置产液能力较强;水平段越长,其流线控制的泄油面积越大;水平井与直井连线成45°角时,水平井与正对的两口直井间的驱替强度相对较大;水平井垂直于主渗透率方向时,流线均匀密集地汇聚到生产井,易形成线性驱替;混合注采井网内部水平井偏离中心位置程度越大,流线分布疏密分化越明显.     

Inter-sub-band transitions and binding energies of donor impurities in a modulation-doped quantum well in the presence of electric field

In this study, we have investigated theoretically the effects of the electric field and doping concentration on the optical transitions in a modulation-doped GaAs-AlGaAs quantum well for different well widths. The binding energies of the donor have also been computed using a trial wave function with two parameters in the framework of an effective-mass approximation. The electronic structure of a modulation-doped quantum well under the electric field is determined by solving the Schrödinger and Poisson equations self-consistently in the effective-mass approximation. The results obtained show that inter-sub-band transitions and the energy levels in the modulation-doped quantum well can be significantly modified and controlled by the well width and donor concentration. The sensitivity to the well widths of the absorption coefficient can be used in various optical semiconductor devices’ applications.     

Polaron Energy and Effective Mass in Parabolic Quantum Wells

The energy and effective mass of a polaron in a parabolic quantum well are studied theoretically by using LLP-like transformations and a variational approach. Numerical results are presented for the polaron energy and effective mass in the GaAs/Al0.3Ga0.7As parabolic quantum well. The results show that the energy and the effective mass of the polaron both have their maxima in the finite parabolic quantum well but decrease monotonously in the infinite parabolic quantum well with the increasing well width. It is verified that the bulk longitudinal optical phonon mode approximation is an adequate formulation for the electron-phonon coupling in parabolic quantum well structures.     

An equation of state contribution for dipolar and quadrupolar square-well fluids

A dipolar–quadrupolar contribution to the residual Helmholtz energy for a polar square well (a square well plus either a point dipole or a point quadrupole) fluid is developed based on the Padé approximation. Taking the square well system as reference, the contribution is formulated using an expansion for radial distribution function of the reference system. In addition to square well potential parameters the contribution depends only on dipole and quadrupole moments. This term is added as perturbation to a generalized equation of state for square well fluids. The results are then compared with the available simulation data in the literature. With the new equation obtained, it was possible to predict liquid–vapour equilibrium properties and critical properties of polar square well fluids more accurately than with available perturbation theories for multipolar square well systems. Application of the equation of state to a real dipolar (water) and a real quadrupolar (carbon dioxide) fluid indicated that the polar contribution greatly improved the predictions of saturation properties. Accurate prediction of critical properties for polar square well fluids remains as a challenge. This work can be useful in the development of better equations of state.     

氮化物抛物量子阱中类氢杂质态能量

采用变分方法研究氮化物抛物量子阱(GaN/Al_xGa_1-xN)材料中类氢杂质态的能级,给出基态能量、第一激发态能量、结合能和跃迁能量等物理量随抛物量子阱宽度变化的函数关系.研究结果表明,基态能量、第一激发态能量、基态结合能和1s→2p±跃迁能量随着阱宽L的增大而减小,最后接近于GaN中3D值.GaN/Al_0.3Ga_0.7N抛物量子阱对杂质态的束缚程度比GaAs/Al_0.3Ga_0.7As抛物量子阱强,因此,在GaN/Al_0.3-Ga_0.7N抛物量子阱中束缚于杂质中心处的电子比在GaAs/Al_0.3Ga_0.7As抛物量子阱中束缚于杂质中心处的电子稳定.     

混合井网条件下加密井产能计算模型及应用

对于以直井、水平井混合井网开采的油藏,后期加密的水平生产井产能计算应综合考虑其他油水井的干扰.基于镜像反映原理与微元线汇理论,建立任意混合井网条件下加密水平井稳态产能计算半解析模型,考虑混合井网内部其他油水井干扰及井筒内由于井壁摩擦与流体加速度造成的压力降对加密水平井产能的影响,适用于任意混合井网条件下(井型任意性、井数目任意性、井位任意性)加密水平井产能计算.     

Diffusion and convection after escape from a potential well

The escape by diffusion of a particle from a potential well in one dimension is strongly influenced by the application of a field in the adjacent half-space. At long times the probability distribution becomes a uniformly moving and steadily broadening gaussian in this half-space. The mean time of escape from the well is given by a simple expression in terms of the mean first passage time and the coefficient of the long-time tail in the occupation probability of the well in the absence of the field. Transient effects in space and time are studied in explicit form for a parabolic potential well.     

Resonant Tunnelling in Barrier-in-Well and Well-in-Well Structures

A Schrödinger equation is solved numerically for a barrier in a quantum well and a quantum well in another well structure by the transfer matrix technique. Effect of structure parameters on the transmission probabilities is investigated in detail. The results suggest that symmetry plays an important role in the coupling effect between the quantum wells. The relationship between the width of the inner well and the resonant energy levels in well-in-well structures is also studied. It is found that the ground state energy and the second resonant energy decrease with increasing width of the inner well, while the first resonant energy remains constant.     

Coherence resonance in an excitable potential well

The excitable behaviour is considered as motion of a particle in a potential field in the presence of dissipation. The dynamics of the oscillator proposed in the present paper corresponds to the excitable behaviour in a potential well under condition of positive dissipation. Type-II excitability of the offered system results from intrinsic peculiarities of the potential well, whose shape depends on a system state. Concept of an excitable potential well is introduced. The effect of coherence resonance and self-oscillation excitation in a state-dependent potential well under condition of positive dissipation are explored in numerical experiments.     

Electronic states in a step quantum well in a magnetic field

The quantum states and energy spectrum of an electron in a rectangular step quantum well in a magnetic field parallel to the plane of two-dimensional electronic gas are investigated. It is shown that the joint effect of a magnetic field and confining potential of quantum well results in radical change of the electron energy spectrum. The energy dependencies on the parameters of the quantum well and magnetic field induction are investigated. Numerical calculations are carried out for an AlAs/ GaAlAs/ GaAs/ AlAs step quantum well.     

无限深势阱问题的可视化研究

基于计算软件对一些常见的无限深势阱进行了可视化研究,并设计了GUI界面实现对势阱的选择.在选定势阱后,设置好相应的势阱参数和量子数,便可依次绘制出低维势阱的波函数、概率密度函数和三维势阱中的电子云图像.文中分析了二维和三维势阱中能级的简并度问题,并重点讨论了不同势阱波函数和概率密度函数随量子数的变化规律.将势阱问题可视化可以方便分析不同条件下波函数的物理图像,有助于量子力学课程中的教师教学与学生学习.     

Light propagation characteristics in quantum well structures of photonic crystals

Two-dimensional （2D） closed-cavity single quantum well （SQW） and multiple quantum well （MQW） structures are proposed based on the traditional 2D open-cavity SQW structures of photonic crystals. The numerical calculation results show that the proposed structures can greatly improve the optical characteristics compared with the traditional structures. It is found that the barrier thickness has a great impact on the optical characteristics of the closed-cavity MQW structures： when the barrier thickness is narrower, each resonant peak which appears in the SQW would split, the number of split times is just equal to the number of wells, and each well in the MQW structures is a travelling-wave-well, similar to the well in the open-cavity SQW structures; when the barrier thickness is wider, there is no effect of spectral splitting, and each well in the MQW structures is a standing-wave-well, just like the well in the closed-cavity SQW. The physical origin of different field distributions and the effect of the spectral splitting are provided.     

Electronic molecule-like spectrum of quantum wells in crossed fields

We show that an electron confined to a single finite parabolic quantum well in crossed electric and magnetic fields can behave as a double quantum well system. The magnetic field is parallel to the heterostructure layers and the electric field is perpendicular to those. For a suitable choice of both fields and quantum well width, the electron can be confined to a double quantum well effective potential that is very similar to the electronic potential model for diatomic molecules. The double quantum well spectrum is calculated using a numerical algorithm based on semiclassical methods. A physical interpretation of this quantum system is given based on the analogy to the electrons bound to diatomic molecules.     

Photoionization of a charged exciton in a GaAs/GaAlAs corrugated quantum well

Binding energies of a charged exciton as a function of well width of a GaAs/GaAlAs corrugated quantum well are investigated. The calculations have been performed by the variational method based on a two parametric trial wave function within a single band effective mass approximation. We have also included the effect of nonparabolicity of the conduction band of GaAs. We study the spectral dependence of the charged exciton in a GaAs/GaAlAs corrugated quantum well as a function of well width. The photoionization cross section for the charged exciton placed at the center of the quantum well is computed as a function of normalized photon energy. The cross-section behavior as a function of incident energy is entirely different in the two cases of radiation being x-direction (along the growth direction) or z-direction. The interband emission energy as a function of well width is calculated and the dependence of the photoionization cross section on photon energy is carried out for the charged excitons. The resulting spectra are brought out for light polarized along and perpendicular to the growth direction. The results show that the charged exciton binding energy, interband emission energy and the photoionization cross section depend strongly on the well width. Our results are compared with the other existing literature available.     

WELL-WIDTH DEPENDENCE OF THE EXCITON LIFETIME IN GaAs/AlGaAs QUANTUM WELLS

The dependence of the excitonic lifetime on the well width has been studied in conventional GaAs/AlGaAs quantum wells. Two clearly different variations of the measured excitonic lifetime have been observed. For wide well widths, we find a nearly linear decrease of the lifetime with decreasing well width. However, when the well is further decreased, a saturation and even increase of the lifetime with decreeing well width are observed. The experimental data are compared with the theory of radiative excitonic recombination, and show that well width dependence of the measured photoluminescence lifetime can be attributed mainly to the change of the excitonic effective volume and the overlap integral as well.     

Effects of intersubband interaction on multisubband electron transport in single and double quantum wells

The multisubband electron transport properties are studied for doped single quantum well and gated double asymmetric quantum well structures. The effects due to intersubband interaction and screening of the ionized impurity scattering are also investigated. We show that intersubband coupling plays an essential role in describing the screening properties as well as the effect of ionized impurity scattering on the mobility in a doped single quantum well. For coupled double quantum well structures, negative transconductance is found theoretically which is due to resonant tunneling between the two quantum wells.     

单势阱粒子溢流模型中热力学量的涨落效应

采用相空间积分方法严格导出了各态历经条件下单势阱粒子溢流模型中系统温度和阱内粒子数涨落的解析表达式,着重讨论了热力学量涨落与总粒子数和势阱体积之间的关系.研究表明,系统总粒子数越少以及势阱体积越小,热力学涨落越显著,并且热力学涨落与阱内粒子的溢出密切相关.粒子的溢出和系统负比热及热力学大幅涨落的发生存在一一对应的关系,这一对应关系的根源可以从表观能量逆均分来理解.