Effects of screening of the interaction potential on the mobility characteristics of degenerate surface layers in compound semiconductors at low lattice temperatures

The rates of scattering of the conduction electrons in degenerate two-dimensional electron gas in the surface of compound semiconductors at low lattice temperatures have been obtained for interaction with the piezoelectric and deformation potential acoustic phonons, under different prevailing conditions. The calculations have been carried out taking due account of the screening of the interaction potential at low temperatures where again the phonon energy cannot be neglected in comparison to the average thermal energy of the electrons and, as a result, the equipartition approximation for the phonon distribution can hardly be valid. The scattering rates thus obtained for inversion layers in GaAs and ZnO are found to depend upon the carrier energy, the lattice temperature and the level of degeneracy in quite involved manners, which are very different from what follows if one makes the simplifying approximation of negligible phonon energy or disregards the effects of screening. The mobility characteristics are then obtained using these scattering rates. The results show how the screening of the interaction potential and the finite energy of the intravalley acoustic and piezoelectric phonons significantly change the mobility characteristics of the degenerate surface layers at low lattice temperatures. The inadequacies of the present theory are pointed out and recommendations for possible refinements are discussed.     

Piezoelectric scattering limited mobility characteristics of a degenerate surface layer in compound semiconductors at low lattice temperatures

The theory is developed for piezoelectric scattering rate of carriers in a degenerate surface layer under the condition of low temperature when the approximations of the well-known traditional theory are not valid. The scattering rates thus obtained are then used to estimate the zero-field mobility characteristics for the surface layers under similar condition of low temperature. The results for the surface layers in GaAs and ZnO show that when one takes into account either the degeneracy of the carrier ensemble or the finite energy of the phonons or both, the energy dependence of the scattering rates changes significantly from what follows for a non-degenerate ensemble or from the traditional theory, where one makes use of the high-temperature approximation and thus assumes equipartition law for the phonon distribution, and neglects the phonon energy in the energy balance equation of the electron–phonon system. It is observed that the zero-field mobility characteristics that follow from these scattering rates are interesting in that they are quite different from what turns out either for a non-degenerate ensemble or in the high-temperature approximations.     

Lattice-controlled electron transport characteristics in quantized surface layers at low temperature

A theory of intravalley acoustic scattering of the carriers in a non-degenerate two-dimensional electron gas is developed here under the condition of low lattice temperature when the assumptions of the well-known traditional theory are not valid. The scattering rates thus obtained are then used to estimate the zero-field mobility characteristics in an n-channel Si inversion layer. It is found that the finite energy of the phonons makes the energy and lattice temperature dependence of the scattering rate, and consequently the lattice temperature dependence of the mobility, significantly different from what follows, in the light of traditional theory which assumes equipartition law for the phonon distribution and neglects the phonon energy in comparison to the carrier energy.     

Effects of Screening and Finite Phonon Energy on the Transport in Quantized Layers in Compound Semiconductors

Analytical expressions for the momentum relaxation times of the conduction electrons in a non-degenerate two dimensional electron gas in the surface of a compound semiconductor have been obtained for interactions with the piezoelectric and deformation potential acoustic phonons taking due account of the screening of the perturbing potential under the the condition of low lattice temperature when the phonon energy cannot be neglected in comparison to the average thermal energy of the electrons and for that matter the equipartition approximation for the phonon distribution is hardly valid. The relaxation times calculated for inversion layers in GaAs and ZnO are found to depend upon the carrier energy, the lattice temperature and the impurity concentration in rather complex manners which are significantly different from what follows from the traditional approach of either neglecting the phonon energy or disregarding the process of screening. It is seen how the finite value of the phonon energy and the screening of the perturbing potential change the mobility characteristics significantly at the low lattice temperatures. The temperature dependence of the zero field mobility that one obtains using the relaxation times calculated here is quite different from the traditional laws.     

Lattice controlled transport in quantum wires at low temperatures

Theory of acoustic scattering rate of the carriers in a quantum wire has been developed under the condition of low temperature when the approximations of the traditional theory are hardly valid. The scattering rates thus obtained are then used to estimate the zero-field mobility characteristics in a narrow channel GaAs–GaAlAs quantum wire. On comparison with other available results it is revealed that the finite energy of the acoustic phonons and the complete phonon distribution without any truncation lead to significantly different transport characteristics at low temperatures.     

Mobility as controlled by the transverse component of phonon wave vector in quantum layers at low temperatures

Without resorting to either the Kawaji’s simplified model of interaction with only two-dimensional phonons or to the equipartition approximation for the phonon distribution, the characteristics of the momentum relaxation time of the conduction electrons in a quantized surface layer for interaction with intravalley acoustic phonons have been analysed under the condition of low temperature. The scattering and the mobility characteristics thus obtained for an n-channel (1 0 0)-oriented Si inversion layer are apparently quite different from what follows in the traditional framework.     

Influence of Nonequilibrium LO Phonons on High-frequency Performance of One-dimensional Hot Electrons in Quantum Wires of Polar Semiconductors

Small-signal ac transport of degenerate one-dimensional hot electrons in quantum wires of GaAs and In_0.53Ga_0.47As is studied for lattice temperatures of 77 K and 300 K. The carrier energy loss via polar optic phonons and momentum losses via polar optic phonons, acoustic phonons and ionized impurities are included in the calculations. Alloy disorder scattering in momentum loss is additionally incorporated for (In,Ga)As. The consideration of nonequilibrium optical phonons or hot phonons is found to enhance the 3dB cut-off frequency (f_3dB) considerably, where the ac mobility falls to 0.707 of its low frequency value. f_3dB is generally higher for (In,Ga)As quantum wire than for GaAs.     

Hot electrons in Si inversion layer

The energy losses per electron to phonons (both acoustic and optical) are calculated for Si(100) inversion layer taking the subband structure of electron energy spectrum fully into account. The electron mobility variations with applied field are studied by energy balance method. We examine two extreme cases: (1) the intervalley transitions connect any pair of subbands in respective valleys with the same transition matrix; (2) the intervalley transitions connect only the lowest subbands in each valley. It turns out that we can choose the magnitude of intervalley transition amplitude such that experimental data lie in between the theoretical results in two cases mentioned above at both lattice temperatures T = 77 and 300 K.     

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.     

Semiconducting properties of CuIn5S8 single crystals I. Electrical properties

The electrical resistivity and Hall coefficient of n-type CuIn₅S₈ single crystals were measured in the temperature range from 80 K–500 K. The energy gap at 0 K was determined to be 1.4 eV. The donor levels at 0.017 eV and 0.09 eV below the conduction band are identified. The mobility data are analysed assuming scatterings by acoustic and polar optical phonons and ionized impurities.     

Effect of Miniband Dispersion on Inelastic Scattering of Superlattice Electrons by Acoustic Phonons

Within the framework of the Boltzmann equation, formulas for calculating the effective relaxation time and mobility of superlattice electrons are derived with allowance for inelastic scattering on acoustic phonons and dispersion of the miniband energy spectrum depending on the longitudinal wave vector. The dependences of longitudinal and transverse mobilities of the nondegenerate electronic gas of the GaAs/Al_0.36Ga_0.64As superlattice with the quantum well 5 nm wide on the potential barrier width and temperature are analyzed numerically. It is demonstrated that inelasticity of scattering and miniband dispersion significantly increase the electron mobility, and its temperature dependence becomes more pronounced at low temperatures.     

Electron-phonon interaction and transport in semiconducting carbon nanotubes

We calculate the electron-phonon scattering and binding in semiconducting carbon nanotubes, within a tight-binding model. The mobility is derived using a multiband Boltzmann treatment. At high fields, the dominant scattering is interband scattering by LO phonons corresponding to the corners K of the graphene Brillouin zone. The drift velocity saturates at approximately half the graphene Fermi velocity. The calculated mobility as a function of temperature, electric field, and nanotube chirality are well reproduced by a simple interpolation formula. Polaronic binding give a band-gap renormalization of approximately 70 meV, an order of magnitude larger than expected. Coherence lengths can be quite long but are strongly energy dependent.     

Rate of energy loss to intravalley acoustic modes in a degenerate surface layer at low lattice temperatures

The rate of loss of the energy of non-equilibrium electrons due to inelastic interaction with intravalley acoustic phonons in a degenerate surface layer is calculated for low temperatures when the approximations of the well-known traditional theory are not valid. The loss characteristics for GaAs and Si seem to be significantly different compared to what follows from the traditional approximations.     

纤锌矿AlGaN/AlN/GaN异质结构中光学声子散射影响的电子迁移率

对含有AlN插入层纤锌矿Al_xGa_1-xN/AlN/GaN异质结构,考虑有限厚势垒和导带弯曲的实际 异质结势,同时计入自发极化和压电极化效应产生的内建电场作用,采用数值自洽求解薛定谔方程和泊松方程, 获得二维电子气(2DEG)中电子的本征态和本征能级.依据介电连续模型和Loudon单轴晶体模型, 用转移矩阵法分析该体系中可能存在的光学声子模及三元混晶效应.进一步, 在室温下计及各种可能存在的光学声子散射,推广雷-丁平衡方程方法,讨论2DEG分布及二维电子迁移率的 尺寸效应和三元混晶效应.结果显示: AlN插入层厚度和Al_xGa_1-xN势垒层中Al组分的增加均会 增强GaN层中的内建电场强度,致使2DEG的分布更靠近异质结界面,使界面光学声子强于其他类型的 光学声子对电子的散射作用而成为影响电子迁移率的主导因素.适当调整AlN插入层的厚度和Al组分, 可获得较高的电子迁移率.     

Exciton absorption of light in layer crystals

Anomalies in the temperature dependence of the integral characteristics of exciton light absorption in layer crystals are found. To explain these, the mechanisms of exciton excitation energy relaxation are first proposed which take into account the specific features of a dissipative subsystem in layer crystals, the occurrence of bending waves in the spectrum of acoustic phonons and of low-energy optic phonons.     

Theory of nonlinear effects in semiconductors with a nondiffusion approximation for acoustic phonons

Momentum and energy balance equations in impurity semi-metals and degenerate semiconductors are derived and investigated in a nondiffusion approximation for the acoustic phonons with arbitrary heating and entrainment of electrons and phonons taken into account. It was shown that the diffusion approximation is not satisfied even for relatively weak electrical fields. In cases of thermal entrainment and no heating of the phonons, cases are possible when the electron temperature becomes equal to and less than the lattice temperature, which is associated with radiation obtained from the energy field by electrons in the form of acoustic phonons at a point of acoustic instability. If mutual entrainment and heating of electrons and phonons occurs then the crystal boundaries are the main channel of energy and momentum relaxation. Necessary conditions delimiting the strong changes of all the galvano- and thermomagnetic effects at a point of acoustic instability are found in every specific case.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 11–16, November, 1990.     

Phonon- and impurity-limited dc mobility calculation from frequency derivatives of time correlation functions. I. General formulae derivation

Starting from the first principles expression for the dc electric conductivity, as derived in 1982 by the authors, new expressions for mobility in semiconductors are derived, for the case when the carriers spectrum is parabolic and the scatterers are phonons and point impurities.     

Size dependent ultrasonic absorption in superfluid helium

Ultrasonic waves in liquid He II at temperatures below 0.6°K can be absorbed by thermal phonons in 3- or 4-phonon processes. For the case that the mean free path of thermal phonons is sufficiently long 3-phonon processes are generally excluded because energy and momentum cannot be conserved. The conservation requirements cannot be fullfilled because the group velocity of thermal phonons is lower than the ultrasonic velocity due to dispersion. — The purpose of this note is to point out that insmall samples of liquid the uncertainty in phonon energy prevents a violation of the conservation laws for 3-phonon processes. In small volumes of liquid, ultrasonic waves are therefore strongly absorbed in 3-phonon processes, while in larger volumes of liquid this contribution to the absorption is absent. — A similiar size dependent absorption is to be expected for longitudinal waves at low temperatures in ideal crystals.     

抛物量子点中弱耦合激子的光学声子平均数

研究了电子-体纵光学声子弱耦合情况下,抛物量子点中激子的性质。在有效质量近似下,采用线性组合算符和幺正变换方法研究了抛物量子点中弱耦合激子的基态能量和光学声子平均数。以GaAs半导体为例进行了数值计算,结果表明:弱耦合情况下,激子的光学声子平均数基态的能量和量子点受限强度的增大而减小,随量子点半径的增大而增大。     

Magnetoelectronic transport of the two-dimensional electron gas in CdSe single quantum wells

Hall mobility and magnetoresistance coefficient for the two-dimensional (2D) electron transport parallel to the heterojunction interfaces in a single quantum well of CdSe are calculated with a numerical iterative technique in the framework of Fermi-Dirac statistics. Lattice scatterings due to polar-mode longitudinal optic (LO) phonons, and acoustic phonons via deformation potential and piezoelectric couplings, are considered together with background and remote ionized impurity interactions. The parallel mode of piezoelectric scattering is found to contribute more than the perpendicular mode. We observe that the Hall mobility decreases with increasing temperature but increases with increasing channel width. The magnetoresistance coefficient is found to decrease with increasing temperature and increase with increasing magnetic field in the classical region.