Mobility of electrons in nondegenerate semiconductors considering electron-electron scattering

Spitzer andHärm [1] have investigated the velocity distribution of electrons in the presence of a weak electric field in an ionized gas. Introducing the concept of time of relaxation τ′, due to electron-ion and electron-electron scattering, and using the results ofSpitzer andHärm [1], the authors have obtained an expression for τ′ which is applicable to semiconductors with little modification. In this paper the authors have used this expression for τ′ to obtain the mobility of electrons in nondegenerate semiconductors, taking into account the scattering by lattice vibrations, electron-ion interactions and electron-electron interactions.     

Mobility of nondegenerate two-dimensional electrons in scattering by a correlated distribution of impurity ions

The temperature dependences of the inverse mobility of nondegenerate two-dimensional electrons in scattering by impurity ions in heterostructures with a narrow spacer have been investigated using the Al _x Ga_{1 ? x} As/GaAs heterostructure as an example. Correlations in the arrangement of impurity ions have been taken into account in the model of hard spheres on a plane. The influence of the form of the structure factor in the electron mobility has been considered.     

Mobility of two-dimensional electrons upon scattering by a correlated distribution of impurity ions

Correlation effects in the mobility of two-dimensional electrons upon scattering by a correlated distribution of impurity ions are described in the framework of the hard-sphere model. The theory is developed for the case of partially ionized impurity centers when correlations in the distribution of impurity ions are weakened as the result of a deficit of free positions for impurity holes. The calculations are performed for heterostructures with a wide spacer when small-angle scattering of electrons dominates.     

电子-正电子散射与电子-电子散射的极化效应

计算了电子-正电子散射的16种极化散射截面.根据角分布的特征,它们可以分为三大类,其前向奇性分别是sin~(-4)(θ/2)、sin~(-2)(θ/2)和1.也计算了电子-电子散射的16种极化散射截面,它们既可以按前向奇性分为三大类,也可以按后向奇性分为三大类.三类奇性的特征与电子-正电子散射类似.对于三类奇性的出现给出了直观的物理说明.     

Maximum of the mobility of two-dimensional electrons upon scattering by a correlated distribution of impurity ions

The concentration dependences of the mobility of two-dimensional electrons in heterostructures with selective doping are investigated. Correlations of impurity ions in the volume of the doped layer are considered. The structure factor, which characterizes the influence of correlations in the arrangement of scatterers on the electron mobility, is described by the analytical expression derived in the framework of the hard-sphere model. The effect of oscillations of the structure factor on the electron mobility is evaluated.     

Effect of optical-phonon scattering on the energy distribution of hot electrons in semiconductors at low temperature

Summary The variational method is used in finding the solution of the transport equation for a system of hot electrons inn-Ge atT=20 K in the presence of high electric field. The role of the emission of optical phonons by hot electrons together with the effect of electron capture by repulsive centres on the formulation of the distribution function are studied. It is shown that the emission of optical phonons plays a dominant role in the formulation of the distribution. The influence of electron capture is very small, it may become appreciable at higher trap concentrations. The obtained distribution function is then used in calculating the capture rate of electrons by negatively charged centres. It is shown that the capture rate increases with electric field.

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Riassunto Il metodo variazionale è usato per trovare la soluzione dell'equazione di transporto per un sistema di elettroni caldi inn-Ge aT=20 K in presenza di grande campo elettrico. Si studiano il ruolo dell'emissione di fononi ottici da elettroni caldi insieme con l'effetto della cattura degli elettroni da centri di repulsione sulla formulazione della funzione di distribuzione. Si mostra che l'emissione di fononi ottici svolge un ruolo dominante nella formulazione della distribuzione. L'influenza della cattura degli elettroni è molto piccola, può diventare apprezzabile a piú grande concentrazione di trappole. La funzione di distribuzione ottenuta è quindi usata nel calcolare il rapporto di cattura degli elettroni da centri a carica negativa. Si mostra che il rapporto di cattura cresce col campo elettrico.

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Резюме Используется вариационный метод для нахождения решения транспортного уравнения для системы горячих электронов вn-Ge приT=20 К при наличии сильного электрического поля. Исследуется роля испускания оптических фононов горячими электронами и эффект эахвата электпонов отталкивающими центрами при определении функции распредения. Показывается, что испускание оптических фононов играет доминируюэую роль при образовании функции распределения. Влияние захвата электронов очень мало и становится существенным при более высоких концентрациях ловушек. Полученная функция распределения используется при вычис-лении интенсивности захвата злектпонов отрицательно заряженными центрами. Показывается, что интенсивность захвата увеличивается с возрастанием электрического поля.

     

The pair scattering and the photoemission effect in GaAs

The photoemission effect in GaAs is calculated for photon energies up to 12 eV using a direct transition model and pseudopotential energy bands. The effect of the pair scattering in the energy distribution curves is included using a mean free path approximation and a first order perturbation treatment for the coulombic interaction producing the scattering. The absolute value of the yield function is well reproduced. A detailed discussion of the contribution from scattered and unscattered electrons to the energy distribution curves is performed and their interpretation in terms of the details of the energy bands is given.     

The elastic scattering of low energy electrons from Xenon

Calculations are presented of angular distributions for electrons elastically scattered from xenon in the energy range 5.5 to 10 eV. The potential describing the xenon atom is determined by the X_α-approximation. The relative dependence with energy of the differential cross section at 30° scattering angle has been calculated in the range 30 to 200 eV. The theoretical results are in very good agreement with experimental data.     

To the question on electron-electron scattering in metals

Temperature dependence of the scattering rate in copper and aluminium has been investigated by the radio frequency size effect with the aim of extracting the contribution of electron-electron collisions. The scattering rate is varied by the cubic law on the wide temperature range (1.2–10°K), which is due to the electron-phonon interaction. On the basis of modern representations on the electron-electron interactions, the absence of the quadratic term in the probability of scattering of charge carriers in these metals, close to the transition ones, is discussed.     

Temperature features of electrical resistivity of two-dimensional electrons in scattering by a correlated distribution of impurity ions in doped thin layers

Spatial correlations of impurity ions in doped thin layers at finite temperatures have been considered in the model of hard spheres on a plane. It has been shown that, in systems with separate doping, the correlations in the arrangement of impurity ions are weakened by thermal motion of electrons at sufficiently low temperatures (below the liquid-helium temperature). The temperature dependences of the electrical resistivity of degenerate two-dimensional electrons in heterostructures with separate doping have been investigated using the Al _x Ga_{1 − x} As/GaAs heterostructure as an example.     

Mobility of electrons upon scattering by a multicomponent correlated system of impurity centers

A system that contains two sorts of impurity centers spatially distributed in a random way is considered. Not all impurities of the first sort are ionized, and all the impurities of the second sort are ionized. Spatial correlations in the system of impurity ions of the first sort are investigated under conditions when the correlation radius of an impurity ion is limited from above due to a deficit of neutral impurities. The influence of randomly spatially arranged small-sized donors (impurities of the second sort) on correlations in the system of impurity ions is analyzed. The equations for describing the effect of small-sized donors on correlations in the system of impurity ions are obtained. The electron mobility at zero temperature is calculated by the example of HgSe: Fe (the correlated system of impurity centers consists of iron atoms and small-sized donors whose concentration is higher than the Mott concentration).     

Relativistic Compton scattering from a relativistic maxwellian distribution of electrons

Using an earlier developed relativistic differential cross section formula for Compton scattering of photons from a given momentum distribution of electrons, an expression for the differential cross section is derived for the case of a relativistic Boltzmann distribution.     

Relativistic multiple scattering theory of electrons by ferromagnets

In view of investigating for 3d- and 4f-ferromagnetic crystals the elastic scattering and the emission of polarized low-energy electrons as well as the bulk electronic structure, a relativistic multiple scattering theory has been developed, in which the exchange interaction with the magnetic ground state electrons is treated in a local density functional approximation. In a layer-KKR-type approach, the Dirac equation, which contains an effective magnetic field term, is first solved for a single crystal atom and subsequently for a monoatomic layer and for a semi-infinite crystal. Spin-orbit coupling and magnetic exchange interaction are thus simultaneously taken into account.     

Effect of multiple scattering on the emission of ultrarelativistic electrons in a thin layer of matter

We develop a quantitative theory of the effect of multiple scattering on the bremsstrahlung of ultrarelativistic electrons in a thin layer of matter. The effect is an analog of the Landau-Pomeranchuk-Migdal (LPM) effect of suppression of the radiation emitted by high-energy particles in an infinite amorphous medium, but certain differences do exist. On the basis of our approach we analyze the data recently obtained at SLAC (E-146) in experiments set up to verify the LPM effect. We show that in addition to the LPM effect, this experiment exhibited the suppression of bremsstrahlung in a thin layer of matter, theoretically predicted in our earlier papers. Zh. éksp. Teor. Fiz. 113, 58–70 (January 1998)