Kinetic theory of ionization and electron capture by a charged impurity in a semiconductor

Inelastic electron-phonon scattering in which the electron is captured or escapes from the Coulomb field of an impurity is taken into account in the kinetic equation for conduction electrons. This scattering is shown to become strong in a certain energy range. In this range, the distribution functions of free and bound electrons are correlated in such a way that there is a balance between the trapping and ionization processes. The existence of a region of strong scattering is the decisive factor in calculating the experimentally measurable trapping and ionization coefficients, which enter into the electron balance equation.     

Electron heating through a set of random levels in the conduction band of insulators induced by femtosecond laser pulses

We develop a theory describing the heating of electrons in crystalline insulators irradiated by high-intensity laser pulses. In agreement with photoelectron yield versus intensity measurements, we assume that electrons are excited into the conduction band from defect layers and traps. The electron dynamics due to direct inter-branch transitions within the conduction band is simulated by solving of time-dependant Schr?dinger equation. The set of levels for this equation is supposed to be random with a distribution function equal to the density of states in the conduction band. The influence of different parameters on the electron heating efficiency is studied. The theory is applied for diamond; the theoretical spectrum is in qualitative agreement with the experimental observations.     

Theorie der galvanomagnetischen Erscheinungen bei beliebigen Energieflächen und anisotroper Streuung der Leitungselektronen

A theory of the galvano-magnetic phenomena of conduction electrons is presented for the case of weak magnetic fields, allowing any energy band structure and any anisotropic scattering mechanism. In order to solve the Boltzmann transport equation an iteration — variation —procedure is developed. It is shown that the variety of trial functions can be restricted considerably by taking into account the point symmetry of the problem. Equations for the phenomenological constants are derived for crystals of octahedral symmetry. The theory, simplified for spherical energy surfaces, is used to calculate the temperature dependence of the galvano-magnetic constants of Na and K.     

Electronic band structure and distribution of excited electrons in the conduction band of anatase doped with boron, nitrogen, and carbon

A method for calculating the distribution of excited electrons in the conduction band of semiconductors has been proposed. This method takes into account both the excitation of electrons by means of an external light source and the transitions to the bottom of the conduction band due to the electron-phonon interaction. The interaction of electrons with the light field has been calculated from first principles in the dipole approximation using the linear muffin-tin orbital method. The electron-phonon interaction has been calculated in terms of the density functional perturbation theory. The method has been applied to the calculation of the quasi-steady-state distribution function of excited electrons in anatase doped with boron, nitrogen, and carbon. The correlations of the distribution function with the photocatalytic activity of doped anatase have been discussed.     

Influence of material design parameters on radiative recombination in GaAs doping superlattices grown by MBE

The specific luminescence process in GaAs doping superlattices arises from recombination of electrons populating low-index conduction subbands with holes in the acceptor impurity band across the indirect gap in real space. The luminescence peak energy thus directly reflects the actual value of the tunable gap for the photoexcited state of the superlattice. We have studied the tunability of the effective gap, the recombination rate, and the relative quantum efficiency on superlattice specimen of different material design parameters by means of low-temperature photoluminescence measurements. For optimized design parameters the ratio between luminescence and excitation intensity remains nearly constant over the entire tunability range of the effective gap.     

Relaxation between electrons and surface phonons of a homogeneously photoexcited metal film

The energy relaxation between the hot degenerate electrons of a homogeneously photoexcited metal film and the surface phonons (phonon wave vectors in two dimensions) is considered under Debye approximation. The state of electrons and phonons is described by equilibrium Fermi and Bose functions with different temperatures. Two cases for electron scattering by the metal surface, namely specular and diffuse scattering, are considered.     

Resonant scattering by impurities in metals and the Anderson model

The Anderson Hamiltonian, written in a representation where the extra orbital is not orthogonal to the conduction states, is used to derive a general theory of the electronic structure of dilute alloys. The theory describes both simple impurities in the over-complete or Wolff limit, and transition or rare-earth impurities where the scattering of the conduction electrons has a resonance. The extra-orbital of Anderson is shown to be identical to a bound state extracted from higher bands by the impurity potential, and overlapping the conduction band in energy. The resonant scattering of conduction electrons is described by a pseudopotential, which is singular in energy, in analogy to the theory of band structures of pure transition elements. The position and width of the resonance, as well as a direct scattering potential introduced by the non-orthogonality, are given in terms of Anderson's parameters. The resonance is narrowed by the non-orthogonality and disappears in the over-complete limit.     

Electron-phonon relaxation and excited electron distribution in zinc oxide and anatase

We propose a first-principles method for evaluations of the time-dependent electron distribution function of excited electrons in the conduction band of semiconductors. The method takes into account the excitations of electrons by an external source and the relaxation to the bottom of the conduction band via electron-phonon coupling. The methods permit calculations of the non-equilibrium electron distribution function, the quasi-stationary distribution function with a steady-in-time source of light, the time of setting of the quasi-stationary distribution and the time of energy loss via relaxation to the bottom of the conduction band. The actual calculations have been performed for titanium dioxide in the anatase structure and zinc oxide in the wurtzite structure. We find that the quasi-stationary electron distribution function has a peak near the bottom of the conduction band and a tail whose maximum energy rises linearly with increasing energy of excitation. The calculations demonstrate that the relaxation of excited electrons and the setting of the quasi-stationary distribution occur within a time of no more than 500?fs for ZnO and 100?fs for anatase. We also discuss the applicability of the effective phonon model to energy-independent electron-phonon transition probability. We find that the model only reproduces the trends in the change of the characteristic times whereas the precision of such calculations is not high. The rate of energy transfer to phonons at the quasi-stationary electron distribution also have been evaluated and the effect of this transfer on the photocatalysis has been discussed. We found that for ZnO this rate is about five times less than in anatase.     

Relaxation processes upon photoexcitation of semiconductor CdF<Subscript>2</Subscript> by laser pulses

The microwave-cavity-based technique is used to study the processes of photoionization of electrons from donor levels to the conduction band in semiconductor CdF₂ crystals doped with Y, In, or Ga. The samples were excited by periodic pulses of Nd-laser (λ = 1.06 μm, pulse width ～10 ns) in the temperature range 6–77 K. The transient processes were detected in the absorption and dispersion modes related to variation of the imaginary and real parts of the complex permittivity ?₁ ? i?₂ induced by the light pulses. The observed signals consisted of short peak at t ～ 0, approximately 40–70 ns in length, and a long tail with a duration of ～100 ms. The short peak is likely to be related to the stay of the photoexcited carriers in the conduction band, while the long tail is associated with the processes of excitation relaxation after the electrons coming back to the donor levels of the impurity band. The weak temperature dependence of the width of the peak at t ～ 0 is explained by the tunneling mechanism of relaxation of electrons through the energy (or, probably, spatial) barrier separating the bound and free states of the carriers in the semiconductor CdF₂.     

Modeling of Nonthermal Solid‐to‐Solid Phase Transition in Diamond Irradiated with Femtosecond x‐ray FEL Pulse

In this contribution we review in detail our recently developed hybrid model able to trace simultaneously nonequilibrium electron kinetics, evolution of an electronic structure, and eventually nonthermal phase transition in solids irradiated with femtosecond free‐electron laser pulses. Diamond irradiated with an ultrashort intense x‐ray pulse serves as an example to show how an irradiated material undergoes an ultrafast phase transition on sub‐picosecond timescales. The transition of diamond into graphite is induced by an excitation of electrons from the valence band into the conduction band, which, in turn, induces a rapid change of the interatomic potential. Our theoretical model incorporates: a Monte‐Carlo method for tracing high‐energy electrons and K‐shell holes in diamond; a temperature equation for the valence‐band and low‐energy conduction‐band electrons; a tight binding method for calculation of the evolving electronic structure of the material and potential energy surfaces; and molecular dynamics propagating atomic trajectories. This unified approach predicts the damage threshold of diamond in a good agreement with experimentally measured values. It reveals a multi‐step nature of nonthermal phase transition being an interplay between electronic excitation, changes of the band structure, and atomic reordering. An effect of pulse parameters, such as photon energy and temporal pulse shape, on the phase transition is discussed in detail. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Momentum redistribution times of 2D excitons measured by transient resonantly induced intersubband absorption

We apply a transient interband-pump–intersubband-probe technique, to directly measure the time it takes for resonantly photoexcited excitons in GaAs/AlGaAs superlattices to redistribute in momentum space. We determine the redistribution time and its excitation density and superlattice periodicity dependence from the temporal evolution of the conduction intersubband absorption spectrum.We find that resonantly excited heavy-hole excitons, at moderate densities, redistribute slowly and reach thermal distribution within a few tens of ps after the pulsed excitation. This redistribution time is nearly inversely proportional to the square root of the initial density of the photoexcited excitons and it depends on the periodicity of the superlattice structure. The smaller the periodicity in direct space is, the longer is the redistribution time. This is due to the relatively inefficient exciton–exciton scattering, and the small momentum that each resonantly excited exciton carries. From measurements performed on three samples of different periodicity we find that the redistribution time increases faster than the superlattice Brillouin-zone length squared.     

Inelastic scattering of slow electrons in solids

A theory of the inelastic scattering of slow electrons in solids due to excitation of interband transitions is developed. It is shown that both nondirect and direct transitions occur which can be described by a generalization of the formalism used in solid state optics. Experiments with 30–200 eV electrons scattered from Si (111) surfaces with well defined surface structures as determined by low energy electron diffraction confirm the theoretical predictions. They indicate that the inelastic scattering of slow electrons can be understood in terms of the three-dimensional band structure of solids and suggest the use of inelastic low energy electron scattering as a tool for band structure analysis.     

Transport of nonequilibrium electrons in photoemission from semibounded medium

The equation is formulated and accurately solved for the problem of the transport of photoexcited electrons which undergo scattering before reaching vacuum, with the formation of an electron-hole pair, as well as multiple scattering of elastic type. The analytical expressions obtained permit calculations of the spectral composition of the emitted-electron flux and the quantum yield of photoemission. The limiting expression for the probability that secondary electrons will reach the vacuum which is obtained when the elastic-scattering mechanism is switched off is compared with literature data.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 86–92, October, 1987.     

Electronic structure of cubic uranium compounds

Self-consistent cellular multiple scattering techniques and photoemission energy distribution curves obtained at 20<hv<80 eV are used to study the density of states of UN and US. The calculations are based on a model using a finite cluster of atoms in a condensed-matter-like boundary potential. The main results refer to the mixing of thes, p, d, andf-states of uranium into a valence and a conduction band. Thef-states form orbitals with the ligands, within the valence and conduction bands. In the nitride the amount off character in the valence band is only 0.3 electrons and thef electrons are in two resonant levels (of each spin) in the conduction band. Only the first of these levels is occupied for the local, alternate from atom to atom, majority spin. In the sulfide the amount off character in the valence band is 0.59 electrons and the rest of thef-levels are in a resonance state (of majority spin) at the beginning of the conduction band. The conduction band is mainly of localized uranium 6d character. The theoretical results compare favorably with the photoemission data reported here.     

Electron scattering and transport phenomena in small-gap zinc-blende semiconductors

We give expressions for electrical conductivity, thermoelectric power and thermal conductivity of conduction band electrons in small-gap zinc-blende semiconductors, obtained by solving the Boltzmann equation by a variational procedure. The term resulting from the phonon-drag is included in the Boltzmann equation. The following electron scattering mechanisms are investigated: inter and intraband scattering by optical phonons via polar and nonpolar interactions, scattering by charged centers (ionized defects and heavy holes) and by neutral centers, as well as scattering by acoustic phonons. Particular attention is paid to the screening of the electron-optical phonon polar interaction by free carriers, which is particularly important in the case of a linear energy band. The formula for the intraband RPA dielectric function for the case of the linear band is given.The general formulation of all the problems investigated permits direct application of the results given in this paper to both intrinsic or n-type HgTe-type and InSb-type semiconductors, including mixed crystals, e.g. Cd_xHg_1?xSe near the cross point.     

Analysis of electrical conduction in an <Emphasis Type="BoldItalic">n</Emphasis> -type GaAs epilayer

The magnetic field dependence of conductivity tensor components, magnetoresistance, and the Hall coefficient have been analyzed in an n-type Si-doped GaAs epilayer at temperatures from 11 to 295 K. Carriers from the conduction band and the impurity band take part in the electrical conduction. The conduction band is located in the epilayer and the impurity band is located in a narrow layer, less than 0.1 m thick, between the GaAs buffer and GaAs semi-insulating substrate. At temperatures below 20 K the localization and magnetic freeze-out of the conduction band electrons have been taken into account as quantum corrections to the electrical conduction. The dependence of the mobility on energy has been considered in the analysis of the experimental data. A wide peak of partial conductions versus mobility appears in the mobility spectrum. From the analysis of the mobility spectrum of conduction band electrons it follows that at low temperatures the mobility of non-degenerated conduction band electrons is limited by scattering on screened charge centers. The mobility spectrum technique has been used as a tool for interpolation and extrapolation of the experimental data beyond the experimentally investigated magnetic field range. PACS 72.20.-i; 72.60.+g