V. D. Kagan

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.

Quantum oscillations of the resistivity and hall coefficient and the quantum limit in Bi0.93Sb0.07 alloys in a magnetic field along the trigonal axis

The dependences of the electrical resistivity ρ and the Hall coefficient R on the magnetic field have been measured for single-crystal samples of the n-Bi0.93Sb0.07 semiconductor alloys with electron concentrations in the range 1 × 1016 cm−3 < n < 2 × 1018 cm−3. It has been found that the measured dependences exhibit Shubnikov-de Haas quantum oscillations. The magnetic fields corresponding to the maxima of the quantum oscillations of the electrical resistivity are in good agreement with the calculated values of the magnetic fields in which the Landau quantum level with the number N intersects the Fermi level. The quantum oscillations of the Hall coefficient with small numbers are characterized by a significant spin splitting. In a magnetic field directed along the trigonal axis, the quantum oscillations of the resistivity ρ and the Hall coefficient R are associated with electrons of the three-valley semiconductor and are in phase with the magnetic field. In the case of a magnetic field directed parallel to the binary axis, the quantum oscillations associated both with electrons of the secondary ellipsoids in weaker magnetic fields and with electrons of the main ellipsoid in strong magnetic fields (after the overflow of electrons from the secondary ellipsoids to the main ellipsoid) are also in phase. In magnetic fields of the quantum limit ħωc/2 ≥ EF, the electrical conductivity increases with an increase in the magnetic field: σ22(H) ∼ Hk. A theoretical evaluation of the exponent in this expression for a nonparabolic semiconductor leads to values of k close to the experimental values in the range 4 ≤ k ≤ 4.6, which were obtained for samples of the semiconductor alloys with different electron concentrations. A further increase in the magnetic field results in a decrease of the exponent k and in the transition to the inequality σ22(H) ≤ σ21(H).

Redistribution of electrons between ellipsoids in a magnetic field in the quantum limit range in n-Bi-Sb alloys

The magnetoresistivities ρ22(H) and ρ32(H) and the Hall coefficient R32.1 for single-crystal samples of the n-Bi0.93Sb0.07 semiconducting alloy have been measured at low temperatures in magnetic fields up to H=14 T at H∥C2. The samples with three electron concentrations n1=1.25 × 1016 cms-3, n2=3.5×1016 cms-3, and n3=1.6×1017 cms-3 have been studied. The strong anisotropy of the electron spectrum of the alloys has made it possible to observe quantum oscillations of the magnetoresistivity ρ22(H) at H∥C2 for electrons of the secondary ellipsoids with the transition to the quantum limit in high magnetic fields. However, in the same magnetic fields, the quantization condition for electrons of the main ellipsoid is not satisfied. An increase in the energy of electrons of the secondary ellipsoids in the magnetic fields of the quantum limit leads to their migration to the main ellipsoid. After the complete migration, the Fermi energy for the alloy samples with the electron concentrations n1, n2, and n3 increases from 7.0 to 11.3 meV, from 11.0 to 17.1 meV, and from 20.2 to 30.6 meV, respectively. After the migration, the magnetoresistivity for electrons of the main ellipsoid increases with an increase in the magnetic field and the specific features in the behavior of the kinetic coefficients are observed in the vicinity of the magnetic field H=10 T. Therefore, the electronic topological transition from the three-valley electron spectrum to the single-valley electron spectrum occurs in the Bi0.93Sb0.07 single crystals for H∥C2 at low temperatures in the range of magnetic fields of the quantum limit.

Phonon drag thermopower in doped bismuth

The low-temperature (2<T<80 K) thermopower in bismuth doped by tellurium, a donor impurity (0<c≤0.07 at. % Te), is dominated by the phonon component, which shifts to higher temperatures with increasing dopant concentration. The temperature and concentration dependences of the phonon thermopower of doped bismuth are satisfactorily described by the theory of phonon drag of electrons. The theory is developed for a strongly anisotropic electron spectrum and includes both direct and two-step phonon drag.

Beats of quantum oscillations of the hall coefficient and resistivity in semiconductor alloys n-Bi0.93Sb0.07 at a small deviation of the magnetic field direction from the trigonal axis

Quantum oscillations of the resistivity ρ22 and Hall coefficient R12.3 in the semiconductor alloy n-Bi0.93Sb0.07 have been studied at H ‖ C3 and j ‖ C1 in magnetic fields to 14 T and at temperatures of 1.5, 4.5, 10, and 20 K. At temperatures of 1.5 and 4.5 K, beats of quantum oscillations of ρ22 and R12.3 due to a small deviation of the magnetic field H from the crystallographic C3 axis have been observed. To determine the oscillation period Δi, cyclotron mass mci, cyclotron frequency ωci, and extreme section Sextri, experimentally measured quantum oscillation beats have been compared with the model beats of oscillations of three harmonic functions, two of which have close frequencies. The deviation of the parameters Δi, mci, and Sextri from the same parameters when the magnetic field H exactly coincides with the trigonal C3 axis has made it possible to estimate the magnetic field H deflection angle from the trigonal C3 axis, which is ∼1°.

Nonmonotonic magnetic-field dependence of transport coefficients for n-Bi-Sb semiconducting alloys

The transport coefficients of tellurium-doped n-Bi1 − xSbx semiconducting alloys (0.07 ≤ x ≤ 0.15) are studied for single-crystal samples in the temperature range 1.5 ≤ T ≤ 40 K and in magnetic fields 0 ≤ H < 20 kOe. The theory developed in this study attributes the specific features in the behavior of the transport coefficients observed in a magnetic field to a strong anisotropy of the electron spectrum and anisotropy in the electron relaxation time. It is found that the dependences of the transport coefficients on the magnetic field for H ∥ C3 can be theoretically expressed through one anisotropy parameter δ, and those for H ∥ C2, by means of several anisotropy parameters, namely, γ, η, ζ, and m3/m1. It is established that the anisotropy parameter δ in the n-Bi-Sb semiconducting alloys can be estimated from measurements of the electrical resistivity ρ22(∞)/ρ22(0) ℞ δ and the Hall coefficient R12.3(∞)/R12.3(H → 0) ℞ δ in a magnetic field H ∥ C3. It is shown that the observed increase in the thermoelectric efficiency by a factor of 1.5–2.0 in the transverse magnetic fields H ∥ C3 and H ∥ C2 originates from the nonmonotonic dependence of the diffusion component of the thermopower Δα22(H)(∇T ∥ C1) on the magnetic field. The nonmonotonic dependence of the diffusion thermopower in n-Bi-Sb semiconducting alloys is associated with the strong anisotropy of the electron spectrum, the anisotropy in the electron relaxation time, and the many-valley pattern of the spectrum.

Electron capture by charged impurities in semiconductors under conditions of spatial diffusion

The capture of electrons by charged impurities in semiconductors due to spatial diffusion is investigated theoretically. In a semiconductor, an electron either can be captured by the field of a charged impurity if this electron loses energy by emitting phonons or can be ionized from the trapping state if it acquires energy by absorbing phonons. The electron trapping is governed by a change in the distribution function of electrons in both coordinate and momentum space. The trapping coefficient is calculated under the condition where it is determined by the diffusion redistribution of the electron density in the field of a charged impurity.

Low-temperature thermal conductivity of tellurium-doped bismuth

Phonon thermal conductivities κ22 (∇T ‖ C1) and κ33 (∇ T ‖ C3) of tellurium-doped bismuth with an electron concentration in the range 1.8 × 1019 ≤ nL ≤ 1.4 × 1020 cm−3 were studied in the temperature interval 2 < T < 300 K. The temperature dependence of the phonon thermal conductivity obtained on doped bismuth samples of both orientations exhibits two maxima, one at a low temperature and the other at a high temperature. The effect of various phonon relaxation mechanisms on the dependence of both phonon thermal conductivity maxima on temperature, impurity concentration, and electron density is studied.

Electric-field-induced impact ionization of excitons in GaN and GaN/AlGaN quantum wells

Impact ionization of exciton states in epitaxial GaN films and GaN/AlGaN quantum-well structures was studied. The study was done using an optical method based on the observation of exciton photoluminescence quenching under application of an electric field. It was established that electron scattering on impurities dominates over that from acoustic phonons in electron relaxation in energy and momentum. The mean free path of the hot electrons was estimated. The hot-electron mean free path in GaN/AlGaN quantum wells was found to be an order of magnitude larger than that in epitaxial GaN films, which is due to the electron scattering probability being lower in the two-dimensional case.

Analysis of the spin splitting of maxima of quantum oscillations of the resistivity of n-Bi-Sb semiconductor alloys in a magnetic field parallel to the bisector axis

In samples of semiconductor alloys n-Bi0.93Sb0.07 with different electron concentrations (n1 = 8 × 1015 cm−3, n2 = 1.2 × 1017 cm−3, and n3 = 1.9 × 1018 cm−3), dependences of the electrical resistivity on magnetic fields up to 45 T parallel to the current and the bisector axis (H ‖ C1 ‖ j) have been measured at temperatures of 1.5, 4.5, and 10 K. The obtained dependences ρ22(H) demonstrate quantum oscillations of the resistivity (Shubnikov-de Haas effect), and, in high magnetic fields, there is a resistivity maximum far away from other maxima. On assumption that this maximum is related to the spin-split Landau level N = 0− for electrons of the main ellipsoid, the spin-splitting parameters are calculated for electrons of the main ellipsoid: γ1 = 0.87, γ2 = 0.8, and γ3 = 0.73. Using these values, the oscillation maxima can be reliably related to the numbers of split Landau levels for electrons of the main and secondary ellipsoids. The dependences of the resistivity ρ11 and the Hall coefficient R31.2 on magnetic field have been measured in a transverse magnetic field at H ‖ C1 and j ‖ C2 on the sample with the electron concentration n4 = 1.4 × 1017 cm−3. Using similar analysis, the spin-splitting parameter is found to be γ4 = 0.85, which is close to the value of γ2 = 0.8 obtained for the sample with close electron concentration (n2 = 1.2 × 1017 cm−3) during the measurements in a longitudinal magnetic field. The quantum oscillation maxima of Hall coefficient R31.2 are shifted to the range of high magnetic fields as compared to the quantum oscillation maxima of resistivity ρ11.