Модель стационарной миграции свободных и прыгающих между акцепторами дырок в кристаллическом полупроводнике

In the diffusion-drift approximation, we have constructed a phenomenological theory of the coexisting migration of v-band holes and holes by means of hopping from hydrogen-like acceptors in the charge state (0) to acceptors in the charge state (−1). A p-type crystalline semiconductor is considered at a constant temperature, to which an external stationary electric field is applied. In the linear approximation, analytical expressions for the screening length of the static electric field and the length of the diffusion of v-band holes and the holes quasilocalized on acceptors are obtained for the first time. The presented relations, as special cases, contain well-known expressions. It is shown that the hopping migration of holes via acceptors leads to a decrease in the screening length and in the diffusion length.В диффузионно-дрейфовом приближении построена феноменологическая теория сосуществующих миграции дырок v-зоны и миграции дырок посредством прыжков с водородоподобных акцепторов в зарядовом состоянии (0) на акцепторы в зарядовом состоянии (−1). Рассматривается кристаллический полупроводник p-типа при постоянной температуре, к которому приложено внешнее стационарное электрическое поле. В линейном приближении впервые получены аналитические выражения для длины экранирования статического электрического поля и длины диффузии дырок v-зоны и дырок, квазилокализованных на акцепторах. Представленные соотношения как частные случаи содержат известные выражения. Показано, что прыжковая миграция дырок по акцепторам приводит к уменьшению и длины экранирования, и длины диффузии

Локализация внешним магнитным полем электронов на ионах водородоподобных доноров в невырожденных полупроводниках

In the quasi-classical approximation of quantum mechanics a model for the localization of conduction electrons on the ions of hydrogen-like donors in an external magnetic field was developed. The thermal ionization energy of donors in lightly doped and moderately compensated crystals of gallium arsenide and indium antimonide of n-type was calculated depending on the induction of the external magnetic field. In contrast to the known theoretical works (which use variational methods for solving the Schrödinger equation), a simple analytical expression is proposed for the ionization energy of the donor in the magnetic field, which quantitatively agrees with the known experimental data. It is shown that the magnitude of the magnetic field induced by the orbital motion of the electron around the ion core of the donor is negligible compared to the external field and does not contribute to the ionization energy of donors.В квазиклассическом приближении квантовой механики развита модель локализации электронов проводимости на ионах водородоподобных доноров во внешнем магнитном поле. Проведен расчет термической энергии ионизации доноров в слабо легированных и умеренно компенсированных кристаллах арсенида галлия и антимонида индия n-типа в зависимости от индукции внешнего магнитного поля. В отличие от известных теоретических работ (с использованием вариационных методов решения уравнения Шредингера) предложено простое аналитическое выражение для энергии ионизации донора в магнитном поле, которое количественно согласуется с известными экспериментальными данными. Показано, что величина магнитного поля, индуцированного орбитальным движением электрона вокруг ионного остова донора, пренебрежимо мала по сравнению с внешним полем и не вносит вклада в энергию ионизации доноров

Квазиклассическая модель статической электропроводности сильно легированных вырожденных полупроводников при низких температурах / Н. А. Поклонский, С. А. Вырко, А. Н. Деревяго

Germanium, silicon, gallium arsenide, and indium antimonide n-type crystals on the metal side of the insulator–metal transition (Mott transition) are considered. In the quasi-classical approximation, the static (direct current) electrical conductivity and the drift mobility of electrons of the c band, and electrostatic fluctuations of their potential energy and the mobility edge are calculated. It is considered that a single event of the elastic Coulomb scattering of a mobile electron occurs only in a spherical region of the crystal matrix with an impurity ion at the center. The results of calculations using the proposed formulas without using fitting parameters are numerically consistent with experimental data in a wide range of concentrations of hydrogenlike donors at their weak and moderate compensation by acceptors.This study was supported by the Belarusian National Research Program “Mattekh”.Рассматриваются кристаллы германия, кремния, арсенида галлия и антимонида индия n-типа на металлической стороне перехода изолятор–металл (перехода Мотта). В квазиклассическом приближении рассчитываются статическая (на постоянном токе) электрическая проводимость и дрейфовая подвижность электронов c-зоны, а также электростатические флуктуации их потенциальной энергии и порог подвижности. Считается, что единичный акт упругого кулоновского рассеяния подвижного электрона происходит только в сферической области кристаллической матрицы, в центре которой расположен ион примеси. Результаты расчетов по предложенным формулам без использования подгоночных параметров численно согласуются с экспериментальными данными в широком диапазоне концентраций водородоподобных доноров при слабой и умеренной их компенсации акцепторами

Drift-diffusion model of hole migration in diamond crystals via states of valence and acceptor bands

Ionization equilibrium and dc electrical conductivity of crystalline diamond are considered, for the temperature T_j in the vicinity of which valence band (v-band) conductivity is approximately equal to hopping conductivity via acceptors. For the first time, we find explicitly (in the form of definite integrals) the fundamental ratio of diffusion coefficient to drift mobility for both v-band holes and holes hopping via hydrogen-like acceptors for the temperature T_j. The known ratios follow from the obtained ones as particular cases. The densities of the spatial distributions of acceptors and hydrogen-like donors as well as of holes are considered to be Poissonian and the fluctuations of electrostatic potential energy are considered to be Gaussian. The dependence of exchange energy of v-band holes on temperature is taken into account. The thermal activation energy of hopping conduction as a function of the concentration of boron atoms (as acceptors) is calculated for temperature T_3 ≈ T_j/2. Without the use of any adjustable parameters, the results of calculations quantitatively agree with data obtained from the measurements of hopping conductivity of diamond with boron concentration from 3×10^17 to 3×10^20 cm^−3, i.e. on the insulating side of the Mott phase transition.The work was partially supported by the Belarusian Republican Foundation for Fundamental Research (Grant no. F17RM-091), by the Belarusian National Research Program ‘Mattekh’ and by the EU Framework Programme for Research and Innovation Horizon 2020 (Grant No. H2020-MSCA-RISE-2015-691010 HUNTER and Grant No. H2020-MSCA-RISE-2015-690968 NANOGUARD2AR)

Effect of neutron irradiation on the hydrogen state in CVD diamond films

The effects of high temperature, up to 1680 °C, and annealing in vacuum on the optical properties of fast neutron irradiated chemical vapour (CVD) deposited polycrystalline diamond films (CVD DFs) are examined. It is shown that at least fifteen relatively narrow (full width at half-height from 10 to 25 cm^−1) CH_x stretching vibration bands with maxima close to 2800, 2818, 2834, 2849, 2855, 2875, 2899, 2906, 2924, 2936, 2950, 2966, 2985, 3012 and 3034 cm^−1, as well as a 3123 cm^−1 band due to the NVH^0 centers, are observed in the IR absorption spectra of the films. The transformation of the CH_x stretching vibration bands in the absorption spectra of fast neutron irradiated (with a fluence of F = 2×10^19 cm^−2) diamond films is investigated with successive isochronous annealing runs. It is found that the neutron irradiation significantly (by ~200°) increases the temperature above which the graphitization (darkening) of the samples starts. That threshold is determined by the temperature of graphitization of intercrystallite (grain) boundaries due to the break of C-H bonds. The phenomena observed are explained by the effect of radiation damage on the structure of grain boundaries in the diamond films

Features of the 1640 cm−1 band in the Raman spectra of radiation-damaged and nano-sized diamonds

Raman spectra of irradiated with fast neutrons or MeV ion-implanted radiation-damaged natural and CVD diamonds and chemically purified detonation nanodiamonds are investigated. The influence of radiation damage level and effects of high-temperature annealing on the intensity and spectral shape of the 1640 cm−1 band is studied. It is shown that in radiation-damaged diamonds this band consists of at least six Gaussian peaks, the intensity of which varies one to one both with the level of radiation disordering and the temperature of the subsequent annealing. The “1640” band in radiation-damaged diamonds is completely annealed at temperatures above 1000 °C, while in detonation nanodiamonds annealing up to 1200 °C does not significantly affect its shape and intensity.This work was partially supported by Russian Foundation for Basic Research, grants no. 19-52-04008, 18-02-01103 and by Belarusian Republican Foundation for Fundamental Research, grant no. F19RM-054