V. I. Chmyrev

Thermally stimulated currents in semiconductors: Analysis of rate equations for a single-level model and thermally stimulated currents in Si

Thermally stimulated currents (TSCs) in semiconductors are analyzed theoretically. The rate equations describing TSCs are solved numerically for various heating profiles, which makes it possible to evaluate the ionization energy, concentration, and capture cross section of traps. The slow and fast retrapping approximations are examined for an arbitrary heating profile. A new approach to TSC data processing is proposed: cleaning of a peak from the lower temperature peak by storing the preilluminated material in the dark at the relaxation temperature of the lower temperature peak. It is shown that heating (constant-rate or exponential) followed by isothermal holding makes it possible to determine the ionization energy of traps without knowing the retrapping mechanism. This approach is adapted for the case when the retrapping time is comparable to the carrier lifetime. Partially compensated silicon with impurity photoconductivity is prepared by doping with gold and phosphorus. It is shown that, using resonance photoexcitation, one can identify the nature (electron or hole) of traps and evaluate their ionization energy. The depths and capture cross sections of three trapping centers in Si were evaluated.

Band structure of silicon carbide nanotubes

Using the linear augmented cylindrical wave method in the muffin-tin approximation, we have calculated the band structure of (n, n) and (n, 0) silicon carbide nanotubes for n = 5–10. In the range n = 7–10, (n, n) nanotubes are semiconductors, and their band gap decreases steadily with increasing n: 0.28 eV at n = 7, 0.26 eV at n = 8, 0.19 eV at n = 9, and 0.11 eV at n = 10. Nanotubes with n = 5 and 6 are metallic. At n = 7–9, (n, 0) nanotubes are semiconductors, and their band gap increases steadily with n: 0.39 eV at n = 7, 0.46 eV at n = 8, and 0.62 eV at n = 9. Nanotubes with n = 5 and 6 have metallic conductivity according to our results.

Doping effect on the optical, electro-optic, and photoconductive properties of Bi12MO20 (M = Ge, Si, Ti)

The doping effect on the optical, electro-optic, and photoconductive properties of Czochralski-grown Bi12MO20 (M = Ge, Si, Ti) sillenite-structure single crystals was studied. The dopants were introduced into the growth charge in the form of oxides. Bi12TiO20 crystals were doped with V, Zn, Cu, P, and Nb; and Bi12SiO20 crystals were doped with Cd and Mo. The results indicate that the doping level has a significant effect on the photoconductivity of the Bi12TiO20〈Zn〉, Bi12TiO20〈Cu〉, Bi12SiO20〈Cd〉, and Bi12SiO20〈Bi24CdMoO40〉 crystals, which may exceed that of undoped crystals at low doping levels and may be substantially lower than it, down to zero, at increased dopant concentrations. Niobium doping of bismuth titanate has no effect on its photosensitivity and electro-optic properties. Phosphorus and vanadium enhance the photosensitivity of bismuth titanate over the entire composition range studied but have little effect on its electro-optic coefficient r41. A slight increase in r41 was only observed at high vanadium concentrations. The axial impurity distribution in the crystals is shown to be nonuniform, which reflects in their photoresponse: the photoconductivity of the copper-doped crystals near the seed end is 3 times that near the tail end.

Analysis of Differential Equations of Thermally Stimulated Currents in Semiconductors: Arbitrary Heating Profile

The thermally stimulated current (TSC) rate equations are solved for an arbitrary heating profile. The equations are analyzed for fast and slow retrapping regimes in the case when the sample is rapidly heated at a constant rate to the set temperature and held there until the current fully decays.

Thermally Stimulated Currents in Si〈P,Au〉: Exponential Heating Profile

The equations of thermally stimulated currents were derived for an exponential heating profile. The applicability of this approach was checked using experimental data for Si〈P,Au〉. The ionization energies of two trap levels in Si〈P,Au〉 were determined to be 0.25 and 0.40 eV.

Effect of Long-Term Heat Treatment on the Acceptor Behavior of Gold in Silicon

Data are presented on the electrical activity of Au in Czochralski Si heat-treated and diffusion-doped under various conditions. The results are interpreted in terms of force fields responsible for changes in the concentration of electrically active centers. Long-term heat treatment between 700 and 1050°C is shown to have a significant effect on the acceptor behavior of Au in diffusion-doped Si. The concentration of Au acceptors is sensitive to the surface condition in the course of heat treatment: a tungsten coating increases the Au concentration in the bulk of diffusion-doped Si.

Effect of interaction between deep impurity traps on thermally stimulated currents in semiconductors

We demonstrate that the problem of determining the concentrations of free and trapped charge carriers in wide-gap semiconductors from their thermally stimulated current (TSC) curves for m interacting levels in an implicit difference scheme for numerically solving differential rate equations of TSCs reduces to finding the roots of an algebraic equation of degree m + 1. For two interacting trap levels of the same nature (electron or hole traps), we present an algorithm for numerically solving differential rate equations of TSCs which allows the concentrations of free and trapped charge carriers to be determined. TSC curves can be divided into four types according to their shape (dependent on trap parameters and experimental conditions): “splitting” (two well-resolved peaks separated by a temperature range), “saddle” (a well-defined minimum between two peaks), shoulder (on the high- or low-energy side), and “coalescence-absorption” (one peak). The modeling results are used to interpret an experimental TSC curve for semiconducting InSe and to demonstrate that, to adequately interpret experimental TSC data, one should use a model for the interaction between levels.

Evaluation of impurity concentration in semiconductors from the relaxation of thermally stimulated currents

The rate equations of thermally stimulated currents due to isothermal detrapping are analyzed. The results demonstrate that, at small trap population, isothermal detrapping follows an exponential law, independent of the trapping rate: fast, slow, or intermediate (the trapping time is comparable to the recombination time). Expressions are derived for determining the density of charged traps in the course of detrapping and assessing the trap density from known trap parameters and thermally stimulated current spectra.

Nonuniform Impurity and Electric-Field Distributions in High-Resistivity Si〈W,Au〉, Bi12GeO20, and CdS Crystals

The impurity and electric-field distributions in high-resistivity Si〈W,Au〉, Bi12GeO20, and CdS semiconductors are studied by the local PC method. The applicability of this method to assessing impurity and field distributions is analyzed. For n-Si〈W,Au〉, with the Au dopant completely compensated by shallow donors, the distribution of empty gold centers along the sample is obtained. At low temperature, the electric-field distribution is nonuniform, which is probably due to exclusion at the semiconductor contacts. Both the field and impurity distributions along the Bi12GeO20 and CdS crystals are found to be nonuniform.

Effect of long-term annealing on accumulation of impurities

The occurrence of changes in impurity accumulation after a long-term annealing preceding the in-diffusion of impurities is shown experimentally. Atoms of Au as acceptors affecting the resistivity and photoconductivity decay time were used as indicators in studies of these changes.