Calculation of the impurity distribution for diffusion in a solid crystal with inhomogeneous layers

A solution is obtained for the diffusion from a constant source at a surface in a solid crystal with an inhomogeneity in the form of a layer with high diffusion coefficient of arbitrary thickness. The expressions obtained may be used, depending on the choice of the inhomogeneous layer thickness, to investigate surface diffusion or diffusion at grain boundaries or dislocations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 104–108, October, 1977.     

Phenomenological model of the diffusion of impurity atoms in ultrathin silicon layers with a nonuniform distribution of temperatures

The influence of fluxes of intrinsic nonequilibrium semiconductor defects on impurity diffusion in a nonuniform temperature field is considered in the framework of the phenomenological theory of irreversible processes. The mass transfer coefficient defined as the ratio of the concentrations of nonequilibrium and equilibrium defects is introduced to take the excessive concentration of nonequilibrium defects into account. The introduction of this coefficient into equations for matter and heat fluxes makes it possible to express the parameters of the process of thermal diffusion (the diffusion coefficient and the heat of transport) as a time-dependent function of the excessive concentration of intrinsic nonequilibrium semiconductor defects.     

Percolation mechanism of the diffusion of impurity atoms in dense surface layers

The molecular dynamics method is used to study the migration of an impurity atom on an unfilled square lattice. The calculations are performed on a lattice containing 2¹² × 2¹⁴ sites at various values of the ratio p of the frequencies of jumps impurity and lattice atoms and various relative concentrations of vacancies ? _V . In the limit of vanishingly small concentrations of vacancies, ? _V ? 1, the present simulation results are in agreement with our previous analytical results. With increasing ? _V , the diffusion coefficient of impurity atoms predicted by the simulations exceeds the result of the analytical theory, a behavior that can be explained by the growing influence of vacancy clusters, voids on the surface, in which the impurity atom can travel long distances. This is most clearly seen in the case of highly mobile impurity atoms (p ? 1), where within the characteristic time of displacement of impurity atoms, lattice atoms remain practically immobile, and the problem appears to be closely related to the percolation problem. In this case, up to ? _V ≈ 0.3, the diffusion coefficient is independent of p; then, such a dependence appears, and the diffusion coefficient increases sharply with ? _V .     

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.     

Comparison of spin and electron diffusion coefficients in a two-dimensional electron gas

The results from femtosecond four-wave-mixing experiments carried out in two-dimensional gas at the GaAs/AlGaAs heterojunction boundary under room temperature conditionsare presented. The obtained values of the spin and electron diffusion coefficients are 163.2 and 200 cm²/s respectively. The spin and electron relaxation times are found to be 50.7 ps and 3 ns respectively.     

Integral equation for the angular distribution function of an anisotropic fluid taking account of short-range order in a quasichemical approximation

An integral equation for the one-particle angular distribution function of nonspherical molecules is formulated on the basis of the thermodynamically closed system of equations obtained earlier for the occupation numbers of a multicomponent mixture of molecules with internal degrees of freedom. It is shown that this equation goes over into a known equation of Vlasov-Onsager type for large coordination numbers (for strongly elongated molecules), and yields a known rigorous result which does not contain a phase transition into the anisotropic state in the one-dimensional case. The criterion for such a transition is formulated in the form of an eigenvalue problem for the kernel of the equation obtained. In the case of single-axis molecules, an explicit expression is given for its kernel which takes account of the anisotropy in both the attraction and repulsion as well as the finite compressibility of the substance. For a binary liquid-crystal mixture, an equation is obtained in explicit analytic form within the framework of the XYZ-model for the transition line of an isotropic fluid (IF) into a nematic liquid crystal (NLC), which agrees with experiment for individual NLC. Formulas are hence obtained for a computation of the parameters of the interaction anisotropy in terms of the IF-NLC transition line parameters, and also specific results for para-azoxyanisole (PAA).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 114–118, September, 1977.The author is grateful to V. K. Semenchenko for kindly providing the necessary publications of experimental material and to B. U. Chotchaev for assistance in processing the results of the experiment.     

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.     

Study of the evolution of a finely dispersed liquid aerosol,taking into account the effect of hardly evaporable impurity

The effect of evaporation on disperse characteristics of the aerosol prepared by explosive dispersion of cavitated liquid is studied. The effect of a salt impurity is considered. Disperse characteristics of the aerosol after evaporation and at the formation point are presented. Experimental and calculated results are compared.     

Gradient-norm-based histogram equalization taking account of HSV color space distribution

In the present paper, we propose an image contrast enhancement method that can enhance the contrast of a color image naturally by taking account of a color space shape. The proposed method realizes the natural enhancement based on two kinds of intensity histograms: a gradient-norm-based histogram and an ideal histogram derived from the shape of a color space. The former histogram is used to suppress over-enhancement in the flat regions of an image and the latter histogram is used to prevent the whole image from being darken. Concretely, the aforementioned intensity histograms are appropriately mixed into a histogram with a weight based on the average intensity of the input image. The contrast enhancement of the input image is realized using the cumulative histogram of the mixed histogram as an intensity transform function. To verify the validity of the proposed method, in experiments, the proposed method is applied to a variety of images and experimental results are evaluated qualitatively and quantitatively.     

Kinetics of the diffusion of an impurity atom on a square lattice

An analytical study of the migration of an embedded impurity atom over a solid surface under the influence of the diffusion of vacancies is presented. The case of small surface coverages of both vacancies ϑ _v and impurity atoms ϑ _i , with ϑ _i ≪ ϑ _v ≪ 1, is considered. It is shown that the realization of multiple collisions of a single impurity atom with vacancies imparts a Brownian character to its motion. At long times, the dependence of the mean square displacement on the time differs little from the linear, whereas the spatial density distribution is close to the Gaussian, features that makes it possible to introduce a diffusion coefficient. For the latter, an analytical expression is derived, which differs from the product of the diffusion coefficient of vacancies and their relative concentration only by a numerical factor η. The dependence of the diffusion coefficient of an impurity atom on the ratio of the frequency of its jumps to the frequency of jumps of vacancies is analyzed. In the kinetic mode, at ω ≪ 1, the diffusion coefficient of impurity atoms depends linearly on ω, whereas at ω ≫ 1, a saturation is observed; i.e., the dependence on the frequency of jumps of the impurity atom disappears. Nevertheless, the value of η remains less than unity, and no total entrainment of impurity atoms with vacancies occurs.     

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.     

Accurate measurement of translational diffusion coefficients: a practical method to account for nonlinear gradients

For NMR probes equipped with pulsed field gradient coils, which are not optimized for gradient linearity, the precision and accuracy of experimentally measured translational diffusion coefficients are limited by the linearity of the gradient pulses over the sample volume. This study shows that the accuracy and precision of measured diffusion coefficients by the Stejskal--Tanner spin-echo pulsed field gradient experiment can be significantly improved by mapping the gradient z-profile and by using the mapped calibration parameters in the data analysis. For practical applications the gradient distribution may be approximated by a truncated linear distribution defined by minimum and maximum values of the gradient. By including the truncated linear gradient distribution function in the Stejskal--Tanner equation, the systematic deviation between the fitted curve and the experimental attenuation curve decreases by an order of magnitude. The gradient distribution may be calibrated using an intense NMR signal from a sample with a known diffusion coefficient. The diffusion coefficient of an unknown sample may then be determined from a two-parameter fit, using the known gradient distribution function.     

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.     

Analysis of impurity distribution in n-GaAs layers by photoconductivity and cyclotron resonance measurements

High-purity GaAs layers of 8 to 80 μm thickness on semi-insulating substrates have been investigated. From the 1s-2p transition of shallow donors the dopants are identified and the exact transition energies determined.

Using the relation Δω √N_I from cyclotron emission measurements the total ionized impurity density N_I was determined. In homogeneous samples a good agreement between the impurity density determined from the cyclotron resonance linewidth with total impurity density values obtained from Hall mobility data is found.

The photoconductivity and transmission measurements show the same linewidth on impurity dependence for the different types of shallow donors.     

Mobility of 2D-electrons in scattering on a correlated distribution of impurity ions in doped thin layers

The spatial correlations of impurity ions in doped thin layers have been considered. A model of hard spheres on the plane has been developed for describing the correlations. In this model, an analytical expression has been obtained for the structure factor of 2D-electrons. The concentration dependences of the mobility of 2D-electrons in heterostructures with separate doping have been investigated using Al _x Ga_{1 − x} As/GaAs as an example.     

On the structure of the two-dimensional spatially periodic inner transition layers in a gas-discharge plasma

We investigate the structure of the spatially periodic inner boundary layers in the plasma of a positive glow-discharge column produced in a long cylindrical tube with an electropositive gas inside. Asymptotic methods, namely, the method of boundary functions, are used to analyze the initial mathematical model. We consider the formation of contrast burst-type structures. We have found all principal terms of the boundary-layer asymptotics of the solution. The results obtained are compared with the available probe measurements of basic physical parameters of ionization waves (strata) in neon at low pressures.