Effect of temperature on the validity of the einstein relation in heavily doped semiconductors
TL;DR: In this paper, an analytical expression of the modified form of the Einstein relation in heavily doped semiconductors in which Gaussian band tails are formed near the lower limit of heavy doping is derived for studying the temperature dependence of the diffusivity-mobility ratio of the carriers.
Abstract: An analytical expression of the modified form of the Einstein relation in heavily doped semiconductors in which Gaussian band tails are formed near the lower limit of heavy doping is derived for studying the temperature dependence of the diffusivity-mobility ratio of the carriers in such semiconductors. It is found that, with increasing temperature from relatively low values, the ratio first increases in a nonlinear manner and then decreases till, at high temperatures, it approaches its value corresponding to the non-degenerate condition resulting in a peak over a narrow range of temperatures.
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TL;DR: In this paper, the ratio of the diffusion coefficient of electrons to their mobility is kT/q, in close analogy with a result first obtained by Einstein for Brownian motion.
Abstract: For pt.II see ibid., vol.2, p.213 (1981). The ratio of the diffusion coefficient of electrons to their mobility is kT/q, in close analogy with a result first obtained by Einstein for Brownian motion. A similar relation holds for electrons and holes in semiconductors and it has been generalised in various ways. It also enters into theories for the screening length and for the velocity of sound in solids.
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TL;DR: In this paper, an attempt was made to study the Einstein relation for the diffusivity-mobility ration of the electrons of narrow-gap semiconductors under strong magnetic quantization in accordance with the three-band Kane model by incorporating spin and broadening.
32 citations
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TL;DR: In this paper, a general formalism and some special results are outlined which seek to show that, provided one proceeds in an appropriate and consistent manner, either formulation is permissible for electronic flow in solids.
Abstract: An introduction to the problem in the title of the paper is attempted, D being a diffusion constant for particles of concentration ν. A general formalism and some special results are outlined which seek to show that, provided one proceeds in an appropriate and consistent manner, either formulation is permissible. The main area of application envisaged is to electronic flow in solids. The mathematical results also hold for atomic flow.
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TL;DR: In this article, nonlinear terms in relations for current densities are treated macroscopically, semimicroscopic and microscopically and a set of such relations which emerge consistently from such a treatment is given.
Abstract: Nonlinear terms in relations for current densities are treated macroscopically, semimicroscopically and microscopically. In the macroscopic treatment, terms in phi 2, E2, (grad n)2,(del)2n, and E.grad n are included, where phi is the electrostatic potential, n is the carrier concentration and E is the electric field. The power series expansion of the current density is valid for equilibrium and yields conductivity-diffusion type Einstein relations. In the semimicroscopic approach, a perturbation theory for the density matrix is used, and Einstein relations are then derived by equating the average of the current density operator to zero. In the microscopic approach a Kubo formalism is developed, based on a local nonequilibrium distribution function due to Mori (1958). This leads to Einstein relations via correlation functions and Liouville's equation. A set of such relations which emerge consistently from such a treatment is given.
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TL;DR: In this paper, the density of states in highly impure semiconductors is studied using a semiclassical or Thomas-Fermi type approximation, where the local density is assumed to be proportional to the local potential.
Abstract: The density of states in highly impure semiconductors is studied using a semiclassical or Thomas-Fermi type approximation The "local" density of states is assumed proportional to ${(E\ensuremath{-}\mathcal{U})}^{\frac{1}{2}}$, where $\mathcal{U}$ is the local potential The problem then reduces to the calculation of the distribution function for the potential, which is found to be a Gaussian in the high-density limit It is clear that this approach predicts tails on both band edges which are identical except for a multiplying factor of ${({m}^{*})}^{\frac{3}{2}}$, the density-of-states mass The important contributions to the potential variation near the average potential are shown to arise from fluctuations in impurity clusters whose volume is of the order of the cube of the screening length For energies far below the average potential the important cluster sizes are much smaller than the screening length cubed Their size is determined by the kinetic energy of localization, an effect which is not accounted for by the ${(E\ensuremath{-}\mathcal{U})}^{\frac{1}{2}}$ assumption The Thomas-Fermi method involves a number of approximations, all of which are valid in the limit of high density The most serious approximation results from the improper treatment of the kinetic energy of localization which requires ${(n{{a}_{0}}^{*3})}^{\frac{1}{12}}\ensuremath{\gg}1$ for validity Because of this requirement, the method is never highly accurate in any attainable concentration range The effect of potential fluctuations on tunnel diode $I\ensuremath{-}V$ characteristics is also studied The results agree satisfactorily with experimental studies of silicon junctions by Logan et al
470 citations
IBM1
TL;DR: In this paper, the shapes of impurity emission lines are calculated for the case of randomly distributed ions in a semiconductor and the shape of the spectral lines emitted by electrons or holes captured in these bands.
Abstract: The shapes of deep-lying bands of impurity states broadened by fluctuations in the local Coulomb potential are calculated for the case of randomly distributed ions in a semiconductor and are shown to determine the shapes of the spectral lines emitted by electrons or holes captured in these bands. The distribution function for the local potential is described in terms of its Laplace transform, and expressions for its first few moments, $\overline{E}$, ${〈{(E\ensuremath{-}\overline{E})}^{2}〉}_{\mathrm{av}}$, etc., are calculated for screened Coulomb potentials. An approximate form is given for this function and is shown to be resonably accurate for materials having a high degree of compensation or a large screening length. From the results of this analysis it is shown that the shapes of impurity emission lines can be used to aid in the identification of the nature of the states and transitions involved. In particular, the width of a line is determined principally by the product of the ion density and the screening length in the luminescent region, while the sense of its skewness depends on the signs of the domination and of the carrier which is captured. Numerical examples are given for GaAs diodes containing approximately ${10}^{18}$ ions/${\mathrm{cm}}^{3}$.
225 citations