# Hot electron diffusion

TL;DR: In this article, a simple expression relating the hot-electron diffusion constant with the differental mobility is derived, and it is found that for some conditions the constant may be even negative.

Abstract: A simple expression relating the hot-electron diffusion constant with the differental mobility is derived. It is found that for some conditions the constant may be even negative.

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TL;DR: In this paper, it was shown that the distribution function for hot carriers may be a displaced Maxwellian only if τ (k) is k independent, which does not hold for most of the situations of physical interest.

Abstract: The differential relaxation time τ (k,F) defined in a previous paper for isotropic semiconductors in the hot‐carrier range is shown to depend on the orientation with respect to the field force F. τ (k,F) is expressed using the collision operator and the distribution function. In the Ohmic range τ (k,F=0) is found to be equal to the usual relaxation time τ (k) related to transition probabilities per unit time. Longitudinal τN(k,E) and transverse τn(k,E) differential relaxation times are numerically computed for p‐type germanium and are found to be actually different although of the same order of magnitude, namely 10−12–10−13 sec. It is proved that the distribution function for hot carriers may be a displaced Maxwellian only if τ (k) is k independent, which does not hold for most of the situations of physical interest. It is shown that the differential relaxation times involved in longitudinal D∥(E) and transverse D⊥(E) diffusion coefficients are τ∥(k,E) and τ⊥(k,E). D∥(E) and D⊥(E) are numerically computed...

20 citations

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TL;DR: In this article, a Monte Carlo simulation of electron transport and noise in GaAs rectangular quasi-one-dimensional quantum wire structures at low temperatures is presented. And the authors show that with the heating of electron gas the efficiency of acoustic phonon scattering decreases and the mobility increases.

Abstract: We have employed a Monte Carlo technique for the simulation of electron transport and noise (diffusion) in GaAs rectangular quasi‐one‐dimensional quantum wire structures at low temperatures. It is demonstrated that with the heating of electron gas the efficiency of acoustic phonon scattering decreases and the mobility increases. The increase of electron mobility appears as a superlinear region on velocity‐field dependence. It is shown that electron noise increases in the superlinear region. The transition from superlinear transport to the regime close to electron streaming with a further increase of electric fields is reflected on the diffusivity‐frequency dependence by the appearance of a separate peak at the streaming frequency. The electron streaming regime which takes place at higher fields causes the collapse of the diffusion coefficient (noise spectral density) to the streaming frequency.

12 citations

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TL;DR: In this paper, the geodesics deviation equation (GDE) is itroduced in "adiabatic" approximation and Perturbation theory in general case is formulated.

Abstract: Geodesics deviation equation (GDE) is itroduced. In "adiabatic" approximation exact solution of the GDE if found. Perturbation theory in general case is formulated. Geometrical criterion of local instability which may lead to chaos is formulated.

10 citations

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TL;DR: In this article, a geodesic deviation equation is introduced and a geometrical criterion of local instability which may lead to chaos is formulated, and its exact solution is found in an "adiabatic" approximation.

Abstract: A geodesic deviation equation is introduced. In an “adiabatic” approximation its exact solution is found. Perturbation theory in general case is formulated. A geometrical criterion of local instability which may lead to chaos is formulated.

10 citations

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TL;DR: In this paper, the authors focus on mathematical aspects of determining local instability by using invariant characteristics of an internal Riemannian geometry with a Jacobi metric and give formulae for determining the sign of the sectional curvature and the separation rate of nearby trajectories for systems with a natural lagrangian.

Abstract: In this work we focus on mathematical aspects of determining local instability by using invariant characteristics of an internal Riemannian geometry with a Jacobi metric. We give formulae for determining the sign of the sectional curvature and the separation rate of nearby trajectories for systems with a natural lagrangian. We apply this to N -body systems.

7 citations

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TL;DR: In this article, the properties of uniformly propagating stable domains in gallium arsenide are calculated on the basis of recently computed velocity-field and diffusion-field characteristics, and the maximum velocity difference increases with decreasing resistivity and is about 25% of the drift velocity in 1 Ω cm material.

Abstract: The properties of uniformly propagating stable domains in gallium arsenide are calculated on the basis of recently computed velocity-field and diffusion-field characteristics. The field dependence of the diffusion coefficient makes the domain velocity larger than the electron drift velocity outside the domain. The velocity difference becomes small when the drift velocity approaches its minimum value because the domain leading edge then approaches total depletion. The velocity difference also becomes small when the drift velocity approaches its peak value. This latter behaviour is qualitatively different from that predicted previously and is due to the close proximity of the peaks of the diffusion-coefficient-field and velocity-field characteristics. The maximum velocity difference increases with decreasing resistivity and is about 25% of the drift velocity in 1 Ω cm material. Plots against outside field of domain velocity, width, peak field, potential, and maximum and minimum electron concentrations are given for sample resistivities of 1, 5 and 10 Ω cm.

57 citations

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TL;DR: The properties of uniformly propagating stable domains are calculated using a constant diffusion coefficient of 178 cm2 sec-1 and an analytic approximation to a recently computed static velocity-field characteristic for gallium arsenide as mentioned in this paper.

Abstract: The properties of uniformly propagating stable domains are calculated using a constant diffusion coefficient of 178 cm2 sec-1 and an analytic approximation to a recently computed static velocity-field characteristic for gallium arsenide The static characteristic has a steep slope in the negative resistivity range and then saturates at high fields Consequently the peak domain field initially increases slowly as the domain velocity is reduced from its maximum value and then increases indefinitely as the domain velocity approaches the saturated drift velocity Domain shapes are given for a resistivity ρ0 = 1 ω cm The extreme degrees of depletion and accumulation, the widths of the depletion and accumulation layers and the domain potential are all plotted against the field outside the domain for ρ0 = 1, 5 and 10 ω cm The domain has a rounded triangular shape which is asymmetric and shows large departures from neutrality at large domain voltages (except when ρ0 << 1 ω cm) but which becomes symmetrical and nearly neutral everywhere at low domain potentials, with a diffusion-limited width of 19 ρ01/2 μm The domain potential increases slowly at first, with an initial slope of 453 ρ01/2 μm, as the outside field is reduced below threshold and then increases rapidly as the minimum outside field is approached Consequently the length dependence of the domain potential for a fixed average field is less sensitive to resistivity variations than was found previously (using a schematic three-line static characteristic) and is in better agreement with the experimental data

45 citations

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TL;DR: In this article, a phenomenological equation for the motion of carriers in a Gunn diode is written in terms of an average drift velocity and an average diffusion coefficient, both of which are functions of the field only.

Abstract: A phenomenological equation for the motion of carriers in a Gunn diode is written in terms of an average drift velocity and an average diffusion coefficient, both of which are functions of the field only. The equation can be reduced to a simple form in the case of a steady‐state dipole domain with a flat top. Various properties of the domain can be deduced using only elementary analytical methods. As an example, it is found that although the domain boundary shapes change with carrier concentration the domain velocity remains constant and equal to the drift velocity of the carriers in the uniform field regions, provided the mobility is independent of concentration.

26 citations