Peter J. Price

Electron transport in polar heterolayers

Abstract The theory of two-dimensional scattering processes in polar heterolayers is developed, and applied to mobility. The quantities involved are investigated numerically in terms of a model of the electron wavefunctions. Screening effects are discussed.

Hot electrons in a GaAs heterolayer at low temperature

The theory of hot electrons is developed for high‐mobility GaAs heterolayers at low temperature, where the electron system is two‐dimensionally itinerant with a highly degenerate distribution, and the scattering is predominantly elastic. The inelastic scattering which controls the electron heating is by acoustic‐mode phonons, with both deformation and piezoelectric coupling to the electrons. Both ‘‘equipartition’’ and ‘‘Bloch’’ temperature ranges are considered. The assumption of an electron temperature, for the hot distribution, is critically investigated.

Monte Carlo calculations on hot electron energy tails

A Monte Carlo procedure which makes it practicable to extend the calculation of hot electron distribution functions to rarely occupied ranges of the electron state is described. The method is illustrated by a calculation of the energy distribution, for semiconductor electrons in an electric field, as a function of distance in the drift direction from the initial position. For energies comparable to the ultimate average energy, the ’’thermalization’’ of the distribution occurs close to the starting point, but with increasing energy it occurs at increasing distances.

Temperature dependence of the electron mobility in GaAs‐GaAlAs heterostructures

We have studied the temperature dependence of the mobility of two‐dimensional electron gases formed at the interface of high‐quality GaAs‐GaAlAs heterostructures, focusing on the temperature range 4–40 K. The inverse mobility is shown to increase linearly with temperature, with a slope which increases with the electron density and is independent of the zero‐temperature mobility. The results are consistent with a theoretical model for the acoustic‐phonon mobility that includes screening, indicating that the temperature dependence in high mobility GaAs‐GaAlAs structures is dominated by phonons rather than ionized impurities. A good agreement between theory and experiment is found using a value of 13.5 eV for the deformation potential of GaAs.

Hybrid method for hot electron calculations

Abstract A new method for precise computations on hot electrons in semiconductors is introduced. It combines attributes of Monte Carlo and distribution-function-based methods. Exploratory calculations, with a model semiconductor, are reported, including time dependence of drift velocity, steady-state longitudinal diffusivity and avalanche rate.

On the flow equation in device simulation

The nonlocal effect of an inhomogeneous electric field on the carrier drift velocity is considered with particular reference to n‐Si. A field‐dependent phenomenological length constant, giving the first‐order effect of the field gradient, is discussed in terms of the Boltzmann equation. It is also shown how this constant may be calculated from the actual effect of a small ‘‘step’’ in an otherwise homogeneous field, by a formula which extends a previously given formula for this case.

Resonant tunneling properties of heterostructures

Abstract A general theory of resonance tunneling in planar structures, independent of the detailed form of the “well”, is developed. The transmission probability versus energy is Lorentzian, near each quasi-local level, with a width that is simply related to the lifetime for escape from the local state, the wave-packet transit time, and the dynamical response time. The charge-accumulation effect is estimated.

Hot electron effects in heterolayers

Abstract Phenomena of interaction in the direction perpendicular to the layer planes, for hot electrons in heterolayer structures such as may be grown by molecular beam epitaxy, are discussed. In particular, energy transfer between electrons in neighboring heterolayers, due to mutual coulomb scattering, and escape of electrons from a heterolayer, due to phonon scattering processes, are analyzed; and it is shown that substantial rates are possible.

Calculation of hot electron phenomena

Abstract Analytical formulas are generally able to give a better account of a physical phenomenon than can be provided by a numerical description. The latter may be necessary for hot electrons, however, because of the inability of simple physical principles to truly encompass the dynamics of the distribution function, and because of complexity in the band and scattering scheme of the solid, of the particular phenomenon studied, or geometry of the situation. The traditional phenomenon of interest is the steady state with spatial homogeneity, and independent nondegenerate electrons. In suitable conditions the Boltzmann equation then reduces to one in a single variable (energy) which can be solved by relatively simple means. More generally, for this case, we need a numerical computation of the distribution function. Either the latter is represented by its values on a grid of points in the space of the electron variables, and the operators of the Boltzmann equation by operations on this array, or the “history” of a single electron is simulated by a Monte Carlo scheme. The former method has advantages within its range of applicability. Monte Carlo has been extensively applied, because of its greater ability to deal with band and scattering details. It is also applicable, by elaboration of the computational procedures, to a range of phenomena including time dependence; diffusion; impact ionization; effects of carrier-carrier interaction; field-effect surface scattering; thermalization of drifting carriers; semiconductor junctions; effect of degeneracy.

Direct Microscopic Simulation of Gunn‐Domain Phenomena

An elaboration of the Monte Carlo computation of hot‐electron states, such as to represent a time‐dependent ensemble, is applied to the study of the instabilities associated with negative differential conductance. A two‐band semiconductor model, approximately equivalent to GaAs, is used; and the instantaneous space‐charge field parallel to the applied field is included in the particle dynamics. Spontaneous Gunn domains, successively traveling from cathode to anode at the expected speed, are obtained. This method should be suitable for investigating the instability phenomena on space and time scales shorter than are appropriate for the macroscopic theories.