Theoretical investigations of reduced size effects in gallium-arsenide and heterostructure electron devices

In this thesis physical effects due to the reduced size of semiconductor devices are investigated theoretically. Effects due to statistical fluctuations and boundary conditions at heterointerfaces are examined, specifically, electron transport models are developed for the effects of impurity fluctuations, contacts, and heterostructure barriers. The investigations are carried out for the GaAs - Al{dollar}sb{lcub}rm x{rcub}{dollar}Ga{dollar}sb{lcub}rm 1-x{rcub}{dollar}As material system.; The effect of impurity fluctuations on impact ionization was analyzed by combining Monte Carlo simulations with a three dimensional Poisson solver, on a reversed biased GaAs p{dollar}sp{lcub}+{rcub}{dollar}/n junction. In the region after the dead space, large and rapid changes in the electric field are averaged out and result in only small and spatially delayed changes in the average energy and the ionization rate. The effects of impurity fluctuations on planar doped barriers were determined from the solution of Poisson's equation at 4.2 K. A spread in values of the barrier height over a range of about 30 meV was found for a structure with an average barrier of 206 meV.; Monte Carlo simulations of the effects of reflecting Schottky barrier contacts on the high field transport in GaAs are performed. It is found that the energy and momentum dependencies of the reflection probability must be included to describe the transport through the contact quantitatively, especially when tunneling is involved, and there is a relatively high spread in electron energy and momentum due to scattering.; Current-voltage characteristics of triple barrier resonant tunneling diodes are modeled. The model consisted of a self-consistent solution of Poisson's and Schroedinger's equations to determine the potential energy profiles and resonant energy levels in each of the two quantum wells. Peaks in the current as a function of applied bias are found to occur whenever a resonant energy level in either of the quantum wells coincides with the bottom of the conduction band in the emitting contact.; A two conduction state behavior of the Heterostructure Hot Electron Diode is demonstrated using ensemble Monte Carlo simulations. The results are consistent with the tunneling, self-consistent field theory which divides transport in the HHED into a low conductivity tunneling mode and a high conductivity thermionic emission mode. The electron distribution function at the drift region/barrier heterointerface indicates that the electrons are all in the {dollar}Gamma{dollar} valley during the tunneling mode and mostly in the satellite valleys during the thermionic emission mode. The difference is significant since the Al{dollar}sb{lcub}rm x{rcub}{dollar}Ga{dollar}sb{lcub}rm 1-x{rcub}{dollar}As presents a large barrier to {dollar}Gamma{dollar} valley electrons but not to electrons in the L and X valleys for Al mole fractions above 0.4.