The objective of this thesis work is twofold: to present a theoretical framework to study high-field carrier transport in semiconductor materials and to provide a deep understanding of the transport properties of GaN and HgCdTe. The validation of this model is performed by applying it to the study of Avalanche Photodiodes.

The model we developed is based on Monte Carlo techniques and it includes the full details of the band structure, derived from the empirical pseudopotential method (EPM), and a numerically calculated impact ionization transition rate based on a wave-vector dependent dielectric function. The nonpolar carrier-phonon interaction is treated within the framework of the rigid pseudoion (RPI) approximation using ab initio techniques to determine the phonon dispersion relation. The calculated phonon scattering rates are consistent with the electronic structure and the phonon dispersion relation thus removing adjustable parameters such as deformation potential coefficients. Band-to-band carrier tunneling has been treated by solving the time-dependent multiband Schroedinger equation. The multiband description predicts a considerable increase of the impact ionization coefficients compared with simulations not considering tunneling.

Specifically, the present model has been applied to the study of two distinct semiconductor materials: GaN and HgCdTe. The former is a wide bandgap while the second is a narrow bandgap semiconductor. In spite of their constantly increasing technological reliability both materials lack theoretical understanding of high-field carrier transport.

Avalanche photodiodes (APDs) offer an ideal environment to test and validate the model developed in this thesis work because of the large electric field involved in these devices. APDs based on both GaN and HgCdTe are investigated, consistently with the physics-based models described above. Key quantities such as gain, breakdown voltage, bandwidth and noise characteristics are estimated. The results are found to be in good agreement with experimental data available in literature.