Calculations of band-to-band impact ionisation rates performed in the semi-classical Fermi’s Golden Rule approximation are presented here for the semiconductors GaAs, In(_0.53)Ga(_0.47)As and Si(_0.5)Ge(_0.5) at 300K. The crystal band structure is calculated using the empirical pseudopotential method. To increase the speed with which band structure data at arbitrary k-vectors can be obtained, an interpolation scheme has been developed. Energies are quadratically interpolated on adapted meshes designed to ensure accuracy is uniform throughout the Brillouin zone, and pseudowavefunctions are quadratically interpolated on a regular mesh. Matrix elements are calculated from the pseudowavefunctions, and include the terms commonly neglected in calculations for narrow band gap materials and an isotropic approximation to the full wavevector and frequency dependent dielectric function. The numerical integration of the rate over all distinct energy and wavevector conserving transitions is performed using two different algorithms. Results from each are compared and found to be in good agreement, indicating that the algorithms are reliable. The rates for electrons and holes in each material are calculated as functions of the k-vector of the impacting carriers, and found to be highly anisotropic. Average rates for impacting carriers at a given energy are calculated and fitted to Keldysh-type expressions with higher than quadratic dependence of the rate on energy above threshold being obtained in all cases. The average rates calculated here are compared to results obtained by other workers, with reasonable agreement being obtained for GaAs, and poorer agreement obtained for InGaAs and SiGe. Possible reasons for the disagreement are investigated. The impact ionisation thresholds are examined and k-space and energy distributions of generated carriers are determined. The role of threshold anisotropy, variation in the matrix elements and the shape of the bands in determining characteristics of the rate, particularly the softness of the rate's threshold behaviour are investigated.

Modulation doped heterostructures have revolutionized the operation of field effect devices by increasing the speed of operation. One of the factors that affects the speed of operation of these devices is the mobility of the carriers, which is intrinsic to the material used. Mobility of electrons in silicon based devices has improved drastically over the years, reaching as high as 50.000cm2/Vs at 4.2K and 2600cm2/Vs at room temperature. However, the mobility of holes in p-type silicon devices still remains comparatively lesser than the electron mobility because of large effective masses and complicated valence band structure involved. Germanium is known to have the largest hole mobility of all the known semiconductors and is considered most suitable to fabricate high speed p-type devices. Moreover, it is also possible to integrate germanium and its alloy (Si1_zGex ) into the existing silicon technology. With the use of sophisticated growth techniques it has been possible to grow epitaxial layers of silicon and germanium on Si1_zGex alloy layers grown on silicon substrates. In tills thesis we investigate in detail the electrical properties of p-type germanium and n-type silicon thin films grown by these techniques. It is important to do a comparative study of transport in these two systems not only to understand the physics involved but also to study their compatibility in complementary field effect devices (cMODFET). The studies reported in this thesis lay emphasis both on the low and high field transport properties of these systems. We report experimental data for the maximum room temperature mobility of holes achieved m germanium thin films grown on Si1_zGex layers that is comparable to the mobility of electrons in silicon films. We also report experiments performed to study the high field degradation of carrier mobility due to "carrier heating" in these systems. We also report studies on the effect of lattice heating on mobility of carriers as a function of applied electric field. To understand the physics behind the observed phenomenon, we model our data based on the existing theories for low and high field transport. We report complete numerical calculations based on these theories to explain the observed qualitative difference in the transport properties of p-type germanium and ii-type silicon systems. The consistency between the experimental data and theoretical modeling reported in this work is very satisfactory.