6. Summary

The influence of strain on the electron transport in strained bulk $\textrm {Si}_{1-x}\textrm {Ge}_{x}$ grown on relaxed $\textrm {Si}_{1-y}\textrm {Ge}_{y}$ substrates with an arbitrary orientation has been studied. The description of the electron transport has been based on the semiclassical model described in Chapter 2. This model includes both the quantum and classical nature of electrons in solids. It uses classical trajectories and treats scattering processes quantum mechanically. Additionally, the quantum mechanical Pauli exclusion principle is taken into account within this transport model. The solids are considered as quantum mechanical objects described through their band structure and quantization of ion vibrations by quasi-particle description. The same quasi-particle concept is used for the electronic system itself at high densities through the plasmon picture. The most general description of semiclassical kinetics is covered by the Boltzmann transport equation with a scattering term including all specific scattering mechanisms. Acoustic phonons, intervalley phonon scattering, plasmon scattering, alloy scattering and ionized impurity scattering have been included in this study of transport in SiGe. To account for the Pauli exclusion principle the scattering term has also been modified leading to a nonlinear form of the Boltzmann equation.

Strain effects have been considered in Chapter 3. The linear theory of deformation-potentials have been applied to the conduction band of SiGe. Within this theory the shape of the bands is kept unchanged while the shift of different valleys leads to a splitting of the equivalent conduction band minima. The influence of the substrate orientation on this splitting has been taken into account. This results in non-zero non-diagonal elements of the strain tensor, which leads to various possible splittings. Finally, the scattering processes have been modified to account for the change of the band structure. The phonon scattering rate has been changed by modifying its prefactor due to the change of the number of final equivalent minima. In addition the energy argument of the delta-function changes due to the splitting. The influence on the ionized impurity scattering has been taken into account through the screening parameters. The Fermi energy is found from the solution of a nonlinear equation. The screening length and the dielectric function are obtained by a proper modification of the expressions known from the unstrained case.

The Monte Carlo approach has been chosen to solve the nonlinear Boltzmann kinetic equation. To study the low field electron mobility tensor in strained semiconductors and in particular in strained SiGe a zero field Monte Carlo algorithm has been developed in Chapter 4. The algorithm allows the whole mobility tensor to be obtained from one simulation, which is an advantage over standard low field Monte Carlo approaches. It has been found that at high electron densities the inelastic scattering processes reverse. This has been explained as a quantum mechanical effect caused by of the Pauli exclusion principle. Finally, the algorithm has been extended to a small signal algorithm for semiconductors in the high field regime. A rejection technique has been proposed to solve the first order perturbation equation. This method is able to deal with an arbitrary shape of the static distribution function and is not limited to the equilibrium distribution as is the case for the zero field algorithm.

The results of Monte Carlo simulation of strained SiGe layers have been discussed in Chapter 5. Both undoped and doped layers have been considered. The influence of repopulation effects in undoped layers caused by energy splitting has been studied. The interplay between the Pauli exclusion principle and strain effects has been observed in doped strained layers. Finally, small signal analyses have been performed for relaxed and strained Si layers.

S. Smirnov: