The effect of strain in pseudomorphicp-silicon(1-x)germanium(x): Physics and modeling of the valence bandstructure and hole transport

The physics of hole transport in pseudomorphic Si{dollar}sb{lcub}1-x{rcub}{dollar}Ge{dollar}sb{lcub}x{rcub}{dollar}//(001)Si is investigated by Monte Carlo simulation. The Monte Carlo method developed in this work takes into account several aspects of the strained p-type system which qualitatively distinguish it from an n-type system. These include: (1) the valence band system is described using a three band {dollar}vec kcdotvec p{dollar} method which gives an accurate representation of the strongly coupled heavy hole, light hole and split-of hole states; (2) the valence band deformation potential theory is used to determine both the strain effects on the bandstructure and the hole--phonon scattering rates in both strained and unstrained materials; (3) the scattering rates are anisotropic, depending upon the direction of flight and are calculated on a mesh which exploits the symmetry of the system and (4) the post-scattering states are determined from a probability distribution which depends not only on the scattering angle, but also upon the initial direction of flight. The Monte Carlo method is used to make a detailed study of the effect of strain and alloying on hole transport in light to moderately doped pseudomorphic Si{dollar}sb{lcub}1-x{rcub}{dollar}Ge{dollar}sb{lcub}x{rcub}{dollar}(0 {dollar}leq xleq{dollar} 0.4) grown on (001)Si, subjected to electric fields in the range of 1-20 kV/cm, at 300 K. The scattering mechanisms considered are: alloy scattering, acoustic phonon scattering and both Si-Si and Ge-Ge optical phonon scattering. Each of these mechanisms can drive both intra- and interband scattering within and between all of the top three valence bands. The combined effects of strain and alloying are found to produce a monotonic increase in hole mobility and temperature, which at the highest Ge content alloy studied, Si{dollar}sb{lcub}0.6{rcub}{dollar}Ge{dollar}sb{lcub}0.4{rcub}{dollar}//(001)Si, are comparable to the hole mobility and temperature in bulk Ge. A slight greater carrier velocity is found for in-plane transport than for perpendicular transport. The results of this analysis are used to estimate the high frequency performance of an npn Si/Si{dollar}sb{lcub}1-x{rcub}{dollar}Ge{dollar}sb{lcub}x{rcub}{dollar}/Si DHBT, where an approximate two-fold increase in {dollar}fsb{lcub}max{rcub}{dollar} is found over that in a comparable state of the art Si BJT. The work concludes with a brief analysis of hole transport in strained GaAs. This being a polar semiconductor results in qualitatively different hole transport characteristics, which are contrasted with the findings for the covalent Si{dollar}sb{lcub}1-x{rcub}{dollar}Ge{dollar}sb{lcub}x{rcub}{dollar}.