Hole transport theory in pseudomorphic Si1-xGex alloys grown on Si(001) substrates.

Abstract

The physics of hole transport in pseudomorphic ${\mathrm{Si}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Ge}}_{\mathrm{x}}$/Si(001) is investigated by Monte Carlo simulation. The Monte Carlo method developed in this work takes into account several aspects of the strained p-type system which qualitatively distinguish it from an n-type system. (1) The valence-band system is described with use of a three-band k\ensuremath{\cdot}p method which gives an accurate representation of the strongly coupled heavy-hole, light-hole, and split-off--hole states. (2) The valence-band deformation-potential theory is used to determine both the strain effects on the band structure and the hole-phonon scattering rates in both strained and unstrained materials. (3) The scattering rates are anisotropic, depending upon the direction of flight and are calculated on a mesh which exploits the symmetry of the system. (4) The postscattering states are determined from a probability distribution which depends not only on the scattering angle, but also upon the initial direction of flight. The Monte Carlo method is used to make a detailed study of the effect of strain and alloying on hole transport in lightly doped pseudomorphic ${\mathrm{Si}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Ge}}_{\mathrm{x}}$ (0\ensuremath{\le}x<=0.4) grown on Si(001), 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 intraband 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, ${\mathrm{Si}}_{0.6}$${\mathrm{Ge}}_{0.4}$/Si(001), are comparable to the hole mobility and temperature in bulk Ge. A slightly greater carrier velocity is found for in-plane transport than for perpendicular transport.