Monte Carlo simulations of hole transport and relaxation in the valence bands of a semiconductor quantum well
This thesis describes the development, from first principles, of a set of Monte Carlo programs to simulate the transport and relaxation of quantum confined holes. We have examined the particular case of hole dynamics in a lOOAGaAs/AlAs single quantum well. Information on the valence band energy dispersions and hole wavefunctions in the quantum well is obtained from a 4-band k.p calculation. We derive expressions for the quantum confined hole-phonon matrix elements and scattering rates which incorporate the 4-band k.p bandstructure, and present detailed results for intra- and inter-band scattering in the first four valence subbands of the quantum well. We consider scattering by acoustic (deformation potential), non-polar optical, polar optical and piezoelectric phonons. The scattering matrix elements in all cases show marked variations with the wavevectors of the scattering states, due to strong heavy - light hole mixing in the valence subbands. The phonon scattering rates show additional structure related to the regions of extremely large densities of states which exist in subband energy minimalocated away from the Brillouin zone centre. We have carried out simulations of steady state electric field heating of the quantum confined holes. The structure in the scattering rates is reflected in the low energy portions of the carrier energy distributions, and large carrier populations are found in the off-zone-centre band minima. Using the high energy tails of these distributions, we have been able to define effective temperatures for carriers in each subband. The similarity of these temperatures indicates that intersubband scattering is important in carrier thermalisation. We have obtained values for the hole energy loss rates in the steady state, which we are able to compare with experimental results. We have also undertaken a detailed study of the transient cooling of quantum confined holes, for a range of initial conditions. We use an approximate model of inelastic acoustic scattering, and include, in our results, the time dependent energy loss rates resolved into components due to intra- and inter-band scattering by optical and acoustic phonons. The relative efficiency of cooling via different numbers of subbands is compared, and the possibility of carrier trapping in the subband energy minima is critically investigated. The influence of features peculiar to the quantum well valence bandstructure, in particular, the presence of off-zone-centre energy minima, is also examined.