TRANSMISSION AND REFLECTION OF HOLES FROM BARRIERS AND WELLS IN SEMICONDUCTOR HETEROSTRUCTURES

The quantum mechanical problem of tunnelling and reflection of holes f rom barriers and wells in semiconductor heterojunctions has been analy sed. By using the Luttinger Hamiltonian to describe the dynamics of ho les, the inherent anisotropy, non-parabolicity and heavy- and light-ho le mixing at the top of the valence band has been taken into account. The symmetries of the hole scattering matrix are worked out, from whic h very general relations among the reflectivities and transmissivities are obtained. These analytical results are complemented by numerical calculations for several different situations; within the range of par ameters investigated, no resonant unity transmission above the barrier is found. We do find that the transmission is zero (anti-resonances) in the well configuration for particular values of the energy of the i ncoming heavy hole.