Resonant over-barrier hole states in multiple quantum wells

We demonstrate an explicit numerical method for accurate calculation of the scattering matrix, and its poles, and apply this method to describing the multi-channel holes scattering in multiple-quantum-wells (MQW) structures. The results of calculations show that in contrast to the single quantum-well case, at some values of MQW parameters the number of S-matrix poles may exceed that of the absolute reflection peaks, and at different values of parameters the absolute reflection peak corresponds to different resonant states. At some values of MQW parameters there is in fact a long-living over-barrier resonant hole state. Lifetimes of resonant states depend drastically on the quantum-well potential depth. In the case of sufficiently shallow quantum wells there is a single long-living resonant state.