The Over-Barrier Resonant States and Multi-Channel Scattering in Multiple Quantum Wells


  • A Polupanov
  • A Kruglov



We demonstrate an explicit numerical method for accurate calculation of the scattering matrix and its poles, and apply this method to describe the multi-channel scattering in the multiple quantum-wells structures. The S-matrix is continued analytically to the unphysical region of complex energy values. Results of calculations show that there exist one or more S-matrix poles, corresponding to the over-barrier resonant states critical for the effect of the absolute reflection of holes in the energy range where only the heavy ones may propagate over barriers in a structure. Light- and heavy-hole states are described by the Luttinger Hamiltonian matrix. In contrast to the single quantum-well case, at some parameters of a multiple quantum-wells structure 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. The imaginary parts of the S-matrix poles and hence the lifetimes of resonant states as well as the widths of resonant peaks of absolute reflection depend drastically on the quantum-well potential depth. In the case of shallow quantum wells there is in fact a long-living over-barrier resonant hole state.


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How to Cite

Polupanov, A. and Kruglov, A. (2012) “The Over-Barrier Resonant States and Multi-Channel Scattering in Multiple Quantum Wells”, The International Journal of Multiphysics, 6(2), pp. 99-106. doi: 10.1260/1750-9548.6.2.99.