Quasistationary-energy-level calculation for thin double-barrier GaAs-${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As heterostructures

A band-structure calculation for thin double-barrier GaAs-${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Al}}_{\mathrm{x}}$As heterostructures is developed by identifying quasistationary energy levels with resonances in the transmission coefficient, which is obtained with the transfer-matrix technique. The results are compared with calculations for isolated quantum wells and superlattices. Exact numerical calculations for the broadening and the shift of energy levels with decreasing barrier width are presented. Changes in the curvature of the band structure are found. An approximate formula for the energy levels and widths of the quasistationary states of double-barrier systems is developed. The formalism is based on a Fano-type configuration interaction between the eigenstates of appropriate subsystems.