Lifetime of the quasi-bound state in the quantum well in a double-barrier structure with a localized imaginary potential

Abstract

Tunneling in a double-barrier structure with a localized recombination channel is modeled by a spatially dependent imaginary potential. The general properties of nonhermitian Hamiltonians with an imaginary potential are examined. For a localized imaginary potential, the eigenvalues are found to be real for the extended states. The eigenstates with different eigenvalues are found to be nonorthogonal in general and this nonorthogonality is related to the nonconservation of matter. A continuity equation is derived from the Schrödinger equation showing explicitly a sink of carrier density at the imaginary potential. The lifetime of the quasi-bound state in the quantum well in a double-barrier structure is calculated from the width of the resonance peak in the transmission spectrum of the structure and is found to be decreasing linearly with the magnitude of the imaginary potential. The dependence agrees with a relation derived from the rate equation describing the tunneling and recombination process. A numerical simulation of the tunneling escape of a wavepacket localized initially inside the quantum well in this potential illustrates the loss of matter through the imaginary potential. The lifetime of the electron in the quantum well, the recombination time, and the tunneling time obtained from the simulation are in agreement with those calculated from the width of the resonance peak.