Tunneling escape of electrons from a double-barrier structure

The lifetime ${\mathrm{\tau }}_{\mathit{e}}$ of an electron occupying the quasibound state in an ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs double-barrier structure has been calculated with both the tunneling Hamiltonian approach and the complex eigenvalue method. It is found that ${\mathrm{\tau }}_{\mathit{e}}$ is dominated by the barrier width, but is insensitive to the well width and the bias. We have also investigated the effect of the electron–LO-phonon interaction on the dynamics of the electron in the quasibound state. Under the condition of perfect interfaces, the tunneling mechanism does not depend on the momentum component parallel to the interfaces. As a consequence, the total probability of the electron remaining in the quantum well obeys a sum rule, and the tunneling escape rate is the same for both the coherent and the incoherent tunneling process. The estimated time scale of the electron–LO-phonon scattering is comparable to ${\mathrm{\tau }}_{\mathit{e}}$ for typical double-barrier structures used in high-speed electronic devices. Our theoretical curve of ${\mathrm{\tau }}_{\mathit{e}}$ vs the barrier width reproduces the characteristic features of the experimental results, where the observed temperature dependence is due to the electron-hole recombination, which has been ignored in our theory.