Coherent model for resonant tunneling of electrons in double quantum wells under electric fields

Taking the inhomogenous broadening of the electron energy levels into account, a coherent model of the resonant tunneling (RT) of electrons in double quantum wells is presented. The validity of the model is confirmed with the experiments [M. Nido et al., Proc. SPIE 1268, 177 (1990)], and shows that the tunneling process can be explained by the simple coherent theory even in the presence of the carrier scattering. We have discussed the dependence of resonant tunneling on the barrier thickness ${\mathit{L}}_{\mathit{B}}$ by introducing the contrast ratio Λ and the full width at half depth of the RT valley, and found that Λ first increases with increasing barrier thickness, reaches a maximum, and then decreases with a further increase of ${\mathit{L}}_{\mathit{B}}$, in striking contrast to the Fabry-Pérot model where a monotonic increase of the peak-to-valley ratio is predicted. We attribute the reduction of Λ with large ${\mathit{L}}_{\mathit{B}}$ to the energy broadening resulting from the carrier scattering. A monotonic decrease of the full width at half depth of the RT valley with an increase of ${\mathit{L}}_{\mathit{B}}$ is also found.