Theory of interface-roughness scattering in resonant tunneling

We have calculated the effects of interface-roughness scattering on resonant tunneling through a GaAs-${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As double-barrier structure. In our calculation we treat the double-barrier potential exactly. The interface-roughness scattering is dealt with nonperturbatively by means of the self-consistent Born approximation, which preserves unitarity. In the presence of scattering, the peak current is reduced by ∼10%, but not more, even though a tunneling electron may be scattered many times while inside the quantum well. The valley current, on the other hand, is increased by several orders of magnitude due to the scattering if the barriers are thick enough. For thin barriers, the calculated peak-to-valley (P/V) ratios increase exponentially with the barrier thickness. At a barrier thickness of ≊100 Å the P/V ratio crosses over to a much slower increase, and eventually reaches a maximum, after which the P/V ratio decreases somewhat. This qualitative behavior is in good agreement with recent experimental results. A surprising result of this work is that nonperturbative and perturbative calculations give practically identical results for the valley current for realistic parameter values for the interface roughness.