We examine the effect of interface roughness on resonant tunneling in
double barrier structures using an exactly solvable real-space three-d
imensional supercell model. We find that scattering of off-resonance s
tates into on-resonance states provides the dominant contribution to i
nterface roughness assisted tunneling. Our analysis of the sensitivity
of scattering strength to interface layer configurations reveals pref
erential scattering into k(parallel-to) almost-equal-to 2pi/lambda sta
tes, where lambda is the island size. We attribute the broadening and
shifting of transmission resonances to lateral localization of wave fu
nctions, which we demonstrate directly. We also show that the degree o
f localization increases with island size.