Abstract
A two-dimensional (2D) finite-difference time-domain model based on wave-packet propagation has been formulated. This method, which is capable of treating arbitrary potential profiles, is applied to the problem of finding the momentum (k) relaxation rates for each subband due to interface roughness scattering in disordered quantum wires as a function of wire width, electron energy, disorder correlation length (Λ), and disorder penetration depth. Results from the general 2D numerical approach are compared with those from 1D calculations based on the adiabatic approximation and the Born approximation. The error introduced by the Born approximation is found to be as much as a factor of 2.5 for small correlation lengths (Λk<1), and becomes significantly greater for large correlation lengths (Λk≫:1) owing to the predominance of higher-order scattering processes. If only intrasubband scattering is effective, the adiabatic approximation agrees to within 50% with the more general 2D results for a wide range of disorder parameters. However, the relaxation time decreases significantly at higher energies with the onset of scattering to higher electron subbands, which the adiabatic approximation is incapable of treating. For electron energies lower than the average disorder-induced potential barriers, the electron wave packet becomes localized with slow probability density decay due to tunneling.
DOI:https://doi.org/10.1103/PhysRevB.55.4494
©1997 American Physical Society