Transport in quantum wells in the presence of interface roughness

The effective Hamiltonian for two-dimensional quantum wells with rough inte rfaces is formally derived. Two terms are generated. The first term is iden tified with local energy-level fluctuations, and was introduced phenomenolo gically in the literature for interface roughness scattering, however, is n ow shown to be valid only for an infinite potential well or Hamiltonians wi th one single length scale. The other term is shown to modulate the wave fu nction and cause fluctuations in the charge density. This will further redu ce the electron mobility to a magnitude that is close to the experimental r esult.