Transport in quantum wells in the presence of interface roughness

The effective Hamiltonian for two-dimensional quantum wells with rough interfaces is formally derived. Two terms are generated. The first term is identified with local energy-level fluctuations, and was introduced phenomenologically in the literature for interface roughness scattering, however, is now shown to be valid only for an infinite potential well or Hamiltonians with one single length scale. The other term is shown to modulate the wave function and cause fluctuations in the charge density. This will further reduce the electron mobility to a magnitude that is close to the experimental result.