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 new terms are generated. The first term is identified to the local energy level fluctuations, which was introduced phenomenologically in the literature for interface roughness scattering but 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 wavefunction and cause fluctuations in the charge density. This will further reduce the electron mobility to the magnitude that is close to the experimental result.