Effect of interface roughness on the density of states of finite barrier height quantum wells

We calculate the density of states of a 2D electron gas in finite barrier height quantum wells with the explicit inclusion of the interface roughness effect. By using Feynman path-integral method, the analytic expression is derived. The results show that the 2D density of states is dependent on the RMS of the fluctuation potential. The interface roughness causes localized states below the subband edge. We also apply the theory to model the finite barrier height quantum wells in AlxGa1−xAs/GaAs.