We present a theory of the band-bending effects on two-dimensional (2D) carriers confined in a modulation-doped square quantum well. We develop a tractable variational evaluation of several physical quantities that are important in the theory of 2D systems. Analytic expressions of the envelope wave function and the 2D screening form factor allow us to compute various electronic properties such as electrical mobility, density of states in the presence or in the absence of magnetic fields, and Landau level broadening. We prove that in the case of the interface roughness scattering, the band-bending effects lead to a peak in the channel-width dependence of the mobility and a minimum in the Landau level broadening. Our modeling explains recent measurements for a 2D hole gas.

• Received 13 December 2007

DOI:https://doi.org/10.1103/PhysRevB.77.125335