Dependence of Modulation Amplitude on Electron Density in Unidirectional   Lateral Superlattices: The Effect of the Thickness of the Two-dimensional   Electron Gas
  The amplitude V_0 of unidirectional periodic potential modulation introduced by a surface grating into a two-dimensional electron gas (2DEG) formed at AlGaAs/GaAs heterointerface is measured as a function of electron density n_e by analyzing commensurability oscillation of the magnetoresistance. The electron density is varied either by applying a bias to a metallic back gate or by illumination. The amplitude decreases with increasing density, with the rate |dV_0/dn_e| roughly an order of magnitude larger for the former method. The result is interpreted in terms of the rate, dE_1/d(delta E_c), of the change in the first subband level E_1 in response to the variation of the conduction-band edge delta E_c above the heterointerface. The rate crucially depends on the thickness of the 2DEG. 
Akira Endo and Yasuhiro Iye