A minimal model for the calculation of surface charges in GaAs/AlGaAs heterostructures

We derive an analytical model to calculate charges accumulated at the surface of GaAs in a doped GaAs/AlGaAs heterostructure that is based on the electrostatics of the structure when biased under different voltages at its surface. We compare our results to self-consistent Poisson-Schrödinger calculations, performed using an in-house 1D solver. This model allows for the calculation of doping densities and charges accumulated in the 2DEG, even in cases where they are not directly measurable using experimental means. Our model reveals that the contribution of the spread of charges away from the interface has a more pronounced effect in shifting the voltage required to form the 2DEG at the surface of GaAs than the occupancy of the subbands.