Airy function based model for 2-DEG charge and surface potential in N-polar Gallium Nitride heterostructures

A systematic, analytical method to obtain the charge density and surface potential in an N-polar GaN/AlGaN heterostructure is presented. This method also provides the wave functions, sub-band energies, and band diagram. The model accounts for the greater leakage of the wave functions into the spacer and barrier layers in the N-polar structure as compared to the Ga-polar structure. The framework is based on the solution of Schrodinger-Poisson equations for an approximately triangular well potential with finite confinement, achieved using first-order perturbation theory. No fitting parameters are used. Results obtained using our model are in good agreement with numerical results (obtained using the finite difference method) for a wide range of bias conditions.