This paper presents an analytical method for determining the electron mobility in N-polar GaN het-erostructures. The wave function, charge density, and Fermi potential are obtained analytically by combining Airy functions in the channel and spacer regions and utilizing first-order perturbation theory. Importantly, this approach does not rely on any external input such as charge density or electric field. The analytically obtained wave function, charge density, and Fermi potential are then utilized to estimate the scattering rates resulting from various processes in N-polar MIS-HEMTs. Matthiessen's rule is applied to combine the individual scattering rates. The obtained results are validated against experimentally measured mobilities for both conventional GaN and composite GaN-InGaN het-erostructures over a range of channel layer thicknesses.

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.

A closed-form model to calculate the 2-DEG charge density and surface potential in an N-polar GaN/AlGaN heterostructure is presented.