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, subband 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 Schrödinger–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 (from OFF- to ON-states) and Al
_x
Ga
$_{{1}-{x}}\text{N}$
spacer mole fractions.