A Closed-Form Model for 2-DEG Charge and Surface Potential in N-Polar Gallium Nitride Heterostructures

A closed-form model to calculate the 2-D electron gas (2-DEG) charge density and surface potential in an N-polar GaN/AlGaN heterostructure is presented. The proposed model is developed from the solution of Schrödinger’s equation for a finite triangular potential well. Asymptotic expressions of Airy functions are used to compute an initial value of subband energy. A new, unified expression to update the surface potential due to Poisson’s equation is presented. The modified Fang–Howard (M.F.H.) function is then employed to develop a closed-form correction to the subband energy using first-order perturbation theory. No fitting parameters are used. The results from our model are validated with numerical data for a wide range of bias conditions, channel layer thickness, and spacer layer mole fraction. Finally, the gate capacitance of the heterostructure is evaluated using automatic differentiation and validated against experimental data.