first-order perturbation theory

The closed form model to calculate the charge density and surface potential in an N-polar GaN/AlGaN heterostructure is presented. The proposed model is developed from the solution of Schrodinger’s equation for a finite triangular potential well. 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.