Analytical analysis of a p-n junction with arbitrary shaped doping profile

Analysis of a p-n junction with arbitrary value of the grading coefficient is conduced. Presented solution is linking the grading coefficient of widely used diode´s depletion layer capacitance equation with analytically defined impurity doping profile. Derivations are verified against numerical simulations based on the finite element method which experimentally prove the correctness. Also, analytical expressions for other physical quantities of a diode, like electric field, charge, potential, space charge region width, follow straightforwardly.