Depletion approximation analysis of an exponentially graded semiconductor p-n junction

Estimation of important properties of p-n junctions such as reverse leakage current and capacitance is greatly facilitated by the depletion approximation. Computation of the electrostatic potential and electron and hole concentrations within this approximation are commonplace in the microelectronics industry. The depletion approximation requires appropriate and accurate boundary conditions. Thus far, such reasonable boundary conditions have been widely applied only for the case in which the p-type and n-type impurity concentrations are spatially uniform. The author derives the solution of the depletion approximation with appropriate boundary conditions for the case in which the impurity concentration on one side of the diode decays exponentially with distance. He plots the potential and charge density of this exponential depletion approximation and compares these results to full numerical solution of the semiconductor equations. The agreement between the proposed approximation and the numerical solution validates this approximation scheme