A Quantum–Mechanical View on the Capacitance of a Silicon p-n Junction

We have calculated the capacitance of a silicon p-n junction from a self-consistent solution to the effective-mass Schroumldinger and Poisson equations. Although the p-n product and the charge distribution deviate strongly from the semiclassical calculations, the quantum mechanically calculated capacitance of the silicon p-n junction differs only weakly from the semiclassical result. We show that the deviation from the semiclassical result can be approximated as band-gap narrowing in the quasi-neutral regions due to the exchange-energy term in the effective-mass Schroumldinger equation