Transition region capacitance of diffused p-n junctions

The classical capacitance-voltage relations based on abrupt space-charge edge approximations, while adequate at large reverse bias, do not adequately describe the capacitance near zero bias. This paper presents explicit capacitance-voltage relations valid near zero bias for linearly graded and exponential-constant profiles. For linearly graded junctions, the intercept in a 1/C³versus voltage plot is shown to be well approximated by the "gradient voltage" defined by Vg= 2/3 kT/q ln a²εkT/q/8qni³. Also presented is an accurate numerical technique for machine computation of the transition region capacitance for any doping profile. Explicit relations obtained by dimensional considerations and curve fitting on numerical solutions are free of singularities, hence useful in computer-aided device design and doping profile determination.