Transition-capacitance calculations for double-diffused p-n junctions

A study of the depletion-layer characteristics of double-diffused p-n junctions, formed by successive diffusion of opposite type impurities into a semiconductor, is presented. The general form of the impurity profile is taken to be N(r) = N_SA e^?ar(ar+2k) where N_S, A, a and k are constants and r is the distance. This general form reduces to Gaussian, erfc and two-step diffusion profiles as particular cases. Results are shown graphically for typical values of these constants.It is shown that the double-diffused junctions can be well approximated by equivalent double-exponential profiles in the impurity range of practical interest and C-V relations are obtained analytically. The results obtained are convenient for ready engineering calculations. The accuracy and the range of validity of the approximation are discussed.A simple and accurate analytical method is outlined for the calculation of reverse-biased sidewall capacitance of double-diffused structures, with special reference to the emitter junction of a planar transistor. It is shown that by approximating the impurity profiles by Gaussian distributions, the metallurgical junction formed is given by an ellipse and this leads to a simple evaluation of the sidewall capacitance. An expression obtained for the impurity gradient along the sidewall enables the computation of forward-biased depletion-layer capacitance when the mobile carriers in the depletion region are to be considered.