Transverse Averaging Technique for Depletion Capacitance of Nonuniform PN-Junctions

This article evolves an analytical theory of nonuniform PN-junctions by employing the transverse averaging technique (TAT) to reduce the three-dimensional semiconductor equations to the quasione-dimensional (quasi-1D) form involving all physical quantities as averaged over the longitudinallyvarying cross section S(z). Solution of the quasi-1D Poisson’s equation shows that, besides the usual depletion capacitance Cp and Cn due to the pand n-layers, there is an additional capacitance Cs produced by nonuniformity of the cross-section area S(z). The general expressions derived yield the particular formulas obtained previously for the abrupt and linearly-graded junctions with uniform cross-section. The quasi-1D theory of nonuniform structures is demonstrated by applying the general formulas to the PN-junctions of exponentially-varying cross section S(z) = S0 exp(αz) as most universal and applicable to any polynomial approximation S(z) ≃ S0(1 + αz) .