Large-signal and high-frequency analysis of nonuniformly doped or shaped pn-junction diodes

Abstract

An analytical theory of nonuniformly doped or shaped PN-junction diodes submitted to largesignals at high frequencies is presented. The resulting expressions can be useful to evaluate the performance of semiconductor device modeling software. The transverse averaging technique is employed to reduce the three-dimensional charge carrier transport equations into the quasi-onedimensional form, with all physical quantities averaged out over the longitudinally-varying cross section. Although, it is assumed an axial symmetry, this approach gives rise to useful analytic expressions for the static current-voltage characteristics, the diffusion conductance, and diffusion capacitance as a function of the signal amplitude and the cross section non-uniformity.

Systematic oil flow modeling in the Quasi-3D approximation yields additional terms that allows for variable cross-section area tubing

“…Defining the average of a scalar, φ( r, z), and the average of a vector, V ( r, z), over the cross-section area for a axially symmetric wellbore [21,22]. Differently from the local instant formulation [18], there is no need to assume the area is constant along the longitudinal direction.…”

“…Frequently, conservation of particles, conservation of momentum and conservation of energy equations are used to provide insight into many physical problems. Phenomena ranging from flow of charge carriers in a semiconductor device to flow of oil and gas in a well can be described within such theoretical framework [18][19][20][21][22].…”

“…In a previous work, we have demonstrated how to break the problem into 1D + 2D dimensions by applying the transverse averaging technique (TAT), and we have used this approximation to study the nonuniformly doped or shaped p-n junction diodes. In the occasion the TAT technique was applied to the conservation of particles equation for holes and electrons [21,22]. In TAT, the cross-section area is not necessarily held constant.…”