OVERVIEW

In our discussion of the two-terminal MOS structure in Sec. 2.5, we have focused on inversion and have adopted the charge sheet and depletion approximations. As is mentioned in Sec. 2.4, though, it is possible to analyze the structure without making such assumptions, allowing for the presence of both electrons and holes throughout the semiconductor, with distributions dictated from semiconductor physics. Such analysis will be valid in all operating regimes (accumulation, depletion, and inversion). In inversion, it accounts for the fact that the hole concentration decreases continuously as one goes from the bulk toward the surface, and allows for the spreading of the inversion layer below the surface. Here we provide the main steps and results of this general analysis. In using relations from Appendix B, x will be replaced by y since quantities vary in the vertical direction, assuming the orientation we have adopted in drawing the MOS two-terminal structure in Chap. 2. A p-type substrate is assumed.

Let us refer to Fig. 2.4a. The charge density at depth y in the semiconductor, including holes, electrons, and ionized acceptor atoms, is given by (2.4.15) repeated here for convenience:

From (2.4.13) and (2.4.14) we have

where ?( y) is the potential with respect to the bulk at y. Deep in the bulk the charge density is zero, so (F.1) gives p _o ? n _o = N _A. Using N _A from this and also (F.2) and (F.3) in...