Compact MOSFET Models for VLSI Design

2

Ideal Metal Oxide Semiconductor Capacitor

2.1 Physical Structure and Energy Band Diagram

A Metal Oxide Semiconductor (MOS) capacitor realized on a silicon substrate, is a two terminal device shown schematically in Figure 2.1(a) where the insulator, conventionally a thermally grown silicon-dioxide (SiO₂) film, is sandwiched between a conducting electrode called the gate (G) at one end, and a silicon substrate connected through an ohmic contact acting as the other electrode (B)[1–3]. In modern MOS technology the gate is formed by a highly doped polysilicon material which is accessed through an ohmic contact. The MOS capacitor shows non-linear C–V characteristics as against a conventional capacitor which is a linear element.

For the purpose of illustration and discussion we shall consider a p-type silicon substrate. The physical concepts developed are applicable for an n-type substrate as well. Figure 2.1(b) shows the energy band diagram of an ideal MOS capacitor structure. We use ideality to mean that the structure is simple, and some of inherent complexities are not considered. Further, the structure has assumed attributes such as uniform substrate doping, charge free oxide, and equal work function for the substrate and the polysilicon gate electrode. Though these conditions do not hold good for real structures, the assumptions help us to focus on the basic physics of the structure to which corrections can be introduced later for the deviation from the so-called ideality.

The ...