Compact MOSFET Models for VLSI Design

3

Non-ideal and Non-classical MOS Capacitors

3.1 Introduction

The metal–oxide–semiconductor structure discussed in the previous chapter was considered to be ideal due to several assumptions. It was assumed that the work functions of gate and substrate materials are identical, the oxide is free of charges, and the substrate is uniformly doped. In practical MOS structures, there is deviation from such idealized assumptions due to the reasons outlined below.

• Gate–substrate work function difference. The work function of the gate material will, in general, not be equal to that of the substrate, as the Fermi level of the semiconductor depends on its conductivity and doping. The type of polysilicon conductivity and its doping in polysilicon gate technology is governed by technological considerations. The work function difference, ϕ_gs = ϕ_g − ϕ_Si, disturbs the flat-band condition assumed for the ideal case [1].
• Fixed charges in oxide. SiO₂ is not free from structural defects, particularly near the SiO₂ interface. In a MOS structure, there is a transition region at the oxide–silicon interface where a fixed positive charge is observed to be located. The location and magnitude of this charge make it dominant in disturbing the flat-band condition. In fact, any charge that enters within the insulator, or is located at the interface, affects the flat-band condition.
• Inhomogeneity of the substrate doping. The substrate is considered homogeneously doped, a condition hardly satisfied in MOS device ...