Quantum Effects on the Gate Capacitance of Trigate SOI MOSFETs

Scaling effects on the gate capacitance of trigate MOS field-effect transistors are studied by means of analytical models and numerical self-consistent solutions of the 2-D Schrödinger and Poisson equations. Special attention is paid to the quantum capacitance, which is related to the density of states. We show that, although the quantum capacitance strongly decreases when the channel dimensions are scaled, the gate capacitance is not reduced relative to the oxide capacitance in trigate MOS structures. This is due to the fact that both the oxide capacitance and the quantum capacitance scale with the channel cross section. From Schrödinger-Poisson simulations, we actually observe a relative increase in the gate capacitance when the silicon cross section is scaled below 7 nm × 7 nm, whereas the opposite trend is obtained from classical calculations. We relate this mainly to the differences between quantum-mechanical and classical electron distributions in real space. Quantization effects on the quantum capacitance are found to have less effect on the gate capacitance except for very small silicon cross sections in the order of 2 nm × 2 nm.