2.2.4 MOS Charge Control Model

2.2.4 MOS Charge Control Model

Well above threshold, the charge density of the mobile carriers in the inversion layer can

be calculated using the parallel plate charge control model of (2.28). This model gives an

adequate description for the strong inversion regime of the MOS capacitor, but fails for

applied voltages near and below threshold (i.e. in the weak inversion and depletion

regimes). Several expressions have been proposed for a unified charge control model

(UCCM) that covers all the regimes of operation, including the following:

where, a i c » c is approximately the insulator capacitance per unit area (with a small

correction for the finite vertical extent of the inversion channel), n0 = ns(V = VT) is the

density of minority carriers per unit area at threshold, and h is the socalled

subthreshold ideality factor, also known as the subthreshold swing parameter. The ideality factor

accounts for the subthreshold division of the applied voltage between the gate insulator

and the depletion layer, and the 1/h represents the fraction of this voltage that contributes

to the interface potential. A simplified analysis gives

This expression reproduces the correct limiting behaviour both in strong inversion and

the subthreshold regime, although it deviates slightly from (2.34) near threshold. The

various charge control expressions of the MOS capacitor are compared in the above

figure.