SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

9.4. CAPACITANCE-VOLTAGE CHARACTERISTICS OF THE MOS 449

Oxide Silicon

Cs

MOS CAPACITOR

Capacitance per unit area

Cox =εdox

ox

Figure 9.11: A simple equivalent capacitance model for the MOS capacitor.

As shown in figure 9.11, the capacitance of the MOS structure is the series combination of the
oxide capacitanceCoxand the semiconductor capacitanceCs. The semiconductor capacitance
per unit area is, by definition

Cs=

dQs

dVs

(9.4.1)

and the capacitance of the MOS capacitor is

Cmos=

CoxCs

Cox+Cs

(9.4.2)

In the accumulation region (negativeVGS), the holes accumulate at the surface andCsis much
larger thanCox. This is because a small change in bias causes a large change inQsin the
accumulation regime. The MOS capacitance becomes

Cmos∼=Cox=

ox

dox

(9.4.3)

As the gate voltage becomes positive and the channel is depleted of holes, the depletion ca-
pacitance becomes important. The depletion capacitance is simply given bys/W, and the total
capacitance

Cmos=

Cox

1+CCoxs

=

ox

dox+oxsW

(9.4.4)

With greater bias, the value ofCmosdecreases, as shown in figure 9.12. At the strong in-
version condition, the depletion width reaches its maximum valueWmax. At this point there is
essentially negligible free carrier density. The minimum capacitance takes the value

Cmos(min)=

ox

dox+oxWsmax

(9.4.5)