6.8 p-MOS and general equations

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p-MOS equations
General equations

6.8.1 p-MOS equations

p-MOS capacitors have an n-type substrate, a positive charge in the depletion layer and a positive charge in the inversion layer. Since the Fermi energy is a distance qf_F above the midgap energy level, the work function difference is given by:

with

The expression for the depletion layer width is similar to that of n-MOS capacitors, namely:

while the threshold is typically negative due to the positive charge in the depletion layer width.

Note that the relation between the flatband voltage and the workfunction difference still applies:

6.8.2 General equations

General equations which are valid for n-MOS and p-MOS capacitors are provided below. The type is directly linked to the net doping density of the substrate, N_a - N_d, which is positive for a p-type substrate (n-MOS capacitor) and negative for an n-type substrate (p-MOS capacitor). The workfunction difference is then given by:

where the built-in potential is positive for p-type substrates and negative for n-type substrates and is given by:

The depletion layer width at threshold is then:

and the threshold voltage is given by:

These equations are of interest when parameters of n-MOS as well as p-MOS capacitors are to be calculated. The equations eliminate the problem of the variable signs and possible mistakes and confusion, at the expense of the added complexity. These equations have been implemented in the active figures.

In a MOSFET structure it is possible to apply a voltage to the channel, V_C relative to the voltage at the bulk contact to the substrate, V_B. This affects the width of the depletion layer width at threshold:

as well as the threshold voltage itself:

This expression will be needed to derive the variable depletion layer model of the MOSFET.

6.7 ¬ ® 7.