6.4 Inversion layer charge

Table of Contents - Glossary - Study Aids - Ź Ž

In this Section

Basic assumption
Numeric solution

Next: 6.5 The MOS capacitor analysis

6.4.1 Basic assumption

The basis assumption as needed for the derivation of the MOSFET models is that the inversion layer charge is proportional with the applied voltage starting at the threshold voltage, while the inversion layer charge is zero at and below that threshold voltage.

The linear proportionality can be explained by the fact that as a positive voltage is applied to the gate of a p-substrate MOS capacitor, a negative charge (electrons) will be attracted to the opposite side of the gate oxide as in any capacitor. The proportionality constant between the charge and the applied voltage is therefore expected to be the gate oxide capacitance.

Because of the energy band gap of the semiconductor, the electrons can only exist if the p-type semiconductor is first depleted. The voltage at which the electron inversion layer forms is refered to as the threshold voltage.

6.4.2 Numeric solution

A numeric solution is needed to justify this assumption. The numeric solution is obtained from the exact analytical solution for the MOS capacitor. A solution is shown below, where the solid line is calculated using the analytical solution while the dotted line represents our basic assumption.

mosexact.xls - moscharg.gif

Fig. 6.4.1

Charge density due to electrons in the inversion layer of an MOS capacitor. Compared are the analytic solution (solid line) and our basic assumption (dotted line) for N_a = 10¹⁷ cm^-3 and t_ox = 20 nm.

While their is a clear difference between the curves, the difference is small. We will therefore use our basic assumption when deriving the different MOSFET models since it dramatically simplifies the derivation, be it while losing some accuracy.

6.3 Ź Ž 6.5

Š Bart J. Van Zeghbroeck, 1996, 1997