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Chapter 2   : Operating Principles of MOS Transistors

The factor 2 comes due to the fact that in the bulk, the semiconductor is p-type, where EI is above EF by , while at the inverted n-type region at the surface EI is below EF by , and thus the amount of the band bending is 2 . This is the second component of the threshold voltage. The potential difference between EI and EF is given as

where k: Boltzmann constant, T: temperature, q : electron charge NA : acceptor concentration in the p-substrate and n i : intrinsic carrier concentration. The expression kT/q is 0.02586 volt at 300 K.

The applied gate voltage must also be large enough to create the depletion charge. Note that the charge per unit area in the depletion region at strong inversion is given by

where is the substrate permittivity. If the source is biased at a potential VSB with respect to the substrate, then the depletion charge density is given by