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Chapter 2   : Operating Principles of MOS Transistors

The component of the threshold voltage that offsets the depletion charge is then given by -Qd /Cox , where Cox is the gate oxide capacitance per unit area, or Cox = (ratio of the oxide permittivity and the oxide thickness).

A set of positive charges arises from the interface states at the Si-SiO2 interface. These charges, denoted as Qi , occur from the abrupt termination of the semiconductor crystal lattice at the oxide interface. More importantly, alkali metal ions like Na+ introduce positive charges in the fixed oxide. The component of the gate voltage needed to offset this positive charge (which induces an equivalent negative charge in the semiconductor) is –Qi /Cox where Qi accounts for various fixed oxide and interface charges. On combining all the four voltage components, the threshold voltage VT0 , for zero substrate bias, is expressed as

For non-zero substrate bias, however, the depletion charge density needs to be modified to include the effect of VSB on that charge, resulting in the following generalized expression for the threshold voltage, namely

The generalized form of the threshold voltage can also be written as