Past exam of the quantum condensed matter course of the University of Cambridge / 2004 / Section B / B9 / c / Solution

An n-channel MOSFET has two heavily n-doped source and drain regions in a p-type body, with an insulated gate above the intervening surface. A positive gate voltage first depletes surface electron holes and then induces an electron semiconductor inversion layer. Above threshold $V_T$ this layer connects source to drain. Gate voltage controls the channel charge through the oxide capacitance, while the insulating gate permits a very small steady gate current.

For the long-channel MOSFET current law, let $C_{\mathrm{ox}}$ be oxide capacitance per area, $W,L$ channel width and length, and use constant mobility ${\mu }_n$. In the gradual-channel approximation,At larger drain voltage the ideal channel pinches off near the drain and the current saturates atCarriers still flow through the pinch-off region; pinch-off does not mean zero drain current. These formulas neglect channel-length modulation, short-channel effects and velocity saturation. A p-channel device reverses the carrier type and operating polarities. Gate control makes MOSFETs useful as electronic switches and amplifiers.