Threshold voltage theory for a short-channel MOSFET using a surface-potential distribution model

A detailed expression of the threshold voltage for a short-channel MOSFET is derived from a model of surface-potential distribution under the gate using a relationship of surface-channel charge neutrality. The theory is compared with the measured threshold voltages. The theoretical curves for threshold voltage over a wide range of drain and backgate voltage are in good agreement with experimental results. It is shown for a MOSFET having a channel length less than 2 μm that the body-bias constant increases as the drain voltage increases. The theory also predicts that the increase in backgate voltage leads to the reduction in short-channel effect for the shorter-channel case.