lec12draincur

# lec12draincur - 6.012 Electronic Devices and Circuits Fall...

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6.012 - Electronic Devices and Circuits Fall 2003 MOSFET Drain Current Modeling In the Gradual Channel Model for the MOSFET we write the drain * current, i D , as the product of q N (y) , the inversion layer sheet charge density at position y along the channel; s y (y), the net drift velocity of the inversion layer carriers there (electrons in the n-channel device we are modeling), and W, the channel width: * i D = - q N (y) s y( y) W with e ox dv CS (y) * q N (y) = - t ox [v GB - V T (y)] and s y (y) = - µ e E y = µ e dy Substituting these expressions yields: dv CS (y) i D = W µ C * [v GB - V T (y)] dy ox * where we have identified the gate capacitance per unit area, C ox ,as e ox /t ox and where the threshold voltage is given by 1 V T (y) = V FB + |2 f p | +v CB (y) + C * 2 e Si qN A [|2 f p |+v CB (y) ox 2 e Si qN A * Defining the body factor, g ,as /C ox , and writing v CB (y) as v CS (y) ­ v BS, we can rewrite this as V T (y) = V FB + |2 f p | +v CS (y) - v BS + g |2 f p |+v CS BS (y)-v and thus we can write i D as |2 f p |+v

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lec12draincur - 6.012 Electronic Devices and Circuits Fall...

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