{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MIT6_012F09_lec11_drain

# MIT6_012F09_lec11_drain - 6.012 Microelectronic Devices and...

This preview shows pages 1–2. Sign up to view the full content.

6.012 - Microelectronic Devices and Circuits Fall 2009 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 ε ox dv CS (y) q N * (y) = - [v GB - V T (y)] and s y (y) = - µ e E y = µ e dy t ox Substituting these expressions yields: dv CS (y) i D = W µ C ox * [v GB - V T (y)] dy where we have identified the gate capacitance per unit area, C ox * , as ε ox /t ox and where the threshold voltage is given by V T (y) = V FB + |2 φ p | +v CB (y) + 1 2 ε Si qN A [|2 φ p | + v CB (y) C ox * Defining the body factor, γ , as 2 ε Si qN A /C ox * , and writing v CB (y) as v CS (y) - v BS, we can rewrite this as V T (y) = V FB + |2 φ p | +v CS (y) - v BS + γ |2 φ p | + v CS (y) - v BS and thus we can write i D as dv CS (y) i D = W µ e C * [v GS -V FB - |2 φ p |- v CS (y) - γ |2 φ p | + v CS (y) - v BS ] dy ox

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}