Assumption 6

Let us assume that the diffusion current is negligible so that all the current flow is due to drift only. This is a fairly good assumption provided the device is in strong inversion, that is, the gate voltage is greater than the threshold voltage ( V _{g s} > V _th). If the diffusion current is neglected then, from Eq. (6.2), it is easy to see that

(6.38)

Comparing this equation with Eq. (6.7) we find that for a device in strong inversion, we can write

and therefore, from Eq (6.9) it follows that

(6.39)

where ? _s(0) is the surface potential at y = 0 (source end). For the sake of algebraic manipulation, it is more convenient to write

where V( y) now varies from 0 at the source end to V _ds at the drain end. With this assumption, Eq. (6.39) can be rewritten as

(6.40)

where we have replaced ? _s(0) by 2 ? _f, the classical criterion for strong inversion, while Eq. (6.14) reduces to

(6.41)

Thus, to calculate I _ds we need to calculate Q _i. We will now derive a simple and more useful expression for Q _i using a charge balance equation given by Eq. (6.28). It is interesting to note that Eq. (6.41) can...