6.1 INTRODUCTION

In the previous chapter we assumed that the transistors under consideration had a channel sufficiently long and wide, so that "edge" effects along the four sides of the channel could be neglected. This allowed us to assume that the electric field lines were everywhere perpendicular to the surface (i.e., they had components only along the y direction), and we performed what is called a one-dimensional analysis by using the gradual-channel approximation. The equations we derived based on such assumptions fail to characterize adequately devices with short and/or narrow channels. If the channel is short (i.e., L is not much larger than the sum of the source and drain depletion widths), a significant part of the electric field lines will have components along both the y and the x directions, the latter being the direction along the channel's length. Thus, a two-dimensional analysis will be needed. If the channel is instead narrow (i.e., W is not much larger than the depletion region depth under the gate), a significant part of the field lines will have components along the y and z directions, the latter being the direction along the channel's width. Again, a two-dimensional analysis must be employed. If the channel is short and narrow, field lines will, in general, have components along the x, y, and z directions; now a three-dimensional