TABLE OF CONTENTS In this model Q i( y) is calculated numerically by integrating the electron concentration in the x direction. Equation (6.12) can be rewritten as
| (6.15) |  |
where ? s is the surface potential ( ? = ? s at x = 0) and is position dependent due to the voltage applied between the source and drain terminals. Note the lower limit of integration is ? f. This is because electron charge comes mostly from the area where electron concentration exceeds the hole concentration, the inversion layer therefore ends at a point where ? = ? f. In the equation above 
is the field in the x direction and is obtained by solving the Poisson equation (6.5). In analogy with an MOS capacitor [cf. Eq. (4.47)], the Poisson equation for a MOSFET can be written as
| (6.16) |  |
The only difference between Eq. (6.16) and the corresponding Eq. (4.47) for the MOS capacitor is the presence of the potential V cb( y) in the exponent and the position dependence of ?( y) in the y direction [cf. Eq. (6.10)]. Integrating Eq. (6.16) in the x direction, and following the same procedure as was used in solving Eq. (4.47), we get the field 
in silicon for the case of a MOSFET as
| (6.17) |  |
where
| (6.18) |  |
is essentially a function describing the electric field in which the term 
is contributed by the majority...
