SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

9.5. MOSFET OPERATION 455

Oxide

p-Si

z

y

x

(b)

(a)

Source Gate Drain

n-channel

p-Si

n+ n+

L

Z

Gate width

x = 0 x = L

S G D

n-channel

n+––––––––––––––––– n+

SGD

VDS = 0 VDS = 0

• –––––––––––

dox

Figure 9.14: a) A schematic of the MOSFET structure. b) a cross-section of the NMOSFET.

as a one-dimensional problem. The induced charge per unit area, once we are in the inversion
region, is
Qs=Cox[VGS−VT−Vc(x)] (9.5.1)

We know that

Vc(x)=0 at the source

= VDS at the drain (9.5.2)

We also assume that the body bias is zero. The case of finite body bias will be discussed later.
The current is given by (current = surface charge density×mobility×electric field×gate
width)

ID=Qsμn

dVc(x)

dx

Z (9.5.3)

whereZis the width of the device. The currentIDis constant at any cross-section of the channel.
The above equation may be rewritten as

IDdx=QsμndVc(x)Z (9.5.4)

The integration of this equation from the source (x=0) to the drain (x=L) after using the