9.6. IMPORTANT ISSUES IN REAL MOSFETS 473
by equation 9.3.5. Thus, if the sheet chargensincreases the surface field also increases. The
increased electric field forces electrons closer to the Si-SiO 2 interface. As a result, the electrons
suffer a greater degree of scattering from the interface roughness and oxide impurities, and the
mobility degrades.
Mobility Variation with Channel Field
The mobility of electrons (holes) in silicon is not independent of longitudinal field as well,
but is high at low field and becomes smaller at high fields where the velocity saturates. Velocity
saturation typically occurs because at higher fields the rate of phonon emission increases and the
rate of energy gained form the electric field equals the rate of energy loss to the crystal primarily
through phonons. This phenomenon has a classical analog in the terminal velocity achieved by a
person in a parachute or rain drops etc.. As a result, the current calculated by our simple model is
much larger than the current observed in real devices. More realistic device modeling approaches
use a more accurate description of the velocity-field relationship. A common expression used
for the velocity-field relation is (see figure 9.26a)
v(E)=μE
1+μvEs(9.6.1)
wherevsis the saturation velocity(∼ 107 cm/s) andEis the local longitudinal field in the
channel. Use of this expression in calculating drain current causes a reduction in current by a
factor of∼(1 +μVDS/vsL).
In figure 9.26 we show a comparison of the current-voltage relations calculated using the
constant-mobility model and the more accurate saturation velocity model.
Channel Length Modulation in Saturation Region
In our simple model, onceVDSexceedsVD(sat)and the channel pinches off at the drain end,
the current is assumed to remain independent ofVDS. The current in the channel is inversely
proportional to the channel length. We have so far assumed that the channel length is the met-
allurgical channel length. However, theLthat appears in the current-voltage relation represents
the distance under the gate from the source side to the pinch-off point, as shown in figure 9.27a.
AsVDSincreases beyondVD(sat), the pinch-off point comes closer to the source side, thus
effectively decreasing the channel length. This produces a change in the channel lengthΔL(see
figure 9.27b) and the current increases as
ID=L
L−ΔL(VDS)
ID(sat) (9.6.2)whereID(sat)is the current calculated assuming a fixed channel length. The effect results in
an increase in the output conductance of the device. A similar effect occurs in MESFETs and
JFETs. It is common to represent the increase in drain current arising from channel-length
modulation by an expression
ID=ID(L=fixed)(1 +λVDS) (9.6.3)