SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

9.6. IMPORTANT ISSUES IN REAL MOSFETS 467

ln IDS

60 mV/decade of current

VG-Vth

0

Figure 9.20: Observation: The device current does not abruptly turn-ff below threshold but
decreases monotonically at a slope of 60 mV/decade of current.

the source and the drain for the case above threshold and below threshold. ForVg>Vthand in
the linear region, the full channel remains in strong inversion. The electron quasi-Fermi level in
the channel follows the voltage variation and therefore drops by an amount equal to the channel
potential,Vc(x), and subsequently the band bending required to sustain inversion increases by
this value. The current flow in this case is given by electron drift and

Jn=σch(x)E(x)

everywhere in the channel. This increased band bending increasesVthas af(x)by an amountVc
and hence the channel charge decreases monotonically, given bynsinv(x)=Cox(Vg−Vth(x)).
One critical element in the diagram is that the oxide voltage decreases and the band bending in
the semiconductor increases as we go toward the drain. This can also be understood as the de-
crease in the channel inversion charge (negative) results in a reduced positive image charge on
the gate and therefore a reduced band bending in the oxide.
The analysis of current transport in the subthreshold regime is less clear than the case above
threshold. figure 9.22 shows the band diagram of the device operating in the subthreshold regime
with zero bias on the source and drain regions. On applying a bias to the drain relative to the
source, current could be carried either by diffusion, drift or a combination of both. figure 9.23
shows the band diagram assuming that the dominant current transport is by drift and figure 9.24
shows the case if the current transport is mainly by diffusion. The first case assumes that the
applied bias drops uniformly along the channel and the second assumes that the bias drops pri-
marily adjacent to the drain with very little drop along the channel. We will now show that the
latter, diffusive transport dominates. In the weak inversion regime the maximum charge in the
inversion layer is small (less than the bulk majority carrier concentration). If drift were to be
true the band bending in the semiconductor has to increase continuously toward the drain which
because of the constant gate voltage requires that the band bending in the oxide decreases by the
same amount. The only manner that the oxide voltage can decrease is by having the inversion