24.5 MOSFETs
713
Fig. 24.20 a Schematic
geometry of a MOSFET
and its band diagram for b
flat-band conditions for
zero gate voltage (and
V D = 0), c thermodynamic
equilibrium with reverse
gate voltage (weak
inversion, still V D = 0) and
d nonequilibrium with
nonzero drain voltage and
gate voltages (with most of
the channel being inverted,
the depletion region is
indicated). Adapted
from [2061]
source
drain
gate
+
+
n
n
+
+
E C
E F
E i
E V
E C
E i
E V
E F
p
n
+
p
n
n
+
+
p
n
+
F n
F n
F p
F p
source
drain
gate
depletion
region
L
X Y
(a)
(b)
(c)
(d)
are the substrate doping N A , the insulator thickness d and the depth r j of the n-type regions. Around
the MOSFET structure is an oxide to insulate the transistor from neighboring devices.
24.5.1 Operation Principle
When there is no applied gate voltage, only the saturation current of the pn-diode(s) between source and
drain flows. In thermodynamic equilibrium (Fig. 24.20c), the necessary surface potential for inversion
at the MIS diode is
inv
s ≈ 2 B . If there is a finite drain voltage, a current flows and there is no longer
equilibrium. In this case, the quasi-Fermi level of the electrons (or generally of the minority carriers)
is lowered and a higher gate voltage is needed to create inversion. The situation at the drain is depicted
in Fig. 24.21.
In nonequilibrium, the depletion layer width is a function of the drain voltage V D . In order to reach
strong inversion at the drain, the surface potential must be at least
inv
s ≈ V D + 2 B .