714
24 Transistors
Fig. 24.21 Charge-carrier
distribution (top) and band
diagram (bottom) at the
inverted p-region of a
MOSFET for a
thermodynamic
equilibrium (V D = 0) and
b nonequilibrium at drain
x
x
E C
Q n
Q d
Q d
-eN A
-eN A
Q n
E V
E F
E i
x
E C
E V
E Fp
E i
x
eV D
E Fn
e S
(a)
(b)
E
E
e S
If the gate voltage is such that an inversion channel is present from source to drain, a current will flow
for a small drain voltage (Fig. 24.22a). Initially, the current will increase linearly with V D , depending
on the conductivity of the channel. With increasing drain voltage, the quasi-Fermi level of the electrons
is lowered until, finally at V D = V D,sat , the inversion channel depth becomes zero (pinch-off at the
point denoted with an arrow in Fig. 24.22b). The current at this condition is denoted as I D,sat . For a
further increase of V D , the pinch-off point moves closer to the source contact and the channel length
(inverted region) is shortened (arrow in Fig. 24.22c). The voltage at the pinch-off point remains V D,sat
and thus the current in the channel remains constant at I D,sat .
24.5.2 Current–Voltage Characteristics
We assume now that the potential V (y) varies along the channel from V = 0 at y = 0 to V = V D at
y = L. In the gradual-channel approximation, the voltage drop V i across the oxide is
V i (y) = V G − s (y) ,
(24.58)
where s is the surface potential in the semiconductor (see Fig. 21.34). The total charge induced in the
semiconductor (per unit area) is, using (21.92), given by
Q s (y) = − [V G − s (y)] C i ,
(24.59)
with C i being the insulator capacitance (per unit area), as given in (21.93).
The inversion surface potential can be approximated by s (y) ≈ 2 B + V (y) (see Fig. 24.21).
With (21.97) the depletion-layer charge is
Q d (y) = −e N A w m = −
2 s e N A [2 B + V (y)] ,
(24.60)
24 Transistors
Fig. 24.21 Charge-carrier
distribution (top) and band
diagram (bottom) at the
inverted p-region of a
MOSFET for a
thermodynamic
equilibrium (V D = 0) and
b nonequilibrium at drain
x
x
E C
Q n
Q d
Q d
-eN A
-eN A
Q n
E V
E F
E i
x
E C
E V
E Fp
E i
x
eV D
E Fn
e S
(a)
(b)
E
E
e S
If the gate voltage is such that an inversion channel is present from source to drain, a current will flow
for a small drain voltage (Fig. 24.22a). Initially, the current will increase linearly with V D , depending
on the conductivity of the channel. With increasing drain voltage, the quasi-Fermi level of the electrons
is lowered until, finally at V D = V D,sat , the inversion channel depth becomes zero (pinch-off at the
point denoted with an arrow in Fig. 24.22b). The current at this condition is denoted as I D,sat . For a
further increase of V D , the pinch-off point moves closer to the source contact and the channel length
(inverted region) is shortened (arrow in Fig. 24.22c). The voltage at the pinch-off point remains V D,sat
and thus the current in the channel remains constant at I D,sat .
24.5.2 Current–Voltage Characteristics
We assume now that the potential V (y) varies along the channel from V = 0 at y = 0 to V = V D at
y = L. In the gradual-channel approximation, the voltage drop V i across the oxide is
V i (y) = V G − s (y) ,
(24.58)
where s is the surface potential in the semiconductor (see Fig. 21.34). The total charge induced in the
semiconductor (per unit area) is, using (21.92), given by
Q s (y) = − [V G − s (y)] C i ,
(24.59)
with C i being the insulator capacitance (per unit area), as given in (21.93).
The inversion surface potential can be approximated by s (y) ≈ 2 B + V (y) (see Fig. 24.21).
With (21.97) the depletion-layer charge is
Q d (y) = −e N A w m = −
2 s e N A [2 B + V (y)] ,
(24.60)