U. Glaeser

E nfog (z)
E C (z)
FIGURE 41.3
FIGURE 41.4
V S
V Source
In the first approximation, take E = ( Vd
− Vs)
/ L,
where Vd,
Vs,
and L are the drain voltage, the source
voltage, and the gate channel length. The total charge can be approximated as Q = WCo∆V,
where W and
Co
are the channel width and the oxide capacitance of the actual corresponding MOSFET transistor,
respectively. Now, ∆V
corresponds to the voltage difference between the average water surface ( Vd
+ Vs)
/ 2
and the channel potential Vch
= ( Vg
− Vth).
That is, ∆V
= ( Vd
+ Vs)
/ 2 − Vch.
Hence, since Q = WCo∆V,
the equivalent amount Q of the water (or
charge) under the gate is given as Q = [( V + ) / 2 − ], where = ( V − ), E = ( V − ) / L.
© 2002 by CRC Press LLC
MOSFET at Onset VG
= Vth.
Vch
V th (V BB ,V S ) = V FB + {B + V S − V BB } + γ
V FB = V BB − (kT/q) In{ N c N A /n i 2 } − {χsi − φm }/q + Q SS /C OX
K = q ε Si N A /C 2 OX
Source gate
Drain
n+
p-Si
n+
kT In(N c /N d + )
dQ
MOSFET I-V characteristics.
0
e−
q ∆ V
L
WC
o
V Gate
d
VSf (x)
= (V Drain + V Source)/2
γ = 2K
V
s
V G = V th (V BB ,V S )
φ S (inv)
V BB′
V
ch
{B + V S − V BB }
VDrain
Q = WCo {Vch − }
= WCo {VGate − Vth − (VDrain + VSource)/2} B = 2(kT/q) In(N A /n i )
L
V
ch
z
I = µQE
I = (W/2L) µCo{2(VG − Vth) − (VDrain + VSource)} (VDrain − VSource) ISat = (W/2L) µCo(VDrain − VSource) 2 for VG > (VDrain + Vth)
g
E = (V Drain − V Source)/L
Q = WC o ∆V
V
th
z
E nfog (z)
Vch = (VGate − Vth)
E C (z)
V D
= WC o (V ch - V Sf)
d
V
s