ELECTRONICS II VLSI DESIGN FALL 2013 LECTURE 4 INSTRUCTOR: L.M. HEAD, PhD ELECTRICAL & COMPUTER...
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Transcript of ELECTRONICS II VLSI DESIGN FALL 2013 LECTURE 4 INSTRUCTOR: L.M. HEAD, PhD ELECTRICAL & COMPUTER...
ELECTRONICS II VLSI DESIGNFALL 2013
LECTURE 4INSTRUCTOR: L.M. HEAD, PhDELECTRICAL & COMPUTER ENGINEERINGROWAN UNIVERSITY
MOSFET Symbols
Cross-section used to identify capacitances.
Accumulation
Depletion – no channel
poly
SiO2
P-type substrate
GND
V << Vth
Depletion region
Depletion – sub threshold channel
Inversion
Capacitance to ground
MOSFET Capacitance Model
Threshold Voltage
Calculating the Threshold Voltage1. Develop the depletion region
2. Create a channel at the gate oxide/substrate interface
3. Account for any source to body voltage
4. Neutralize defect charge
5. Neutralize material dependent potential difference
'
'
ox
bBC C
QV Begin with the definition of voltage due
to a charge stored on a capacitor.
+Qb’ is the charge on the gate and -Qb’ is the charge under the gate oxide.
Calculating the Threshold Voltage
i
afp
a
fpssi
d
n
NkTV
where
qN
VVX
ln
2
From these equations:
fpsAsidAb VVqNXqNQ 2'
If the surface potential, Vs is equal to the electrostatic potential in the semiconductor bulk there is no charge stored in a depletion region. As Vs increases, the depletion region grows.
First, we determine the charge in the depletion region.
fpAsibo VqNQ 22'
Next, we determine the additional charge due to the channel.
Vs increases with an increase in VGS. When VS reaches -Vfp negative charge has accumulated at the oxide semiconductor interface. In fact, at that point the interface area (channel) is as n-type as the bulk semiconductor is p-type.
Taking into consideration any source to body potential:
If the body of the MOSFET is not tied to the source, the potential between the interface and the bulk is not only dependent upon VGS. Now the charge under the gate totals,
SBfpAsib VVqNQ 22'
CBox
bBC VV
C
QV
'
'
fpC VV 2fp
ox
bB VC
QV 2
'
'
The total potential across the gate-oxide capacitance:
Since the change in voltage to obtain the channel is:
Then*,
*Remember, Vfp is a negative number!
An additional source of charge is defects at the oxide interface:
fpox
ssbB V
C
QQV 2
'
''
And finally, there is the inherent potential difference between the gate and the substrate:
i
A
i
polyD
fpGms
n
N
q
kT
n
N
q
kT
VVV
lnln ,
fpSBfpox
Asi
ox
ssbofpms
ox
bbo
ox
ssbofpms
msfpox
ssbTHN
VVVC
Nq
C
QQVV
C
C
QQVV
VVC
QQV
222
2
2
2
''
''
'
''
'
''
'
''
Combining these components to get the final version of the threshold voltage:
fpSBfpTHNTHN
ox
Asi
ox
ssbofpmsTHN
VVVVV
C
Nq
C
QQVVV
22
2
2
0
'
'
''
0
Note error in equation 6.17
Now we come to the I-V Characteristics