Transcript lecture 4

ELECTRONICS II
VLSI DESIGN
FALL 2013
LECTURE 4
INSTRUCTOR: L.M. HEAD, PhD
ELECTRICAL & COMPUTER ENGINEERING
ROWAN UNIVERSITY
MOSFET Symbols
Cross-section used to identify
capacitances.
Accumulation
Depletion – no channel
V << Vth
poly
SiO2
Depletion region
P-type substrate
GND
Depletion – sub threshold channel
Inversion
Capacitance to ground
MOSFET Capacitance Model
Threshold Voltage
Calculating the Threshold Voltage
1.
2.
3.
4.
5.
Develop the depletion region
Create a channel at the gate oxide/substrate
interface
Account for any source to body voltage
Neutralize defect charge
Neutralize material dependent potential difference
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.
VBC
'
b
'
ox
Q

C
Calculating the Threshold Voltage
First, we determine the charge in the depletion region.
Xd 
2 si Vs  V fp
qN a
where
V fp  kT ln
Na
ni
From these equations:
Qb'  qN A X d  2 si qN A Vs  V fp
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.
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.
Qbo'  2 si qN A  2V fp
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,
Qb'  2 si qN A  2V fp  VSB
The total potential
across the gate-oxide
capacitance:
VBC
Qb'
 '  VB  VC
Cox
Since the change in voltage to obtain the channel is:
VC  2V fp
Then*,
Qb'
VB  '  2V fp
Cox
An additional source of charge is defects at the
'
'
oxide interface:
b
ss
B
fp
'
ox
Q Q
V 
 2V
C
*Remember, Vfp is a
negative number!
And finally, there is the inherent potential difference between the gate and
the substrate:
Vms  VG  V fp
kT  N D , poly  kT  N A 
 


ln 
ln 
q  ni  q  ni 
Combining these components to get the final version of the threshold voltage:
VTHN
Qb'  Qss'

 2V fp  Vms
'
Cox
'
'
Qbo
 Qss' Qbo
 Qb'
 Vms  2V fp 

'
Cox
Cox'
'
2q si N A 
Qbo
 Qss'
 Vms  2V fp 

2V fp  VSB  2V fp 
'
'


Cox
Cox
VTHN 0
'
Qbo
 Qss'
 Vms  2V fp 
Cox'
2q si N A

Cox'
VTHN  VTHN 0    2V fp  VSB  2V fp 


Note error in equation 6.17
Now we come to the I-V Characteristics