EE143 F2010
Lecture 22
Electrical Characteristics of MOS Devices
• The MOS Capacitor
x
– Voltage components
– Accumulation, Depletion, Inversion Modes
– Effect of channel bias and substrate bias
– Effect of gate oxide charges
– Threshold-voltage adjustment by implantation
– Capacitance vs. voltage characteristics
• MOS Field-Effect Transistor
– I-V characteristics
– Parameter extraction
ox
Professor N Cheung, U.C. Berkeley
VG
+
“metal”
oxide
semiconductor
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EE143 F2010
Lecture 22
1) Reading Assignment
Streetman: Section of Streetman Chap 8 on MOS
2) Visit the Device Visualization Website
http://jas.eng.buffalo.edu/
and run the visualization experiments of
1) Charge carriers and Fermi level,
2) pn junctions
3) MOS capacitors
4) MOSFETs
Professor N Cheung, U.C. Berkeley
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EE143 F2010
Lecture 22
Work Function of Materials
METAL
SEMICONDUCTOR
Eo
Work function
= q
Ef
Vacuum
energy level
q
Ef
Eo
EC
EV
qM is determined
qS is determined
by the metal material
by the semiconductor material,
the dopant type,
and doping concentration
Professor N Cheung, U.C. Berkeley
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EE143 F2010
Lecture 22
Work Function (qM) of MOS Gate Materials
Eo = vacuum energy level
Ef = Fermi level
EC = bottom of conduction band EV = top of conduction
band
q = 4.15eV (electron affinity)
Eo
Eo
Eo
qM
qM
q = 4.15eV
q = 4.15eV
EC
EC
Ef
0.56eV
0.56eV
qM
Ef
Examples:
Al = 4.1 eV
TiSi2 = 4.6 eV
Ei
Ei
0.56eV
EV
n+ poly-Si
(Ef = EC)
Professor N Cheung, U.C. Berkeley
0.56eV
Ef
EV
p+ poly-Si
(Ef = EV)
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EE143 F2010
Lecture 22
Work Function of doped Si substrate
F
* Depends on substrate concentration NB
Eo
kT  N B 


ln
q
 ni 
Eo
qs
Ef
Ei
q = 4.15eV
EC
0.56eV
|qF|
qs
Ei
Ef
0.56eV
q = 4.15eV
EC
0.56eV
|qF|
0.56eV
EV
n-type Si
s (volts) = 4.15 +0.56 - |F|
Professor N Cheung, U.C. Berkeley
EV
p-type Si
s (volts) = 4.15 +0.56 + |F|
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EE143 F2010
Lecture 22
The MOS Capacitor
VG
+
+
_
xox
“metal”
oxide
VFB
+
_
+
_
Vox (depends on VG)
Vsi (depends on VG)
semiconductor
VG  VFB  Vox  VSi
 ox
C ox 
xox
[in Farads /cm2]
Oxide capacitance/unit area
Professor N Cheung, U.C. Berkeley
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EE143 F2010
Lecture 22
Flat Band Voltage
• VFB is the “built-in” voltage of the MOS:
VFB   M   S
• Gate work function M:
Al: 4.1 V; n+ poly-Si: 4.15 V; p+ poly-Si: 5.27 V
• Semiconductor work function S :
s (volts) = 4.15 +0.56 - |F| for n-Si
 s (volts) = 4.15 +0.56 + |F| for p-Si
• Vox = voltage drop across oxide (depends on VG)
• VSi = voltage drop in the silicon (depends on VG)
Professor N Cheung, U.C. Berkeley
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EE143 F2010
Lecture 22
MOS Operation Modes
A) Accumulation: VG < VFB for p-type substrate
M
O
Si (p-Si)
holes
Charge Distribution
Thickness of accumulation layer ~0
VSi  0, so Vox = VG - VFB
QSi’ = charge/unit area in Si
=Cox (VG - VFB )
Professor N Cheung, U.C. Berkeley
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EE143 F2010
Lecture 22
MOS Operation Modes
• B) Flatband Condition : VG = VFB
No charge in Si (and hence no charge in metal gate)
•
VSi = Vox = 0
M
O
S (p-Si)
Charge Distribution
Professor N Cheung, U.C. Berkeley
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EE143 F2010
Lecture 22
MOS Operation Modes (cont.)
C) Depletion: VG > VFB
Charge Distribution
M
Depletion
Layer
xd 
thickness
2Si VSi
qN B
O
S (p-Si)
xd
qNB
VG  VFB
qN Bx d qN Bx d


Cox
2s
Note: NBxd is the total
charge in Si /unit area
Professor N Cheung, U.C. Berkeley
Vox
VSi
2
Depletion layer
(For given VG, can solve for xd)
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EE143 F2010
Lecture 22
Depletion Mode :Charge and Electric Field Distributions
by Superposition Principle of Electrostatics
 (x)
Q'
M etal
 (x)
Q'
Oxide
Semiconductor
x=xo + x
d
x
M etal
 (x)
Q'
Oxide
Semiconductor
x=0
E(x)
Metal
Oxide Semiconductor
Metal
E (x)
Oxide
x=xo
x=xo
Professor N Cheung, U.C. Berkeley
x=0
Semiconductor
=
Metal
x
x=x + x
o d
x=xo + x
d
x=0

- Q'
x=xo
x
Semiconductor
x=xo + x
d x
Oxide
x

x=0
M etal
x=0
x=x
o
E(x)
Oxide
x=xo
Semiconductor
+
x
x=x + x
o d
x=0
x=x
o
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EE143 F2010
Lecture 22
MOS Operation Modes (cont.)
D) Threshold of Inversion: VG = VT
This is a definition
for onset of
nsurface = NB (for p-type substrate)
strong inversion
=> VSi = 2|F|
M
O
S (p-Si)
xdmax
qNB
Q’n
VG  VT  VFB 
Professor N Cheung, U.C. Berkeley
2 s ( 2  F )qN B
C ox
 2 F
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EE143 F2010
Lecture 22
MOS Operation Modes (cont.)
E) Strong Inversion: VG > VT
xdmax is approximately unchanged
xd max 
4 Si  F
qN B
when VG> VT
M
O
S (p-Si)
xdmax
Vox 
qN B xd max  Qn
C ox
Qn  C ox (VG  VT )
Professor N Cheung, U.C. Berkeley
qNa
Q’n
electrons
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EE143 F2010
Professor N Cheung, U.C. Berkeley
Lecture 22
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EE143 F2010
Professor N Cheung, U.C. Berkeley
Lecture 22
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EE143 F2010
Lecture 22
p-Si
Professor N Cheung, U.C. Berkeley
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EE143 F2010
Lecture 22
Voltage drop = area under E-field curve
Accumulation
Vox = Qa/Cox
VSi ~ 0
Vox =qNaxd/Cox
Depletion
VSi = qNaxd2/(2s)
Vox = [qNaxdmax+Qn]/Cox
Inversion
VSi = qNaxdmax2/(2s)
= 2|F|
* For simplicity, dielectric constants assumed to be same for oxide and Si in E-field sketches
Professor N Cheung, U.C. Berkeley
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EE143 F2010
Lecture 22
Suggested Exercise
Most derivations for MOS shown in lecture notes
are done with p-type substrate (NMOS)
as example.
Repeat the derivations yourself for n-type substrate
(PMOS) to test your understanding of MOS.
Professor N Cheung, U.C. Berkeley
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EE143 F2010
Lecture 22
p-Si substrate (NMOS)
Accumulation
(holes)
strong inversion
(electrons)
depletion
VFB
VT
VG
(more
positive)
n-Si substrate (PMOS)
VG
(more
negative)
Strong inversion
(holes)
Professor N Cheung, U.C. Berkeley
VT
Accumulation
(electrons)
depletion
VFB
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EE143 F2010
Professor N Cheung, U.C. Berkeley
Lecture 22
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EE143 F2010
Professor N Cheung, U.C. Berkeley
Lecture 22
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EE143 F2010
Professor N Cheung, U.C. Berkeley
Lecture 22
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EE143 F2010
Professor N Cheung, U.C. Berkeley
Lecture 22
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EE143 F2010
Professor N Cheung, U.C. Berkeley
Lecture 22
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EE143 F2010
Lecture 22
C-V Characteristic
C/Cox
a
C/Cox
e
e
1
1
b
p-type
substrate
a
b
c
c
d
d
VG
VT
n-type
substrate
VG
VT
a) accumulation: Cox
b) flatband: ~Cox (actually a bit less)
c) depletion: Cox in series with the Cdepl
d) threshold: Cox in series with the minimum Cdepl
e) inversion: Cox (with some time delay!)
Professor N Cheung, U.C. Berkeley
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EE143 F2010
Lecture 22
Small signal charge response Q due to VG
Q
Q
All frequencies
Accumulation
C = Cox
Q
Depletion
All frequencies
Q
1/C = 1/Cox + xd/s
Q
Q
Q
Q
Inversion
Low frequency
C = Cox
Professor N Cheung, U.C. Berkeley
High frequency
1/C = 1/Cox + xdmax/s
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EE143 F2010
Lecture 22
Effect of Substrate Bias VB and Channel Bias VC
VG
VC
inversion
electrons
M
O
depletion
region
n+
n+
p-Si
VB
VG  VB   VFB
 Vox  VSi
net bias across MOS
Professor N Cheung, U.C. Berkeley
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EE143 F2010
Lecture 22
At the onset of strong inversion, where VG is defined
as the threshold voltage
M
O
Si
Ei
Efs
qp
q(VC-VB)
qp
Efn
2
1 qN a X
VSi 
2
s
d max
VSi  2  p  VC  VB 
2
qN a X d max 1 qN a X d max
VG  VB   VFB 

C OX
2
s
Professor N Cheung, U.C. Berkeley
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EE143 F2010
Lecture 22
At threshold: VG – VB = VFB+Vox+VSi
But VSi = 2|p| + (VC - VB ) =>
xdmax is different from no-bias case
2 SiVSi
xd max 
qN B
VT -VB = VFB +
2sqNB(2|F| + VC-VB)
+ 2|F| + VC - VB
Cox
Vox
Professor N Cheung, U.C. Berkeley
VSi
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EE143 F2010
Lecture 22
Flat Band Voltage with Oxide charges
VFB is the Gate voltage required to create no charge in the Si
1 x ox ( x)
VFB   M   S 

dx

Cox Cox 0 xox
xox
Qf
ox (x)
M
Qf
S
O
x=0
Professor N Cheung, U.C. Berkeley
x = xox
ox (x) due to alkaline
contaminants or trapped
charge
Qf due to broken bonds
at
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EE143 F2010
Lecture 22
VT Tailoring with Ion Implantation
Qi
VT 
COX
Shallow implanted
Qi = q  implant dose in Si
dopant profile at Si-SiO2
Nsub
interface (approximated as
a delta function)
• Acceptor implant gives positive shift (+ VT)
• Donor implant gives negative shift - VT
Algebraic sign of VT shift is independent of n or p substrate !
Professor N Cheung, U.C. Berkeley
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EE143 F2010
Lecture 22
The delta-function approximation of implanted profile
* Valid if thickness of implanted dopants << xdmax
implanted acceptors
SiO2
SiO2
p-Si
xdmax
Na
p-Si
Qd
Qn
Doping Profile After Implantation
Qd (due to implanted acceptors)
Charge Distribution for V G > VT
The VT shift can be viewed as the extra gate voltage nee
deplete the implanted dopants ~ Qi/Cox
Professor N Cheung, U.C. Berkeley
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EE143 F2010
Lecture 22
Summary : Parameters Affecting VT
1 M
6  OX & Q f
2
n+
Qn
Na
xox
n+
VC
5
3
4 VB
7
Dopant implant near Si/SiO2 interface
Professor N Cheung, U.C. Berkeley
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EE143 F2010
Lecture 22
M increases
|VCB| increases
B threshold implant
Xox increases
Xox increases
As or P threshold implant
+ Qf or Qox
Professor N Cheung, U.C. Berkeley
|VCB| increases
M decreases
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EE143 F2010
Lecture 22
Summary of MOS Threshold Voltage (NMOS, p-substrate)
• Threshold voltage of MOS capacitor:
VT = VFB +
2sqNB(2|F|)
Qi
+ 2|F| Cox
Cox
• Threshold voltage of MOS transistor:
2sqNB(2|F| + |VC-VB|)
Qi
VT = VFB +
+ 2|F| + VC Cox
Cox
Note 1: At the onset of strong inversion, inversion charge is negligible
and is often ignored in the VT expression
Note 2: VT of a MOSFET is taken as the VT value at source ( i.e., VC =VS)
Note 3 : Qi = (q  implant dose ) is the charge due to the ionized donors
or acceptors implanted at the Si surface. Qi is negative for acceptors
and is positive for donors
Professor N Cheung, U.C. Berkeley
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EE143 F2010
Lecture 22
Summary of MOS Threshold Voltage (PMOS, n-substrate)
• Threshold voltage of MOS capacitor:
VT = VFB -
2sqNB(2|F|)
Qi
- 2|F| Cox
Cox
• Threshold voltage of MOS transistor:
VT = VFB -
2sqNB(2|F| + |VC-VB|)
Qi
- 2|F| + VC Cox
Cox
* Yes, + sign for VC term but VC (<0) is a negative bias for PMOS because the
inversion holes have to be negatively biased with respect to the n-substrate
to create a reverse biased pn junction.
Professor N Cheung, U.C. Berkeley
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