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Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
1
( ) SioxFBBG VVVVV ++=−
net bias across MOS
MO
p-Si
VVG
C
inversionelectrons
depletionregion
VB
n+n+
Effect of Substrate Bias VB and Channel Bias VC
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
2
( )
( )s
da
OX
daFBBG
BCpSi
XqNC
XqNVVV
VVV
ε
φ
max2
max
21
2
++=−
−+=
M O SiEi
Efs
q(VC-VB)
Efn
pqφ
pqφ
s
daSi
XqNV
εmax
2
21
=
At the onset of strong inversion, where VG is defined as the threshold voltage
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
3
At threshold: VG – VB = VFB+Vox+VSi But VSi = 2|Φp| + (VC - VB ) => xdmax is different from no-bias case
B
SiSid qN
Vx
ε2=max
VT -VB = VFB + 2εsqNB(2|φF| + VC-VB)
Cox + 2|φF| + VC - VB
VoxVSi
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
4
Flat Band Voltage with Oxide charges
VFB is the Gate voltage required to create no charge in the Si
dxx
xxCC
QV
oxx
ox
ox
oxox
fSMFB ∫−−Φ−Φ≡
0
)(1 ρ
x = 0 x = xox
M O S
ρox (x)Qf
ρox (x) due to alkaline contaminants or trapped charge
Qf due to broken bonds at Si-SiO2 interface
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
5
VT Tailoring with Ion Implantation
Nsub
Shallow implanted dopant profile at Si-SiO2interface (approximated asa 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 !
OX
iT C
QV =∆
Qi = q • implant dose in Si
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
6
p-Si
implanted acceptors
Na
SiO2
Doping Profile After Implantation
SiO2
xdmax
Q
Qd
d
Qn
p-Si
(due to implanted acceptors)
Charge Distribution for V G > VT
* Valid if thickness of implanted dopants << xdmax
The VT shift can be viewed as the extra gate voltage needed todeplete the implanted dopants ~ Qi/Cox
The delta-function approximation of implanted profile
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
7
Summary : Parameters Affecting VT
6
7
n+
Na
VB
5
1
2
4
3
Dopant implant near Si/SiO2 interface
fOX Q&ρ Mφ
xox
VCQn n+
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
8
+ Qf or Qox
B threshold implant
As or P threshold implant
Xox increases
Xox increases
ΦM increases
ΦM decreases
|VCB| increases
|VCB| increases
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
9
Summary of MOS Threshold Voltage (NMOS, p-substrate)
• Threshold voltage of MOS capacitor:
• Threshold voltage of MOS transistor:
Note 1: At the onset of strong inversion, inversion charge is negligible and is often ignored in the VT expressionNote 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 donorsor acceptors implanted at the Si surface. Qi is negative for acceptors and is positive for donors
VT = VFB + 2εsqNB(2|φF|)
Cox + 2|φF| -
QiCox
VT = VFB + 2εsqNB(2|φF| + |VC-VB|)
Cox + 2|φF| + VC -
QiCox
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
10
Summary of MOS Threshold Voltage (PMOS, n-substrate)
• Threshold voltage of MOS capacitor:
• Threshold voltage of MOS transistor:
* Yes, + sign for VC term but VC (<0) is a negative bias for PMOS because theinversion holes have to be negatively biased with respect to the n-substrateto create a reverse biased pn junction.
VT = VFB - 2εsqNB(2|φF|)
Cox - 2|φF| -
QiCox
VT = VFB - 2εsqNB(2|φF| + |VC-VB|)
Cox - 2|φF| + VC -
QiCox
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
11
Negligible electron concentration underneath Gate region; Source-Drain is electrically open
High electron concentration underneath Gate region; Source-Drain is electrically connected
VG < Vthreshold VG > Vthreshold
Metal -Oxide-Semiconductor Transistor [ n-channel]
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
12
MOSFET I-V Analysis
n+ n+
VS VG
W
VB=0
VD
ID
L
Qn
N-MOSFET
•In general, inversion charge Qn (∝ [VG-VT]) decreases from Source towardDrain because channel potential VC increases.
VT increases
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
13
Let VT defined to be threshold voltage at Source
( )
−−=
−=
+
2V
VVC
)average(VVC)average(Q2
VV~)average(V
DSTGOX
TGOXn
DSTT [ This is an approximation ]
ID = Wt • (-q n vdrift)= W• Qn • vdrift
Inversion layer thickness Inversion layer concentration
Approximate Analysis
Note: ID is constant for all positionsalong channel
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
14
LV
EvWith DSnndrift
µ≈µ−=
DSDS
TGOXD V2
VVVC
LW
I
−−µ=
VDS
ID
Linear with VDS
Quadratic with VDS
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
15
VD saturation
n+ n+
VS=0
VD
Qn=0 at the drain
Lateral E-field → ∞Electrons moves
saturation velocity
VDsat is defined to be the value of VDwith Qn=0 at drain.
From Qn = Cox (VG -VT -VD), we get VDsat =VG-VT
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
16
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
17
VD
ID
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
18
DSDS
TGOXn
D VV
VVCLW
I
−−=
2µ
MOSFET I-V Characteristics Summary
For VD < VDsat
( )2
2 TGOXn
DsatD VVCLW
II −==µ
For VD > VDsat
Note: VDsat = VG - VT
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
19
E x
SiO2inversionlayer
Mobility of inversion charge carriers
*Carrier will experience additional scattering at theSi/SiO2 interface
*Channel mobility is lower than bulk mobility
* µ(effective) is extracted from MOSFET I-V characteristics* Typically ~0.5 of µ(bulk)
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
20
Parameter Extraction from MOSFET I-V
(A) VT VD
ID
D
S
( )
.
0
221
2
'
'
modesaturationinisMOSFEToffpinchatisDrain
VV
VqNC
VV
drainatV
VVVFor
TG
DpasOX
pDFB
T
TGD
⇒−⇒
<−⇒
++
++=
>=
φε
φ
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
21
( )2TDDsatD VV
LW
kII −==∴
VDVT
DI
LkW
slope=
VG
µnCOX
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
22
Alternative way to extract VT
•Measure ID versus VG for a fixed small VDS (say <100mV)
The intercept of ID versus VG plot on VG-axis is VT.
( ) DSTGOXn
DSDS
TGOXn
D
VVVCLW
V2
VVVC
LW
I
−µ
≈
−−
µ=
VT
VG
ID
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
23
VD
ID
VB(varies)
VD
VB =0 VB1 VB2
VT0 VT1 VT2
DI
( ) ( )
OX
as
pSBp
SBTSBT
CqN
V
VwithVVwithV
ε
φφγ
2
22
00
=
−+
=−≠≡
(B) Body Coefficient γ
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
24
ID
VD
VG2
VG1
(C)
VD
( ) DTGOXnD
D
DD
TGOXnD
VsmallforVVL
WC
VI
VV
VVCL
WI
−=∂∂
−−=
µ
µ2
ID
VG slope
LW
COXnµ
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
25
(D) Transconductance gm
(a) For VDS<VDsat
(b) For VDS > VDsat
DVfixedG
Dm V
Ig
∂∂
≡
DSOXnG
D
DSDS
TGOXn
D
VL
WC
VI
VV
VVCLW
I
⋅=∂∂
∴
−−=
µ
µ2
( )
( )TGOXn
G
D
TGOXn
DsatD
VVCLW
VI
VVCLW
II
−⋅=∂∂
−==
µ
µ 2
2
ID
VDS
VG1+∆VG
VG1
VDsat
[gm varies with VDS]
[gmsat varies with VG]
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
26
ID
VD
VDsat
real
ideal
n+ n+
Qn
( ) ( )1
2
)(01.01.0~
12
−
+−=
volttoTypically
VVVk
I DSTGDsat
λ
λ
(E) Channel Modulation Parameter λ
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
27
Short Channel Effect on VT
VT
idealanalysis
Ldepletionchargecontrolledby gate.
n+ n+
VG
pdepletion layer
L
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
28
n+ n+
VS=0 VD=0
Wo
x
WoXj+Wo
Xj
Xj
Xj
L’
L
( )[ ]
−+−=
−−+−=
−=
12
12
2
2'22
j
oj
jooj
XW
XL
XWWXL
xLL Note: Wo is xdmax
Sameelectric potentialbecause of heavily doped n+
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
29
fXW
LX
WWLL
Nq
j
oj
ideal
actual
oa
≡
−+−=
=∴
⋅⋅+
⋅⋅=
12
11
21
Area of gate charge distribution
“Yau Model” for short-channel effect.
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
30
•Implantation at low energy•Small Dt.•Minimize channeling and transient enhance diffusion
To make f 1
Xj
Wo •Increase Na
L large
S/D S/D
L small
S/DS/D
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
31
VT
L
Large VDS
VDS ~ 0
Effect of VDS on VT Lowering
Large VDS ⇒ Larger S/D depletion charge at the drain side ⇒ Smaller depletion region charge contributed by gate⇒ VT starts to decrease at larger L
n+ n+
VG
depletion layer
Depletion charge contributedby gate
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
32
parasiticchargewhich has to be createdby gate bias
∴VT is larger than ideal analysis.
Fox Fox
W
Ideal Depletion charge
W
Narrow Width Effect (related to W)
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
33
VT
W
VT
L
Narrow Width Effect
Narrow Channel Effect
Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
34
Small Geometry Effects Summary
W
L
Actual gate control charge
Idealgate controlcharge