lec_23 effect of substrate bias vb and channel bias vc
TRANSCRIPT
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1Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
( ) 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
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2Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
( )
( )s
da
OX
daFBBG
BCpSi
XqNCXqNVVV
VVV
ε
φ
max2
max
21
2
++=−
−+=
M O SiEi
Efs
q(VC-VB)
Efn
pqφ
pqφ
s
daSi
XqNVε
max2
21
=
At the onset of strong inversion, where VG is defined as the threshold voltage
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3Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
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
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4Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
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
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5Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
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
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6Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
p-Si
implanted acceptors
NaSiO2
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
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7Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
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+
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8Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
+ Qf or Qox
B threshold implant
As or P threshold implant
Xox increases
Xox increases
ΦM increases
ΦM decreases
|VCB| increases
|VCB| increases
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9Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
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
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10Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
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
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11Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
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]
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12Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
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
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13Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
Let VT defined to be threshold voltage at Source
( )
−−=
−=
+
2VVVC
)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
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14Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
LVEvWith DSn
ndriftµ
≈µ−=
DSDS
TGOXD V2
VVVCLWI
−−µ=
VDS
ID
Linear with VDS
Quadratic with VDS
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15Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
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
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16Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
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17Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
VD
ID
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18Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
DSDS
TGOXn
D VVVVCLWI
−−=
2µ
MOSFET I-V Characteristics Summary
For VD < VDsat
( )22 TGOXn
DsatD VVCLWII −==
µ
For VD > VDsat
Note: VDsat = VG - VT
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19Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
Ex
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)
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20Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
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
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21Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
( )2TDDsatD VVLWkII −==∴
VDVT
DI
LkWslope=
VG
µnCOX
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22Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
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
VVVCLWI
−µ
≈
−−
µ=
VTVG
ID
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23Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
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
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24Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
ID
VD
VG2
VG1
(C)
VD
( ) DTGOXnD
D
DD
TGOXnD
VsmallforVVL
WCVI
VVVVCL
WI
−=∂∂
−−=
µ
µ2
ID
VG slope
LWCOXnµ
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25Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
(D) Transconductance gm
(a) For VDS<VDsat
(b) For VDS > VDsat
DVfixedG
Dm V
Ig∂∂
≡
DSOXnG
D
DSDS
TGOXn
D
VL
WCVI
VVVVCLWI
⋅=∂∂
∴
−−=
µ
µ2
( )
( )TGOXn
G
D
TGOXn
DsatD
VVCLW
VI
VVCLWII
−⋅=∂∂
−==
µ
µ 2
2
ID
VDS
VG1+∆VG
VG1
VDsat
[gm varies with VDS]
[gmsat varies with VG]
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26Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
ID
VDVDsat
real
ideal
n+ n+
Qn
( ) ( )1
2
)(01.01.0~
12
−
+−=
volttoTypically
VVVkI DSTGDsat
λ
λ
(E) Channel Modulation Parameter λ
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27Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
Short Channel Effect on VT
VT
idealanalysis
Ldepletionchargecontrolledby gate.
n+ n+
VG
pdepletion layer
L
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28Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
n+ n+
VS=0 VD=0
Wo
x
WoXj+Wo
Xj
Xj
Xj
L’
L
( )[ ]
−+−=
−−+−=
−=
1212
2
2'22
j
oj
jooj
XWXL
XWWXL
xLL Note: Wo is xdmax
Sameelectric potentialbecause of heavily doped n+
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29Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
fXW
LX
WWLLNq
j
oj
ideal
actual
oa
≡
−+−=
=∴
⋅⋅+
⋅⋅=
1211
21
Area of gate charge distribution
“Yau Model” for short-channel effect.
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30Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
•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
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31Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
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
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32Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
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)
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33Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
VT
W
VT
L
Narrow Width Effect
Narrow Channel Effect
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34Professor N Cheung, U.C. Berkeley
Lecture 23EE143 S06
Small Geometry Effects Summary
W
L
Actual gate control charge
Idealgate controlcharge