UNIVERSITY OF CALIFORNIA, BERKELEY
BSIM4.3.0 Model
Enhancements and Improvements Relative to
BSIM4.2.1
Xuemei (Jane) Xi, Jin He, Mohan Dunga,
Ali Niknejad, Chenming Hu
University of California, Berkeley
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UNIVERSITY OF CALIFORNIA, BERKELEY
OUTLINE
New Features of BSIM4.3.0 beta’ release
vStress effect model
vNew temperature model
vHolistic noise model enhancement
vUnified current saturation model
q Velocity
saturation
q Velocity
overshoot
q Source
injection thermal velocity limit
vNew document for multi-layer gate tunneling
vForward body bias
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Model for Isolation-induced
Stress Effects
L
Trench isolation
edge
SB
SA
W
LOD
SD
Instance parameters added: SA, SB, SD
SD is neighbour finger distance which is constant throughout all the fingers.
Stress effect calculation only if: 1) both SA and SB are given and are larger than 0 for
finger number NF=1; 2) SA, SB and SD are all given and are larger than 0 for NF >1
Intermediate geometry definitions :
LOD = SA + SB + NF ⋅ L + ( NF − 1 ) ⋅ SD
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Mobility Model With STI Stress
Define :
ρ µeff = ∆µ eff / µ effo = ( µ eff − µ effo ) / µ effo
=
So,
µ eff
µ effo
µ eff
µ effo
−1
= 1 + ρ µeff
(relative mobility change due to stress)
(Vth insensitive to Lod, SA and/or SB)
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Stress Effects Model-1/LOD Model
v Simple stress distribution function: 1/(SA+L/2), 1/(SB+L/2)
v
ρ µeff
ρ µeff =
Inv _ sa =
expression with LOD, L, W, and T dependence
ku0
⋅ ( Inv _ sa + Inv _ sb )
Kstress _ u0
1
SA + 0 .5 ⋅ Ldrawn
Inv _ sb =
1
SB + 0.5 ⋅ Ldrawn

LKU0
WKU0
Kstress _ u 0 = 1 +
+
LLODKU0
( W drawn + XW + WLOD )WLODKU0
 ( Ldrawn + XL )
+
( Ldrawn + XL )
LLODKU0
PKU0
⋅ ( Wdrawn + XW + WLOD )WLODKU0
 
Temperatur e  
 × 1 + TKU 0 ⋅ 
− 1 

 TNOM

 
v All data can be fitted well with only one set of parameters (ie.
Global model for LOD effect) and do not need extra binning
parameters if binning is desired.
v For multi-finger device:
Inv _ sa =
1
NF
NF −1
1
+ i ⋅ ( SD + Ldrawn )
drawn
∑ SA + 0. 5 ⋅ L
i= 0
Inv _ sa =
1
NF
NF −1
∑ SB + 0.5 ⋅ L
i =0
drawn
1
+ i ⋅ ( SD + Ldrawn )
v For irregular LOD device:
n
1
sw i
1
=∑
⋅
SAeff + 0.5 ⋅ Ldrawn i=1 Wdrawn sai + 0.5 ⋅ Ldrawn
n
1
sw i
1
=∑
⋅
SBeff + 0.5 ⋅ Ldrawn i =1 Wdrawn sbi + 0 .5 ⋅ Ldrawn
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Stress Effect µeff , υ sat Model
µ eff =
υ sat =
1 + ρ µeff ( SA , SB )
1 + ρ µeff ( SAref , SB ref )
µeffo
1 + K ⋅ ρ µeff ( SA , SB )
1 + K ⋅ ρ µeff ( SAref , SB ref )
υ sato
Where µ effo , υ sato are low field mobility, saturation velocity
at SAref, SBref
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Stress Effect Model to VTH0, K2, ETA0
LKVTH0
WKVTH0
+
( Ldrawn + XL )LLODKVTH ( Wdrawn + XW + WLOD )WLODKVTH
PKVTH0
+
( Ldrawn + XL )LLODKVTH ⋅ ( Wdrawn + XW + WLOD )WLODKVTH
Kstress _ vth0 = 1 +
VTH 0 = VTH 0original +
KVTH0
⋅ (Inv _ sa + Inv _ sb − Inv _ saref − Inv _ sbref )
Kstress_vt h0
STK2
⋅ (Inv _ sa + Inv _ sb − Inv _ sa ref − Inv _ sbref )
Kstress_vt h0LODK2
STETA0
ETA 0 = ETA 0original +
⋅ (Inv _ sa + Inv _ sb − Inv _ sa ref − Inv _ sbref )
Kstress_vt h0LODETA0
K 2 = K 2original +
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Stress Effect Model Verification
Drain current relative change (%) with SAref=5µm
SA=SB
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Stress Effect Model Verification
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Drain current relative change (%) with SAref=5µm
Stress Effect Model Verification
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Temperature Model Enhancement
Temperature mode TEMPMOD created:
qTEMPMOD = 0: current model with VFB enhancement
qTEMPMOD = 1: New format for vsat, prt, ua, ub, uc:
PARAM ( T ) = PARAM ( TNOM ) ⋅ [1 + TEMP _ COEFF ⋅ (T − TNOM )]
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Holistic Thermal Noise Model Enhancement
Refer to Chapter 9 of BSIM4 manual
θ tnoi

= RNOIB ⋅ 1 + TNOIB ⋅ Leff


 V
⋅  gsteff
 E sat Leff





2

= RNOIA ⋅ 1 + TNOIA ⋅ Leff


 Vgsteff
⋅ 
 E sat Leff




2
β tnoi




(9.2.5)




(9.2.6)
Default RNOIA=0.577; RNOIB=0.37
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Unified Current Saturation
-Velocity Overshoot Model
Price’s approximation to HD model:
λ ∂E y
∂n
J = qn µE y ( 1 +
) + qD
µE y ∂x
∂x
Approximate solution of Price’s equation yields unified current
expression that includes velocity saturation and velocity
overshoot:
I DS 0
I DS , HD =
V dseff
1+
OV
Leff E sat
where
E OV
sat

 V ds − Vdseff
1 +

Esat ⋅ litl
 LAMBDA 
= E sat 1 +
⋅
Leff ⋅ µ eff  V ds − V dseff

1 +

Esat ⋅ litl

2


 − 1 


2


 + 1 



Vdseff

I DS 0 = I DS ( BSIM 4.2.1 ) ⋅ 1 +
 L E
eff
sat





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Unified Current Saturation:
-Source–end Velocity Limit
and Quasi-Ballistic Transport
v sHD =
HD transport source carrier velocity:
v sBT =
Ballistic transport source carrier velocity:
r=
where VTL: thermal velocity,
Leff
I DS , HD
Wq s
1− r
VTL
1+ r
XN ⋅ Leff + LC
XN ≥ 3.0
Unified current expression with velocity saturation, velocity
overshoot and source velocity limit:
I DS =
[1+ (v
I DS ,HD
/ v sBT )
2 MM
sHD
]
1 / 2 MM
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Direct Tunneling through MultipleLayer Gate Stacks
v Gate Current modeled as
JG = Q INV ⋅ fIMP ⋅ T
T ∝ exp( −αt oxe )
v For two layer case T ∝ exp( −α new t oxe )
v For a single layer
α double = α 1 ⋅ f + α 2 ⋅ ( 1 − f ) + f ⋅ ( 1 − f ) ⋅
V ox
3h
where

 K 1 ⋅ qm 1 − K 2 ⋅ qm 2

2φ B 1
2φ B 2





α is the tunneling attenuation coefficient already modeled in BSIM4, f = Toxe1 / Toxe
v Stands for multiple layers(N≥2) as well.
v Using new tunneling attenuation coefficient and interpreted with
tunneling equations in BSIM4, BSIM4 is now capable of
modeling multi-layer gate tunneling.
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Verification
v Verified with data of
existing gate stack of
HfO2 and silicon
oxynitride.
v Very good fit observed
using BSIM model.
v BSIM4 direct tunneling
equation thus models the
multi-layer case.
Gate
1st layer
2nd layer
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Forward Body Bias
To ensure a good model behavior of body effect, body bias is usually
bounded between (Vbsc, and φs0 where φ s0 = 0.95 φs ). BSIM4.2.1
already has the smooth function for Vbs low bound. Following is the
upper bound smooth function:
(
)
2
'
'
Vbseff = 0.95Φs − 0.5 0.95Φs −Vbseff
− δ1 + 0.95Φs − Vbseff
− δ1 + 4δ1 .0.95Φs 


Where:
Vbseff = Vbc + 0. 5 ⋅  (Vbs − Vbc − δ1 ) +

(Vbs − Vbc − δ 1 )2 − 4δ1 ⋅Vbc 

Is the low bound smooth function. d 1 = 0.001V, and Vbc is the maximum
allowable Vbs and found from dVth/dVbs= 0 to be

K 12
Vbc = 0 .9 Φ s −
4 K 22




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Gate Current Partition Bugfix
From Original:
Igcs = Igc ⋅
and
Igcd = Igc ⋅
To:
Igcs = Igc ⋅
Igcd = Igc ⋅
PIGCD ⋅ Vds + exp(− PIGCD ⋅Vds ) −1 + 1.0e − 4
2
PIGCD 2 ⋅ Vds + 2.0e − 4
1 − (PIGCD ⋅ Vds + 1)⋅ exp(− PIGCD ⋅Vds ) + 1.0e − 4
2
PIGCD 2 ⋅Vds + 2.0e − 4
PIGCD ⋅Vdseff + exp(− PIGCD ⋅Vdseff ) − 1 + 1.0e − 4
PIGCD 2 ⋅Vdseff + 2.0e − 4
2
1 − (PIGCD ⋅Vdseff + 1)⋅ exp(− PIGCD ⋅ Vdseff )+ 1.0e − 4
PIGCD 2 ⋅ Vdseff + 2.0e − 4
2
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Gate Current Partition Bugfix
-11
2.0x10
Igc with bugfix
Original Igc
-11
1.8x10
-11
IGC(A)
1.6x10
-11
1.4x10
-11
1.2x10
VDS increase
-11
1.0x10
-12
8.0x10
-12
6.0x10
1.00
1.02
1.04
1.06
1.08
1.10
1.12
VGS(V)
Effect of gate current
bug fix
Comparison with experimental data
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New Parameters in BSIM4.3.0
-Stress Effect
Parameter
Name
Description
Default
Value
Binnab
le?
Note
SA
INSTANCE parameter: Distance between
OD edge to Poly from one side
0.0
If not given or (≤0.0), stress
effect will be turned off
SB
INSTANCE parameter: Distance between
OD edge to Poly from the other side
0.0
If not given or (≤0.0), stress
effect will be turned off
SD
INSTANCE parameter: Distance between
neighbour fingers
0.0
for NF >1: if not given or (≤0.0),
stress effect will be turned off
saref
Reference distance between OD edge to
poly of one side
Reference distance between OD edge to
poly of the other side
1.E-06[m]
no
>0.0
1.E-06[m]
no
>0.0
wlod
Width parameter for stress effect
0.0 [m]
no
ku0
Mobility degradation/enhancement
coefficient for stress effect
0.0 [m]
no
kvsat
Saturation velocity
degradation/enhancement parameter for
stress effect
0.0[m]
no
tku0
Temperature coefficient of ku0
0.0
no
lku0
Length dependence of ku0
0.0 [m llodku0]
no
sbref
-1 ≤ kvsat ≤ 1
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New Parameters in BSIM4.3.0
-Stress Effect
Parameter
Name
Description
Default Value
Binnable
?
Note
wku0
Width dependence of ku0
0.0 [m wlodku0]
no
pku0
Cross-term dependence of ku0
0.0[m llodku0+wlodku0]
no
llodku0
Length parameter for u0 stress effect
0.0
no
>0
wlodkuo
Width parameter for u0 stress effect
0.0
no
>0
kvth0
Threshold shift parameter for stress effect
0.0[V*m]
no
lkvth0
Length dependence of kvth0
0.0[V*mllodku0]
no
wkvth0
Width dependence of kvth0
0.0[V*mwlodku0]
no
pkvth0
Cross-term dependence of kvth0
0.0[V*mllodku0+wlodku0]
no
llodvth
Length parameter for Vth stress effect
0.0
no
>0
wlodvth
Width parameter for Vth stress effect
0.0
no
>0
stk2
K2 shift factor related to Vth0 change
0.0[m]
no
lodk2
K2 shift modification factor for stress effect
1.0
no
steta0
eta0 shift factor related to Vth0 change
0.0[m]
no
lodeta0
eta0 shift modification factor for stress effect
1.0
no
>0
>0
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New Model Parameters in BSIM4.3.0
-Unified Current Saturation
Parameter
Name
Description
Default
Value
Binnable
?
Note
LAMBDA
Velocity overshoot coefficient
0.0
yes
If not given or (≤0.0), velocity
overshoot will be turned off
VTL
Thermal velocity
2.0e5 [m/s]
yes
LC
Velocity back scattering
coefficient
0.0[m]
no
If not given or (≤0.0), source
end thermal velocity limit will
be turned off
~5e-9(m) at room temperature
XN
Velocity back scattering
coefficient
3.0
yes
Temperature Model
TEMPMOD
Temperature mode selector
0
no
If=0, original model will be used
If=1, new format will be used
Holistic Thermal Noise
RNOIA
Thermal noise coefficient
0.577
no
RNOIB
Thermal noise coefficient
0.37
no
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