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![Page 1: EE5342 – Semiconductor Device Modeling and Characterization Lecture 25 April 19, 2010 Professor Ronald L. Carter ronc@uta.edu](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697bfa71a28abf838c98e49/html5/thumbnails/1.jpg)
EE5342 – Semiconductor Device
Modeling and Characterization
Lecture 25April 19, 2010
Professor Ronald L. [email protected]
http://www.uta.edu/ronc/
![Page 2: EE5342 – Semiconductor Device Modeling and Characterization Lecture 25 April 19, 2010 Professor Ronald L. Carter ronc@uta.edu](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697bfa71a28abf838c98e49/html5/thumbnails/2.jpg)
L25 04/19/10 2
MOSFET equivalentcircuit elements
OxOxOxgdOxgs 'WLCC ,C31
C ,C32
C
Fig 10.51*
![Page 3: EE5342 – Semiconductor Device Modeling and Characterization Lecture 25 April 19, 2010 Professor Ronald L. Carter ronc@uta.edu](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697bfa71a28abf838c98e49/html5/thumbnails/3.jpg)
L25 04/19/10 3
n-channel enh.circuit model
G
D
B
SCgs
Cgd
Cgb
CbsCbd
RD
RG
RB
RB
RDS
IdrainDSS DSD
![Page 4: EE5342 – Semiconductor Device Modeling and Characterization Lecture 25 April 19, 2010 Professor Ronald L. Carter ronc@uta.edu](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697bfa71a28abf838c98e49/html5/thumbnails/4.jpg)
L25 04/19/10 4
MOS small-signal equivalent circuitFig 10.52*
![Page 5: EE5342 – Semiconductor Device Modeling and Characterization Lecture 25 April 19, 2010 Professor Ronald L. Carter ronc@uta.edu](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697bfa71a28abf838c98e49/html5/thumbnails/5.jpg)
L25 04/19/10 5
MOSFET circuitparameters
region ohmic ,VL
'CWg
saturation ,VVL
'CWg
V
Ig
cetancTranscondu
DSOxn
mL
TGSOxn
ms
VGS
Dm
DS
![Page 6: EE5342 – Semiconductor Device Modeling and Characterization Lecture 25 April 19, 2010 Professor Ronald L. Carter ronc@uta.edu](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697bfa71a28abf838c98e49/html5/thumbnails/6.jpg)
L25 04/19/10 6
MOSFET circuitparameters (cont)
ohmic ,VVVL
'CWg
saturation ,0g
VI
g
econductanc drain or Output
DSTGSOxn
dL
ds
VDS
Dd
GS
![Page 7: EE5342 – Semiconductor Device Modeling and Characterization Lecture 25 April 19, 2010 Professor Ronald L. Carter ronc@uta.edu](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697bfa71a28abf838c98e49/html5/thumbnails/7.jpg)
L25 04/19/10 7
Substrate bias effect on VT (body-effect)
pSBpOx
aSiSBT
SBTTa
SBpmaxd,
Ox
maxd,apFBST
T
2V2'C
Nq20VV
VVV so , qN
V22x
where , 'C
xNq2VVV
Source to relative be ncalculatio V Letting
![Page 8: EE5342 – Semiconductor Device Modeling and Characterization Lecture 25 April 19, 2010 Professor Ronald L. Carter ronc@uta.edu](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697bfa71a28abf838c98e49/html5/thumbnails/8.jpg)
L25 04/19/10 8
Body effect dataFig 9.9**
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L25 04/19/10 9
Fully biased n-channel VT calc
0V ,
qN
VV22x
,xNqQ' ,0Nn
lnV
VV'C
'Q2VVV
VV :substratep
a
sBpmaxd,
maxd,amaxd,a
itp
FBOx
max,dpFBsT
Tthreshold at ,G
![Page 10: EE5342 – Semiconductor Device Modeling and Characterization Lecture 25 April 19, 2010 Professor Ronald L. Carter ronc@uta.edu](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697bfa71a28abf838c98e49/html5/thumbnails/10.jpg)
L25 04/19/10 10
Values for ms
with silicon gate
i
dt
g
d
Ct
d
CtSi
gSims
i
at
g2i
aCt
2i
aCtSiSims
nN
lnVq2
E
NN
lnV :Note
NN
lnVq
E :Si-n to poly p
nN
lnVq2
E
n
NNlnV :Note
n
NNlnV :Si-p to poly n
![Page 11: EE5342 – Semiconductor Device Modeling and Characterization Lecture 25 April 19, 2010 Professor Ronald L. Carter ronc@uta.edu](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697bfa71a28abf838c98e49/html5/thumbnails/11.jpg)
L25 04/19/10 11
Q’d,max and xd,max forbiased MOS capacitor
Fig 8.11**
xd
,max (
mic
ron
s)
|Q’ d
,max|/
q (
cm-2
)
![Page 12: EE5342 – Semiconductor Device Modeling and Characterization Lecture 25 April 19, 2010 Professor Ronald L. Carter ronc@uta.edu](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697bfa71a28abf838c98e49/html5/thumbnails/12.jpg)
L25 04/19/10 12
I-V relation for n-MOS
2TGSOxn
sat,D
sat,DSDS
Lys,sat,DS
sat,DSTGDS
2DSDSTG
OxnD
VVLW
2'C
I
VV for const is
curr. channel that assume
0n' ,V At
physical.-non is result
,VVVV
for Note .VVVV2LW
2'C
I
ID
VDSVDS,sat
ID,sat
ohmic
non-physical
saturated
![Page 13: EE5342 – Semiconductor Device Modeling and Characterization Lecture 25 April 19, 2010 Professor Ronald L. Carter ronc@uta.edu](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697bfa71a28abf838c98e49/html5/thumbnails/13.jpg)
L25 04/19/10 13
MOS channel-length modulationFig 11.5*
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L25 04/19/10 14
Analysis of channellength modulation
DS2
TGSOxn
satD
satDSDSDSsatDSp
DSsatDSpa
Si
DD
V1VVLW
2C
I
VVV , V2
VV2qN2
L
ILL
LI so ,modulation length
channel the change DR the Assume
'
'
,
,,
,
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L25 04/19/10 15
Channel length mod-ulated drain charFig 11.6*
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L25 04/19/10 16
Associating theoutput conductance
ID
VDSVDS,sat
sat,D
DS
sat,Dsat,ds
VDS
Dd
DS2
TGSOxn
sat,D
I
V1
Ig
VI
g
V1VVLW
2'C
I
GS
sat,dsg
slopeID,sat
![Page 17: EE5342 – Semiconductor Device Modeling and Characterization Lecture 25 April 19, 2010 Professor Ronald L. Carter ronc@uta.edu](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697bfa71a28abf838c98e49/html5/thumbnails/17.jpg)
L25 04/19/10 17
MOSFET circuitparameters
region ohmic ,VL
'CWg
saturation ,VVL
'CWg
V
Ig
cetancTranscondu
DSOxn
mL
TGSOxn
ms
VGS
Dm
DS
![Page 18: EE5342 – Semiconductor Device Modeling and Characterization Lecture 25 April 19, 2010 Professor Ronald L. Carter ronc@uta.edu](https://reader035.fdocuments.us/reader035/viewer/2022062217/5697bfa71a28abf838c98e49/html5/thumbnails/18.jpg)
L25 04/19/10 18
Estimating LAMBDA
0V,
qN
VV22x
,V
x
x1
VL
L1
is of tioninterpreta The
V1VVLW
2'C
I
SBa
SBDSp
maxd,
DS
max,d
max,dDS
DS2
TGSOxn
sat,D
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L25 04/19/10 19
e-e- e- e- e- + + + + + + + + + +
+ +
n-channel enhancementMOSFET in ohmic region
0< VT< VG
VB < 0
EOx,x> 0
Acceptors
Depl Reg
VS = 0 0< VD< VDS,sat
n+ n+
p-substrate
Channel
e- channel ele + implant ion
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L25 04/19/10 20
Subthreshold conduction• Below O.S.I., when the total band-
bending < 2|p|, the weakly inverted channel conducts by diffusion like a BJT.
• Since VGS>VDS, and below OSI, then Na>nS >nD, and electr diffuse S --> D
t
DS
t
GSsubthresh,D V
Vexp1
VV
expI
Electron concentration at Source
Concentration gradient driving diffusion
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L25 04/19/10 21
Subthreshold current data
Figure 11.4*
Figure 10.1**
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L25 04/19/10 22
Mobility variationdue to Edepl
Figures 11.7,8,9*
31
0
eff0eff E
E
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L25 04/19/10 23
Velocity saturationeffects
L2v
f
vWCg
E as vv So
v
E1
vv limit" speed"
satT
satOxsat,m
sat
212
sat
eff
eff
thsat
Figure 11.10*
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L25 04/19/10 24
SPICE mosfet Model Instance CARM*, Ch. 4, p. 290M MOSFET
General Form
M<name> <drain node> <gate node> <source node>+ <bulk/substrate node> <model name>+ [L=<value>] [W=<value>]+ [AD=<value>] [AS=<value>]+ [PD=<value>] [PS=<value>]+ [NRD=<value>] [NRS=<value>]+ [NRG=<value>] [NRB=<value>]+ [M=<value>]
Examples
M1 14 2 13 0 PNOM L=25u W=12uM13 15 3 0 0 PSTRONGM16 17 3 0 0 PSTRONG M=2M28 0 2 100 100 NWEAK L=33u W=12u+ AD=288p AS=288p PD=60u PS=60u NRD=14 NRS=24 NRG=10
L = Ch. L. [m]W = Ch. W. [m]AD = Drain A [m2]AS = Source A[m2]NRD, NRS = D and S diff in squares
M = device multiplier
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L25 04/19/10 25
CARM*, Ch. 4, p. 99Model Forms
.MODEL <model name> NMOS [model parameters]
.MODEL <model name> PMOS [model parameters]
As shown in Figure 11, the MOSFET is modeled as an in tr insic MOSFET with ohmic resistances in series with the drain , source, gate, and bulk (substrate). There is also a shunt resistance (RDS) in parallel with the drain-source channel.
[L=<value>] [W=<value>] cannot be used in conjunction with Monte Carlo analysis .
The simulator provides four MOSFET device models, which differ in the formulation of the I-V characteristic. The LEVEL parameter selects between di fferent models :
LEVEL=1 is the Shichman-Hodges model (see reference [1])LEVEL=2 is a geometry-based, analytic model (see reference [2])LEVEL=3 is a semi-empirical, short-channel model (see reference [2])LEVEL=4 is the BSIM model (see reference [3])LEVEL=5 is the BSIM3 model (see reference [7] Version 1.0)LEVEL=6 is the BSIM3 model (see reference [7] Version 2.0)
L and W are the channel length and width, and are decreased to get the effective channel length and width. L and W can be specified in the device, model, or .OPTIONS statements. The value in the device statement supersedes the va lue in the model sta tement, which supersedes the value in the .OPTIONS statement.
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L25 04/19/10 26
SPICE mosfet model levels• Level 1 is the Schichman-Hodges
model• Level 2 is a geometry-based,
analytical model• Level 3 is a semi-empirical, short-
channel model• Level 4 is the BSIM1 model• Level 5 is the BSIM2 model, etc.
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L25 04/19/10 27
SPICE ParametersLevel 1 - 3 (Static)Par am. Parameter Description Def . Typ. Units
VTO Zero-bias Vthresh 1 1 V
KP Transconductance 2.E-05 3.E-05 A/ V 2̂
GAMMA Body-eff ect par. 0.0 0.35 V 1̂/ 2
PHI Surf ace inversion pot. 0.6 0.65 V
LAMBDA Channel-length mod. 0.0 0.02 1/ V
TOX Thin oxide thickness 1.E-07 1.E-07 m
NSUB Substrate doping 0.0 1.E+15 cm̂ -3
NSS Surf ace state density 0.0 1.E+10 cm̂ -2
LD Lateral diff usion 0.0 8.E-05 m
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L25 04/19/10 28
Par am. Parameter Description Def . Typ. Units
TPG Type of gate material* 1 1
UO Surf ace mobility 600 700 cm̂ 2/ V-s
I S Bulk j ctn. sat. curr. 1.E-14 1.E-15 A
J S Bulk j ctn. sat. curr. dens. A/ m̂ 2
PB Bulk junction potential 0.8 0.75 V
RD Drain ohmic resistance 0 10 Ohms
RS Source ohmic resistance 0 10 Ohms
RSH S/ D sheet ohmic res. 0 10 Ohms/ sq
SPICE ParametersLevel 1 - 3 (Static)
* 0 = aluminum gate, 1 = silicon gate opposite substrate type, 2 = silicon gate same as substrate.
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L25 04/19/10 29
SPICE ParametersLevel 1 - 3 (Q & N)Par am. Parameter Description Def . Typ. Units
CJ Zero-bias bulk cap./ A 0 1.E-09 Fd/ m̂ 2
MJ Bulk j ctn. grading coeff . 0.5 0.5
CJ SW Zero-bias perimeter C/ l 0 1.E-09 Fd/ m
MJ SW Per. C grading coeff . 0.5 0.5
FC For.-bias cap. coeff . 0.5 0.5
CGBO Gate-bulk overlap C/ L 0 2.E-10 Fd/ m
CGDO Gate-drain overlap C/ L 0 4.E-11 Fd/ m
CGSO G-S overlap C/ L 0 4.E-11 Fd/ m
AF Flicker-noise exp. 1 1.2
KF Flicker-noise coeff . 0.0 1.E-26
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L25 04/19/10 30
Level 1 Static Const.For Device EquationsVfb = -TPG*EG/2 -Vt*ln(NSUB/ni)
- q*NSS*TOX/eOxVTO = as given, or
= Vfb + PHI + GAMMA*sqrt(PHI)KP = as given, or = UO*eOx/TOXCAPS are spice pars., technological
constants are lower case
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L25 04/19/10 31
Level 1 Static Const.For Device Equations = KP*[W/(L-2*LD)] = 2*K, K not spiceGAMMA = as given, or = TOX*sqrt(2*eSi*q*NSUB)/eOx2*phiP = PHI = as given, or = 2*Vt*ln(NSUB/ni)ISD = as given, or = JS*AD
ISS = as given, or = JS*AS
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L25 04/19/10 32
Level 1 Static Device Equationsvgs < VTH, ids = 0VTH < vds + VTH < vgs, id = KP*[W/(L-2*LD)]*[vgs-VTH-vds/2] *vds*(1 + LAMBDA*vds)VTH < vgs < vds + VTH, id = KP/2*[W/(L-2*LD)]*(vgs - VTH)^2 *(1 + LAMBDA*vds)
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L25 04/19/10 33
SPICE ParametersLevel 2Par am. Parameter Description Def . Typ. Units
NEFF Total channel chg coeff . 1 5
UCRI T Critical E-fi eld f or mob. 1.E+04 1.E+04 V/ cm
UEXP Expon. coeff . f or mob. 0 0.1
UTRA Transverse fi eld coeff . 0 0.5
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L25 04/19/10 34
SPICE ParametersLevel 2 & 3Par am. Parameter Description Def . Typ. Units
NFS Surf ace-f ast state dens. 0.0 1.E+10 cm̂ -2
XJ Metallurgical j ctn. depth 0.0 1.E-06 m
VMAX Max. drif t v of carr. 0.0 5.E+04 m/ s
XQC Coeff . of ch. Q share 0.0 0.4
DELTA Width eff . on Vthresh 0.0 1.0
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L25 04/19/10 35
Level 2 StaticDevice EquationsAccounts for variation of channel
potential for 0 < y < LFor vds < vds,sat = vgs - Vfb - PHI +
2*[1-sqrt(1+2(vgs-Vfb-vbs)/2]
id,ohmic = [/(1-LAMBDA*vds)] *[vgs - Vfb - PHI - vds/2]*vds -2[vds+PHI-vbs)1.5-(PHI-vbs)1.5]/3
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L25 04/19/10 36
Level 2 StaticDevice Eqs. (cont.)For vds > vds,sat
id = id,sat/(1-LAMBDA*vds)
where id,sat = id,ohmic(vds,sat)
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L25 04/19/10 37
Level 2 StaticDevice Eqs. (cont.)Mobility variationKP’ = KP*[(esi/eox)*UCRIT*TOX /(vgs-VTH-UTRA*vds)]UEXP
This replaces KP in all other formulae.
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L25 04/19/10 38
SPICE ParametersLevel 3Par am. Parameter Description Def . Typ. Units
KAPPA Saturation fi eld f actor 0.2 1.0
ETA Stat. f eedbk on Vthresh 0.0 1.0
THETA Mobility modulation 0.0 0.05 1/ V
DELTA Width eff . on Vthresh 0.0 1.0
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L25 04/19/10 39
References
• CARM = Circuit Analysis Reference Manual, MicroSim Corporation, Irvine, CA, 1995.
• M&A = Semiconductor Device Modeling with SPICE, 2nd ed., by Paolo Antognetti and Giuseppe Massobrio, McGraw-Hill, New York, 1993.
• **M&K = Device Electronics for Integrated Circuits, 2nd ed., by Richard S. Muller and Theodore I. Kamins, John Wiley and Sons, New York, 1986.
• *Semiconductor Physics and Devices, by Donald A. Neamen, Irwin, Chicago, 1997