l27 23apr021 semiconductor device modeling and characterization ee5342, lecture 27 -sp 2002...
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L27 23Apr023 Source of Ebers- Moll Equations (E)TRANSCRIPT
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L27 23Apr02 1
Semiconductor Device Modeling and CharacterizationEE5342, Lecture 27 -Sp 2002
Professor Ronald L. [email protected]
http://www.uta.edu/ronc/
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L27 23Apr02 2
Ebers-Moll Model(No G-R curr)
-JEAE
= IE
JCAC = IC
E
B
C
RIRFIF
(Fig. 9.30 Semiconductor Physics & Devices, by Neamen, Irwin, Chicago, 1997, * throughout)
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L27 23Apr02 3
Source of Ebers-Moll Equations (E)
SFFB0BRR
E
ESB0BE0EES
B0BnE
E0EpE
nEpEE
/exp /sinhnqD
/exp
/tanhnqD
/tanhpqD
/sinh/exp
/tanh/expnqDJ
1exp/tanhpqDJ
/JJJ
IVVf
AJLxL
AVVf
AJAI
LxLLxLJ
LxVVf
LxVVf
L
VV
LxL
AI
tBEBBBtBC
BBBEEE
BB
tBC
BB
tBE
B
t
BE
EEE
EE
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L27 23Apr02 4
Source of Ebers-Moll Equations (C)
StBCBBBtBE
C
CS
BBBCCC
BB
tBE
BB
tBC
B
t
BC
CCC
CC
IVVf
AJLxL
AVVf
AJAI
LxLLxLJ
LxVVf
LxVVf
L
VV
LxL
AI
/exp /sinhnqD
/exp
/tanhnqD
/tanhpqD
/sinh/exp
/tanh/expnqDJ
1exp/tanhpqDJ-
/JJJ
RRB0BFF
B0BC0CCS
B0BnC
C0CpC
nCpCC
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L27 23Apr02 5
Common emitter current gain,
lim. , V2VexpDn2
xxn , xDNxDN
L2x
lim. , V2VexpDn2
xxn , L2x
xDNxDN
limited. or limited is BJT a Usually,V2VexpDn2
xxnL2x
xDNxDN
1 so , 1 ; III with ,II
TtBE
0BBOBBEi
EBEBEB
2B
2B
tBE
0BBOBBEi
2B
2B
EBEBEB
T
1
tBE
0BBOBBEi
2B
2B
EBEBEB
00
0CBEBC
0
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L27 23Apr02 6
Charge componentsin the BJT
From Getreau, Modeling the Bipolar Transistor,Tektronix, Inc.
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L27 23Apr02 7
Gummel-Poon Staticnpn Circuit Model
C
E
BB’
ILC
ILE IBFIBR ICC - IEC =
IS(exp(vBE/NFVt) -exp(vBC/NRVt)/QB
RC
RE
RBB
IntrinsicTransistor
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L27 23Apr02 8
Recombination/GenCurrents (FA)
CBCB
BCeff,
1gen
BCeff,BCbiC
BCgen
BCiGC
1rec
BEt
BErec
iBERE
NNNNN and
rate, ionrecombinat the is and DR CB
the is qNVV2W where ,2
WqnJ
.rate ionrecombinat the is and DR
EB the is W where ,V2Vexp2
nqWJ
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L27 23Apr02 9
Gummel Poon npnModel Equations
IBF = IS expf(vBE/NFVt)/BFILE = ISE expf(vBE/NEVt)
IBR = IS expf(vBC/NRVt)/BRILC = ISC expf(vBC/NCVt)
ICC - IEC = IS(exp(vBE/NFVt - exp(vBC/NRVt)/QB
QB = { + + (BF IBF/IKF + BR IBR/IKR)1/2} (1 - vBC/VAF - vBE/VAR )-1
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L27 23Apr02 10
+
-+
-
VAF ParameterExtraction (fEarly)
iCiB
vCEvBE
0.2 < vCE < 5.00.7 < vBE < 0.9
Forward Active Operation
iC = ICC =(IS/QB)exp(vBE/NFVt),
where ICE = 0, andQB
-1 =
(1-vBC/VAF-vBE/VAR )* {IKF terms}-1,
so since vBC = vBE - vCE,VAF = iC/[iC/vBC]vBE
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L27 23Apr02 11
iE = - IEC =(IS/QB)exp(vBC/NRVt),
where ICC = 0, andQB
-1 =
(1-vBC/VAF-vBE/VAR ) {IKR terms}-1,
so since vBE = vBC - vEC,VAR = iE/[iE/vBE]vBC
VAR ParameterExtraction (rEarly)
+
-+
-
iEiB
vECvBC
0.2 < vEC < 5.00.7 < vBC < 0.9
Reverse Active Operation
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L27 23Apr02 12
BJT CharacterizationForward GummelvBCx= 0 = vBC + iBRB - iCRC
vBEx = vBE +iBRB +(iB+iC)RE
iB = IBF + ILE = ISexp(vBE/NFVt)/BF
+ ISEexpf(vBE/NEVt)iC = FIBF/QB =
ISexp(vBE/NFVt) (1-vBC/VAF-vBE/VAR )
{IKF terms}-1
+
-
iC RC
iB
RE
RB
vBEx
vBC
vBE
++
-
-
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L27 23Apr02 13
Definitions ofNeff and ISeff• In a region where iC or iB is approxi-
mately a single exponential term, theniC or iB ~ ISeffexp (vBEext /(NFeffVt)
whereNeff = {dvBEext/d[ln(i)]}/Vt,
and ISeff = exp[ln(i) - vBEext/(NeffVt)]
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L27 23Apr02 14
Region a - IKFIS, RB, RE, NF, VAR
Region b - IS, NF, VAR, RB, RE
Region c - IS/BF, NF, RB, RE
Region d - IS/BF, NFRegion e - ISE, NE
Forward GummelData Sensitivities
1.E-121.E-101.E-081.E-061.E-041.E-02
0.1 0.3 0.5 0.7 0.9iC(A),iB(A) vs. vBE(V)
iC
vBCx = 0
iB
a
b
c
d
e
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L27 23Apr02 15
Simple extractionof IS, ISE from data
1.E-16
1.E-14
1.E-12
1.E-10
0.1 0.3 0.5 0.7 0.9
Data set used • IS = 10f• ISE = 10E-14Flat ISeff for iC data =
9.99E-15 for 0.230 < vD < 0.255
Max ISeff value for iB data is 8.94E-14 for vD = 0.180ISeff vs. vBEext
iB data
iC data
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L27 23Apr02 16
Simple extraction of NF, NE from fg data
Data set used NF=1NE=2
Flat Neff region from iC data = 1.00 for 0.195 < vD < 0.390
Max Neff value from iB data is 1.881 for 0.180 < vD < 0.181
0.91.11.31.51.71.92.1
0.1 0.3 0.5 0.7 0.9NEeff vs. vBEext
iB data
iC data
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L27 23Apr02 17
0
25
50
75
100
1.E-10 1.E-06 1.E-02
Simple extractionof BF from data
• Data set used BF = 100
• Extraction gives max iC/iB = 92 for 0.50 V < vD < 0.51 V 2.42A < iD < 3.53A
• Minimum value of Neff =1 for slightly lower vD and iD
iC/iB vs. iC
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L27 23Apr02 18
BJT CharacterizationReverse Gummel
+
-
iE
RC
iB
RE
RB
vBCxvBC
vBE
++
-
-
vBEx= 0 = vBE + iBRB - iERE
vBCx = vBC +iBRB +(iB+iE)RC
iB = IBR + ILC = (IS/BR)expf(vBC/NRVt)
+ ISCexpf(vBC/NCVt)iE = RIBR/QB =
ISexpf(vBC/NRVt)(1-vBC/VAF-vBE/VAR )
{IKR terms}-1
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L27 23Apr02 19
1.E-10
1.E-08
1.E-06
1.E-04
1.E-02
0.1 0.3 0.5 0.7 0.9
Sample rg data forparameter extraction
• IS=10f• Nr=1• Br=2• Isc=10p • Nc=2• Ikr=.1m• Vaf=100• Rc=5• Rb=100
iE, iB vs. vBCext
iB data
iE data
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L27 23Apr02 20
0.0
0.5
1.0
1.5
2.0
1.E-10 1.E-06 1.E-02
Simple extractionof BR from data
• Data set used Br = 2
• Extraction gives max iE/iB = 1.7 for 0.48 V < vBC < 0.55V 1.13A < iE < 14.4A
• Minimum value of Neff =1 for same range
iE/iB vs. iE
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L27 23Apr02 21
1.E-16
1.E-14
1.E-12
1.E-10
0.2 0.4 0.6
Simple extractionof IS, ISC from data
Data set used • IS = 10fA• ISC = 10pAMin ISeff for iE data =
9.96E-15 for vBC = 0.200
Max ISeff value for iB data is 8.44E-12 for vBC = 0.200ISeff vs. vBCext
iB data
iE data
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L27 23Apr02 22
0.91.11.31.51.71.92.1
0.1 0.3 0.5 0.7 0.9
Simple extraction of NR, NC from rg data
Data set used Nr = 1Nc = 2
Flat Neff region from iE data = 1.00 for 0.195 < vBC < 0.375
Max Neff value from iB data is 1.914 for 0.195 < vBC < 0.205NEeff vs. vBCext
iB data
iE data
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L27 23Apr02 23
Fully biased n-MOScapacitor
0y
L
VG
Vsub=VB
EOx,x> 0
Acceptors
Depl Reg
e- e- e- e- e- e- n+
n+
VS VD
p-substrate
Channel if VG > VT
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L27 23Apr02 24
Flat band with oxidecharge (approx. scale)
Ev
Al SiO2 p-Si
EF
m
Ec,Ox
Eg,ox~8eV EFp
Ec
Ev
EFi
'Ox
'ssmsOxmsFB
OxOxc
Ox
'ssx
ssm
ss
CQVV
xV
dxdE
q1QE
surface gate the onis Q'Q' charge
a cond FB at thenbound, Ox/Si the at
is Q' charge a If
q(fp-ox)
q(Vox)
q(m-ox)
q(VFB) VFB= VG-VB, when Si bands
are flat
Ex
+<--Vox-->-
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L27 23Apr02 25
Flat-band parametersfor p-channel (n-subst)
0nNlnVq2
EnNNlnV
qE gate, Si-poly p a For
den chg Ox/Si the is 'Q ,x'C
change) (no 'C'QV :substraten
idt
g2i
dvtms
gsms
ssOxOx
Ox
OxssmsFB
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L27 23Apr02 26
Fully biased n-channel VT calc
0V ,qN
VV22x
,xNqQ' ,0NnlnV
VV'C'Q2VVV
VV :substratep
aCBp
d,max
d,maxad,maxaitp
FBOx,maxd
pFBCT
Tthreshold at ,G
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L27 23Apr02 27
Fully biased n-channel VT calc
0V ,qNVV22x
,xNqQ' ,0NnlnV
VV'C'Q2VVV
VV :substratep
a
sBpmaxd,
maxd,amaxd,a
itp
FBOx
max,dpFBsT
Tthreshold at ,G
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L27 23Apr02 28
Q’d,max and xd,max forbiased MOS capacitor
Fig 8.11**
x d,m
ax (m
icron
s)
|Q’ d,
max
|/q (c
m-2
)
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L27 23Apr02 29
2Emax.damax,d
Eamax,dmax,d
21
EE
Emax.d
E
Ep
21
a
pmaxd,
cm/coul936.8XqNQ102.5Nx m31.1x
144196.1264.021485.87.112x
mV2641045.1144ln02586.0
qN022x
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L27 23Apr02 30
Fully biased p-channel VT calc
0V ,qNVV22x
,xNqQ' ,0nNlnV
VV'C'Q2VVV
VV :substraten
dBCn
d,max
d,maxdd,maxidtn
FBOx,maxd
nFBCT
Tthreshold at ,G
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L27 23Apr02 31
I-V relation for n-MOS (ohmic reg)
2TGSOxn
sat,D
sat,DSDS
Lys,sat,DS
sat,DSTGDS
2DSDSTG
OxnD
VVLW
2'CI
VV for const iscurr. channel that assume
0n' ,V Atphysical.-non is result
,VVVVfor Note .VVVV2L
W2'CI
ID
VDSVDS,sa
t
ID,sat
ohmic non-physical
saturated
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L27 23Apr02 32
Universal draincharacteristic
9ID1
ID
4ID1
ID1VGS=VT+1V
VGS=VT+2V
VGS=VT+3V
2DS
Oxnsat,D VLW
2'CI
VDS
2Oxn1D V1LW
2'CI
saturated, VDS>VGS-VTohmic
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L27 23Apr02 33
Characterizing then-ch MOSFET
VD
IDDSG B
2TGSOxn
sat,D
TGSDSTGSDS
VVLW
2'CI
so , VVV0V , VV
VGSVT
DI
LW
2'CslopeOxn
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L27 23Apr02 34
Substrate bias effect on VT (body-effect)
pSBpOx
aSiSBT
SBTTa
SBpmaxd,
Ox
maxd,apFBST
T
2V2'CNq20VV
VVV so , qNV22x
where , 'CxNq2VVV
Source to relative be ncalculatio V Letting
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L27 23Apr02 35
Body effect dataFig 9.9**
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L27 23Apr02 36
EqQ,CQV
0.097V
cm/F 986cm/coul98.36- - C
Qcm/nf 86
7401485.89.3
tCcm740m940t
ssox
ssms FB
2E
E
ox
max,d
2E
Eoxox
ox
EEox
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L27 23Apr02 37
V186.09E86E19E6.1
CQ-
-0.817V 10E45.1
14E419E8.2ln02586.0
'ox
'ss
2ms
2
iactssms n
NNlnVXX
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L27 23Apr02 38
Values for ms
with silicon gate
idt
g
dCt
dCtSi
gSims
iat
g2i
aCt
2i
aCtSiSims
nNlnVq2
ENNlnV :Note
NNlnVq
E :Si-n to poly p
nNlnVq2
EnNNlnV :Note
nNNlnV :Si-p to poly n
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L27 23Apr02 39
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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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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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*ADISS = as given, or = JS*AS
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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*[W/(L-2*LD)]*(vgs - VTH)^2 *(1 + LAMBDA*vds)
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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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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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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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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