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Semiconductor Device Modeling and Characterization EE5342, Lecture 20 -Sp 2002. Professor Ronald L. Carter [email protected] http://www.uta.edu/ronc/. Equivalent circuit above OSI. Depl depth given by the maximum depl = x d,max = [2 e Si |2 f p |/(qN a )] 1/2 - PowerPoint PPT Presentation
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L20 28Mar02 1
Semiconductor Device Modeling and CharacterizationEE5342, Lecture 20 -Sp 2002
Professor Ronald L. [email protected]
http://www.uta.edu/ronc/
L20 28Mar02 2
Equivalent circuitabove OSI• Depl depth given by the maximum depl = xd,max
= [2Si|2p|/(qNa)]1/2
• Depl cap, C’d,min = Si/xd,max
• Oxide cap, C’Ox = Ox/xOx
• Net C is the series comb
Ox,mindtot 'C1
'C1
'C1
C’Ox
C’d,min
L20 28Mar02 3
MOS surface states**p- substr = n-channel
VGS s Surf chg Carr Den
VGS < VFB < 0 s < 0 Accum. ps > Na
VGS = VFB < 0 s = Neutral ps = Na
VFB < VGS s > 0 Depletion ps < Na
VFB < VGS < VTh s = |p| I ntrinsic ns = ps = ni
VGS < VTh s > |p| Weak inv ni< ns < Na
VGS = VTh s = 2|p| O.S.I . ns = Na
L20 28Mar02 4
n-substr accumulation (p-channel)Fig 10.7a*
L20 28Mar02 5
n-substrate depletion(p-channel)Fig 10.7b*
L20 28Mar02 6
n-substrate inversion(p-channel)Fig 10.7*
L20 28Mar02 7
Ideal 2-terminalMOS capacitor/diode
x
-xox
0SiO2
silicon substrate
Vgate=VG
Vsub=VB
conducting gate,area =
LW
tsub
0y
L
L20 28Mar02 8
Band models (approx. scale)
Eo
Ec
Ev
qox
~ 0.95 eV
metal silicon dioxide p-type s/c
qm= 4.28 eV for Al
Eo
EF
m
EFp
Eo
Ec
Ev
EFi
qs,p
qSi= 4.0eV
Eg,ox
~ 8 eV
L20 28Mar02 9
Flat band with oxidecharge (approx. scale)
Ev
Al SiO2p-Si
EF
m
Ec,Ox
Eg,ox
~8eV EFp
Ec
Ev
EFi
'Ox
'ss
msOxmsFB
Ox
Oxc
Ox
'ss
x
ssm
ss
CQ
VV
xV
dxdE
q1Q
E
surface gate the on
is Q'Q' charge
a cond FB at then
bound, 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-->-
L20 28Mar02 10
Values for gate workfunction, m
V 17.5q/E :Si-poly p
V 05.4 :Si-poly n
V 55.4 :W ,Tungsten
V 65.5 :Pt ,Platinum
V 6.4 :Mo ,Molybdenum
V 1.5 :Au ,Gold
V 28.4 :Al ,umminAlu
gSim
Sim
m
m
m
m
m
L20 28Mar02 11
Values for ms
with metal gate
02586.0V ,12.1E ,19E8.2N
10E45.1n ,05.4 ,28.4
NN
lnV :Si-n to Al
nN
lnVq2
E
n
NNlnV :Note
n
NNlnV :Si-p to Al
tgC
iSiAlm,
d
CtSiAlm,ms
i
at
g2i
aCt
2i
aCtSiAlm,ms
L20 28Mar02 12
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
L20 28Mar02 13
Experimental valuesfor msFig 10.15*
L20 28Mar02 14
Calculation of thethreshold cond, VT
Ox the across Q induce to added
voltage the isV where V,VV
sub)-p sub,-(n xNqQ is
charge extra the and x of value
the reached has region depletion
The inverted. is surface the when
reached is condition threshold The
d,max
FBT
d,maxBd,max
d,max
L20 28Mar02 15
Equations forVT calculation
substr-n for 0 substr,- p for 0V
qN
22x ,xNqQ
,0nN
lnV ,0Nn
lnV
C
Q2VV :substrn,p
d,a
n,pd,maxd,maxa,dd,max
i
dtn
a
itp
Ox
',maxd
n,pFBT
L20 28Mar02 16
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
L20 28Mar02 17
Effect of contacts,VS and VD
material type-n induced allyelectronic
the contacts V and type-p the
contacts V since ,VV2VV
bend-band total let size, D.R. compute To
... ,VV21
V where ,VVyV
so ,V at not are regions contact The
C
BCBpabi
DSavgC,CGOx
B
L20 28Mar02 18
Computing theD.R. width at O.S.I.
Ex
Emax
x
aSi
x Nq
dxdE
a
CBpSi,maxd qN
VV22x
CBp VV2area
,maxda,maxd xqNQ
L20 28Mar02 19
Computing thethreshold voltage
DR the charge
and channel the invert to
required is where ,
'
'2 ,max
VVV
C
QVVV
FB
Ox
dSpFBT
L20 28Mar02 20
)VV(2/1V or VVV
VV,V
DsGsGox
BDs
)VV(2 Bending Band Total
VVVVV
)n/Nln(V2
NnN,NN 2V
from goes BB Total
sBp
sBnsidepsidea
iat
asdaapbi
L20 28Mar02 21
aqN
))sVBV(p2(E2
max,dX
O.S.I. At
xE
maxE
max,dXX
max,damax.d XqNQ
)VV(2area sBp E
aqNdxdE
L20 28Mar02 22
oxmax,dFB...ThGBBT
BsGT
oxmax,dsPFBT
C/)Q(BB.TVVVV
chosen values V&V for VV
C/)Q(V2VV
L20 28Mar02 23
Fully biased MOScapacitor in inversion
0y
L
VG>VT
Vsub=VB
EOx,x> 0
Acceptors
Depl Reg
e- e- e- e- e- e- n+
n+
VS=VC VD=VC
p-substrate
Channel
L20 28Mar02 24
Flat band with oxidecharge (approx. scale)
Ev
Al SiO2p-Si
EF
m
Ec,Ox
Eg,ox
~8eV EFp
Ec
Ev
EFi
'Ox
'ss
msOxmsFB
Ox
Oxc
Ox
'ss
x
ssm
ss
C
QVV
xV
dxdE
q1Q
E
surface gate the on
is Q'Q' charge
a cond FB at then
bound, 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-->-
L20 28Mar02 25
Flat-band parametersfor n-channel (p-subst)
0nN
lnVq2
E
n
NNlnV
gate, Si-poly n a For
den chg Ox/Si the is 'Q ,x
'C
'C'Q
V :substratep
i
at
g2i
actms
sms
ssOx
OxOx
Ox
ssmsFB
L20 28Mar02 26
MOS energy bands atSi surface for n-channel
Fig 8.10**
L20 28Mar02 27
Fully biased n-channel VT calc
0V ,
qN
VV22x
,xNqQ' ,0Nn
lnV
VV'C
'Q2VVV
VV :substratep
a
CBpd,max
d,maxad,maxa
itp
FBOx
,maxdpFBCT
Tthreshold at ,G
L20 28Mar02 28
References
* Semiconductor Physics & Devices, by Donald A. Neamen, Irwin, Chicago, 1997.
**Device Electronics for Integrated Circuits, 2nd ed., by Richard S. Muller and Theodore I. Kamins, John Wiley and Sons, New York, 1986