EE 5340 Semiconductor Device Theory Lecture 24 – Spring 2011 Professor Ronald L. Carter
22
EE 5340 Semiconductor Device Theory Lecture 24 – Spring 2011 Professor Ronald L. Carter [email protected] http://www.uta.edu/ronc
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©rlc L24-19Apr20113 Band models (approx. scale) EoEo EcEc EvEv q ox ~ 0.95 eV metalsilicon dioxidep-type s/c q m = 4.1 eV for Al EoEo E Fm E Fp EoEo EcEc EvEv E Fi q s,p q Si = 4.05eV E g,ox ~ 8 eV
Transcript of EE 5340 Semiconductor Device Theory Lecture 24 – Spring 2011 Professor Ronald L. Carter
EE 5340Semiconductor Device TheoryLecture 24 – Spring 2011
Professor Ronald L. [email protected]
http://www.uta.edu/ronc
©rlc L24-19Apr2011
2
Ideal 2-terminalMOS capacitor/diode
x
-xox
0SiO2
silicon substrate
Vgate
Vsu
b
conducting gate,area =
LW
tsub
0y
L
©rlc L24-19Apr2011
3
Band models (approx. scale)
Eo
Ec
Ev
qcox
~ 0.95 eV
metal silicon dioxide p-type s/c
qfm= 4.1 eV for Al
Eo
EF
mEFp
Eo
EcEvEFi
qfs,p
qcSi= 4.05eV
Eg,ox
~ 8 eV
©rlc L24-19Apr2011
4
Flat band condition (approx. scale)
Ec,Ox
Ev
Al SiO2 p-Siq(fm-cox)= 3.15 eV
EF
m EFp
Ec
Ev
EFi
q(cox-cSi)=3.1eV
Eg,ox
~8eV
cond band-flat forVVV8.0
V
eV8.0EEThen
eV85.0EEIf
sgMS
fpfmFB
fpfm
fpc
f
ff
qffp= 3.95e
V
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5
Depletion for p-Si, Vgate> VFB
SiO2
p-type Si
Vgate> VFB
Vsub = 0
EOx,x> 0
x
-xox
0
tsu
b
x,OxSi
OxSi
SiSix,OxOxOxOx
x,Ox
E31E
39.37.11
EE
0xVE
AcceptorsDepl Reg
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Depletion forp-Si, Vgate> VFBFig 10.4b*
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Equivalent circuitfor depletion• Depl depth given by the usual
formula = xdepl = [2Si(Vbb)/(qNa)]1/2
• Depl cap, C’depl = Si/xdepl
• Oxide cap, C’Ox = Ox/xOx
• Net C is the series comb
Oxdepltot 'C1
'C1
'C1
C’Ox
C’depl
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8
Inversion for p-SiVgate>VTh>VFB
Vgate> VFB
Vsub = 0
EOx,x> 0
inversion for threshold above
E Induced depletes 0
E Induced
0xVE
Si
SiOxOx
x,Ox
Acceptors
Depl Reg
e- e- e- e- e-
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Inversion for p-SiVgate>VTh>VFBFig 10.5*
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Approximation concept“Onset of Strong Inv”• OSI = Onset of Strong Inversion
occurs when ns = Na = ppo and VG = VTh
• Assume ns = 0 for VG < VTh
• Assume xdepl = xd,max for VG = VTh and it doesn’t increase for VG > VTh
• Cd,min = Si/xd,max for VG > VTh • Assume ns > 0 for VG > VTh
©rlc L24-19Apr2011
11
MOS Bands at OSIp-substr = n-channelFig 10.9*
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12
Equivalent circuitabove OSI• Depl depth given by the maximum
depl = xd,max = [2Si|2fp|/(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
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13
MOS surface states**p- substr = n-channel
VGS fs Surf chg Carr DenVGS < VFB < 0 fs < 0 Accum. ps > Na
VGS = VFB < 0 fs = Neutral ps = Na
VFB < VGS fs > 0 Depletion ps < Na
VFB < VGS < VTh fs = |fp| I ntrinsic ns = ps = ni
VGS < VTh fs > |fp| Weak inv ni< ns < Na
VGS = VTh fs = 2|fp| O.S.I . ns = Na
©rlc L24-19Apr2011
14
n-substr accumulation (p-channel)Fig 10.7a*
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n-substrate depletion(p-channel)Fig 10.7b*
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n-substrate inversion(p-channel)Fig 10.7*
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17
Values for gate workfunction, fm
V 17.5q/E :Si-poly pV 05.4 :Si-poly n
V 55.4 :W ,TungstenV 65.5 :Pt ,Platinum
V 6.4 :Mo ,MolybdenumV 1.5 :Au ,Gold
V 28.4 :Al ,umminAlu
gSim
Sim
mm
m
m
m
cf
cf
f
f
f
f
f
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Values for fms
with metal gate
02586.0V ,12.1E ,19E8.2N10E45.1n ,05.4 ,28.4
NNlnV :Si-n to Al
nNlnVq2
EnNNlnV :Note
nNNlnV :Si-p to Al
tgC
iSiAlm,
dCtSiAlm,ms
iat
g2i
aCt
2i
aCtSiAlm,ms
cf
cff
cff
©rlc L24-19Apr2011
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Values for fms
with silicon gate
ccf
ccf
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
©rlc L24-19Apr2011
20Fig 10.15*
fms
(V)
NB (cm-3)
Typical fms values
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21
Flat band with oxidecharge (approx. scale)
Ev
Al SiO2 p-Si
EF
m
Ec,Ox
Eg,ox
~8eV EFp
Ec
Ev
EFi
'Ox
'ss
msOxmsFB
Ox
Oxc
Ox
'ss
x
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
ff
q(ffp-cox)q(Vox
)q(fm-
cox)
q(VFB
) VFB= VG-VB, when Si bands
are flat
Ex
+<--Vox-->-
©rlc L24-19Apr2011
22
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
