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EE 5340Semiconductor Device TheoryLecture 25 - Fall 2010
Professor Ronald L. Carterronc@uta.edu
http://www.uta.edu/ronc
L25 17Nov2010 2
Ideal 2-terminalMOS capacitor/diode
x
-xox
0SiO2
silicon substrate
Vgate
Vsu
b
conducting gate,area =
LW
tsub
0y
L
L25 17Nov2010 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
L25 17Nov2010 4
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
L25 17Nov2010 5
Flat-band parametersfor p-channel (n-subst)
0nN
lnVq2
E
n
NNlnV
q
E gate, Si-poly p a For
den chg Ox/Si the is 'Q ,x
'C
change) (no 'C'Q
V :substraten
i
dt
g2i
dvtms
gsms
ssOx
OxOx
Ox
ssmsFB
L25 17Nov2010 6
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-->-
L25 17Nov2010 7
Equivalent circuitfor accumulation• Accum depth analogous to the
accum Debye length = LD,acc = [Vt/(qps)]1/2
• Accum cap, C’acc = Si/LD,acc
• Oxide cap, C’Ox = Ox/xOx
• Net C is the series comb
Oxacctot 'C1
'C1
'C1
C’Ox
C’acc
L25 17Nov2010 8
Equivalent circuitfor Flat-Band• Surface effect analogous to the
extr Debye length = LD,extr = [Vt/(qNa)]1/2
• Debye cap, C’D,extr = Si/LD,extr
• Oxide cap, C’Ox = Ox/xOx
• Net C is the series comb
Oxextr,Dtot 'C1
'C1
'C1
C’Ox
C’D,extr
L25 17Nov2010 9
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
L25 17Nov2010 10
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
L25 17Nov2010 11
Differential chargesfor low and high freq
From Fig 10.27*
high freq.
L25 17Nov2010 12
Ideal low-freqC-V relationship
Fig 10.25*
L25 17Nov2010 13
Comparison of lowand high freq C-VFig 10.28*
L25 17Nov2010 14
Effect of Q’ss onthe C-V relationshipFig 10.29*
L25 17Nov2010 15
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
L25 17Nov2010 16
MOS Bands at OSIp-substr = n-channel
Fig 10.9*
2q|p|
qp
xd,max
L25 17Nov2010 17
Computing the D.R. W and Q at O.S.I.
Ex
Emax
x
aSi
x Nq
dxdE
a
pSid qN
x
22
,max
parea 2
,max,max' dad xqNQ
L25 17Nov2010 18
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
L25 17Nov2010 19
Equations forVT calculation
substr-n for 0 substr,- p for 0V
qN
22x ,xNqQ'
0nN
V 0Nn
V
C
Q2VV substrnp
da
npd,maxd,maxa,dd,max
i
dtn
a
itp
Ox
dnpFBT
,
,
',max
,
,ln,ln
':,
L25 17Nov2010 20
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
L25 17Nov2010 21
MOS energy bands atSi surface for n-channel
Fig 8.10**
L25 17Nov2010 22
Computing the D.R. W and Q at O.S.I.
Ex
Emax
x
aSi
x Nq
dxdE
a
SBpSid qN
VVx
)(22,max
)(2 SBp VVarea
,maxda,maxd xqNQ
L25 17Nov2010 23
Q’d,max and xd,max forbiased MOS capacitor
Fig 8.11**
xd,max
(m) )2-
d,max
(cm
q
Q'
L25 17Nov2010 24
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
L25 17Nov2010 25
n-channel VT forVC = VB = 0
Fig 10.20*
L25 17Nov2010 26
Fully biased p-channel VT calc
0V ,
qNVV22
x
,xNqQ' ,0nN
lnV
VV'C
'Q2VVV
VV :substraten
d
BCnd,max
d,maxdd,maxi
dtn
FBOx
,maxdnFBCT
Tthreshold at ,G
L25 17Nov2010 27
p-channel VT forVC = VB = 0
Fig 10.21*
L25 17Nov2010 28
n-channel enhancementMOSFET in ohmic region
0< VT< VG
VB < 0
EOx,x> 0
Acceptors
Depl Reg
VS = 0 0< VD<
VDS,sate-e- e- e- e- n+
n+
p-substrate
Channel
L25 17Nov2010 29
Conductance ofinverted channel• Q’n = - C’Ox(VGC-VT)
• n’s = C’Ox(VGC-VT)/q, (# inv elect/cm2)
• The conductivity n = (n’s/t) q n
• G = n(Wt/L) = n’s q n (W/L) = 1/R, so
• I = V/R = dV/dR, dR = dL/(n’sqnW) WdV VVV'CdLI nTCG
L
0
V
VOx
D
S
L25 17Nov2010 30
Basic I-V relationfor MOS channel
2TGOxn
satDD
TGsatDSDS
satDSDD
nTGsatDSDS
TGDS2
DSDSTGOxn
D
VVL2CW
II
so VVVV for
,VI by given be I let so
Sat0LyQ' VVVV At
VVV VVVV2L2CW
I
'
.,
,'
,
,
,
,
L25 17Nov2010 31
I-V relation for n-MOS (ohmic reg)
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
L25 17Nov2010 32
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