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EE 5340Semiconductor Device TheoryLecture 27 – Spring 2011
Professor Ronald L. Carterronc@uta.edu
http://www.uta.edu/ronc
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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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MOS energy bands atSi surface for n-channel
Fig 8.10**
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Computing the D.R. W and Q at O.S.I.
Ex
Emax
x
aSi
x NqdxdE
a
SBpSid qN
VVx
)(22,max
)(2 SBp VVarea
,maxda,maxd xqNQ
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Q’d,max and xd,max forbiased MOS capacitor
Fig 8.11**
xd,max
(mm) )2-
d,max
(cmq
Q'
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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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n-channel VT forVC = VB = 0
Fig 10.20*
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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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p-channel VT forVC = VB = 0
Fig 10.21*
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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
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Conductance ofinverted channel• Q’n = - C’Ox(VGC-VT)• n’s = C’Ox(VGC-VT)/q, (# inv
elect/cm2)• The conductivity sn = (n’s/t) q mn
• G = sn(Wt/L) = n’s q mn (W/L) = 1/R, so
• I = V/R = dV/dR, dR = dL/(n’sqmnW) WdV VVV'CdLI nTCGL
0
V
VOx
D
Sm
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Basic I-V relationfor MOS channel
2TGOxn
satDD
TGsatDSDS
satDSDD
nTGsatDSDS
TGDS2
DSDSTGOxn
D
VVL2CWII
so VVVV for ,VI by given be I let so
Sat0LyQ' VVVV At
VVV VVVV2L2CWI
m
m
'
.,
,'
,
,
,
,
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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
m
m
ID
VDSVDS,sat
ID,sat
ohmic non-physical
saturated
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Universal draincharacteristic
9ID1
ID
4ID1
ID1VGS=VT+1V
VGS=VT+2V
VGS=VT+3V
2DS
Oxnsat,D VLW
2'CI m
VDS
2Oxn1D V1LW
2'CI
m
saturated, VDS>VGS-VTohmic
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Characterizing then-ch MOSFET
VD
IDDSG B
2TGSOxn
sat,D
TGSDSTGSDS
VVLW
2'CI
so , VVV0V , VV
m
VGSVT
DI
m
LW
2'CslopeOxn
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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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Body effect dataFig 9.9**
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Low field ohmiccharacteristics
DSVVVGS
D
OxnDSTGS
DSTGSOxnD
TGDS
2DSDSTGS
OxnD
VLWKPdV
dI
'C KP , VVVLWKP
VVVLW'CI
that so ,VVV let e,Furthermor region. ohmic for
, VVVV2LW
2'CI
TGDS
m
m
m
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MOSFET circuitparameters
region ohmic ,VVL'CWg
saturation ,VL'CWg
VIg
cetancTranscondu
TGSOxn
mL
DSOxn
ms
VGSD
mDS
m
m
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MOSFET circuitparameters (cont)
ohmic ,VVVL'CWg
saturation ,0gVIg
econductanc drain or Output
DSTGSOxn
dL
ds
VDSD
dGS
m
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OxOxOxgdOxgs 'WLCC ,C31C ,C3
2C
Fig 10.51*
MOSFET equivalentcircuit elements
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MOS small-signal equivalent circuitFig 10.52*
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MOS channel-length modulationFig 11.5*
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Analysis of channellength modulation
DD
sat,DSDSDS
sat,DSp
DSsat,DSpa
Si
ILLL'I
VVVV2
VV2qN2L
mod length the as same theis change DR the Assume
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Channel length mod-ulated drain charFig 11.6*
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e-e- e- e- e- + + + + + + + + + +
+ +
Implanted n-channel enhance-ment MOSFET (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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Si & SiO2
AlSi3N4
Si
Al & SiO2
Si3N4
Range
RP
Ion implantation*
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“Dotted box” approx**
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curve dottedunder area curve dashedunder area
iaiimpl XNdxN 0
'ox
iit
iait
CxqNΔV so
xand Nget implant to desired, as Vget To
FBTmaxd,i V V then , x xIf
dii
aiiiibeforessss xQQ
NNNN
qN 'impl ,
'
Calculating xi and VT
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aiaiSBppsa
iai
msxdaiaid
a
aiips
ad
NNxqVqN
xqN
xqNxqNQ
NNx
qNx
22
,
2
2
2
If xi ~ xd,max
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i
idiath
i
iaiathps
aiaiSBppsaOx
pspOx
iai
Ox
ssmsT
nxNNV
nxNNV
NNxqVqNC
CxqN
CQV
lnor , ln
21 22'
''
'
Calculating VT
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Implanted VT
Vt per Eq. 9.1.23 in M&K for a MOSFET with an 87-nm-thick gate oxide, Qff/q = 1011 cm-2, N’ = 3.5 X 1011 cm-2, and Na = 2 X 1015 cm-3. Both VS and VB = Figure 9.8 (p. 441)
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Mobilities**
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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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Body effect dataFig 9.9**
35
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M&K Fig. 9.9 (Eq. 9.1.23)
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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
tDS
tGS
subthresh,D VVexp1V
VexpI
Electron concentration at Source
Concentration gradient driving diffusion
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M&K Fig.9.10 (p.443)
Band diagram along the channel region of an n-channel MOSFET under bias, indicating that the barrier qΦB at the source depends on the gate voltage.
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M&K Fig. 9.11 (p.444)
Measured subthreshold characteristics of an MOS transistor with a 1.2 μm channel length. The inverse slope of the straight-line portion of this semilogarithmic plot is called the drain-current subthreshold slope S (measured in mV/decade of drain current).
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Subthreshold current data
Figure 11.4*Figure 10.1**
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Mobility variationdue to Edepl Figures 11.7,8,9*
31
0eff
0eff EE
mm
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Velocity saturationeffects
L2vf
vWCg E as vv So
vE1
vv limit" speed"
satT
satOxsat,msat
212
sateff
effthsat
m
mm
Figure 11.10*
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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