Semiconductor Device Modeling and Characterization – EE5342 Lecture 35 – Spring 2011 Professor Ronald L.
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Transcript Semiconductor Device Modeling and Characterization – EE5342 Lecture 35 – Spring 2011 Professor Ronald L.
Semiconductor Device Modeling
and Characterization – EE5342
Lecture 35 – Spring 2011
Professor Ronald L. Carter
[email protected]
http://www.uta.edu/ronc/
Flat-band parameters
for p-channel (n-subst)
n substrate : VFB ms
Q'ss
(no change)
C'Ox
Ox
C'Ox
, Q'ss is the Ox/Si chg den
xOx
For a p poly - Si gate, s m s
NvNd Eg
Nd
ms Vt ln 2 Vt ln 0
ni 2q
ni
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Eg
q
Fully biased pchannel VT calc
n substrate : VG, at threshold VT
VT VC VFB 2n
Q'd,max
C'Ox
VFB V
Nd
n Vt ln 0, Q'd,max qNdxd,max ,
ni
22 n VC VB
xd,max
, V 0
qNd
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p-channel VT for
VC = VB = 0
Fig 10.21*
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Ion implantation
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“Dotted box” approx
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Nimpl dx NaiXi
0
area under
dashed curve
'
Qss
area under dotted
curve
Na
Qss , before impl qNaiXi
, F NaiX
Nd
di
di
Xi Xd, max
'
To get Vt as desired, implant Nai Xi
qNaiXi
to get Vt 2.43, etc
'
Cox
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Mobilities
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Differential charges
for low and high freq
high freq.
From Fig 10.27*
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Ideal low-freq
C-V relationship
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Fig 10.25*
Comparison of low
and high freq C-V
Fig 10.28*
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Effect of Q’ss on
the C-V relationship
Fig 10.29*
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n-channel enhancement
MOSFET in ohmic region
0< VT< VG
Channel
VS = 0
0< VD< VDS,sat
EOx,x> 0
n+
Depl Reg
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e-e- e- e- e-
p-substrate
VB < 0
n+
Acceptors
Conductance of
inverted 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)
L
VD
0
VS
I dL C'Ox VG VC VT mnWdV
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Basic I-V relation
for MOS channel
WmnCOx
2
ID
2VG VT VDS VDS
, VDS VG VT
2L
At VDS VDS,sat VG VT , Q'n y L 0 Sat.
so let ID be given by ID VDS,sat ,
for VDS VDS,sat VG VT so
ID ID,sat
WmnCOx
VG VT 2
2L
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I-V relation for
n-MOS
(ohmic
reg)
m C'
W
2
ID
2VG VT VDS VDS
. Note for
2
L
ohmic
VDS VG VT VDS,sat ,
ID
non-physical
result is non - physical.
ID,sat
At VDS,sat , n's, y L 0
n Ox
assume that channel curr.
is const for VDS VDS,sat
ID,sat
mnC'Ox W
VGS VT 2
2
L
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saturated
VDS,sat
VDS
Universal drain
characteristic
mnC'Ox W
ID1
1V 2
2
L
ID
VGS=VT+3V
9ID1
ohmic
4ID1
ID1
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mnC'Ox W 2
ID,sat
VDS
2
L
saturated, VDS>VGS-VT
VGS=VT+2V
VGS=VT+1V
VDS
Characterizing the
n-ch MOSFET
VD
ID
ID
D
G
S
slope
B
mnC'Ox W
L
2
VDS VGS , VT 0
VDS VGS VT , so
mnC'Ox W
VGS VT 2
ID,sat
2
L
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VT
VGS
Low field ohmic
characteristics
mnC'Ox W
2
ID
2VGS VT VDS VDS
,
2
L
for ohmic region. Furthermore, let
VDS VG VT , so that
W
ID mnC'Ox VGS VT VDS
L
W
KP VGS VT VDS , KP mnC'Ox
L
dID
W
KP VDS
dV
L
GS V V V
DS
G
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T
MOSFET Device
Structre
Fig. 4-1, M&A*
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4-7a
(A&M)
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Figure 4-7b
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(A&M)
Figure 4-8a
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(A&M)
Figure 4-8b
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(A&M)
Body effect data
Fig 9.9**
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MOSFET equivalent
circuit elements
Fig 10.51*
Cgs
2
1
COx , Cgd COx , COx WLC'Ox
3
3
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n-channel enh.
circuit model
G
RG
S
RB
Cgs
RDS
Cgd
Cbs
Idrain
DSS DSD
Cbd
RB
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B
RD D
Cgb
MOS small-signal
equivalent circuit
Fig 10.52*
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MOSFET circuit
parameters
Transconduc tan ce
ID
gm
VGS
VDS
Wmn C'Ox
VGS VT , saturation
gms
L
Wmn C'Ox
gmL
VDS , ohmic region
L
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MOSFET circuit
parameters (cont)
Output or drain conductanc e
ID
gd
VDS V
GS
gds 0, saturation
gdL
Wmn C'Ox
VGS VT VDS , ohmic
L
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Substrate bias effect
on VT (body-effect)
Letting VT calculatio n be relative to Source
VT VS VFB 2 p
xd,max
VT VSB
qNa xd,max
2 2 p VSB
qNa
2 SiqNa
0
C'Ox
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C'Ox
, where
, so VT VT VSB
2
p
VSB 2 p
Body effect data
Fig 9.9**
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Fully biased nchannel VT calc
p substrate : VG, at threshold VT
VT Vs VFB 2p
Q'd,max
VFB V
C'Ox
ni
p Vt ln 0, Q'd,max qNa xd,max ,
Na
xd,max
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2 2 p VB Vs
qNa
, V 0
Values for ms
with silicon gate
n
poly to p - Si : ms
NCNa
Si Si Vt ln 2
ni
NCNa Eg
Na
Note : Vt ln 2 Vt ln
ni
ni 2q
Eg
NC
p poly to n - Si : ms Si Si Vt ln
q
Nd
NC Eg
Nd
Note : Vt ln Vt ln
Nd 2q
ni
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Fig 8.11**
|Q’d,max|/q (cm-2)
xd,max (microns)
Q’d,max and xd,max for
biased MOS capacitor
I-V relation
formn-MOS
C'
W
2
ID
2VG VT VDS VDS
. Note for
2
L
ohmic
VDS VG VT VDS,sat ,
ID
non-physical
result is non - physical.
ID,sat
At VDS,sat , n's, y L 0
n Ox
assume that channel curr.
is const for VDS VDS,sat
ID,sat
mnC'Ox W
VGS VT 2
2
L
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saturated
VDS,sat
VDS
MOS channellength modulation
Fig 11.5*
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Analysis of channel
length modulation
Assume the DR change the channel
L
length modulation, so I'D
ID
L L
2Si
L
2 p VDS,sat VDS
qNa
2 p VDS,sat , VDS VDS VDS,sat
mn C'Ox W
VGS VT 2 1 VDS
ID,sat
2 L
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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
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