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  2n 
Q'd,max
C'Ox
 VFB  V
 Nd 
n  Vt ln   0, Q'd,max  qNdxd,max ,
 ni 
22 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 
2VG  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 
2VG  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 
2VGS  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  2p 
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 
2VG  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
2Si
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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