Lecture #38
OUTLINE
The MOSFET:
• Bulk-charge theory
• Body effect parameter
• Channel length modulation parameter
• PMOSFET I-V
• Small-signal model
Reading: Finish Chapter 17, 18.3.4
Spring 2007
EE130 Lecture 38, Slide 1
Problem with the “Square Law Theory”
Qinv  Coxe VG  VT  VS  VC 
• Ignores variation in depletion width with distance y
Spring 2007
EE130 Lecture 38, Slide 2
Modified (Bulk-Charge) Model
VG  VT
• linear region: VD  VDsat 
m
W
m
I Dlin  Coxe  eff (VG  VT  VDS )VDS
L
2
• saturation region: VD  VDsat
I Dsat
where m  1 
Spring 2007
VG  VT

m
W

Coxe  eff (VG  VT ) 2
2mL
Cdm
3T
 1  oxe
Coxe
WT
EE130 Lecture 38, Slide 3
since  Si  3 SiO2
MOSFET Threshold Voltage, VT
The expression that was previously derived for VT is the
gate voltage referenced to the body voltage that is
required reach the threshold condition:
2qN A Si (2F  VSB )
VT  VFB  VSB  2F 
Cox
Usually, the terminal voltages for a MOSFET are all
referenced to the source voltage. In this case,
2qN A Si (2F  VSB )
VT  VFB  2F 
Cox
and the equations for IDS are
W
m
Coxe eff (VGS  VT  VDS )VDS
L
2
VDS  VDSsat  VGS  VT  / m
I Dlin 
Spring 2007
EE130 Lecture 38, Slide 4
W
Coxe  eff (VGS  VT ) 2
2mL
 VDSsat  VGS  VT  / m
I Dsat 
VDS
The Body Effect
Note that VT is a function of VSB:
2qN A Si (2F  VSB )
VT  VFB  2F 
Cox
2qN A Si (2F )
2qN A Si (2F )
2qN A Si (2F  VSB )
 VFB  2F 


Cox
Cox
Cox



2qN A Si
 VT 0 
2F  VSB  2F  VT 0  g 2F  VSB  2F
Cox
where g is the body effect parameter

When the source-body pn junction is reverse-biased, |VT|
is increased. Usually, we want to minimize g so that IDsat
will be the same for all transistors in a circuit
Spring 2007
EE130 Lecture 38, Slide 5
MOSFET VT Measurement
• VT can be determined by plotting IDS vs. VGS,
using a low value of VDS
IDS
VGS
Spring 2007
EE130 Lecture 38, Slide 6
Channel Length Modulation Parameter, l
• Recall that as VDS is increased above VDsat, the width DL of
the depletion region between the pinch-off point and the
drain increases, i.e. the inversion layer length decreases.
1
1  DL 
I Dsat 
 1 

L  DL L 
L 
DL  VDS  VDSsat
DL
 l VDS  VDSsat 
L
I Dsat 
Spring 2007
W
Coxe  eff (VGS  VT ) 2 1  l VDS  VDSsat 
2mL
EE130 Lecture 38, Slide 7
P-Channel MOSFET
• The PMOSFET turns on when VGS < VTp
– Holes flow from SOURCE to DRAIN
 DRAIN is biased at a lower potential than the SOURCE
VG
VS
• VDS < 0
VD
GATE
P+
IDS
P+
N
VB
• IDS < 0
• |IDS| increases with
• |VGS - VTp|
• |VDS| (linear region)
• In CMOS technology, the threshold voltages
are usually symmetric: VTp = -VTn
Spring 2007
EE130 Lecture 38, Slide 8
PMOSFET I-V
• Linear region: 0  VDS 
I DS
VGS  VTp
m
W
m
  Coxe  p ,eff (VGS  VTp  VDS )VDS
L
2
• Saturation region: VDS 
I DS  I Dsat
VGS  VTp
m
W

Coxe  p ,eff (VGS  VTp ) 2
2mL
m = 1 + (3Toxe/WT) is the bulk-charge factor
Spring 2007
EE130 Lecture 38, Slide 9
Small Signal Model
id  g d vd  g m vg
• Conductance parameters:
gd 
I D
VD V
 lI Dsat0
G  const
I D
gm 
VG V
Spring 2007
EE130 Lecture 38, Slide 10

D  const
Weff Coxe
mL
(VGS  VT )
Inclusion of Additional Parasitics
Spring 2007
EE130 Lecture 38, Slide 11
Cutoff Frequency
• fmax is the frequency where the MOSFET is
no longer amplifying the input signal
– Obtained by considering the small-signal model
with the output terminals short-circuited, and
finding the frequency where |iout / iin| = 1
f max
Weff
gm
1


(VGS  VT ) 
2Coxe 2mL
L
 Increased MOSFET operating frequencies are
achieved by decreasing the channel length
Spring 2007
EE130 Lecture 38, Slide 12