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Lecture 20
OUTLINE
The MOSFET (cont’d)
• Long-channel I-V characteristics
Reading: Pierret 17.2; Hu 6.6
Derivation of NMOSFET I-V
• VD > VS
• Current in the channel flows by drift
• Channel voltage VC(y) varies continuously between the source
and the drain
2qN A Si (2F VCB ( y))
VT ( y) VFB VCB ( y) 2F
Cox
• Channel inversion charge density
Qdep ( y )
Qinv ( y ) Coxe VG VFB VCB ( y) 2S
Coxe
W
EE130/230A Fall 2013
Lecture 20, Slide 2
R. F. Pierret, Semiconductor Device Fundamentals, Figs. 17.6
1st-Order Approximation
• If we neglect the variation of Qdep with y, then
Qdep 2qN A Si (2F VSB )
2qN A Si (2F VSB )
VT ( y) VFB VCB ( y) 2F
VSB VSB
Cox
VT ( y) VT VSB VCB ( y )
where VT is defined to be the threshold voltage at the source end:
2qN A Si (2F VSB )
VT VFB VSB 2F
Cox
The inversion charge density is then
Qinv Coxe VG VT VSB VCB ( y) Coxe VG VT VS VC ( y)
EE130/230A Fall 2013
Lecture 20, Slide 3
NMOSFET Current (1st-order approx.)
• Consider an incremental length dy of the channel. The voltage
drop across this region is
dVC I DS dR I DS
L
0
dy
WTinv
I DS
I DS dy
dy
q eff nWTinv
Qinv eff W
VD
I DS dy eff WQinv (VC )dVC
I DS
I DS
VS
VD
W
eff Qinv (VC )dVC
VS
L
VD
W
eff Coxe VG VT VS VC dVC
VS
L
VDS
W
eff Coxe VG VT
VDS in the linear region
L
2
EE130/230A Fall 2013
Lecture 20, Slide 4
Saturation Current, IDsat
(1st-order approximation)
C. C. Hu, Modern Semiconductor Devices for Integrated Circuits, Figure 6-16
IDS saturates when VD reaches VG-VT
Set VD = VG-VT in the equation for ID
I Dsat
W
Coxe eff (VG VT ) 2
2L
for VD VDsat VG VT
2qN A Si (2F VSB )
VT VFB VSB 2F
Cox
EE130/230A Fall 2013
Lecture 20, Slide 5
Problem with “Square Law Theory”
• Ignores variation in depletion width with distance y:
Qinv Coxe VG VT VS VC
2qN A Si (2F VSB )
where VT VFB VSB 2F
Cox
EE130/230A Fall 2013
Lecture 20, Slide 6
Modified (Bulk-Charge) I-V Model
VG VT
In linear region: VD VDsat
m
W
m
I Dlin Coxe eff (VG VT VDS )VDS
L
2
In saturation region: VD VDsat
I Dsat
where m 1
EE130/230A Fall 2013
Cdep,min
Coxe
1
VG VT
m
W
Coxe eff (VG VT ) 2
2mL
3Toxe
WT
Lecture 20, Slide 7
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 (2F VSB )
VT VFB VSB 2F
Cox
Usually, the terminal voltages for a MOSFET are all
referenced to the source voltage. In this case,
2qN A Si (2F VSB )
VT VFB 2F
Cox
and the equations for IDS are
W
m
Coxe eff (VGS VT VDS )VDS
L
2
VDS VDsat VGS VT / m
I Dlin
EE130/230A Fall 2013
Lecture 20, Slide 8
W
Coxe eff (VGS VT ) 2
2mL
VDsat VGS VT / m
I Dsat
VDS
The Body Effect
Note that VT is a function of VSB:
2qN A Si (2F VSB )
VT VFB 2F
Cox
2qN A Si (2F )
2qN A Si (2F )
2qN A Si (2F VSB )
VFB 2F
Cox
Cox
Cox
2qN A Si
VT 0
2F VSB 2F VT 0 g 2F VSB 2F
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.
EE130/230A Fall 2013
Lecture 20, Slide 9
MOSFET VT Measurement
• VT can be determined by plotting IDS vs. VGS, using a
low value of VDS
IDS
VGS
EE130/230A Fall 2013
Lecture 20, Slide 10
Long-Channel MOSFET I-V Summary
• In the ON state (VGS>VT for NMOS; VGS<VT for PMOS),
the inversion layer at the semiconductor surface forms
a “channel” for current to flow by carrier drift from
source to drain
In the linear region of operation (VDS < (VGSVT)/m):
VDS
I DS I Dlin WQinvv WQ inv eff WQ inv eff
L
mVDS
Qinv Coxe VGS VT
2
m 1
Cdep,min
Coxe
eff f VGS
In the saturation region of operation (VDS > (VGSVT)/m):
W
I DS I Dsat
Coxe eff (VGS VT ) 2 1 VDS VDSsat
2mL
EE130/230A Fall 2013
Lecture 20, Slide 11