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 (2F  VCB ( y))
VT ( y)  VFB  VCB ( y)  2F 
Cox
• Channel inversion charge density

Qdep ( y ) 
Qinv ( y )  Coxe VG  VFB  VCB ( y)  2S 

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 (2F  VSB )
2qN A Si (2F  VSB )
VT ( y)  VFB  VCB ( y)  2F 
 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 (2F  VSB )
VT  VFB  VSB  2F 
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 (2F  VSB )
VT  VFB  VSB  2F 
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 (2F  VSB )
where VT  VFB  VSB  2F 
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 (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  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 (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.
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 < (VGSVT)/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 > (VGSVT)/m):
W
I DS  I Dsat 
Coxe  eff (VGS  VT ) 2 1   VDS  VDSsat 
2mL
EE130/230A Fall 2013
Lecture 20, Slide 11