Lecture 20
OUTLINE
The MOSFET (cont’d)
• Qualitative theory
• Field-effect mobility
• Long-channel I-V characteristics
Reading: Pierret 17.2, 18.3.4; Hu 6.3-6.6
Qualitative Theory of the NMOSFET
VGS < VT :
depletion layer
The potential barrier to electron flow from the source
into the channel region is lowered by applying VGS> VT Inversion-layer
“channel” is formed
VGS > VT :
Electrons flow from the
source to the drain by drift,
when VDS>0. (IDS > 0)
VDS  0
The channel potential
varies from VS at the source
end to VD at the drain end.
VDS > 0
EE130/230M Spring 2013
Lecture 20, Slide 2
MOSFET Linear Region of Operation
For small values of VDS (i.e. for VDS << VGVT),
I DS  WQinvv  WQ inv m eff

 VDS 
 WQ inv meff 

 L 
where meff is the effective carrier mobility
Hence the NMOSFET can be modeled as a resistor:
RDS
VDS
L


I DS Wmeff Coxe (VG  VT )
EE130/230M Spring 2013
Lecture 20, Slide 3
Field-Effect Mobility, meff
Scattering mechanisms:
• Coulombic scattering
• phonon scattering
• surface roughness
scattering
EE130/230M Spring 2013
Lecture 20, Slide 4
MOSFET Saturation Region of Operation
VDS = VGS-VT
VDS > VGS-VT
ID
• When VD is increased to be equal
to VG-VT, the inversion-layer
charge density at the drain end
of the channel equals 0, i.e. the
channel becomes “pinched off”
• As VD is increased above VG-VT,
the length DL of the “pinch-off”
region increases. The voltage
applied across the inversion layer
is always VDsat=VGS-VT, and so the
current saturates.
I Dsat  I DS V
EE130/230M Spring 2013
DS VDsa t
• If DL is significant compared to L,
then IDS will increase slightly with
VDS
increasing VDS>VDsat, due to
“channel-length modulation”
Lecture 20, Slide 5
Ideal MOSFET I-V Characteristics
Enhancement-Mode N-channel MOSFET
Linear
region
EE130/230M Spring 2013
Lecture 20, Slide 6
Impact of Inversion-Layer Bias
• When a MOS device is biased into inversion, a pn junction
exists between the surface and the bulk.
• If the inversion layer contacts a heavily doped region of the
same type, it is possible to apply a bias to this pn junction.
N+ poly-Si
+ + + + + + + +
SiO2
N+
- - - - - - - - -
p-type Si
EE130/230M Spring 2013
• VG is biased so that surface is inverted
• n-type inversion layer is contacted by N+
region
• If a bias VC is applied to the channel, a
reverse bias (VB-VC) is applied between
the channel and body
Lecture 20, Slide 7
Effect of VCB on fS, W and VT
• Application of a reverse body bias  non-equilibrium
 2 Fermi levels (one in n-type region, one in p-type region)
are separated by qVBC  fS is increased by VCB
• Reverse body bias widens W, increases Qdep and hence VT
2qN A Si (2fF  VCB ( y))
VT ( y)  VFB  VCB ( y)  2fF 
Cox
EE130/230M Spring 2013
Lecture 20, Slide 8
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 (2fF  VCB ( y))
VT ( y)  VFB  VCB ( y)  2fF 
Cox
• Channel inversion charge density
Qdep ( y) 

Qinv ( y)  Coxe VG  VFB  VCB ( y)  2fS 

C
oxe 

W
EE130/230M Spring 2013
Lecture 20, Slide 9
1st-Order Approximation
• If we neglect the variation of Qdep with y, then
Qdep  2qN A Si (2fF  VSB )
2qN A Si (2fF  VSB )
VT ( y)  VFB  VCB ( y)  2fF 
 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 (2fF  VSB )
VT  VFB  VSB  2fF 
Cox
The inversion charge density is then
Qinv  Coxe VG  VT  VSB  VCB ( y)  Coxe VG  VT  VS  VC ( y)
EE130/230M Spring 2013
Lecture 20, Slide 10
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

qm eff nWTinv
Qinv m eff W
VD
I DS dy    m eff WQinv (VC )dVC
I DS
I DS
VS
VD
W
  m eff  Qinv (VC )dVC
VS
L
VD
W
  m eff   Coxe VG  VT  VS  VC dVC
VS
L
VDS 
W

 m eff Coxe VG  VT 
VDS in the linear region

L
2 

EE130/230M Spring 2013
Lecture 20, Slide 11
Saturation Current, IDsat
(1st-order approximation)
IDS saturates when VD reaches VG-VT
 Set VD = VG-VT in the equation for ID
I Dsat
W

Coxe m eff (VG  VT ) 2
2L
for VD  VDsat  VG  VT
2qN A Si (2fF  VSB )
VT  VFB  VSB  2fF 
Cox
EE130/230M Spring 2013
Lecture 20, Slide 12
Problem with “Square Law Theory”
• Ignores variation in depletion width with distance y:
Qinv  Coxe VG  VT  VS  VC 
2qN A Si (2fF  VSB )
where VT  VFB  VSB  2fF 
Cox
EE130/230M Spring 2013
Lecture 20, Slide 13
Modified (Bulk-Charge) I-V Model
VG  VT
In linear region: VD  VDsat 
m
W
m
I Dlin  Coxe m eff (VG  VT  VDS )VDS
L
2
In saturation region: VD  VDsat
I Dsat
where m  1 
EE130/230M Spring 2013
Cdep,min
Coxe
 1
VG  VT

m
W

Coxe m eff (VG  VT ) 2
2mL
3Toxe
WT
Lecture 20, Slide 14
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 (2fF  VSB )
VT  VFB  VSB  2fF 
Cox
Usually, the terminal voltages for a MOSFET are all
referenced to the source voltage. In this case,
2qN A Si (2fF  VSB )
VT  VFB  2fF 
Cox
and the equations for IDS are
W
m
Coxe meff (VGS  VT  VDS )VDS
L
2
VDS  VDsat  VGS  VT  / m
I Dlin 
EE130/230M Spring 2013
Lecture 20, Slide 15
W
Coxe m 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 (2fF  VSB )
VT  VFB  2fF 
Cox
2qN A Si (2fF )
2qN A Si (2fF )
2qN A Si (2fF  VSB )
 VFB  2fF 


Cox
Cox
Cox



2qN A Si
 VT 0 
2fF  VSB  2fF  VT 0  g 2fF  VSB  2fF
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.
EE130/230M Spring 2013
Lecture 20, Slide 16

MOSFET VT Measurement
• VT can be determined by plotting IDS vs. VGS, using a
low value of VDS
IDS
VGS
EE130/230M Spring 2013
Lecture 20, Slide 17
Channel Length Modulation
• 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  VDsat
DL
  VDS  VDsat 
L
IDS
I Dsat 
W
Coxe m eff (VGS  VT ) 2 1   VDS  VDsat 
2mL
VDS
EE130/230M Spring 2013
Lecture 20, Slide 18
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 m eff  WQ inv m eff 

 L 

mVDS 

Qinv  Coxe VGS  VT 

2


m  1
Cdep,min
Coxe
m eff  f VGS 
In the saturation region of operation (VDS > (VGSVT)/m):
W
I DS  I Dsat 
Coxe m eff (VGS  VT ) 2 1   VDS  VDSsat 
2mL
EE130/230M Spring 2013
Lecture 20, Slide 19