Lecture #36
OUTLINE
The MOSFET:
• Qualitative theory
• Long-channel I-V (“Square-Law” Theory)
Reading: Textbook Chapter 17.2, 18.3.4
Spring 2007
EE130 Lecture 36, Slide 1
Qualitative Theory of the NMOSFET
VGS < VT:
depletion layer
The potential barrier to electron flow from the source
into the channel is lowered by applying VGS> VT
VGS > VT :
Electrons flow from the
source to the drain by drift,
when VDS>0. (IDS > 0.)
VDS  0
VDS > 0
V 
I DS  WQinvv  WQ inv  eff   WQ inv  eff  DS 
 L 
Spring 2007
EE130 Lecture 36, Slide 2
The channel potential
varies from VS at the
source end to VD at the
drain end.
(The inversion layer can be
modeled as a resistor.)
VGS > VT :
VDS = VGS-VT
VDS > VGS-VT
When VD is increased to be equal to
VG-VT, the inversion-layer charge
density at the drain end of the
channel equals zero, 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
DS VDsa t
If DL is significant compared to L, then
IDS will increase slightly with increasing
VDS>VDsat, due to “channel-length
modulation”
Spring 2007
EE130 Lecture 36, Slide 3
Ideal MOSFET I-V Characteristics
(Enhancement Mode NMOS Transistor)
Saturation
region
Linear
region
Spring 2007
EE130 Lecture 36, Slide 4
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
• VG is biased so that surface is inverted
+ + + + + + + +
SiO2
N+
- - - - - - - - -
p-type Si
Spring 2007
• 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 & body
EE130 Lecture 36, Slide 5
Effect of VCB on fS, W, and VT
• Application of a reverse body bias  non-equilibrium
– 2 Fermi levels (one for n-region, one for p-region)
• separation = qVBC fS is increased by VCB
• Reverse body bias widens W, increases Qdep
Qinv decreases with increasing VCB, for a given VGB
Spring 2007
2qN A Si (2fF  VCB )
VT  VFB  VCB  2fF 
Cox
EE130 Lecture 36, Slide 6
NMOSFET I-V Characteristics
• 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  VFB  VCB ( y)  2fF 
Cox
• Channel inversion charge density
Qdep ( y) 

Qinv ( y)  Coxe VG  VFB  VCB ( y)  2fS 

C
oxe 

W
Spring 2007
EE130 Lecture 36, Slide 7
1st-Order Approximation
• If we neglect the variation of Qdep with y, then
Qdep  2qN A Si (2f F  VSB )
 Qinv  Coxe VG  VT  VSB  VCB 
Qinv  Coxe VG  VT  VS  VC 
where VT = threshold voltage at the source end:
2qN A Si (2fF  VSB )
VT  VFB  VSB  2fF 
Cox
Spring 2007
EE130 Lecture 36, Slide 8
NMOSFET Current (1st-order approx.)
• Consider an incremental length dy in 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
VS
VD
W
I DS    eff  Qinv (VC )dVC
VS
L
VDS 
W

I DS   eff Coxe VG  VT 
VDS in the linear region

L
2 

W
I DS  I Dsat 
Coxe  eff (VG  VT ) 2 in the saturation region
2L
Spring 2007
EE130 Lecture 36, Slide 9
Saturation Current, IDsat
• saturation region:
VD  VDsat  VG  VT
I Dsat
W

Coxe  eff (VG  VT ) 2
2L
2qN A Si (2fF  VSB )
VT  VFB  VSB  2fF 
Cox
Spring 2007
EE130 Lecture 36, Slide 10