Lecture 20
description
Transcript of Lecture 20
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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
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Qualitative Theory of the NMOSFETdepletion layer
The potential barrier to electron flow from the source into the channel region is lowered by applying VGS> VT
Electrons flow from the source to the drain by drift, when VDS>0. (IDS > 0)
The channel potential varies from VS at the source end to VD at the drain end.
VGS < VT :
VGS > VT :
VDS 0
VDS > 0
EE130/230M Spring 2013 Lecture 20, Slide 2
Inversion-layer “channel” is formed
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MOSFET Linear Region of OperationFor small values of VDS (i.e. for VDS << VGVT),
where eff is the effective carrier mobility
Hence the NMOSFET can be modeled as a resistor:
L
VWQWQvWQI DS
effinveffinvinvDS
)( TGoxeeffDS
DSDS VVCW
L
I
VR
EE130/230M Spring 2013 Lecture 20, Slide 3
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Field-Effect Mobility, eff
Scattering mechanisms:
• Coulombic scattering
• phonon scattering
• surface roughness scattering
EE130/230M Spring 2013 Lecture 20, Slide 4
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• 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 L of the “pinch-off” region increases. The voltage applied across the inversion layer is always VDsat=VGS-VT, and so the current saturates.
• If L is significant compared to L, then IDS will increase slightly with increasing VDS>VDsat, due to “channel-length modulation”
DsatDS VVDSDsat II
VDS = VGS-VT
VDS > VGS-VT
EE130/230M Spring 2013 Lecture 20, Slide 5
ID
VDS
MOSFET Saturation Region of Operation
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Ideal MOSFET I-V Characteristics
Linearregion
Enhancement-Mode N-channel MOSFET
EE130/230M Spring 2013 Lecture 20, Slide 6
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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
p-type Si
-- - - --
+ + + + + +
N+
+ +
-- -SiO2
• 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
EE130/230M Spring 2013 Lecture 20, Slide 7
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Effect of VCB on S, 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 S is increased by VCB
• Reverse body bias widens W, increases Qdep and hence VT
ox
CBFSiAFCBFBT C
yVqNyVVyV
))(2(22)()(
EE130/230M Spring 2013 Lecture 20, Slide 8
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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
• Channel inversion charge density
oxe
depSCBFBGoxeinv C
yQyVVVCyQ
)(2)()(
ox
CBFSiAFCBFBT C
yVqNyVVyV
))(2(22)()(
W
EE130/230M Spring 2013 Lecture 20, Slide 9
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1st-Order Approximation• If we neglect the variation of Qdep with y, then
where VT is defined to be the threshold voltage at the source end:
The inversion charge density is then
)2(2 SBFSiAdep VqNQ
)()(
)2(22)()(
yVVVyV
VVC
VqNyVVyV
CBSBTT
SBSBox
SBFSiAFCBFBT
EE130/230M Spring 2013 Lecture 20, Slide 10
)()( yVVVVCyVVVVCQ CSTGoxeCBSBTGoxeinv
ox
SBFSiAFSBFBT C
VqNVVV
)2(22
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NMOSFET Current (1st-order approx.)• Consider an incremental length dy of the channel. The voltage
drop across this region is
DSDS
TGoxeeffDS
V
V CCSTGoxeeff
V
V CCinveffDS
V
V CCinveff
L
DS
effinv
DS
inveffDS
invDSDSC
VV
VVCL
WI
dVVVVVCL
W
dVVQL
WI
dVVWQdyI
WQ
dyI
nWTq
dyI
WT
dyIdRIdV
D
S
D
S
D
S
2
)(
)(0
in the linear region
EE130/230M Spring 2013 Lecture 20, Slide 11
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2)(2 TGeffoxeDsat VVCL
WI
IDS saturates when VD reaches VG-VT
Saturation Current, IDsat (1st-order approximation)
TGDsatD VVVV for
ox
SBFSiAFSBFBT C
VqNVVV
)2(22
EE130/230M Spring 2013 Lecture 20, Slide 12
Set VD = VG-VT in the equation for ID
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Problem with “Square Law Theory”• Ignores variation in depletion width with distance y:
where
CSTGoxeinv VVVVCQ
EE130/230M Spring 2013 Lecture 20, Slide 13
ox
SBFSiAFSBFBT C
VqNVVV
)2(22
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Modified (Bulk-Charge) I-V Model
T
oxe
oxe
dep
W
T
C
Cm
311 min, where
23 since OSiSi
DSDSTGeffoxeDlin VVm
VVCL
WI )
2(
2)(2 TGeffoxeDsat VVCmL
WI
In saturation region:m
VVVV TG
DsatD
In linear region:m
VVVV TG
DsatD
EE130/230M Spring 2013 Lecture 20, Slide 14
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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:
ox
SBFSiAFSBFBT C
VqNVVV
)2(22
Usually, the terminal voltages for a MOSFET are all referenced to the source voltage. In this case,
and the equations for IDS areox
SBFSiAFFBT C
VqNVV
)2(22
DSDSTGSeffoxeDlin VVm
VVCL
WI )
2( 2)(
2 TGSeffoxeDsat VVCmL
WI
mVVVV TGSDsatDS / mVVVV TGSDsatDS /EE130/230M Spring 2013 Lecture 20, Slide 15
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The Body EffectNote that VT is a function of VSB:
where is the body effect parameter
When the source-body pn junction is reverse-biased, |VT| is increased. Usually, we want to minimize so that IDsat will be the same for all transistors in a circuit.
FSBFTFSBFox
SiAT
ox
SBFSiA
ox
FSiA
ox
FSiAFFB
ox
SBFSiAFFBT
VVVC
qNV
C
VqN
C
qN
C
qNV
C
VqNVV
22222
)2(2)2(2)2(22
)2(22
00
EE130/230M Spring 2013 Lecture 20, Slide 16
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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
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Channel Length Modulation• Recall that as VDS is increased above VDsat, the width L of the
depletion region between the pinch-off point and the drain increases, i.e. the inversion layer length decreases.
L
L
LLLIDsat 1
11
DsatDS VVL
DsatDS VVL
L
DsatDSTGSeffoxeDsat VVVVCmL
WI 1)(
22
EE130/230M Spring 2013 Lecture 20, Slide 18
IDS
VDS
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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):
In the saturation region of operation (VDS > (VGSVT)/m):
L
VWQWQvWQII DS
effinveffinvinvDlinDS
DSsatDSTGSeffoxeDsatDS VVVVCmL
WII 1)(
22
2DS
TGSoxeinv
mVVVCQ
oxe
dep
C
Cm min,1 GSeff Vf
EE130/230M Spring 2013 Lecture 20, Slide 19