Lecture 20
description
Transcript of Lecture 20
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 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
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
Field-Effect Mobility, eff
Scattering mechanisms:
• Coulombic scattering
• phonon scattering
• surface roughness scattering
EE130/230M Spring 2013 Lecture 20, Slide 4
• 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
Ideal MOSFET I-V Characteristics
Linearregion
Enhancement-Mode N-channel MOSFET
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
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
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
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
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
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
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
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
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
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
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
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 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
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