Madan Mohan Malaviya Univ.

of Technology, Gorakhpur

VLSI Design (BEC-41)

(Unit-1, Lecture-3)

Presented By:
Prof. R. K. Chauhan
Department of Electronics and Communication Engineering
16-07-2020 Side 1
MOSFET operation: linear region
• The MOSFET consists
– A MOS capacitor, two pn junction adjacent to the channel
– The channel is controlled to the MOS gate
• The carrier (electron in nMOSFET)
– Entering through source, controlling by gate, leaving through drain
• To ensure that both p-n junctions are reverse-biased initially
– The substrate potential is kept lower than the other three terminal potentials
• When 0<VGS<VT0
– G-S region depleted, G-D region depleted
– No current flow
• When VGS>VT0
– Conduction channel formed
– Capable of carrying the drain current
– As VDS=0
• ID=0
– As VDS>0 and small
• ID proportional to VDS
• Flowing from S to D through the conducting channel
• The channel act as a voltage controlled resistor
• The electron velocity much lower than the drift velocity limit
• As VDS↑ the inversion layer charge and the channel depth at the drain end start to
decrease

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MOSFET operation: saturation region
• For VDS=VDSAT
– The inversion charge at the drain is
reduced to zero
– Pitch off point
• For VDS>VDSAT
– A depleted surface region forms
adjacent to the drain
– As further increases VDS this
depletion region grows toward the
source
– The channel-end remains essentially
constant and equal to VDSAT
– The pitch-off (depleted) section
• Absorbing most of the excess voltage
drop, VDS-VDSAT
• A high-field forms between the
channel-end of the drain boundary
– Accelerating electrons, usually
reaching the drift velocity limit

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MOSFET current-voltage characteristics-gradual
channel approximation (GCA)(1)
• Considering linear mode operation
– VS=VB=0, the VGS and VDS are the external parameters controlling the drain
current ID
– VGS > VT0 (assume constant through the channel) to create a conducting inversion layer
– Defining
• X-direction: perpendicular to the surface, pointing down into the substrate
• Y-direction: parallel to the surface
– The y=0 is at the source end of the channel
– Channel voltage with respect to the source, Vc(y)
– Assume the electric field Ey is dominant compared with Ex
• This assumption reduced the current flow in the channel to the y-direction only
– Let QI(y) be the total mobile electron charge in the surface inversion layer
• QI(y)=-Cox[VGS-Vc(y)-VT0]

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MOSFET current-voltage characteristics-gradual
channel approximation (GCA)(2)
Assumeing that all mobile electrons in the inversion layer has a constant surfacr mobility μn
dy
dR = − (mimus sign is due to the negative polarity of the inversion layer charge QI )
W ⋅ μn ⋅ QI (y)
The electron surface mobility μn dependents on the doping concentration of the channel region,
and its magnitude is typically about one - half of that of the bulk electron mobility
ID
dVC = I D ⋅ dR = - ⋅ dy
W ⋅ μn ⋅ QI (y)
L VDS
∫
0
I D ⋅ dy = − W ⋅ n ∫0
QI ( y ) ⋅ dVC
VDS
ID ⋅ L = W ⋅ n ⋅ Cox ∫ VGS − VC − VT 0 ⋅ dVC
0

⋅ Cox W
ID = ⋅ ⋅ 2 ⋅ VGS − VT 0 VDS − VDS
n 2

2 L
k' W
I D = ⋅ ⋅ 2 ⋅ VGS − VT 0 VDS − VDS2
where k ' = μnCox
2 L
k W
I D = ⋅ 2 ⋅ VGS − VT 0 VDS − VDS
2
where k = k ' ⋅
2 L

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Example 4

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MOSFET current-voltage characteristics-gradual
channel approximation (GCA)-saturation region

• For VDS≥VDSAT=VGS-VT0
– ⋅ Cox W 2
I D ( sat ) = n
⋅ ⋅ 2 ⋅ VGS − VT 0 ⋅ VGS − VT 0 − VGS − VT 0
2 L
⋅C W 2
= n ox ⋅ ⋅ VGS − VT 0
2 L
– The drain current becomes a function only of VGS, beyond the saturation
boundary

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 Channel length modulation
The inversion layer charge at the source end of the channel is
QI (y = 0 ) = -Cox ⋅ VGS -VT 0
and the inversion layer charge at the drain end of the channel is
QI (y = L) = -C ox ⋅ VGS -VT 0 − VDS
Note that at the edge of saturation , VDS = VDSAT = VGS -VT 0
The inversion layer charge at the drain end become very small
QI (y = L) ≈ 0
The effective channel length L' = L-Δ-
where ΔΔ is the length of the channel segment wi th QI = 0
μn Cox W 2
I D(sat) = ⋅ ' ⋅ VGS − VT 0
2 L
⎛ ⎞
⎜ 1 ⎟μC W
=⎜ ⎟ n ox ⋅ ' ⋅ VGS − VT 0 2
I D(sat)
⎜ 1 − ΔL ⎟ 2 L
⎜ ⎟
⎝ L ⎠
ΔL ∝ VDS − VDSAT
ΔL
We use 1 − ≈ 1 − λ ⋅ VDS , λ channel length modulation coefficient
L
Assuming that λλ DS << 1
μn ⋅ Cox W 2
I D(sat) = ⋅ ⋅ VGS − VT 0 ⋅ 1 + λVDS
2 L

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Substrate bias effect
• The discussion in the previous has been done under the assumption
– The substrate potential is equal to the source potential, i.e. VSB=0
• On the other hand
– the source potential of an nMOS transistor can be larger than the substrate
potential, i.e. VSB>0
– VT (VSB ) = VT 0 + ⋅ 2 F + VSB − 2 F
⋅ Cox W
I D ( lin ) = n
⋅ ⋅ 2 ⋅ VGS − VT (VSB ) VDS − VDS
2

2 L
⋅C W 2
I D ( sat ) = n ox ⋅ ⋅ VGS − VT (VSB ) ⋅ 1 + ⋅VDS
2 L

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Current-voltage equation of n-, p-channel MOSFET

For n - channel MOSFET

I D = 0, for VGS < VT
⋅ Cox W
I D ( lin ) = n
⋅ ⋅ 2 ⋅ VGS − VT VDS − VDS
2
for VGS ≥ VT
2 L
and VDS < VGS -VT
⋅ Cox W 2
I D ( sat ) = n
⋅ ⋅ VGS − VT ⋅ 1 + ⋅ VDS for VGS ≥ VT
2 L
and VDS ≥ VGS -VT
For p - channel MOSFET
I D = 0, for VGS > VT
⋅ Cox W
I D ( lin ) = n
⋅ ⋅ 2 ⋅ VGS − VT VDS − VDS
2
for VGS ≤ VT
2 L
and VDS > VGS -VT
⋅ Cox W 2
I D ( sat ) = n
⋅ ⋅ VGS − VT ⋅ 1 + ⋅ VDS for VGS ≤ VT
2 L
and VDS ≤ VGS -VT
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Measurement of parameters- kn, VT0, and
• The VSB is set at a constant value
– The drain current is measured for different values of VGS
– VDG=0
• VDS>VGS-VT is always satisfied saturation mode
• Neglecting the channel length modulation effect
– kn 2 kn
I D ( sat ) =
⋅ V GS − V T 0 , I D = ⋅ V GS − V T 0
2 2
– Obtaining the parameters kn, VT0, and γ
– VT (VSB ) − VT 0
=
2 F + VSB − 2 F

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Measurement of parameters-
• The voltage VGS is set to VT0+1
• The voltage VDS is chosen sufficiently large (VDS>VGS-VT0) that the transistor
operates in the saturation mode, VDS1, VDS2
– ID(sat)-(kn/2)(VGS-VT0)2(1+λVDS)
• Since VGS=VT0+1 ID2/ID1=(1+λVDS2)/ (1+λVDS1)
• Which can be used to calculate the channel length modulation coefficient λ
• This is in fact equivalent to calculating the slope of the drain current versus drain
voltage curve in the saturation region
– The slope is λkn/2

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Example 5

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