Today
ESE370: Circuit-Level Modeling, Design,
and Optimization for Digital Systems
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Operating Regions (continued)
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Lec 8: September 18, 2015
MOS Transistor Operating Regions
Part 2
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Drain Induced Barrier Lowering
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Resistive
Saturation
Velocity Saturation
Subthreshold
Vth
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Channel Evolution - Increasing Vgs
Last Time…
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Threshold
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Linear Region
Voltage where strong inversion occurs # threshold
voltage
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Vth ~= 2ϕF
Engineer by controlling doping (NA)
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VGS>Vth and VDS small
#N &
φ F = φT ln% A (
$ ni '
COX =
εOX
tOX
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V2 %
I DS = µ nCOX W $(VGS −Vth ) VDS − DS '
L #
2 &
( )
€
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Voltage along Channel
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Channel Field
What does voltage along the channel look like?
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When voltage gap VG-Vx drops below Vth, drops out
of inversion
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What if VDS > VGS – Vth #VDS – VGS > Vth?
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Upper limit on current, channel is “pinched off”
VD −VS
x = VT
L
VG −VS −VT
V −V
x=
L = GS T L
VD −VS
VDS
VG −V (x) = VG −VS +
VDS > VGS −VT ⇒ x < L
x=0
x=L
VD −VS
x
L
V −V
VG −V (x) = VG −VS + D S x
L
V (x) = VS +
Vd
V(x)
Vs
x
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Saturation
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MOSFET – IV Characteristics
In saturation, VDS-effective=Vx= VGS-VT
VDS <VGS -VTH
" W %)
V2 ,
IDS = µn COX $ '+(VGS − VT )VDS − DS .
# L &*
2 !
VGS -Vth
IDS
Becomes:
VDS ≥VGS -VTH
2
" W %)
2
(VGS − VT ) ,.
IDS = µn COX $ '+(VGS − VT ) −
# L &+*
2
.-
€
IDS =
€
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µn COX " W %
$ ' (V − VT )
2 # L & GS
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VDS
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€
Preclass 1
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New Stuff
What is electrical field in channel?
Leff = 25nm,VDS = 1V
Field =
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VDS
Leff
Velocity:
v = F ⋅ µn
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Electron mobility: µn = 500cm / (V ⋅ s)
What is electron velocity?
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2
Moving Charge
Short Channel
Field =
!1$
I = # &V
"R%
v=µ⋅
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I increases
linearly in V
What’s I?
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ΔQ/Δt
Speed at which charge
moves
VDS
, v = µn ⋅ F
Leff
VDS " µ n
=$
Leff $# Leff
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%
''VDS
&
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Velocity increases
linearly in V
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Short Channel
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At what voltage do we hit the speed limit? (preclass
1d)
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Vdsat = voltage at which velocity (current) saturates
~ 105m/s
How does this relate to preclass 1b calculated
velocity?
Encounter velocity saturation when channel short
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Modern processes, L is short enough to reach this region
of operation
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Velocity Saturation
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Limited by scattering effects
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Increases with voltage
There is a limit to how fast carriers can move
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Velocity Saturation
Model assumes carrier velocity increases with field
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Increases with voltage
Are there limits to how fast things (including
electrons) can move?
What’s a moving
electron?
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Model assumes carrier velocity increases with field
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Velocity Saturation
Once velocity saturates:
! W $(
V2 +
I DS = µ nCOX # &*(VGS −Vth ) VDS − DS " L %)
2 ,
! V
$
(
+
V
VDS = VDSAT ⇒ I DS = # µ n DSAT & COX W *(VGS −Vth ) − DSAT )
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L %
2 ,
(
+
Lv
V
VDSAT ≈ SAT ⇒ I DS ≈ vsat COX W *(VGS −Vth ) − DSAT )
µn
2 ,
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Long Channel
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Short Channel
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Velocity Saturation
Velocity Saturation
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Once velocity saturates we can still increase current
with parallelism
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Effectively make a wider device
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Below Threshold
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Subthreshold
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Transition from insulating to conducting is nonlinear, but not abrupt
Current does flow
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Subthreshold
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If VGS < Vth ,
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W/L dependence follow from resistor behavior
(parallel, series)
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! VGS −Vth $
#
&
" nkT /q %
! VDS $ $
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#
&
#1− e"−kT /q % & (1+ λVDS )
#
&
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%
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Not shown explicitly in text
λ is a channel-length modulation parameter
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Defined empirically
! V −V $
! VDS $ $
#
&
! W $ # GS th & !
I DS = I S # & e" nkT /q % #1− e"−kT /q % & (1+ λVDS )
#
&
"L%
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Current is from the parasitic NPN BJT transistor
when gate is unbiased and there is no conducting
channel
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Subthreshold
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!W $
I DS = I S # & e
"L%
But exponentially dependent on VGS
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Steady State
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Leakage
What current flows in steady state?
What causes (and determines)
the magnitude of current flow?
Which device?
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Subthreshold Slope
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kT
S = n$ ' ln(10)
# q&
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Exponent in VGS determines how steep the turnon
is
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kT
S = n$ ' ln(10)
# q&
Units: V/dec
Every S Volts, IDS is scaled by factor of 10
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€
!W $
I DS = I S # & e
"L%
Units: V/dec
Every S Volts, IDS is scaled by factor of 10
€
! VGS −Vth $
#
&
" nkT /q %
! VDS $ $
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#
&
#1− e"−kT /q % & (1+ λVDS )
#
&
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%
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n – depends on electrostatics
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IDS vs. VGS
n=1 # S=60mV at Room Temp. (ideal)
n=1.5 # S=90mV
Single gate structure showing S=90-110mV
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IDS vs. VGS
(Logscale)
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Subthreshold Slope
Exponent in VGS determines how steep the turnon
is
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Call this steady-state current flow leakage
Idsleak
S
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(Logscale)
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Subthreshold Slope
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If S=100mV and Vth=300mV,
what is Ids(Vgs=300mV)/Ids(Vgs=0V) ?
Threshold
What if S=60mV?
" kT %
S = n$ ' ln(10)
# q&
! V −V $
! VDS $ $
#
&
! W $ # GS th & !
I DS = I S # & e" nkT /q % #1− e"−kT /q % & (1+ λVDS )
#
&
€ "L%
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%
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Threshold
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VDS impact
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In practice, VDS impacts state of channel
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VDS impact
Increasing VDS, already depletes portions of channel
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VDS impact
Describe VT as a constant
Induce enough electron collection to invert channel
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Increasing VDS, already depletes portions of channel
Need less charge, less voltage to create inversion
layer
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Drain-Induced Barrier Lowering (DIBL)
DIBL Impact
VT
VDS
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In a Gate?
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Which device, has large Vds?
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In a Gate
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PMOS
VDS largest for off device
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Easier to turn on
#
&
V
I DS ≈ ν sat COX W %VGS −Vth − DSAT (
$
2 '
Speed of switching?
Leakage?
Penn ESE370 Fall2015 – Khanna
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VDS largest for output charging/discharging device
Vin=Vdd ?
Vin=Gnd ?
How effect
operation?
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In a Gate
What does it impact most?
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Penn ESE370 Fall2015 – Khanna
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Analagous phenomena to NMOS
Signs different
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Reason based on oppositely charged carriers
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Easier to turn on
Leak more
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Negative Vth
! V −V $
! VDS $ $
#
&
! W $ # GS th & !
I DS = I S # & e" nkT /q % #1− e"−kT /q % & (1+ λVDS )
#
&
"L%
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%
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Big Idea
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Admin
3 Regions of operation for MOSFET
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Text 3.3.2 – highly recommend read
Office Hours: M (Khanna), T (Giesen)
HW4 due Wednesday
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Midterm 1 Review session on Thursday
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Midterm 1 Monday 9/28
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Subthreshold
Linear
Saturation
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Pinch Off
Velocity Saturation, DIBL
"  Short channel
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If you haven’t looked at it yet, you’re behind!
5pm? 6pm? 7pm?
No Lecture
Midterms from 2010, 2011, 2012, 2013, 2014
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All online with and without answers
Suggest start without answers
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