noise in short channel mosfetsusers.wpi.edu/~mcneill/papers/cicc_2009_slides.pdf · noise in short...
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Noise in Short Channel MOSFETs
John A. McNeillWorcester Polytechnic Institute (WPI),
Worcester, MA [email protected]
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Overview• Creativity in Analog / Mixed Signal IC Design• DSM CMOS Effects on Analog Design• Fundamental Noise Sources• Applications• Conclusion
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Overview• Creativity in Analog / Mixed Signal IC Design
–Role of Creativity• DSM CMOS Effects on Analog Design• Fundamental Noise Sources• Applications• Conclusion
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Need for Creativity:"… every company is betting on the
ingenuity of its engineers to create theproducts that will conquer the market. Andyet engineers' conferences and travels arecut, as if they don't make any contributionto creativity - the creativity that is required,ironically, at the very moment that itssources of inspiration are being cut."
- Willy Sansen,IEEE SSCS Magazine,
Summer 2009, p.4
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Why be creative?• Need
– Easy problems solved already– Tough problems need creative solution
• Dealing with environment of change– Coping vs. thriving
• Human nature– Fun!
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Career ClassificationCREATIVE USEFUL
GOOD PAY
ENGINEER
PROFESSOR TEACHERNURSE
ARTISTPOET
DOCTORADVERTISING
INVESTMENT BANKERLAWYER
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Creativity Resources
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Creativity Framework
Explorer
Artist
Judge
Warrior
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Example: Time (Stages of project)
Explorer
Artist
Judge
Warrior
Background Research
Brainstorm Options
Choose Solution
Implement Design
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Creativity Framework
Explorer
Artist
Judge
Warrior
Seek out new informationSurvey the landscapeGet off the beaten pathPoke around in unrelated areasGather lots of ideasShift your mindsetDon't overlook the obviousLook for unusual patterns
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Creativity Framework
Explorer
Artist
Judge
Warrior
Create something originalMultiply optionsUse your imaginationAsk "what if" questionsPlay with ideasLook for hidden analogiesBreak the rulesLook at things backwardChange contextsPlay the fool
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Creativity Framework
Explorer
Artist
Judge
Warrior
Evaluate optionsAsk what's wrongWeigh the riskEmbrace failureQuestion assumptionsLook for hidden biasBalance reason and hunchesMake a decision!
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Creativity Framework
Explorer
Artist
Judge
Warrior
Put decision into practiceCommit to a realistic planGet helpFind your real motivationSee difficulty as challengeAvoid excusesPersist through criticismSell benefits not featuresMake it happenLearn from every outcome
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Example: Modes of Thinking
Explorer
Artist
Judge
Warrior
DivergentSoft
Qualitative
ConvergentHard
Quantitative
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Why a Creativity Model?
Education• Standardized-test-numbed students• Paralysis in face of open-ended problem
Designer• Awareness of strengths, weaknesses• Recognize preferences
Not Right or Wrong!• One way of looking at process• Orchard analogy
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Creativity Framework
Explorer
Artist
Judge
Warrior Learn from every outcome
Question assumptions
Survey the landscape
Break the rules
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Overview• Creativity in Analog / Mixed Signal IC Design• DSM CMOS Effects on Analog Design
–Short Channel Effects–Noise Behavior
• Fundamental Noise Sources• Applications• Conclusion
Survey the landscape
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Good Old Days
• Large strong inversion region– "Square law", easy hand analysis
Op 't Eynde and Sansen, "Design and Optimization of CMOS Wideband Amplifiers," CICC 1989
W/L
ID
WEAKINVERSION
VELOCITYSATURATION
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TSMC L=0.25µm process
• Square law• Graphical / numerical analysis
W[µm]
ID [µA]100
101
102
103
104
10-6 10-5 10-4 10-3 10-2
WEAKINVERSION
VELOCITYSATURATION
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MOSFET Noise
Y. Tsividis, "Operation and Modeling of the MOS Transistor" New York: Oxford University Press, 2008.
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MOSFET Noise p.s.d.
• Saturation, strong inversion operation• Where does factor γ=2/3 come from?
[A2/Hz]
!
in2
= 4"kTgm =8
3kTgm
1/f REGION WHITE NOISE REGION
Y. Tsividis, "Operation and Modeling of the MOS Transistor" New York: Oxford University Press, 2008.
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Submicron CMOS: Noise behavior
⇒ Gamma factor γ > 2/3 ?!?Disagreement with long channel model?
Navid, Lee, and Dutton," A Circuit-Based Noise Parameter Extraction Technique for MOSFETs," ISCAS 2007, pp. 3347-3350
Question assumptions
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Overview• Creativity in Analog / Mixed Signal IC Design• DSM CMOS Effects on Analog Design• Fundamental Noise Sources
–Shot Noise–Thermal Noise
• Applications• Conclusion
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Shot Noise• Current noise density for DC current IDC
• Where does this come from?• Key assumption:
–Electron arrivals independent events!
in2
= 2qeIDC
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Shot Noise
• What is current measured by ammeter?
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Shot Noise
• What is current measured by ammeter?
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Ramo-Shockley Theorem
• Current measured by ammeter:–Randomly arriving pulses with area qe
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Poisson Process
• Average arrival rate λ [sec-1]• Average DC current:
• Autocorrelation: time domain description ofrandom process
!
IDC = "qe
!
"qe2
#T
AUTOCORRELATION!
qeIDC
"T=
!
IDC
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Shot Noise Power Spectral Density
• Wiener-Khinchine theorem–Autocorrelation → frequency domain p.s.d
• Frequency domain–For frequencies < 1/τT
!
qeIDC
"T!
2qeIDC
!
qeIDC
!
in2
= 2qeIDC
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Shot Noise Power Spectral Density• Key Points:
–Discrete nature of charge is essential–Carrier transits are independent events–Carriers do not interact with each other or
with any medium–Temperature not a factor
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Thermal Noise
• Current noise density for resistor
• Where does this come from?• Assumption:
–Carriers in thermal equilibrium!
in
2
=4kT
R
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Thermal Noise in Resistor
• Assumption:–Carriers in thermal equilibrium
• Random velocity vectors v• Only vx component contributes to current
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Boltzmann's Constant k• k = 1.38 E-23 J/K Meaning?• Thermodynamics: Equipartition theorem
–Independent energy storage modes in asystem at equilibrium have averageenergy of kT/2
–Equivalent statements:
"Temperaturein this room
is 293K"
"Average kinetic energy (in each of x, y,z directions) for each air molecule in
this room is 2.02E-21 joule"
!
kT
2=1.38E " 23 J K[ ]( ) 293 K[ ]( )
2= 2.02E " 21 J[ ]
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Thermal Noise
0.1 µm/ps vxVelocity (rms) 1 ps τcMean free time0.1 µm lcMean free path
• Approximate collision statistics:
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Thermal Noise
• Consider "slice" equal to mean free path lc• During one mean free time τc
–On average, half of carriers exit each way:IAVG+ = IAVG-
• Shot noise components is+ = -is- correlated–Noise current from "slice" is = 2is+
Sarpeshkar, Delbruck, and Mead, "White noise in MOS transistors and resistors," IEEE Circuits & Devices Magazine, Nov. 1993
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Thermal Noise
• Sum (independent) contributions from slices• Noise current seen by external ammeter im(s)
reduced by current divider factor:ΔR of slice, total resistance R = R1 + ΔR + R2
• Relating to R using mobility definition gives
!
in
2
=4kT
RSarpeshkar, Delbruck, and Mead, "White noise in MOS transistors and resistors," IEEE Circuits & Devices Magazine, Nov. 1993
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Thermal Noise (Alternative)
• Equipartition, rms energy in capacitor:
• Integrate noise p.s.d. over noise bandwidth:
• Equate:
!
kT
C= in
2 1
4RC" in
2=4kT
R
!
1
2Cv
2=kT
2" v
2=kT
C
!
v2 = inR( )
2 "
2
1
2"RC
#
$ %
&
' ( ) v
2 = in2 1
4RC
!
1
2"RC
!
"
2f#3dB
!
inR( )2
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Thermal Noise Power Spectral Density• Key Points:
–Discrete nature of charge is not essential• Can also be derived from equipartition
only (e.g. kT/C noise)–Carrier scattering: interact with medium,
thermal equilibrium–Carrier transits are not independent due to
interaction with medium–Temperature is important to determine
carrier average kinetic energy / velocity
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Overview• Creativity in Analog / Mixed Signal IC Design• DSM CMOS Effects on Analog Design• Fundamental Noise Sources• Application
–MOSFET Noise–Oscillator Jitter
• Conclusion
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!
in2
= 4"kTgm =8
3kTgm
Y. Tsividis, "Operation and Modeling of the MOS Transistor" New York: Oxford University Press, 2008.
MOSFET Channel Noise Density
• Where does this come from?• Assumption:
–Resistive channel segments
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MOSFET Noise Analysis
• Model: Thermal noise dv for differentialsegment dx of MOSFET channel
• Integrate over channel length L• Gamma factor γ = 2/3 falls out of integral
A. Jordan and N. Jordan, "Theory of noise in MOS devices," IEEE Trans. Electron Devices, March, 1965
SOURCEDRAINNOISE
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MOSFET Noise Analysis
• Key assumption:–Carrier behavior in channel determined
by mobility (resistive) behavior
–What if it's not a resistor?
Ask "what if" questions
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Velocity Saturation
• Deviation from mobility model at high field–"High field" ⇔ Small dimensions
Y. Tsividis, "Operation and Modeling of the MOS Transistor" New York: Oxford University Press, 2008.
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MOSFET Potential Energy (L ~ µm)
1. Carrier injection into channel2. Low field motion modeled by mobility3. Velocity saturated region
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MOSFET Potential Energy (L < µm)
• Velocity saturated region is a greaterfraction of channel
• Carriers still interact due to collisions
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MOSFET Potential Energy (L << µm)
• Channel length L ~ mean free path lc• "Ballistic": no interaction due to collisions• No thermal equilibrium
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L < lc "Breaking the Rules"
• L < mean free path lc• No thermal equilibrium• No reason to expect any
validity for a thermalnoise / resistance modelthat assumed mobilityand thermal equilibrium
• Behavior dominated by statistics of carrierinjection at source
– Shot noise! But not full shot noise:– Presence of injected carrier modifies
potential profile; changes probability ofinjection
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Analogy: Bipolar Transistor
• Output current noise ino for isolated bipolartransistor is full shot noise inc of collector current
• With degeneration resistor: Not full shot noise:• Voltage drop across RE modifies vBE ; feedback
reduces variation in ino due to inc
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Submicron CMOS: Noise behavior
⇒ Don't interpret as γ increase⇒ Interpret as shot noise suppression
Navid, Lee, and Dutton," A Circuit-Based Noise Parameter Extraction Technique for MOSFETs," ISCAS 2007, pp. 3347-3350
Shot noiseprediction
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Overview• Creativity in Analog / Mixed Signal IC Design• DSM CMOS Effects on Analog Design• Fundamental Noise Sources• Application
–MOSFET Noise–Oscillator Jitter
• Conclusion
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Jitter Example: Ring Oscillator
• Time-domain noise (jitter)on clock transitions
• Characterized by standarddeviation σ (ps rms)
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Jitter Example: Ring Oscillator
• Plot jitter vs. time interval ∆T• Increases as square root: jitter delay• κ frequency-independent figure-of-merit
McNeill and Ricketts, "The Designer's Guide to Jitter in Ring Oscillators," Springer, 2009
!
" = # $T
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Jitter at the Gate Delay Level
• MOSFET noise adds uncertainty to gate delay Td• Statistics of MOSFET noise can be related to
oscillator figure-of-merit κ
McNeill and Ricketts, "The Designer's Guide to Jitter in Ring Oscillators," Springer, 2009
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How to Improve Jitter?
• Burn more power• Oscillator figure-of-merit κ of form
• Derived from thermal noise model• Intuitively, as oscillator power increases, random
thermal energy is a smaller fraction of waveform
McNeill and Ricketts, "The Designer's Guide to Jitter in Ring Oscillators," Springer, 2009
!
" #kT
POWER
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Oscillator Jitter κ vs. W
• Scales as predicted
!
" # W
!
"
Chengxin Liu, "Jitter in Oscillators …," PhD Dissertation, WPI, 2006
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How to Improve Jitter?
• Burn more power• Oscillator figure-of-merit κ of form
• Derived from thermal noise model• How does this behave as L shrinks?
McNeill and Ricketts, "The Designer's Guide to Jitter in Ring Oscillators," Springer, 2009
!
" #kT
POWER
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Oscillator Jitter κ vs. L
• Deviation from predicted for L < 1µm• Inflection or minimum?
!
" # 1 L
!
"
Chengxin Liu, "Jitter in Oscillators …," PhD Dissertation, WPI, 2006
?
?
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Overview• Creativity in Analog / Mixed Signal IC Design• DSM CMOS Effects on Analog Design• Fundamental Noise Sources• Applications• Conclusion
Learn from every outcome
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DSM CMOS Conclusions
• Survey the landscape–Noise behavior changes for short L
• Question assumptions–Mobility model
• Ask "what if" questions–What if it's not a resistor?
• Learn from every outcome–Jitter example: Scaling may not provide
benefits for analog as one might expectfrom long channel model
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Add Complexity
Eliminate Complexity
Design Drivers in DSM CMOS
Explorer
Artist
Judge
Warrior
Digital
Analog
Environment: Decreasing abilityto predict analog performance
from simple assumptions / models
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Acknowledgments• WPI
–David Cyganski–Chengxin Liu
• Analog Devices–Mike Coln–Bob Adams–Larry DeVito–Colin Lyden
• Carnegie Mellon–David Ricketts
• Columbia University–Yannis Tsividis
• Creativity Resources–Roger von Oech
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ReferencesMOSFET Device Physics
Y. Tsividis, "Operation and Modeling of the MOSTransistor" New York: Oxford University Press, 2008.ISBN 978-0195170153
Creativity
R. Von Oech, "A Whack on the Side of the Head"New York: Warner, 1998. ISBN 0446674559
R. Von Oech, "A Kick in the Seat of the Pants"New York: HarperCollins, 1986. ISBN 0060960248
CMOS Design
Op 't Eynde and Sansen, "Design and Optimization ofCMOS Wideband Amplifiers," Proc. CICC, 1989.
Oscillator Jitter
J. McNeill and D. Ricketts, "The Designer's Guide toJitter in Ring Oscillators" New York: Springer, 2009.ISBN 978-0387765266