Design%20

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Design Analysis of Resonant Power/Clock Drivers
for Adiabatic Logic

• Research Overview
• Michael P. Frank
• Thursday, October 5, 2006
• (Presented to S. Foo, H. Li, J. Zheng)

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Outline

• Motivation
• Device architectural work
• Analog circuit analysis

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Motivation

• Logic performance is increasingly limited by
  power dissipation constraints, with unfortunate
  results
• Over the last few years, clock speeds have been
  increasing rather more slowly than in the past
  (19/yr instead of 58/yr)
• The energy efficiency of traditional digital
  switching schemes is approaching fundamental
  thermodynamic limits
• Today Switching a min-size FET dissipates 200
  eV
• 1 eV dissipation/switching event for any
  reliable FET-based techology
• 18 meV (kT ln 2) for any irreversible technology
• To beat these limits will require an increasing
  amount of energy recovery in switching
• Several types of logic devices that allow this
  are known

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Energy-Recovering Logic in CMOS

• Basic idea Still use ordinary CMOS transistors,
  but switch their state adiabatically
• Gradually, with less dissipation (see later
  analysis)
• We now know how to build fully-adiabatic versions
  of arbitrary combinational and sequential logic
• One requirement Fully adiabatic switching events
  must also be logically reversible
• Perform an invertible transformation of the
  digital state
• Problem with CMOS Energy coefficient Q2R is
  relatively large, results in low cost-performance

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Another Adiabatically Switchable Device The
Quantum-Dot Cell

• Group several quantum dotsclose together into a
  cell
• Separated by tunnel junctions
• Excess electrons in the celloccupy certain
  naturally-stable configurations
• E.g. 2 electrons will tend to settle in opposite
  corners due to Coulombic repulsion
• By electrostatic biasing we can adiabatically
  restore the cell to a neutral polarization
• From which it may be easily induced to switch to
  either state

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Quantum-Dot Cell Automata wire

• Line of neighboring cells are driven in sequence
• Each cell is biased by the neighboring cell to
  take on the same state as its neighbor
• Flow of information along wires can be
  wave-pipelined

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Doing logic with quantum-dot cells

• With a different arrangement of cells, we can
  complement the input signal

a0
q1
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Functional completeness

• This assemblage of cells implements the majority
  function
• q MAJ(a,b,c) ab ac bc
• Using MAJ, we can do AND and OR, and thus (with
  NOT) compute anything

a0
b0
q0
c1
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QCA Full Adder Module
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A more complex circuit
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One potential fabrication process
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QCA structures fabricated at Sandia

• The surface is a SiGe single crystal film on a Si
  (001) substrate.
• The square structures are monolithic groupings of
  four self-assembled SiGe dots surrounding a
  central pit in the film (which elastically binds
  the 4 dots).
• The lateral dimension across each of the
  structures is about 250 nm
• larger than a potential production device, but
  small enough to demonstrate the relevant
  behavior.
• Placement of the four-dot cells into specific
  geometric arrangements needed for QCA is
  accomplished using a Focused Ion Beam (FIB) to
  create preferred nucleation sites.

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Potential Molecular QCA Implementation

• Would work at room temperature due to small dot
  separation and high (eV) barrier energies
• Synthesis of molecules and quantum chemistry
  simulations of electron behavior has been
  completed
• Challenge is to arrange molecules at precise
  locations on a surface

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IBM/Columbia Resonant Clocks
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MultiGigs Rotary Clock
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High-Q MEMS Resonators at U. Mich
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Trapezoidal MEMS Resonator Concept
Arm anchored to nodal points of fixed-fixed beam
flexures,located a little ways away, in both
directions (for symmetry)

z
y
Phase 180 electrode
Phase 0 electrode
Repeatinterdigitatedstructurearbitrarily
manytimes along y axis,all anchored to the
same flexure
x
C(?)
C(?)
0
360
0
360
?
?
(PATENT PENDING, UNIVERSITY OF FLORIDA)
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A Manufacturable Approximation
(Earlydesignw. thinfingers)
Capacitance
Four-finger sensor
Simulated Output Waveform
(PATENT PENDING, UNIVERSITY OF FLORIDA)
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Partially Fabbed Prototype

• Post-etch process was still being fine-tuned.
• Parts were not yet ready for testing
• and then the funding ran out.

Primaryflexure(fin)
Sensecomb
Drive comb
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Clock Distribution Network Design by M. Ottavi
at Sandia, In Progress
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The Present Effort

• A wide variety of resonator design techniques are
  presently being explored
• Each different resonator approach naturally
  delivers a given shape of voltage waveform
• We want to more carefully analyze and understand
  the interplay between
• resonator design,
• waveform shape,
• and the energy efficiency of adiabatic charge
  transfers in the logic

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Initial Circuit Model for Analysis

• Basic lumped-element RC circuit model.

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General Waveform Model
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Cumulative Energy Transferred
t1
Esup
Erec
Ed,tr
Etfr
Ed,cyc
t0
Egap
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Energy Flow Summary
CV2/2
QtfrVgap
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Energy Efficiency Metrics

• Energy transfer efficiency
• Energy transferred to the load, per unit of
  energy dissipated in that transition
• Range is 0, 8)
• Energy recovery efficiency
• The fraction of energy supplied from the source
  terminal during charging that is later returned
  to the source terminal
• Range is 0, 1)
• Resonant quality factor
• Ratio between energy supplied by the source in
  charging and energy dissipated per cycle
• Range is 1, 8)
• Other related metrics could be defined

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Relations Between the Metrics

• The energy transfer efficiency, energy recovery
  efficiency, and quality factor are related to
  each other by

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Particular Wave Shapes Analyzed

• Step function
• Zero-frequency limit of square wave
• Square wave (arbitrary frequency)
• Linear ramp (arbitrary rise time)
• Truncated by flat wave top
• Zero-frequency limit of trapezoidal wave
• Trapezoidal wave (arb. rise time frequency)
• Sinusoidal wave (arbitrary frequency)

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Step Function Results

• Energy transfer efficiency is exactly 1.
• Exactly the same amount of energy (CV2/2) is
  dissipated in each transition as is transferred
  onto or off of the load
• The energy recovery efficiency is exactly 0.
• Lowest possible. CV2 supplied, 0 recovered.
• The quality factor is exactly 1.
• The lowest possible, given that all energy
  dissipated ultimately comes from the source

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General Square Wave Response
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Cumulative Energy Transfers for the Example
Square Wave
Ed,tr
Esup
Ed,cyc
Etfr
Egap
t0
t1
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Results for Square Wave

• Energy transfer efficiency is lt1
• Energy recovery efficiency is still 0.
• And Q is still 1.

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Energy Transfer Inefficiency of Square Wave
Driver as a function of Frequency
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Energy Transfer Efficiency of the Linear Ramp
Driver

• Energy transfer efficiency is gt1
• with r RC/t (t rise time), and e 1/r
  t/RC.
• Clearly approaches 1 as t ? 0 (step function)

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Energy Transfer Inefficiency of Linear Ramp
Driver as a Function of Rise Time
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Energy Recovery Efficiency for Linear Ramp Driver

• Has both upper and lower bounds

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Energy Recovery Efficiencyof the Linear Ramp
Driver
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Trapezoidal waveform example
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Still to do Analysis of Trapezoidal Wave

• Need to determine load voltage range V as a
  function of the source voltage range Vs and the
  wave parameters trise and tcyc.
• Then calculate Esup, Ed,tr, and Etfr for this
  case
• Then calculate the energy efficiencies
• Also, for a given value of tcyc, what value of
  trise gives the best efficiency?
• It may turn out to be a constant fraction of tcyc.

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Analysis of the Sinusoidal Driver

• Load voltage amplitude is given by
• Energy transferred onto the load is thus
• Meanwhile, the energy dissipated per transition
  is

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Energy Transfer Efficiency of the Sinusoidal
Driver

• Energy transfer efficiency is
• Exactly equal to the cycle period divided by the
  characteristic time tc p2RC/2 4.93RC.

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Energy Supplied by theSinusoidal Driver During
Charging

• Present form, needs more simplification
• Then find Erec by subtracting 2Ed,tr
• Then we are in a position to calculate ?E,tr

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Final steps for sinusoidal driver

• How do the energy transfer and recovery
  efficiencies of the sinusoidal wave compare to
  those of the (optimized) trapezoidal wave?
• There may turn out to be just a constant factor
  difference in efficiencies between the two cases
• Which wave shape is more efficient at finite
  frequencies? Does the choice of which is better
  depend on the value of RCf?

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Ideas for Follow-on Work

• Do a variational analysis in terms of stationary
  functionals to find the exact source wave shape
  that maximizes energy efficiency, in terms of
  given values of the relative cycle period tcyc/RC
  and the load voltage swing V.
• Borrow methods used to calculate least-action
  trajectories in physics
• Elaborate the circuit model into some more
  realistic, representative models of particular
  resonator and clock distribution circuits
• Do a systems-engineering type optimization of
  resonator designs together with particular
  classes of logic devices