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![Page 1: Extreme Computing 2005 Center for Nano Science and Technology University of Notre Dame Craig S. Lent University of Notre Dame Molecular QCA and the limits.](https://reader036.fdocuments.in/reader036/viewer/2022070412/56649f115503460f94c233f1/html5/thumbnails/1.jpg)
Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Craig S. LentUniversity of Notre Dame
Molecular QCA and the limits of binary switching logic
Supported by NSF, State of Indiana
Collaborators: Peter Kogge, Mike Niemier, Greg Snider, Patrick Fay, Marya Lieberman, Thomas Fehlner, Alex Kandel
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
The Dream of Molecular Transistors
Why don’t we keep on shrinking transistors until they are each a single molecule?
![Page 3: Extreme Computing 2005 Center for Nano Science and Technology University of Notre Dame Craig S. Lent University of Notre Dame Molecular QCA and the limits.](https://reader036.fdocuments.in/reader036/viewer/2022070412/56649f115503460f94c233f1/html5/thumbnails/3.jpg)
Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Molecular Transistors
Where’s the benefit of small?
Where do you put the next device?
![Page 4: Extreme Computing 2005 Center for Nano Science and Technology University of Notre Dame Craig S. Lent University of Notre Dame Molecular QCA and the limits.](https://reader036.fdocuments.in/reader036/viewer/2022070412/56649f115503460f94c233f1/html5/thumbnails/4.jpg)
Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Dream molecular transistors
V
off
low conductance state
V
high conductance state
on I
1 nm
fmax=1 THz
Molecular densities: 1nm x 1nm 1014/cm2
![Page 5: Extreme Computing 2005 Center for Nano Science and Technology University of Notre Dame Craig S. Lent University of Notre Dame Molecular QCA and the limits.](https://reader036.fdocuments.in/reader036/viewer/2022070412/56649f115503460f94c233f1/html5/thumbnails/5.jpg)
Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Transistors at molecular densities
Suppose in each clock cycle a single electron moves from power supply (1V) to ground.
V
![Page 6: Extreme Computing 2005 Center for Nano Science and Technology University of Notre Dame Craig S. Lent University of Notre Dame Molecular QCA and the limits.](https://reader036.fdocuments.in/reader036/viewer/2022070412/56649f115503460f94c233f1/html5/thumbnails/6.jpg)
Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Transistors at molecular densities
Suppose in each clock cycle a single electron moves from power supply (1V) to ground.
V
Frequency (Hz) 1014 devices/cm2 1013 devices/cm2 1012 devices/cm2 1011 devices/cm2
1012 16,000,000 1,600,000 160,000 16,000
1011 1,600,000 160,000 16,000 1,600
1010 160,000 16,000 1,600 160
109 16,000 1600 160 16
108 1600 160 16 1.6
107 160 16 1.6 0.16
106 16 1.6 0.16 0.016
Power dissipation (Watts/cm2)
ITRS roadmap: 7nm gate length, 109 logic transistors/cm2 @ 3x1010 Hz for 2016
![Page 7: Extreme Computing 2005 Center for Nano Science and Technology University of Notre Dame Craig S. Lent University of Notre Dame Molecular QCA and the limits.](https://reader036.fdocuments.in/reader036/viewer/2022070412/56649f115503460f94c233f1/html5/thumbnails/7.jpg)
Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Transistors at molecular densities
Suppose in each clock cycle a single electron moves from power supply (1V) to ground.
Vdd
Frequency (Hz) 1014 devices/cm2 1013 devices/cm2 1012 devices/cm2 1011 devices/cm2
1012 16,000,000 1,600,000 160,000 16,000
1011 1,600,000 160,000 16,000 1,600
1010 160,000 16,000 1,600 160
109 16,000 1600 160 16
108 1600 160 16 1.6
107 160 16 1.6 0.16
106 16 1.6 0.16 0.016
Power dissipation (Watts/cm2)
ITRS roadmap: 7nm gate length, 109 logic transistors/cm2 @ 3x1010 Hz for 2016
![Page 8: Extreme Computing 2005 Center for Nano Science and Technology University of Notre Dame Craig S. Lent University of Notre Dame Molecular QCA and the limits.](https://reader036.fdocuments.in/reader036/viewer/2022070412/56649f115503460f94c233f1/html5/thumbnails/8.jpg)
Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
The Dream of Molecular Transistors
![Page 9: Extreme Computing 2005 Center for Nano Science and Technology University of Notre Dame Craig S. Lent University of Notre Dame Molecular QCA and the limits.](https://reader036.fdocuments.in/reader036/viewer/2022070412/56649f115503460f94c233f1/html5/thumbnails/9.jpg)
Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Molecular electronics requirements
1) Low power dissipation
2) Real power gain
3) Robustness to disorder
Benefit: functional densities at molecular scale
![Page 10: Extreme Computing 2005 Center for Nano Science and Technology University of Notre Dame Craig S. Lent University of Notre Dame Molecular QCA and the limits.](https://reader036.fdocuments.in/reader036/viewer/2022070412/56649f115503460f94c233f1/html5/thumbnails/10.jpg)
Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Outline• Introduction
• QCA paradigm
• Implementations– Metal-dot QCA– Molecular QCA
• Energy flow in QCA– Power gain– Power dissipation and erasure– Bennett clocking
![Page 11: Extreme Computing 2005 Center for Nano Science and Technology University of Notre Dame Craig S. Lent University of Notre Dame Molecular QCA and the limits.](https://reader036.fdocuments.in/reader036/viewer/2022070412/56649f115503460f94c233f1/html5/thumbnails/11.jpg)
Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Quantum-dot cellular automata
Represent binary information by charge configuration of cell.
“0”
“null”
“1”QCA cell •Dots localize charge
•Two mobile charges
•Tunneling between dots
•Clock signal varies relative energies of “active” and “null” dots
active
Clock need not separately contact each cell.
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
“null”
Quantum-dot cellular automata
Neighboring cells tend to align in the same state.
“1”
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Quantum-dot cellular automata
Neighboring cells tend to align in the same state.
“1” “1”
![Page 14: Extreme Computing 2005 Center for Nano Science and Technology University of Notre Dame Craig S. Lent University of Notre Dame Molecular QCA and the limits.](https://reader036.fdocuments.in/reader036/viewer/2022070412/56649f115503460f94c233f1/html5/thumbnails/14.jpg)
Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Quantum-dot cellular automata
Neighboring cells tend to align in the same state.
“1” “1”
This is the COPY operation.
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Majority Gate
“1”
“1”
“0”
“null”
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Majority Gate
“1”
“1”
“0”
“1”
![Page 17: Extreme Computing 2005 Center for Nano Science and Technology University of Notre Dame Craig S. Lent University of Notre Dame Molecular QCA and the limits.](https://reader036.fdocuments.in/reader036/viewer/2022070412/56649f115503460f94c233f1/html5/thumbnails/17.jpg)
Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Majority Gate
Three input majority gate can function as programmable 2-input AND/OR gate.
“A”
“C”
“B”
“out”
MABC
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Inverter Gate
“1”
![Page 19: Extreme Computing 2005 Center for Nano Science and Technology University of Notre Dame Craig S. Lent University of Notre Dame Molecular QCA and the limits.](https://reader036.fdocuments.in/reader036/viewer/2022070412/56649f115503460f94c233f1/html5/thumbnails/19.jpg)
Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Inverter Gate
“1” “0”
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Inverter Gate
“1”
![Page 21: Extreme Computing 2005 Center for Nano Science and Technology University of Notre Dame Craig S. Lent University of Notre Dame Molecular QCA and the limits.](https://reader036.fdocuments.in/reader036/viewer/2022070412/56649f115503460f94c233f1/html5/thumbnails/21.jpg)
Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Inverter Gate
“0”
![Page 22: Extreme Computing 2005 Center for Nano Science and Technology University of Notre Dame Craig S. Lent University of Notre Dame Molecular QCA and the limits.](https://reader036.fdocuments.in/reader036/viewer/2022070412/56649f115503460f94c233f1/html5/thumbnails/22.jpg)
Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Inverter Gate
“0” “1”
![Page 23: Extreme Computing 2005 Center for Nano Science and Technology University of Notre Dame Craig S. Lent University of Notre Dame Molecular QCA and the limits.](https://reader036.fdocuments.in/reader036/viewer/2022070412/56649f115503460f94c233f1/html5/thumbnails/23.jpg)
Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
QCA single-bit full adder
Hierarchical layout and design are possible.
result of SC-HF calculation with site model
![Page 24: Extreme Computing 2005 Center for Nano Science and Technology University of Notre Dame Craig S. Lent University of Notre Dame Molecular QCA and the limits.](https://reader036.fdocuments.in/reader036/viewer/2022070412/56649f115503460f94c233f1/html5/thumbnails/24.jpg)
Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Adiabatic computing (Landauer)
“null”
“0”
0
0
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Characteristic energy
E=0
kink
E=Ek
We would like “kink energy” Ek > kBT.
ene
rgy
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Molecular Wire
ONIOM/STO-3G (Gaussian 03)
aligned
error
Ene
rgy
Ek = 0.8 eV
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Outline• Introduction
• QCA paradigm
• Implementations– Metal-dot QCA– Molecular QCA
• Energy flow in QCA– Power gain– Power dissipation and erasure– Bennett clocking
![Page 28: Extreme Computing 2005 Center for Nano Science and Technology University of Notre Dame Craig S. Lent University of Notre Dame Molecular QCA and the limits.](https://reader036.fdocuments.in/reader036/viewer/2022070412/56649f115503460f94c233f1/html5/thumbnails/28.jpg)
Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
QCA devices exist
“dot” = metal island
electrometers
70 mK
Al/AlOx on SiO2
Metal-dot QCA implementation
Greg Snider, Alexei Orlov, and Gary Bernstein
![Page 29: Extreme Computing 2005 Center for Nano Science and Technology University of Notre Dame Craig S. Lent University of Notre Dame Molecular QCA and the limits.](https://reader036.fdocuments.in/reader036/viewer/2022070412/56649f115503460f94c233f1/html5/thumbnails/29.jpg)
Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Metal-dot QCA cells and devices
• Majority Gate
MABC
Amlani, A. Orlov, G. Toth, G. H. Bernstein, C. S. Lent, G. L. Snider, Science 284, pp. 289-291 (1999).
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
QCA Shift Register
Gtop
Gbot
electrometers
VIN+
VIN–
VCLK1 V
CLK2
D1 D4
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
QCA Shift Register
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Metal-dot QCA devices exist
• Single electron analogue of molecular QCA• Gates and circuits:
– Wires– Shift registers– Fan-out– Power gain demonstrated– AND, OR, Majority gates
• Work underway to raise operating temperatures
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
From metal-dot to molecular QCA
“dot” = metal island70 mK
Mixed valence compounds
“dot” = redox center
room temperature+
Metal tunnel junctions
Key strategy: use nonbonding orbitals ( or d) to act as dots.
![Page 34: Extreme Computing 2005 Center for Nano Science and Technology University of Notre Dame Craig S. Lent University of Notre Dame Molecular QCA and the limits.](https://reader036.fdocuments.in/reader036/viewer/2022070412/56649f115503460f94c233f1/html5/thumbnails/34.jpg)
Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
4-dot molecule
Each ferrocene acts as a quantum dot, the Co group connects 4 dots.
Fehlner et al(Notre Dame chemistry group)Journal of American Chemical Society125:7522, 2003
5.8 Å
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Bistable configurations
“0” “1”
Guassian-98 UHF/STO-3G/LANL2DZFehlner et al(Notre Dame chemistry group)Journal of American Chemical Society125:7522, 2003
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Switching molecule by a neighboring molecule
Coulomb interaction is sufficient to couple molecular states.
![Page 37: Extreme Computing 2005 Center for Nano Science and Technology University of Notre Dame Craig S. Lent University of Notre Dame Molecular QCA and the limits.](https://reader036.fdocuments.in/reader036/viewer/2022070412/56649f115503460f94c233f1/html5/thumbnails/37.jpg)
Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Molecular 3-dot cell
For the molecular cation, a hole occupies one of three dots.
cationneutral radical
+
neutral radical
+
Three allyl groups form “dots” on alkyl bridge.
![Page 38: Extreme Computing 2005 Center for Nano Science and Technology University of Notre Dame Craig S. Lent University of Notre Dame Molecular QCA and the limits.](https://reader036.fdocuments.in/reader036/viewer/2022070412/56649f115503460f94c233f1/html5/thumbnails/38.jpg)
Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Charge configuration represents bit
isopotential surfaces
“1”“null”
+
“0”
![Page 39: Extreme Computing 2005 Center for Nano Science and Technology University of Notre Dame Craig S. Lent University of Notre Dame Molecular QCA and the limits.](https://reader036.fdocuments.in/reader036/viewer/2022070412/56649f115503460f94c233f1/html5/thumbnails/39.jpg)
Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Clocking field
“1”
“0”
null
E
E
E
or
Use local electric field to switch molecule between active and null states.
active
“null”
![Page 40: Extreme Computing 2005 Center for Nano Science and Technology University of Notre Dame Craig S. Lent University of Notre Dame Molecular QCA and the limits.](https://reader036.fdocuments.in/reader036/viewer/2022070412/56649f115503460f94c233f1/html5/thumbnails/40.jpg)
Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
driver (eÅ)
mol
ecu
le (
eÅ)
“null”
Clocking field alters response function
mol
ecu
le (
eÅ)
driver (eÅ)
“1”
“0”
E
• Clocking field positive (or zero)• Positive charge in top dots• Cell is active – nonlinear
response to input
• Clocking field negative• Positive charge in bottom dot• Cell is inactive – no response
to input
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Clocked Molecular QCA
No current leads. No need to contact individual molecules.
Active Domain
Null Domain
Switching Region
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Molecular clocking
Clocking field is provided by buried wire electrodes (CMOS controlled).
Wire sizes can be 10-100 times larger than molecules.
Hennessey and Lent, JVST (2001)
QCA layer
lockednullactive
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Clocking field: linear motion
![Page 44: Extreme Computing 2005 Center for Nano Science and Technology University of Notre Dame Craig S. Lent University of Notre Dame Molecular QCA and the limits.](https://reader036.fdocuments.in/reader036/viewer/2022070412/56649f115503460f94c233f1/html5/thumbnails/44.jpg)
Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Molecular circuits and clocking wires
Plan view of buried clocking wires
region where perpendicular field is high pushing cells into active state
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Molecular circuits and clocking wires
molecular circuits are on a much smaller length scale (10 –100x)
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Molecular circuits and clocking wires
First: zoom in to molecular level
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Field-clocking of QCA wire: shift-register
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Computational wave: majority gate
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Computational wave: adder back-end
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
XOR Gate
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Permuter
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Wider QCA wires
Internal redundancy yields defect tolerance.
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Molecular circuits and clocking wires
Next: zoom out to dataflow level
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Universal floorplan
Kogge & Niemier
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Outline• Introduction
• QCA paradigm
• Implementations– Metal-dot QCA– Molecular QCA
• Energy flow in QCA– Power gain– Power dissipation and erasure– Bennett clocking
![Page 56: Extreme Computing 2005 Center for Nano Science and Technology University of Notre Dame Craig S. Lent University of Notre Dame Molecular QCA and the limits.](https://reader036.fdocuments.in/reader036/viewer/2022070412/56649f115503460f94c233f1/html5/thumbnails/56.jpg)
Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Power Gain in QCA Cells
• Power gain is crucial for practical devices because some energy is always lost between stages.
• Lost energy must be replaced.– Conventional devices – current from power supply– QCA devices – from the clock
• Unity power gain means replacing exactly as much energy as is lost to environment.
Power gain > 3 has been measured in metal-dot QCA.
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
• Maxwell’s demon (1875) – by first measuring states, could perform reversible processes to lower entropy
• Szilard (1929), Brillouin (1962): measurement causeskBT log(2) dissipation per bit.
• Landauer (1961,1970): only erasure of information must cause dissipation of kBT log(2) per bit.
• Bennett (1982): full computation can be done without erasure.
logical reversibility physical reversibility
Minimum energy for computation
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Theoretical descriptionCoherence vector formalism
Extract the real degrees of freedom from the density matrix ˆˆ( )i iTr ρ
real vector
2ˆ are the 1 generators of SU(n), n=2,3i n
system
environment
ssd
dt
Ω
Equation of motion
ˆ( )eqss itr ρ
1 ˆ( )j itr H
ik ijk jj
f Ω
: structure constants of SU(n)ijkf
( )
Heq
H
e
tr e
ρ
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Computational wave: adder back-end
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
The computational wave
Computation happens here.
Dissipation (if any) happens here.
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Landauer clocking of QCA
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Bennett-style circuit reversibility
En
erg
y/E
k
kBT log(2)
reversibleirreversible
Direct time-dependent calculations shows: Logically reversible circuit can dissipate much less than kBT log(2).
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
“Bennett clocking” of QCA
Output is used to erase intermediate results.
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Bennett clocking of QCA
For QCA no change in layout is required.
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
QCA gate: reversible/irreversible
Direct time-dependent calculations shows: Bennett-clocked circuit can dissipate much less than kBT log(2).
En
erg
y/E
k
kBT log(2)
reve
rsib
le
irre
vers
ible
Be
nne
ttcl
ock
edSame layout
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Power dissipation limits
• QCA can operate at the theoretical limits of low power dissipation.
• For regular clocking: must dissipate kBT log(2) for each erased bit.
• For Bennett-clocking: no fundamental lower limit.Cost: half clock speed, more complicated clocking.
• Makes extreme high densities possible—clocking type is in design space.
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Doesn’t adiabatic mean slow?
Slow compared to what?
– For conventional circuits, < RC
– For molecular QCA, slow compared to electron switching from one side of a molecule to the other
f < fB ~ 10 15 Hz THz operation is feasible
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
QCA Power Dissipation
QCA architectures could operate at densities 1012 devices/cm2 and 100GHz without melting the chip.
QCA Operation Region
100 W/cm2
@1012 devices/cm2
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Outline• Introduction
• QCA paradigm
• Implementations– Metal-dot QCA– Molecular QCA
• Energy flow in QCA– Power gain– Power dissipation and erasure– Bennett clocking
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Is Zettaflops computing possible?
Minimum device size: 1 nm x 1 nm
1014 devices/cm2
Maximum switching speed: 1015 Hz
Total chip area: 10 cm x 10 cm
Maximum devices that could be switching
= 1014 x 1015 x 102 = 1031 switches/sec
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Is Zettaflops computing possible?
Downgrade density
1014 1012 devices/cm2
Downgrade speed
1015 Hz 1012 Hz
Total chip area: 10 cm x 10 cm
Gate op/flop 105
1012 x 1012 x 102 x 10-5 = 1021 FLOPS
Possible…. but challenging
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Extreme Computing 2005Center for Nano Science and TechnologyUniversity of Notre Dame
Main Points• Quantum-dot Cellular Automata (QCA) is transistor-less approach
for solving the challenges of– Scaling devices to molecular dimensions– Avoiding huge power dissipation issues– Power gain (lacking in crossbars)– Robustness against disorder
• QCA is an example of operating at the ultimate limits of low power dissipation.
• Direct calculation of the time evolution of QCA arrays illustrates the Landauer Principle. (no hand-waving required)
• QCA can be operated in a Bennett-clocking mode. • Zettaflops operation is conceivable
Thank you for your attention