![Page 1: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/1.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Craig S. Lent
University of Notre Dame
Quantum-dot Cellular Automata:
beyond transistors to extreme
supercomputing
Supported by DARPA, ONR, NSF, State of Indiana
Collaborators: Peter Kogge, Greg Snider, Patrick Fay,
Marya Lieberman, Thomas Fehlner, Alex Kandel
![Page 2: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/2.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Converging problems
• How can we make the most powerful computer?– Binary
– Most processing elements/cm2 – high functional density
– � molecules as devices
• How can we solve the “heat problem”?– Power dissipation is limiter
– Understand the fundamentals of the issue
– Need to go beyond transistors
– Practical way to do “reversible computation”
There is an approach than may solve both these problems and provide a path forward: QCA
![Page 3: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/3.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Convergence
Molecular electronics
Power dissipation
Quantum-dot cellular
automata (QCA)
smaller
cooler
![Page 4: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/4.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Outline of presentation
• Shrinking electronics & QCA
• The heat problem & QCA
• A path forward
![Page 5: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/5.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Convergence
Molecular electronics
Power dissipation
Quantum-dot cellular
automata (QCA)
smaller
cooler
![Page 6: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/6.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
How is information
represented physically?
![Page 7: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/7.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
on=“1”
Zuse’s paradigm• Konrad Zuse (1941) Z3 machine
– Use binary numbers to encode information
– Represent binary digits as on/off state of a current switch Telephone
relay Z3 Adder
The flow through one switch
turns another on or off.
Electromechanical
relay
Exponential down-scaling
Vacuum tubes Solid-state transistors CMOS IC
off=“0”
![Page 8: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/8.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Problems shrinking the current-switch
To reach the single-molecule level, a new approach to
representing information is required.
Electromechanical
relay
Vacuum tubes Solid-state transistors CMOS IC Molecules
New
idea
Valve shrinks also – hard
to get good on/off
Current becomes small -
resistance becomes high
Hard to turn next switch
Charge becomes quantized
Power dissipation
threatens to melt
the chip.
![Page 9: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/9.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
New paradigm: Quantum-dot
Cellular Automata
Revolutionary, not incremental, approach
Beyond transistors – requires rethinking circuits and architectures
Use molecules, not as current switches, but as structured charge containers.
Represent information with molecular charge configuration.
Zuse’s paradigm
• Binary
• Current switch��
• charge configuration�
![Page 10: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/10.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Quantum-dot Cellular Automata
Represent binary information by
charge configuration
A cell with 4 dots
Tunneling between dots
Polarization P = +1
Bit value “1”
2 extra electrons
Polarization P = -1
Bit value “0”
Bistable, nonlinear cell-cell
response
Restoration of signal levels
Robustness against disorder
cell1 cell2
cell1 cell2
Cell-cell response function
Neighboring cells tend to align.
Coulombic coupling
![Page 11: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/11.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
0 01 1
01 10
A
B
C
Out
Binary wire
InverterMajority gate
MA
B
C
Programmable 2-input
AND or OR gate.
QCA devices
![Page 12: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/12.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
QCA single-bit full adder
Hierarchical layout and design are possible.
result of SC-HF calculation
with site model
![Page 13: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/13.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
QCA devices exist
“dot” = metal island
electrometers
70-300 mK
Al/AlOx on
SiO2
Metal-dot QCA implementation
Greg Snider, Alexei Orlov, and Gary Bernstein
![Page 14: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/14.jpg)
LACSI 10/2004Center for Nano Science and Technology
University 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).
![Page 15: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/15.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Clocked QCA cells
“1”“0” “null”
• Middle dot adds “null” state to cells.
• Applied voltage (clock) alters energy of middle
dots and forces charge into null or “active” dots.
• Energy from clock provides power gain which
restores weakened signals.
![Page 16: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/16.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
+
(0,0,0) neutral
Three-dot QCA latch operation
(0,0,0) →→→→ (0,-1,1) switch to “1”
-VCLK-VIN +VINVCLK=0
(0,-1,1) storage of “1” (0,0,0) ←←←← (0,-1,1) back to null
D1 D3
D2
-VIN=0 +VIN=0
• Clock supplies energy, input defines direction of switching
• Three states of the QCA latch: “0” , “1” and “null”
![Page 17: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/17.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Clocking in QCA
0 1
0
ene
rgy
xClock
Small Input Applied
Clock Applied
Input Removed
Signalis amplified
0
Keyes and Landauer, IBM Journal of Res. Dev. 14, 152, 1970
![Page 18: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/18.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
QCA Shift Register
![Page 19: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/19.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
QCA Shift Register
Gtop
Gbot
electrometers
VIN+
VIN–
VCLK1 V
CLK2
D1 D4
![Page 20: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/20.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Interactive Demos
• link
![Page 21: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/21.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Power gain
Power gain is essential for any practical digital
technology.
– Lacking in cross-bar and lookup-table proposals
– Lacking in randomly self-assembled circuits
– Clocked QCA has power gain.
• Theory: Timler and Lent, J. Appl. Phys. 91, 823 (2002).
• Experiment: Kummamuru et al., Appl. Phys. Lett. 81,
1332 (2002).
Power gain > 3 has been measured.
![Page 22: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/22.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
• Metal-dot QCA
– First QCA devices
– Clocked QCA
• Molecular QCA
– Molecular electronics
– Aviram molecules
– Fe-Ru
– 4-dot Ferrocene molecules
• Implications for architecture
QCA implementations
��
�
![Page 23: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/23.jpg)
LACSI 10/2004Center for Nano Science and Technology
University 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 (π or d) to act as dots.
![Page 24: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/24.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Aviram molecule: simple model system
Aviram JACS 110, 5687 (1988)Hush et al. JACS 112, 4192 (1990)
Use allyl groups as dots
1,4-diallyl butane radical cation
![Page 25: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/25.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Charge configuration represents bit
“1”
isopotentialsurface
“0”
Gaussian 98 UHF/STO-3G
HOMO
Lent, Isaksen, LiebermanJournal of American Chemical Society. 125, 1056 (2003)
![Page 26: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/26.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Molecular wire
“0” “0”
“1” “1”
Quantum chemistry calculation shows line acting as binary wire.
Extended Hückel (Gaussian 03)
![Page 27: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/27.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Experiments on molecular double-dot
Thomas Fehlner et al. (Notre Dame chemistry group)Journal of American Chemical Society,125:15250, 2003
Ru Ru
Fe Fe
“0” “1”
Fe group and Ru group act as two unequal quantum dots.
trans-Ru-(dppm)2(C≡CFc)(NCCH2CH2NH2) dication
![Page 28: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/28.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Surface attachment and orientation
N
Si Si
3.8 Α
2.4 Α106o
PHENYL GROUPS“TOUCHING” SILICON
Molecule is covalent bonded to Si and oriented vertically by “struts.”
Si(111)
moleculeSi-N bonds
“struts”
![Page 29: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/29.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Charge configurations
UHF/STO-3G/LANL2DZ
“1”“0”
Bistable charge configuration.
Ru
Fe
Ru
Fe
![Page 30: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/30.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Switching by an applied field
FeRu
FeRu
Fe Ru
Mobile electron driven by electric field, the effect of counterionsshift the response function.
Click-clack correspond to:
Gaussian
![Page 31: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/31.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
When equalized, capacitance peaks.
Applied field equalizes the energy of the two dots
FeRu Fe Ru Fe
Ru
Si
Hg
Fe
Ru
Si
Hg
Fe
Ru
Si
Hg
Fe
Ru
ac Capacitance
voltage
excited stateswitching
Energy
ground state
applied
potential
Measurement of molecular bistability
layer of molecules
Ru
Fe
Ru
Fe
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
C(oxidized) C(reduced) ΔC
VHg (V)
C (nF)
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
ΔC (nF)
2 counterion charge configurations on surface
![Page 32: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/32.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Molecule-molecule interaction
Can one molecule switch another molecule?
![Page 33: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/33.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Switching by a neighboring molecule
The distance betweenNeighboring molecules:1 nm
External electric field:1.2 V/nm
All counterions attach tothe substrate
One molecule can switch a neighboring molecule.
![Page 34: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/34.jpg)
LACSI 10/2004Center for Nano Science and Technology
University 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 Society
125:7522, 20035.8 Å
![Page 35: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/35.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
4-dot molecule
Self-assembly of 4-dot cell—no legs or struts.
![Page 36: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/36.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Bistable configurations
“0” “1”
Guassian-98 UHF/STO-3G/LANL2DZ
![Page 37: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/37.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Can one molecule switch the other ?
![Page 38: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/38.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Switching molecule by a neighboring molecule
Coulomb interaction is sufficient to couple molecular states.
![Page 39: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/39.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Majority gate
A
B
C
Output
The output cell assumes the value of the majority of the input cells.
![Page 40: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/40.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Calculated response
Majority gate operation confirmed (in theory).
![Page 41: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/41.jpg)
LACSI 10/2004Center for Nano Science and Technology
University 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 42: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/42.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Charge configuration represents bit
isopotential
surfaces
“1”“null”
+
“0”
![Page 43: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/43.jpg)
LACSI 10/2004Center for Nano Science and Technology
University 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 44: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/44.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
µdriver (eÅ)
µmolecule (eÅ
)
“null”
Clocking field alters response
function
µmolecule (eÅ
)
µdriver (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
![Page 45: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/45.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Clocked Molecular QCA
QCA layer
lockednullactive
Active domains can be moved across surface by applying
a time-varying voltage to the clocking wires.
Hennessey and Lent, JVST (2001)
![Page 46: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/46.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Clocking field: linear motion
![Page 47: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/47.jpg)
LACSI 10/2004Center for Nano Science and Technology
University 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
![Page 48: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/48.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Molecular circuits and clocking wires
molecular circuits are on a much
smaller length scale (10 –100x)
![Page 49: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/49.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Molecular circuits and clocking wires
First: zoom in to molecular level
![Page 50: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/50.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Field-clocking of QCA wire:
shift-register
![Page 51: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/51.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Computational wave: majority gate
![Page 52: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/52.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Computational wave: adder back-end
![Page 53: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/53.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
XOR Gate
![Page 54: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/54.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Permuter
![Page 55: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/55.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Triple-Wide Wire
Advantages: easier fabrication, works at higher temperatures
![Page 56: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/56.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Wider QCA wires
Redundancy results in defect tolerance.
![Page 57: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/57.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Molecular circuits and clocking wires
Next: zoom out to dataflow level
![Page 58: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/58.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Clocking field: propagation + loop
![Page 59: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/59.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Universal floorplan
![Page 60: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/60.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Crossing signals in the plane
![Page 61: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/61.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Multiple crossovers
![Page 62: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/62.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Interdisciplinary challenge
• Electrical Engineering
• Computer Science
• Chemistry
• Physics
![Page 63: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/63.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Convergence
Molecular electronics
Power dissipation
Quantum-dot cellular
automata (QCA)
smaller
cooler
![Page 64: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/64.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Convergence
Molecular electronics
Power dissipation
Quantum-dot cellular
automata (QCA)
smaller
cooler
![Page 65: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/65.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
![Page 66: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/66.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Transistors at molecular densities
Suppose in each clock cycle a single electron
moves from power supply (1V) to ground.
Vdd
![Page 67: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/67.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Transistors at molecular densities
Suppose in each clock cycle a single electron
moves from power supply (1V) to ground.
Vdd
1011 devices/cm21012 devices/cm21013 devices/cm21014 devices/cm2Frequency (Hz)
0.0160.161.616106
0.161.616160107
1.6161601600108
16160160016,000109
1601,60016,000160,0001010
1,60016,000160,0001,600,0001011
16,000160,0001,600,00016,000,0001012
Power dissipation (Watts/cm2)
ITRS roadmap:
9nm gate length, 109 logic transistors/cm2@ 3x1010 Hz for 2016
![Page 68: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/68.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Physics of computation
• Is there a fundamental lower limit on energy
dissipation per bit?
• What is the distinguishability criterion in thermal
environment?
![Page 69: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/69.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Landauer
Question: Is there a fundamental lower limit to the
amount of energy that must be dissipated to
compute a bit?
Answer: No.
Question: Isn’t it kBT log(2)?
Answer: No, it isn’t.
There is no fundamental lower limit on the amount of
energy that must be dissipated to compute a bit.
Landauer (1961)
![Page 70: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/70.jpg)
LACSI 10/2004Center for Nano Science and Technology
University 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
See Timler & Lent “Maxwell’s demon and quantum-dot cellular automata” JAP (2003).
Minimum energy for computation
![Page 71: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/71.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Physical reversibility � logical
reversibility
Entropy S=kB log(W)
time
configuration
W=2 W=1
time
configuration
W=2 W=2
![Page 72: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/72.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Boltzmann’s tombstone
![Page 73: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/73.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Physical reversibility � logical
reversibility
Entropy S=kB log(W)Total ΔS > 0. (2nd Law of Thermodynamics)
Reduction of entropy in system must be accompanied by transfer of entropy elsewhere.
Either:
1) information transfers to another system, or
2) free energy ΔF=TΔS=kBT log(2) transfers to environment.
time
configuration
W=2 W=1
time
configuration
W=2 W=2
ΔS=0 ΔS= -kB log(2)
![Page 74: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/74.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Physical reversibility � logical
reversibility
Logical reversibility means that inputs are logically determined by outputs.
Logically reversible computation can be implemented by physically reversible processes.
Logically irreversible computation cannot be implemented by physically reversible process. Example: erasure.
time
configuration
W=2 W=1
time
configuration
W=2 W=2
ΔS=0 ΔS= -kB log(2)
reversible irreversible
1
0null0
1
0
1
![Page 75: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/75.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
QCA system considered
• Driver- provides input bit
• Demon cell (after Maxwell’s Demon)- measures and copies the polarization of the test cell
Test Cell Demon CellDriver
![Page 76: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/76.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Bit erasureErasure with copy to demonErasure without demon
Test Cell
Null
Test Cell Demon Cell
Bit=1 Bit=1
Lower clock
Bit erased
Copy bit
to demon
Lower clock
‘1’
‘1’
‘1’ ‘1’
Null‘1’
Null
![Page 77: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/77.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Bit erasure in a QCA cellErasure with copy to demon
Test Cell
Erasure without demonTest Cell Demon Cell
Bit=1 Bit=1
Lower clock
Bit erased
Copy bit
to demon
Lower clock
![Page 78: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/78.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Erasure dynamics without demon cell
Test CellDriver
Pdriver
0
1
-1
4
8
0
12
-4
Ptest cell
0
1
-1Eclock/Ek
0 100 200 300 400
Without a demon cell, erasing the bit results in
considerable energy dissipation.
( )0/γht
0
410−
Power diss
Ek/(h/γ0)
![Page 79: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/79.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Erasure dynamics with copy to the demon cell
Erasing the bit with a copy to the demon cell, results in very little energy
dissipation.
Pdriver
0
1
-1
48
0
12
-4
PTest Cell
0
1
-1
EClock/Ek
0 100 200 300 400
( )0/γht
Pdemon
Test Cell Demon CellDriver0
1
-1Power bath
Ek/(h/γ0)
0
410−
Tc
![Page 80: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/80.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Ediss without demon
)2log(TkB
Ediss with demon
)(sTc
Energy/Ek
Ek=0.5 eV
T=60K
The demon cell makes the erasure reversible, so energy loss can be
much less than kBT log(2).
Energy loss for erasing a single bit
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
10-14
10- 13
10-12
10- 11
![Page 81: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/81.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Demon to the right: a shift register
![Page 82: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/82.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
QCA gate: reversible/irreversible
Energy/E
k
kBT log(2)
reversibleirreversible
Direct time-dependent calculations shows: Logically
reversible circuit can dissipate much less than kBT log(2).
![Page 83: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/83.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Bennett clocking of QCA
Output is used to erase intermediate results.
![Page 84: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/84.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Bennett clocking of QCA
For QCA no change in layout is required.
![Page 85: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/85.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Landauer clocking of QCA
![Page 86: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/86.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
QCA gate: reversible/irreversible
Direct time-dependent calculations shows: Logically
reversible circuit can dissipate much less than kBT log(2).
Energy/E
k
kBT log(2)
reversible
irreversible
Bennett
clocked
![Page 87: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/87.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
QCA gate: reversible/irreversible
With QCA, reversible computation adds no circuit
complexity. Simply redo clock timing where desired.
Energy/E
k
kBT log(2)
reversible
irreversible
Bennett
clocked
![Page 88: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/88.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Distinguishability
Don’t you need to dissipate more than kBT log(2)
to be able to distinguish a bit in a thermal
environment?
![Page 89: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/89.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Energy flow in QCA cells
![Page 90: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/90.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Energy flow in QCA cells
kBT log(2)
Ein Eout Eclock Ediss
E/Ek
0.6
0.5
0.4
0.3
0.2
0.1
0
Ein Eout
Eclock
Ediss
Switching events in QCA cells can dissipate much less than kBT log(2)
![Page 91: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/91.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Energy flow in QCA cells
Ein Eout Eclock Ediss
E/Ek
0.6
0.5
0.4
0.3
0.2
0.1
0
Ein Eout
Eclock
Ediss
Distinguishability requires Ein> kBT log(2). Ediss can be much less.
kBT log(2)
![Page 92: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/92.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Distinguishability
• Information is physical
• Signal energy must be greater than kBT log(2) for
next stage to be able to distinguish it from thermal
fluctuation. (a “read” criterion)
• The signal energy need not be dissipated.
• What to do with it?
– Bennett: Never throw away information. Reverse
computation to return all energy to inputs.
– Modestly reversible computation. Don’t erase information
needlessly.
![Page 93: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/93.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Double well represents bit
w
Eb
a
“0”
“1”
![Page 94: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/94.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Bit switching
Thermal hop over barrier
dissipates no energy.
Tunneling through barrier
dissipates no energy.
Note: Traversing an energy barrier dissipates no energy.
![Page 95: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/95.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Dissipation: falling down hill
Energy dissipation is determined by energy difference between initial and final state – not barrier height.
![Page 96: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/96.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
What’s wrong with transistors?
Net transport of charge from Vdd to ground (falling downhill).
Energy dissipated each cycle is at least QVdd.
Energy is dissipated even for logically reversible operations.
VddVdd
gnd
Vdd
gnd
Q
Q
![Page 97: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/97.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Apply input biasRemove input bias
Raise clocking potential
QCA adiabatic switching
Keep system always very close to ground state.
Don’t let it fall downhill.
![Page 98: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/98.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Breakdown of adiabaticity
If clock moves up too fast, system cannot get to ground
state without some dissipation.
![Page 99: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/99.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Ediss without demon
)2log(TkB
Ediss with demon
)(sTc
Energy/Ek
Ek=0.5 eV
T=60K
The demon cell makes the erasure reversible, so energy loss can be
much less than kBT log(2).
Energy loss for erasing a single bit
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
10-14
10- 13
10-12
10- 11
![Page 100: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/100.jpg)
LACSI 10/2004Center for Nano Science and Technology
University 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
![Page 101: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/101.jpg)
LACSI 10/2004Center for Nano Science and Technology
University 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
~ ωB = 4 x 10 16 Hz → THz operation is feasible
![Page 102: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/102.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Power dissipation at molecular densities
• Cannot afford to dump charge to ground.
• Must use some version of adiabatic switching.
– Keep system always near ground state (e.g. clocked QCA).
– No fundamental lower limit on energy dissipation per bit
provided information is not erased. (Landauer)
– Must dissipate at least kBT log(2) for each erasure.
• Moderate approach: erase as needed, manage power
budget. “Landauer clocking”
• More radical approach: partition into blocks and only
erase inputs to each block. “Bennett clocking”
![Page 103: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/103.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Convergence
Molecular electronics
Power dissipation
Quantum-dot cellular
automata (QCA)
smaller
cooler
![Page 104: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/104.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Zettaflops
1021 flops� 1025 ops
1 nm2 devices (includes surrounding groups)
1014 devices/cm2 derate for power & redundancy
1012 bits on the move/cm2
1012 bits on the move/cm2 * 1012 Hz= 1024 ops/cm2
10 cm2 chip � 1025 ops
![Page 105: Quantum-dot Cellular Automata: beyond transistors to ...–Understand the fundamentals of the issue ... • KonradZuse(1941) Z3 machine –Use binary numbers to encode information](https://reader030.vdocument.in/reader030/viewer/2022041002/5ea43771020c673938251192/html5/thumbnails/105.jpg)
LACSI 10/2004Center for Nano Science and Technology
University of Notre Dame
Conclusions
• QCA offers path to limits of downscaling – molecular
computing.
• Clocked QCA can operate at lower limits of power
dissipation.
– Only dissipate when information is erased
– Tuned Bennett clocking: hold intermediate results in place
when absolute lowest power dissipation is required
• A clear path, but much research remains to be done.
– Chemistry, physics, electrical engineering, computer science
Thanks for your attention.