1. Exploration of the Synchronization Constraint in Quantum-dot Cellular Automata (QCA)
Frank Sill Torres1,2, Pedro A. Silva3, Geraldo Fontes3, José A. M. Nacif3, Ricardo S. Ferreira3, Omar P. V. Neto4, Jeferson F. Chaves4,5, Rolf Drechsler1,2
1DFKI GmbH (Germany), 2University of Bremen (Germany)
3UFV (Brazil), 4UFMG (Brazil), 5CEFET(Brazil)

2. Outline Trends Quantum-dot Cellular Automata Basics Clocking in QCA
Synchronicity
Impact Analysis
Conclusions

3. Trends Switching Energy (fJ) Gate Delay (ps) LGATE (m) LGATE (m)
CMOS Scaling limits
100
100 10 1 10
0.1
0.01
0.001
Switching Energy (fJ)
Gate Delay (ps) 1
0.1
0.0001
0.01
0.001
0.01
0.1 1
0.001
LGATE (m) 1
LGATE (m)
Current CMOS device scaling close to the ideal limits
Intel/ITRS: Scaling might end between 2021 and 2030 (at 3.5 nm)
Source: Nikonov (Intel), 2013

4. Trends Simple example: Array of novel devices with 1nm x 1nm footprint
Power
Simple example:
Array of novel devices with 1nm x 1nm footprint
→ Density: 1014 devices per cm² (0.1 Peta)
Frequency: 100 GHz
Each device in each clock cycle: single electron has to drop down potential of 0.1V (=energy loss of 0.1eV)
Total Power: 160 kW cm-2

5. Trends Quantum-dot Cellular Automata 10-3 Costs per device 20 nm CMOS
10-7
1 fJ
Power [W]
Ek=100 meV
1 aJ
10-11
QCA Operation Region
Ek – kink energy (energetic costs of two neighboring cells having opposite polarizations)
1 zJ
1 yJ
10-15
10-14
10-11
10-7
Propagation Delay [s]
Source: Lent, 2002

6. Quantum-dot Cellular Automata
What is a Quantum dot?
Nanometer sized structure (1nm – 10nm)
Capable of trapping (confine) electrons in 3 dimensions (due to the high potential required to escape)
Like in Atom: Quantized energy levels due to confinement of electrons (also known as: artificial atom)
Electrical and optical characteristics can be adapted

7. Quantum-dot Cellular Automata
QCA Cell
Basic elements:
4 Quantum dots (shown as circles)
2 Electrons located within quantum dots → can tunnel between dots
Principle:
Quantum dots confine electrons
Coulomb forces repel of electrons
Only two possible states => enables binary logic
Balance between Coulomb forces, dot distance and confinement - - - -
Polarization -1
Polarization +1
Binary 0
Binary 1

8. Quantum-dot Cellular Automata
QCA cell-to-cell Coupling
Two cells placed close to each other with adequate distance d such that:
Electrons cannot tunnel between cells (tunneling probabilities decay exponentially with distance)
Electrons of one cell influence electrons other cell (Coulombic forces decay quadratically) → No current!
Coulombic Interactions d

9. Quantum-dot Cellular Automata
Basic Blocks
Wire
Majority
Coulombic Interactions
‘1’
‘1’
A = 0
B = 1
F = MAJ(A,B,C) = 1
C = 1

10. Quantum-dot Cellular Automata
Boolean Cells
AND:
FAND=MAJ(A,B,C=0)=AB OR
FAND=MAJ(A,B,C=1)=A+B A A B
F = AB B
F = A+B
C = 0
(fix)
C = 1
(fix)

11. Clocking in QCA
Potential barrier manipulation
Problem: How to deal with metastability and how to control data transfer?
Solution: External electric fields (clocks) that control potential barriers of Quantum dots
Potential barriers increased
Potential barriers decreased
Potential
V(x,y)
Source: Goser, 1998

12. Clocking in QCA Switch Barriers raised, cells become polarized
Clocking States
Switch
Barriers raised, cells become polarized
→ processing and information stored in cell
Hold
Barriers are held high
→ stored information remains stable, can act as inputs to next stage
Release
Barriers are lowered
→ Information gets lost
Relax
Cell barriers remain lowered
→ Cell in neutral state

13. Clocking in QCA
Tile-based Design
Four external clocks (1-4), phase-shifted by 90 degrees
QCA cells organized in tiles (can contain wires or logic)
All cells within tile controlled by same clock
Information transfer only between consecutively numbered clocks (1 → 2, 2 → 3, …, 4 → 1)
Tile
Clock number controlling all cells
Possible cell locations

14. 1 1 ↓ ↔ ↓ ↔ ↔ ↓ ↔ X ↓ ↔ Clocking in QCA
Information Transfer
Pipeline-like information transfer
Clock
State 1
Switch 2
Relax 3
Release 4
Hold
Clock
State 1
Hold 2
Switch 3
Relax 4
Release
Clock
State 1
Release 2
Hold 3
Switch 4
Relax 1 1 ↓ ↔ ↓ ↔ ↔ ↓ ↔ X ↓ ↔

15. Synchronicity
Constraint
Common assumption: All data paths in QCA must be of equal length
Complicated Design
Random operations
Source: Campos, 2015

16. Synchronicity Inputs can be hold stable for X clock cycles
Solution
Inputs can be hold stable for X clock cycles
Drawback: Reduced throughput

17. Impact Analysis
Environment
Question: Impact of allowing to break synchronicity constraint?
Modification of bi-directional algorithm for QCA Place-and-Route (P&R)
Output
Output
Gates
Inputs
Inputs

18. Impact Analysis Distances Environment cont’d Failed synchronicity
Synchronicity achieved
Failed synchronicity
Logic levels
Distances

19. Results
Throughput (50%)
Area (33%)
Latency (13%)
(Area)

20. Conclusions
Quantum-dot Cellular Automata (QCA) is promising nanotechnology for ultra-low power applications
Information transfer controlled by external electric clocking fields → circuits may have pipeline-like behavior
Contrast to what is common believe → not a mandatory constraint for QCA circuits
Simulation results for relaxed synchronicity constraint:
Area reductions of up to 70%, Latency improved by up to 25%
Throughput decreases by up to 70%
New degree of freedom for designers

21. Thank you!

22. Exploration of the Synchronization Constraint in Quantum-dot Cellular Automata (QCA)
Frank Sill Torres1,2, Pedro A. Silva3, Geraldo Fontes3, José A. M. Nacif3, Ricardo S. Ferreira3, Omar P. V. Neto4, Jeferson F. Chaves4,5, Rolf Drechsler1,2
1DFKI GmbH (Germany), University of Bremen (Germany)
3UFV (Brazil), 4UFMG (Brazil), 5CEFET(Brazil)