Exploration of the Synchronization Constraint in Quantum-dot - PowerPoint PPT Presentation

Exploration of the Synchronization Constraint in Quantum-dot Cellular Automata (QCA) Frank Sill Torres 1,2 , Pedro A. Silva 3 , Geraldo Fontes 3 , José A. M. Nacif 3 , Ricardo S. Ferreira 3 , Omar P. V. Neto 4 , Jeferson F. Chaves 4,5 , Rolf Drechsler 1,2 1 DFKI GmbH (Germany), 2 University of Bremen (Germany) 3 UFV (Brazil), 4 UFMG (Brazil), 5 CEFET(Brazil) Sill Torres – QCA

Outline  Trends  Quantum-dot Cellular Automata Basics  Clocking in QCA Synchronicity   Impact Analysis  Conclusions Sill Torres – QCA 2

Trends CMOS Scaling limits 100 100 Switching Energy (fJ) 10 10 1 Gate Delay (ps) 0.1 1 0.01 0.001 0.0001 0.1 0.00001 0.01 0.000001 0.001 0.01 0.1 1 0.001 0.01 0.1 1 L GATE ( µ m) L GATE ( µ 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 Sill Torres – QCA 3

Trends Power  Simple example: – Array of novel devices with 1nm x 1nm footprint → Density: 10 14 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 Sill Torres – QCA 4

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

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 Sill Torres – QCA 6

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 Sill Torres – QCA 7

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 Sill Torres – QCA 8

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

Quantum-dot Cellular Automata Boolean Cells  AND :  OR – F AND =MAJ(A,B,C=0)=AB – F AND =MAJ(A,B,C=1)=A+B A A B F = AB B F = A+B C = 0 C = 1 (fix) (fix) Sill Torres – QCA 10

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 Sill Torres – QCA 11

Clocking in QCA 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 Sill Torres – QCA 12

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  Tile 1 2 3 4 1 Clock number Possible cell locations controlling all cells  Information transfer only between consecutively numbered clocks 1 2 3 (1 → 2, 2 → 3, …, 4 → 1) 2 3 4 Sill Torres – QCA 13

Clocking in QCA Information Transfer  Pipeline-like information transfer b b=0 Clock Clock Clock State State State 1 1 ↓ ↔ 0 0 ↔ 0 ↓ 1 1 1 Switch Hold Release s s=1 2 2 1 1 3 3 2 2 2 Switch Relax Hold ↔ 0 0 ↔ 0 ↓ ↔ X ↓ a f f 3 3 3 Release Relax Switch a=0 2 2 3 3 4 4 4 4 4 Release Hold Relax Sill Torres – QCA 14

Synchronicity Constraint  Common assumption: All data paths in QCA must be of equal length In1 In1 A A o1 o1 Random 4 1 1 2 4 2 2 3 3 1 1 2 operations o3 o3 3 3 B B o2 In2 In2 o2 4 4 1 1 2 2 3 3 1 1 2 2 Complicated Design  Source: Campos, 2015 Sill Torres – QCA 15

Synchronicity Solution  Inputs can be hold stable for X clock cycles  Drawback: Reduced throughput In2 B o5 o6 o4 A 1 4 4 2 3 1 2 o3 o7 In1 o1 4 3 4 1 3 2 1 o2 o8 o9 f 3 3 2 2 4 1 4 Clock 1 In1 In1-1 In1-2 In2 In2-1 In2-2 A undef In1-1 In1-2 In2-1 In2-2 B Sill Torres – QCA 16

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 Sill Torres – QCA 17

Impact Analysis Environment cont’d Failed synchronicity Synchronicity achieved o1 o1 2 2 o2 6 o2 4 Logic levels Distances 4 2 o3 6 o3 5 2 2 2 2 o4 o5 o6 o4 o5 o6 o6 o4 o1 o1 1 4 2 3 1 1 3 1 4 2 4 o6 o4 o3 o5 4 4 2 3 1 1 4 3 2 1 4 o5 o3 o2 o2 3 3 2 4 1 3 1 3 2 4 2 Sill Torres – QCA 18

Results 80% 60% Throughput (50%) Reduction 40% Area (33%) 20% Latency (13%) 0% c17 t newtag CLPL FA-AOIG FA-MAJ B1_r2 XOR5_r XOR5_r1 Occ. clock zones Latency Throughput (Area) Sill Torres – QCA 19

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  Sill Torres – QCA 20

Thank you! frasillt@uni-bremen.de Sill Torres – QCA 21

Exploration of the Synchronization Constraint in Quantum-dot Cellular Automata (QCA) Frank Sill Torres 1,2 , Pedro A. Silva 3 , Geraldo Fontes 3 , José A. M. Nacif 3 , Ricardo S. Ferreira 3 , Omar P. V. Neto 4 , Jeferson F. Chaves 4,5 , Rolf Drechsler 1,2 1 DFKI GmbH (Germany), University of Bremen (Germany) 3 UFV (Brazil), 4 UFMG (Brazil), 5 CEFET(Brazil) Sill Torres – QCA