Erik Forsberg Joint Research Center of Photonics

1. The electron waveguide Y-branch switchA review and arguments for its use as a base for reversible logic Erik Forsberg Joint Research Center of Photonics of the Royal Institute of Technology and Zhejiang University Hangzhou 310027, P. R. China 中国杭州浙江大学玉泉校区 erikf@zju.edu.cn

2. Outline • Basic idea • Theoretical • Required switching voltage • Single mode operation • Ballistic switching • Experimental • Logic • Reversible logic • Conclusions

3. 3 2 e- 1 Electron Waveguide Y-Branch Switch (YBS)T. Palm and L. Thylén, Appl. Phys. Lett. 60, 237 (1992) Single mode coherent mode of operation: Envelope of electron wavefunction propagates to either drain depending on the direction of electric field across the branching region. Required switching voltage: • no thermal limit  promises extreme low-power consumption • waveguide device  small is good • monotonic response  tolerant to fabrication inaccuracies • economics … ?

4. Required switching voltageT. Palm, L. Thylen, O. Nilsson, C. Svensson, J. Appl. Phys. 74, 687 (1993) Required change in applied gate bias required to change the state of the YBS: • Example (GaAs): • Sheet carrier concentration 4x1015 m-2 • Interaction length 200 nm •  Theoretically required switch voltage 1 mV Contrast: Sub-thermal switching in YBS just experimentally verified ! L. Worschech et. al., private communication

5. 1 0 -10 0 10 Gate bias [arb. units] Electron transport – Landauer-Büttiker formalism Transmission probability stem  right arm

6. 3 2 e- 1 Space-charge effectsswitching The Self-Gating EffectJ-O J. Wesström Phys. Rev. Lett. 82 2564 (1999)

7. Space charge cont’d...E. Forsberg, J. Appl. Phys, 93, 5687 (2003)E. Forsberg and J.-O. J. Wesström, Solid-State. Electron.48, 1147-1154 (2004). Fully self-consistent simulation tool for simulations of electron waveguide devices developed. • Space-charge can be dominant. • Dependence is complex. • Single parameter model not adequate to model space charge effects • Screening of gatevoltagecan be severe. • Conclusions: • Small charge densities allows for original response • Gate efficiency is a showstopper

8. Set Detecting selfgatingK. Hieke and M. Ulfward, Phys. Rev. B 62, 16727 (2000).L. Worschech et. al., Appl. Phys. Lett. 79, 3287 (2001). Leave stem, W1, floating and measure it’s potential while varying branch voltages Theory then predicts: Expected result Experimental result

9. Ballistic switching modeH. Q. Xu, Appl. Phys. Lett. 78, 2064 (2001). Three star coupled QPCs

10. Recap YBS has three modes of operation • Single mode transport • No thermal limit to switch voltage • Self-gating operation • Switching based on space charge effects • Bi-stable mode of operation • (single mode operation) • Ballistic switching • Multimode mode of operation • Room temperature operation demonstrated

11. Fabrication: Split-gateP. Ramvall, P. Omling, T. Palm, and L. Thylen, "Quantum Confinement: Physics and Application" (Eds. M. Cahay et. al.) (The Electrochemical Society, Inc., 1994). • Simple fabrication technique However… • Confinement too weak

12. Fabrication:In-plane gatesJ. O. Wesström et. al., "Quantum IV: Nanoscale Materials, Devices and Sytems" (Eds. M. Cahay et. al.) (The Electrochemical Society, Inc., 1997).L. Worschech et. al., Appl. Phys. Lett. 78, 3325 (2001).L. Worschech et. al., Physica E 12, 688 (2002).G. M. Jones et. al., Appl. Phys. Lett. 86, 073117 (2005). • Simple fabrication technique • Strong confinement  single mode easily achieved • Demonstrated in • GaAs/AlGaAs • InGaAs/InP • InAs/AlSb • However… • Low gate efficiency

13. Fabrication: Schottky gatesE. Forsberg and K. Hieke, Phys. Scri. T101, 158 (2002). • Strong confinement  single mode easily achieved • Demonstrated in • GaAs/AlGaAs • Better gate efficiency possible However… • Complex fabrication technique

14. YBS-based circuits • Fan-out possible • Tolerant to fabrication defects • Monotonic response • Coherence only required in branching region

15. G D 1 S D 2 S G D1 D2 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 Logic Based on Y-branch Switches T. Palm and L. Thylén, J. Appl. Phys. 79 8076 (1996) E. Forsberg, unpublished Electrical symbol and possible states Inverter NAND gate using asymmetrical Y-branch switches

16. Ballistic YBS logic S. Reitzenstein et. al., Electron. Lett. 38, 951 (2002) H. Q. Xu, IEEE Electron. Dev. Lett 25, 164 (2004).

17. YBS logic • Single mode operation logic • Feasible • Low power operation due to sub-thermal switching • Advantage over CMOS FET ? • Ballistic • Demonstrated @ room temperature • Thermally limited • Advantage of CMOS FET ? • Feasible application: easy integration with III-V semiconductor lasers/modulators • Conclusion: • For conventional logic it is highly questionable if the YBS can ever outperform CMOS FETs in an economically competitive manner. • Other ideas?

18. Comparing numbers Switchenergy for a device with capacitive inputs: ΔVswitch = 1 mV C = 0.1 pF Minimum switch energy for typical YBS is thus of the order0.6 meV. kBT ln 2 = 18 meV @ room temperature. Conclusion: Reversible logic can greatly reduce the power dissipation of YBS-based logic.

19. Reversible YBS logicE. Forsberg, Nanotechnology 15, 298 (2004). ccNOT (Fredkin) gate

20. Implementation • Possible today III-V’s • However, present fabrication techniques limited • Cryogenic operation required • Low gating efficiency • Power dissipation due to information erasure not dominant • Other possibilities • Hexogonal networks – feasible • Carbon nanotubes – possible • Si nanowires – ? A. N. Andriotis et. al., Appl. Phys. Lett. 79, 266 (2001).

21. Moving periodic globalpotential V x Left branch y Data waveguide Ground-state high- probability regions of two electrons’ wave packets x Electrostatic repulsion BasicY-junction“switch gate” Control waveguide Rightbranch TimingM. Frank et. al., private communication

22. Summary • YBS summarized • Recap on theoretical work • Summary of experimental work • Conventional logic based on YBS • Reversible logic based on YBS • The road ahead • Clocking schemes etc • Feasible designs • Fabrication issues • Gating efficiency potential showstopperinvariant of implementation technology