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The electron waveguide Y-branch switch
A review and arguments for its use as a base for reversible logic
Erik ForsbergJoint 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
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Outline
• Basic idea• Theoretical
– Required switching voltage– Single mode operation– Ballistic switching
• Experimental• Logic• Reversible logic• Conclusions
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Electron Waveguide Y-Branch Switch (YBS)T. Palm and L. Thylén, Appl. Phys. Lett. 60, 237 (1992)
e-
1
2 3 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.
no thermal limit promises extreme low-power consumption
waveguide device small is good
monotonic response tolerant to fabrication inaccuracies
economics … ?
Tswitch eV
Required switching voltage:
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Example (GaAs): Sheet carrier concentration 4x1015 m-2
Interaction length 200 nm
Theoretically required switch voltage 1 mV
Required switching voltageT. Palm, L. Thylen, O. Nilsson, C. Svensson, J. Appl. Phys. 74, 687 (1993)
T
YBSS eV
Required change in applied gate bias required to change the state of the YBS:
Sub-thermal switching in YBS just experimentally verified !L. Worschech et. al., private communication
Contrast: e
TkV BFETS )10log(
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Electron transport – Landauer-Büttiker formalism
-10 0 100
1
Gate bias [arb. units]
4
1
4
1
2
14
1
4
1
2
12
1
2
10
22
22
YT
eTER
I rY
r )(1
0
S
gg
V
V tanh
Transmission probability stem right arm
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Space-charge effects switching
e-
1
2 3
4
1
4
1
2
14
1
4
1
2
12
1
2
10
22
22
YT
rY
r VTER
I )(1
0
The Self-Gating EffectJ-O J. Wesström Phys. Rev. Lett. 82 2564 (1999)
S
gg
V
V tanh
S
sggg
V
WV 23tanh
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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).
Space-charge can be dominant. Dependence is complex. Single parameter model not adequate to model space charge effects Screening of gate voltage can be severe.
Fully self-consistent simulation tool for simulations of electron waveguide devices developed.
0
50
100
150
200 0
50
100
150
2000
1
x 10-3
[nm][nm]
[C/m
2 ]
0
50
100
150
200 0
50
100
150
2000
1
x 10-3
[nm][nm]
[C/m
2 ]
Conclusions: Small charge densities allows for original response Gate efficiency is a showstopper
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Detecting selfgatingK. Hieke and M. Ulfward, Phys. Rev. B 62, 16727 (2000).L. Worschech et. al., Appl. Phys. Lett. 79, 3287 (2001).
-6 -4 -2 -0 2 4 6
Branch voltage [a.u.]
0
1
2
3
4
5
Ste
m v
olt
age
[a.u
.]Leave stem, W1, floating and measure it’s potential while varying branch voltages
Setrr WW 23
rr WW 21 Theory then predicts:
2223 1 rWW
Expected result
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
-0.4 -0.2 0 0.2 0.4
right drain voltage (V)
stem
vo
ltag
e (V
)
200 nm
320 nm
Experimental result
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Ballistic switching modeH. Q. Xu, Appl. Phys. Lett. 78, 2064 (2001).
Three star coupled QPCs
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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
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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).
E lectron gas
Split gate
Simple fabrication technique
However… Confinement too weak
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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
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Fabrication: Schottky gatesE. Forsberg and K. Hieke, Phys. Scri. T101, 158 (2002).
Pt:Schottky-gate
E lectron gas
Strong confinement single mode easily achieved Demonstrated in
– GaAs/AlGaAs Better gate efficiency possible
However… Complex fabrication technique
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YBS-based circuits
Fan-out possible Tolerant to fabrication defects
- Monotonic response- Coherence only required in branching region
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Logic Based on Y-branch Switches
Inverter
NAND gate using asymmetrical Y-branch switches
S
D1
G
D2
1011
0101
0010
0000
D2D1GS
Electrical symbol and possible states
T. Palm and L. Thylén, J. Appl. Phys. 79 8076 (1996)E. Forsberg, unpublished
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Ballistic YBS logic
S. Reitzenstein et. al., Electron. Lett. 38, 951 (2002) H. Q. Xu, IEEE Electron. Dev. Lett 25, 164 (2004).
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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?
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Comparing numbers
Switchenergy for a device with capacitive inputs: 2switchswitch VCE
ΔVswitch = 1 mV
C = 0.1 pF
Conclusion: Reversible logic can greatly reduce the power dissipation of YBS-based logic.
Minimum switch energy for typical YBS is thus of the order 0.6 meV.
kBT ln 2 = 18 meV @ room temperature.
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Reversible YBS logicE. Forsberg, Nanotechnology 15, 298 (2004).
A A '
B B '
C C '
A B C A’ B’ C’
0 0 0 0 0 0
0 0 1 0 0 1
0 1 0 0 1 0
0 1 1 0 1 1
1 0 0 1 0 0
1 0 1 1 1 0
1 1 0 1 0 1
1 1 1 1 1 1
ccNOT (Fredkin) gate
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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).
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TimingM. Frank et. al., private communication
Moving periodic globalpotential
x
y
x
V
BasicY-junction“switch gate”Control
waveguide
Data waveguide
Electrostatic repulsion
Ground-state high- probability regions of two electrons’ wave packets
Left branch
Rightbranch
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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 showstopper invariant of
implementation technology