1. The electron waveguide Y-branch switch A 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 , P. R. China
中国杭州浙江大学玉泉校区
Good morning, my name is Erik Forsberg and I come from the JORCEP, which is a collaboration between the Royal Institute of Technology in Sweden and Zhejiang University in China. Main research topic is, as the name implies, photonics.
I’ve been asked to give a presentation on the electron waveguide YBS switch, and this is work that has been done at our group at KTH.

2. Outline Basic idea Theoretical Experimental Logic Reversible logic
Required switching voltage
Single mode operation
Ballistic switching
Experimental
Logic
Reversible logic
Conclusions
The YBS was proposed by our group at KTH (not by me though, I was still in high school at the time) but I’ll present work done by other groups with which we have collaborated with as well.
Basic outline will be this, I’ll start with the basic idea, present some theoretical aspects, discuss fabrication techniques that has been employed and then discuss logic based on the switch.

3. Electron Waveguide Y-Branch Switch (YBS) T. Palm and L. Thylén, Appl
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.
Required switching voltage:
The YBS was proposed in 1992 by Lars Thylen and his, at the time, student, Tomas Palm. The inspiration came from optics, the electron waveguide switch is basically an electronic analogy of the optical YBS.
At the time there were a number of proposal of devices based on electron waveguides, all with the intention of eventually replacing the FET.
The basic idea is simple enough, form a Y-shaped electron waveguide device, send in electrons into the stem, and direct the electrons into either of the two branches depending on the applied gate voltage.
Pretty much at once, the KTH group realized that the YBS had a very appealing feature, which is that the change in the applied gate voltage required to switch the state of the device is not thermally limited.
Also, in contrast to other devices considered it has a monotonic response to the applied gate bias, making it more tolerant to fabrication defects.
no thermal limit  promises extreme low-power consumption
waveguide device  small is good
monotonic response  tolerant to fabrication inaccuracies
economics … ?

4. Required switching voltage T. Palm, L. Thylen, O. Nilsson, C
Required switching voltage T. 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
The fact the required switch voltage is not thermally limited is quite easily understood from intuitive arguments. In the YBS electrons need be stopped as in an FET, you only need to deflect them. And so the limiting value of the switch voltage is determined by the interaction length, or the time the electron wave package is influenced by the gate field.
As an example, we can calculate the minimum required switch voltage in a typical YBS to be of the order of a mV. This can of course be optimized more, so we can consider this to be a conservative number.
This is of the order of 50 times less than for an FET (at room temperature)
I should mention that subtermal switching has just been demonstrate by a group at Wurzburg university headed by Lukas Worschech. I don’t know the details yet, they’re working on a paper right now.
Contrast:
Sub-thermal switching in YBS just experimentally verified !
L. Worschech et. al., private communication

5. Electron transport – Landauer-Büttiker formalism
Transmission probability stem  right arm
-10 10 1
Gate bias [arb. units]
Being an electron waveguide device operating in the single mode coherent regime the electron transport can described using the Landauer-Buttiker formalism, where the current through the device is determined by a transmission probability matrix. And if you design the switch properly the reflections in the stem can be neglected and if so the matrix is dependent on one parameter only. This parameter is of course dependent on the gate bias and has been through simulations and experiments found to tangent hyperbolic function.
As gates are not perfect one normally adds a gate efficiency parameter eta. Delta Vs is a measure of the response.

6. Space-charge effects switching
The Self-Gating Effect J-O J. Wesström Phys. Rev. Lett (1999) e- 1 2 3
Initial work did not consider the effect of space charge inside the device but this is a bit to simplistic. Wesstrom in our group at KTH first considered this, and realized that when you direct the electron flow through one of the branches, you will create an internal field between the branches. The field is in a direction opposite the applied gate field and as such reduce the switching efficiency. Under certain conditions one can also achieve a bi-stability.

7. Space charge cont’d. E. Forsberg, J. Appl. Phys, 93, 5687 (2003) E
Space charge cont’d... E. Forsberg, J. Appl. Phys, 93, 5687 (2003) E. Forsberg and J.-O. J. Wesström, Solid-State. Electron. 48, (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 gate voltage can be severe.
So let’s see, we did some further work on this with more rigorous simulations, which partly supported this but also pointed at a more complex dependence than the one-parameter model predicted.
Conclusions:
Small charge densities allows for original response
Gate efficiency is a showstopper

8. Detecting selfgating K. Hieke and M. Ulfward, Phys. Rev
Detecting selfgating K. Hieke and M. Ulfward, Phys. Rev. B 62, (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:
Set
When proposing the selfgating effect Wesstrom also proposed ways to experimentally verify its existence. Experiments that followed both in our group as well as in the Wurzburg group found something completely different.
The proposal was to while leaving the stem floating, one should set the voltages connecting the branches equal but opposite in sign. When doing so the stem would always follow the more positive of the two, however the experiments showed the exact opposite. The results were also visible at room temperature as well as for high voltages. So it was quite clear that this was another physical process.
Expected result
Experimental result

9. Ballistic switching mode H. Q. Xu, Appl. Phys. Lett. 78, 2064 (2001).
Three star coupled QPCs
The explanation of what was seen was given by Honqi Xu at Lund University with whom we collaborating at the time. By modeling the YBS as a three QPCs one can quite easily reproduce the measured results.
So this then is an very different operating regime of the YBS which has been perused quite a lot by the Lund group.

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
So to shortly recap what I’ve said so far, the YBS has in essence three modes of operation, two variants in the single mode regime and one multimode regime.
A lot of experimental work has also been done. And the first came quite early after the first proposal.

11. Fabrication: Split-gate P. Ramvall, P. Omling, T. Palm, and L
Fabrication: Split-gate P. 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
The simplest way to fabricate a YBS is just take a 2DEG defined in by a heterostructure and place a split gate on top. By a negative voltage on the gates the electron gas below is confined to the regions where there is no gate on top.
This is a simple technique, but that is on the other hand its only virtue. Confinement is too weak to make this a feasible technique.`

12. Fabrication: In-plane gates J. O. Wesström et. al
Fabrication: In-plane gates J. 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, (2005).
Simple fabrication technique
Strong confinement  single mode easily achieved
Demonstrated in
GaAs/AlGaAs
InGaAs/InP
InAs/AlSb
However…
Low gate efficiency
A better method, and the most widely used is to etch trenches using for example reactive ion beam etching, and in this way one can define the switch. An added benefit is that one can use the electron gas next to the defined wire as gates, and these will be automatically aligned. This gives you a strong confinement, but a problem is that the gating efficiency is usually quite low which means that the theoretical limit of required switch efficiency is far away.

13. Fabrication: Schottky gates E. Forsberg and K. Hieke, Phys. Scri
Fabrication: Schottky gates E. 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
A better technique which gives you higher gate efficiency is to electrochemically plate the gate on the side walls of the waveguide, drawback is on the other a quite complex fabrication method.

14. YBS-based circuits Fan-out possible Tolerant to fabrication defects
Monotonic response
Coherence only required in branching region
I single switch is of course not what we want, we want a circuit. This is on the other hand no problem, fan-out is for instance possible and when operating in the single mode coherent regime coherence is only needed in the branching region, not throughout the whole circuit.
So logic based on the YBS has of course been considered …

15. Logic Based on Y-branch Switches
T. Palm and L. Thylén, J. Appl. Phys (1996)
E. Forsberg, unpublished
Electrical symbol and
possible states
Inverter S D 1 G 2
…the first proposal came a few years after the original proposal and discussed conventional devices such as inverters and nand gates. 1 D2 D1 G S
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).
Logic based on the ballistic switching has also been demonstrated both by the Lund group and the group at Wurzburg university.

17. YBS logic Single mode operation logic Ballistic Conclusion:
Feasible
Low power operation due to sub-thermal switching
Advantage over CMOS FET ?
Ballistic
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?
So, logic based on the YBS is no problem…..on the other hand, is there a point. Well, based on the single mode operating regime one could in principle get low power circuits and the ballistic devices can have some specialized applications. But, CMOS is a tough competitor to say the least and when writing my thesis I started to think that just mimicking conventional logic was, well, not innovative enough…
… at the time I also read about reversible computing for the first time. And it turns out that…

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 order 0.6 meV.
kBT ln 2 = 18 room temperature.
…that if you start too look at some numbers one can reach some interesting conclusions. If we calculate the switch energy for a typical, though ideal, YBS using the switch voltage from before we get a switch energy of about half a meV which is about more than an order of magnitude less than the cost of information erasure.
So reversible logic circuits based on YBS switches seemed to me to something quite interesting. So I proposed a fredkin gate based on the YBS…
Conclusion:
Reversible logic can greatly reduce the power
dissipation of YBS-based logic.

19. Reversible YBS logic E. Forsberg, Nanotechnology 15, 298 (2004).1
ccNOT (Fredkin) gate
… which, as I found out during the review process of my paper was in a sense logically equivalent to a proposal of helical logic by Merkle and Drexler. The physical implementation is of course quite different.
Other flavors of reversible logic is should be possible, I think I have an idea of how to do a cSET based on the selfgating effect. Not sure about this one just yet as I thought about it on the plane over here.

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 few words on implementation, reversible circuits can be made today….there are of course a few buts though. Present day YBSs are made in III-V still operate at cryogenic temperatures, not a showstopper perhaps but definitely a drawback. Gating efficiency is also generally low\
Other options for implementation could be in hexagonal networks, something that a group at Hokkaido university has used to demonstrate binary decision diagram logic in, carbon nanotubes is another possibility. Something similar to the ballistic switching has already been demonstrated in a Y-shaped cnt.
Si, well I don’t enough about that, but that would of course be nice
A. N. Andriotis et. al., Appl. Phys. Lett. 79, 266 (2001).

21. Timing M. Frank et. al., private communication
Moving periodic global potential x y V
Basic Y-junction “switch gate”
Control waveguide
Data waveguide
Electrostatic repulsion
Ground-state high- probability regions of two electrons’ wave packets
Left branch
Right branch
Timing will of course be of importance. And Mike here had a good idea of how to solve this using a moving global potential, so I stole this picture from him.

22. Summary YBS summarized Reversible logic based on YBS The road ahead
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
Time is running out so I’d better stop, and just leave some summary and points for further work here and go to questions if you have any.