Single Electron Transistors and Quantum Computers

G5: Norma L. Rangel

Nanotechnology

4/20/2010

Overview of Nano-electronic devices

Ellenbogen 2000

Outline

Conventional TransistorsSingle Electron Transistors

Coulomb IslandCoulomb Blockade Coulomb Gap EnergyTunneling

Applications of SETsQuantum Computers: NATURE, Vol 464, 03-2010

Transistors Transistors

BJT

NPN

Electrons

PNP

holes

FET

JFET

MOSFET

Fundamental component in

almost all electronic devices

• A transistor can be used as a switch and as amplifier

• Manufactured in different shapes but they have three leads: BASE (gate controller device), COLLECTOR (larger electrical supply, source) AND EMITTER (the outlet for that supply)

Junction transistors & field effect transistorsA junction transistor: a thin piece of one type of semiconductor material between two thicker layers of the opposite type.A field effect transistor: Electricity flows through one of the layers, called the channel. The voltage connected to the gate controls the strength of the current in the channel.

http://www.physlink.com/Education/AskExperts/ae430.cfm

Single Electron Transistor (SET)Switching device that uses controlled electron

tunneling to amplify current. A SET is made from two tunnel junctions that share a

common electrode.

An AFM picture of a single-electron transistor (SET). The red region, the island where only single electrons may be admitted.

Schumacher et al.,  Applied Physics Letters

A tunnel junction consists of two pieces of metal separated by a very thin (~1 nm) insulator. The only way for electrons in one of the metal electrodes to travel to the other electrode is to tunnel through the insulator. Since tunneling is a discrete process, the electric charge that flows through the tunnel junction flows in multiples of e, the charge of a single electron.

Single Electron Transistor (SET)Tunnel Junction

Single Electron Transistor (SET)Tunneling

Quantum tunneling refers to the phenomena of a particle's ability to penetrate energy barriers within electronic structures.

Schematic representation of quantum tunnelling through a barrier. The energy of the tunneled particle is the same, only the quantum amplitude (and hence the probability of the process) is decreased.

http://en.wikipedia.org/wiki/Quantum_tunnelling

Dynamics of SETThe SET is made by placing 2 tunnel junctions in seriesThe 2 tunnel junction create what is known as a “Coulomb Island” that electrons can only enter by tunneling through one of the insulators.This device has 3 terminals like the FETs.The cap may seem like a third tunnel junction, but is much thicker than the others so that no electrons could tunnel through it.The cap simply serves as a way of setting the electric charge on the coulomb island.

controlled by light irradiation

Coulomb IslandWhen a capacitor is charged through a resistor, the

charge on the capacitor is proportional to the applied voltage and shows no sign of quantization.

When a tunnel junction replaces the resistor, a conducting island is formed between the junction and the capacitor plate. In this case the average charge on the island increases in steps as the voltage is increased -> Low self capacitance

The steps are sharper for more resistive barriers and at lower temperatures.

ProcedureCharge passes through the island in quantized units. The energy must equal the coulomb energy e^2/2Cg. Coulomb blockade, As the bias voltage between the source and drain is increased, an electron can pass through the island when the energy in the system reaches the coulomb energy.The critical voltage needed to transfer an electron onto the island equal to e/C, is called the coulomb gap energy.

Coulomb BlockadeThe effect in which electron can not pass through the island unless the energy in the system is equal to the coulomb energy e^2/Cg.

The thermal energy kBT must be below the charging energy or the electron will be able to pass the quantum blockade via thermal excitation

Coulomb blockade tries to alleviate any leak by current during the off state of the SET.

For Function SETs

Capacitance of the island must be less than 10^-17 Farads and therefore its size must be smaller that 10 nm.

The wavelength of the electrons is comparable with the size of the dot, which means that their confinement energy makes a significant contribution to the coulomb energy.

Example SET FabricationLocalization of appropriate flakes with optical microscopeContacting with metal electrodes by e-beam LithographyWriting an etch-mask with e-beam lithographyReactive ion etching with Ar/O2 plasmaWire-bonding to contact pins -> testing the deviceFurther etching, if necessary to narrow the graphene structures

Example: Graphene SETConductance G of a device with the central island as a function of Vg in the vicinity

Chaotic Dirac Billiard in Graphene Quantum DotsL. A. Ponomarenko, F. Schedin, M. I. Katsnelson, R. Yang,1 E. W. Hill, K. S. Novoselov, A. K. GeimScience 2008

T = 0.3 K

Review Article

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe & J. L. O’Brien

NATURE, March 2010

Quantum Computers

I think I can safely say that nobody understands quantum mechanics.

“No, you’re not going to be able to understand it. . . . You see, my physics students don’t understand it either. That is because I don’t understand it. Nobody does. ... The theory of quantum electrodynamics describes Nature as absurd from the point of view of common sense. And it agrees fully with an experiment. So I hope that you can accept Nature as She is -- absurd.

Richard Feynman

Quantum Computer:

A machine that would exploit the full complexity of a many-particle quantum wavefunction to solve a computational problem.

A quantum computer will not be a faster, bigger or smaller version of an ordinary computer. Rather, it will be a different kind of computer, engineered to control coherent quantum mechanical waves for different applications.

Light to laser - Computer to QCLight was always ‘incoherent’, meaning that the many electromagnetic waves generated by the source were emitted at completely random times with respect to each other. Quantum mechanical effects, however, allow these waves to be generated in phase, and the light source engineered to exploit this concept was the laser.

Classical Computation: Classical logic bit: “0” and “1”

Quantum Computation: Quantum bit, “Qubit”, can be manipulated using the rules of quantum

physics

To build a quantum computer, need many qubits with long coherence times

Need interactions between qubits to generate entanglement

Bits and Qubits

Quantum State

Two Distinguishable States

a b+

Continuous State Space

Orthogonal quantum states |0> , |1> and their superposition |Ψ> = c0|0> + c1|1>

Potential technologies of QCShor’s quantum algorithm for factoring large numbers. Grover’s Search AlgorithmArtificial nanotechnology: we might use quantum computers to understand and engineer such technology at the atomic level.Quantum communication: sharing of secrets with security guaranteedQuantum metrology: in which distance and time could be measured with higher precision than is possible otherwise.Quantum teleportation

Quantum teleportation

Entanglement-assisted teleportation, is a technique used to transfer quantum information from one quantum system to another. Is a quantum protocol by which a qubit a (the basic unit of quantum information) can be transmitted exactly (in principle) from one location to another.

http://en.wikipedia.org/wiki/Quantum_teleportation

QC Hardware

Many materials under consideration: Quantum bits are often imagined to be constructed from the smallest form of matter, an isolated atom, as in ion traps and optical lattices, but they may likewise be made far larger than routine electronic components, as in some superconducting systems.

QC SoftwareNielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge University Press, 2000).

Implementation of quantum computers: DiVincenzo’s criteria

1. Scalability: A scalable physical system with well characterized parts, usually qubits.

2. Initialization: The ability to initialize the system in a simple “pure” state.

3. Control: The ability to control the state of the computer using sequences of elementary universal gates.

4. Stability: Long decoherence times, together with the ability to suppress decoherence through error correction and fault-tolerant computation.

5. Measurement: The ability to read out the state of the computer in a convenient product basis.

DiVincenzo, Fortschr. Phys. 48, 771 (2000)

Dephasing and Decoherence

An oscillator with frequency varying by trial, as indicated by the differently colored waves, averages to an oscillation decaying with apparent dephasing timescale T2*.

A quantum oscillator interacting with the environment may have phase-kicks in a single trial; these are the processes that harm coherence in quantum computation, and lead to an average

decay process of timescale T2.

Relaxation of non-thermal distribution.

Decay rate of resonance peaks

Dephasing caused by impedance both at level splitting and zero frequency.

Width of resonance peaks

Qubit decoherence can be related to noise in the environment coupled to qubit.

Decoherence

ERRORS

Quantum error correction’ (QEC): NNo system is fully free of decoherence, but small amounts of decoherence may be removed through various techniques

Fault-tolerantfor error probabilities beneath a critical threshold that depends on the computer hardware, the sources of error, and the protocols used for QEC.

Physical requirements

It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions. A Hilbert space is an abstract vector space possessing the structure of an inner product that allows length and angle to be measured.

Scalability. The computer must operate in a Hilbert space whose dimensions can grow exponentially without an exponential cost in resources (such as time, space or energy).Universal logic. The large Hilbert space must be accessible using a finite set of control operations; the resources for this set must also not grow exponentially.Correctability. It must be possible to extract the entropy of the computer to maintain the computer’s quantum state.

Technologies researchers are currently employing

Photons Trapped Atoms Nuclear Magnetic Resonance Quantum Dots and dopants in solids Superconductors Other Technologies

Photons

Photons are relatively free of the decoherenceAllow the encoding of a qubit on the basis of location and timing; quantum information may also be encoded in the continuous phase and amplitude variables of many-photon laser beams.Research Focus: High efficiency single-photon detectors and sources, devices that would enable a deterministic interaction between photons, and chip-scale waveguide quantum circuits.

Photonic quantum

circuitGreen lines show optical waveguides; yellow components are metallic contacts.

Trapped atomsThe best time and frequency standards are based on isolated atomic systems.The energy levels in trapped atoms form very reliable qubits, with T1 and T2 times typically in the range of seconds and longer.Individual atomic ions can be confined in free space with nanometer precision using appropriate electric fields from nearby electrodes

Multi-level linear ion trap chip; the inset displays a linear crystal of several ions fluorescing when

resonant laser light is applied (the ion–ion spacing is 4 mm in the figure).

Neutral atomsAn array of cold neutral atoms may be confined in free space by a pattern of crossed laser beams, forming an optical latticeAdjacent atoms can be brought together depending on their internal qubit levels with appropriate laser forces, and through contact interactions.

Schematic of optical lattice of cold atoms formed by multi-dimensional optical standing wave potentials (J. V. Porto). Image of individual Rb atoms confined in a two-dimensional optical lattice, with atom–atom spacing of 0.64 mm (M. Greiner).

Nuclear Magnetic Resonance (NMR)

Nuclear spins in molecules in liquid solutionsRapid molecular motion helps nuclei maintain their spin orientation for T2 times of many seconds.Immersed in a strong magnetic field, nuclear spins can be identified.Irradiating the nuclei with resonant radio-frequency pulses allows manipulation of nuclei of a distinct frequency, giving generic one-qubit gates. Two-qubit interactions arise from the indirect coupling mediated through molecular electrons.

Nuclear SpinA nucleus with an odd atomic number or an odd mass number has a nuclear spin.The spinning charged nucleus generates a magnetic field.

=>

Two Energy States

The magnetic fields of the spinning nuclei will align either with the external field, or against the field.

A photon with the right amount of energy can be absorbed and cause the spinning proton to flip.

NMR spectrometryA 900MHz NMR instrument with a 21.2 T

magnet at HWB-NMR, Birmingham, UK

•http://en.wikipedia.org/wiki/NMR_spectroscopy•Chapter 13, Nuclear Magnetic Resonance Spectroscopy Organic Chemistry, 5th Edition L. G. Wade, Jr.

Quantum dots and dopants in solidsMotivation: A complication of using single atoms in vacuum is the need to cool and trap them. Need to be integrated into a solid-state host.

Problem: Self-assembled dots are randomly located their optical characteristics vary from dot to dot.

Rapid optical initialization has been demonstrated for both electrons and holes. Qubits may be controlled very quickly, on the order of picoseconds, potentially enabling extremely fast quantum computers.

Electrostatically defined quantum dots, where the confinement is created by controlled voltages on lithographically defined metallic gates. Operate at very low temperatures (~1K) and are primarily controlled electrically, Self-assembled quantum dots, a random semiconductor growth process creates the potential for confining electrons or holes. operate at higher temperatures (~4 K) and are primarily controlled optically.

The negatively charged state of the nitrogen vacancy centre forms a triplet spin system. Under optical illumination, spin-selective relaxations facilitate efficient optical pumping of the system into a single spin state, allowing fast (250 ns) initialization of the spin qubit. The spin state of a N-vacancy centre may then be coherently manipulated with resonant microwave fields, and then detected in a few milliseconds via spin-dependent fluorescence in an optical microscope

The atomic structure of a nitrogen-vacancy centre in the diamond

lattice, with lattice constant 3.6A Å.

Optically active solid-state dopants

Arrays of electrostatically defined dots

Each containing a single electron whose two spin states provide a qubitQuantum logic would be accomplished by changing voltages on the electrostatic gates to move electrons closer and further from each other, activating and deactivating the exchange interactionThe single-electron transistor or quantum point contact allows the measurement of a single electron chargeThe control of individual spins has also been demonstrated via direct generation of microwave magnetic and electric fields.

The carbon-based nanomaterials of fullerenes, nanotubes and graphene have excellent properties for hosting arrays of electron-based qubits. Electrons for quantum computing may also be held in a low-decoherence environment on the surface of liquid helium, or be contained in molecular magnets

Schematic diagram of a graphene double quantum dot. Each dot is assumed to have length L and width W. The structure is based on a ribbon of graphene (grey) with semiconducting armchair edges (white).

Trauzettel, B., Bulaev, D. V., Loss, D. & Burkard, G. Spin qubits in graphene quantum dots. Nature Phys. 3, 192–196 (2007).

Other technologies

Comparing coherence times:

Status of QCRudimentary Quantum Computers existDecember 19, 2001 – IBM performs Shor’s AlgorithmQuantum computing is so complex that expanding on simple operations is still 10 –20 years away.Most well known QC’s based on nuclear magnetic resonance (NMR).

Future Work

Promising techniques for improving coherence timesThe central challenge in actually building quantum computers is maintaining the simultaneous abilities to control quantum systems, to measure them, and to preserve their strong isolation from uncontrolled parts of their environment.

Thanks

Questions?

G5Rebuttal: Quantum mechanical devices

Norma L. Rangel

Norma Rangel – Rebuttal • The featured paper (review) was very recent and potentially interesting to the

audience. Although a bit unorganized, the slides had a fair amount of information and graphics. However, some references were missing or incomplete – Certainly, there were not references in every slide, but somewhere all the sources were cited

in the ppt.• I know the topic was hard, but the speaker constantly apologized instead of focusing

on giving her best effort, projecting confidence and credibility. The speaker gave the impression of not having a good enough knowledge of the basic theory behind the presented technology, although might rather be lack of confidence handling this specific topic.

– I apologize (again) for my lack of confidence, certainly more time was require from myself to successfully cover this topic since it was not in my confidence field.

• A friendlier outline of the presentation would have helped a lot. The sequence of slides was not optimal. For instance, after three slides talking about SET, there was one slide with the schematics of quantum tunneling, where actually the instructor had to intervene to explain it. It would have been better start with slide explaining quantum tunneling , and then follow with the device that uses that principle.

– I fully agree with the reviewer, an outline could have been very helpful but I didn’t use it because I tried to cover two main topics: SET and QC, most of the remaining the topics came out from definitions that I found appropiate to help the audience understand the lecture.

• Generally, the subject was presented with ease of understanding, as this topic can be very hard to understand. However, this led to somewhat lacking depth in the subject.– I tried to made the presentation somehow helpful to undergrads

(majority in the audience) to understand, since a very technical background was needed to follow the topic.

• The connection between the introduction (SET) and the reviewed paper (Quantum Computer) was weak, interrupting the flow of the presentation. Choosing a paper with applications using SET might better induce the flow of the overall presentation.– I agree with the reviewer, I think the connection between the SET and

the quantum computer hardware was lost, my intension of having SETs as an introduction of QCs was because SETs are one of the components of a QC, however I know realize that an introduction only based on concepts could have been more helpful. Also, I believe that since I wanted to define most of the concepts needed for the presentation made the connection between the two components.

G1Review: Quantum mechanical devices

Edson Bellido

The presenter explained how the BJT and FET transistors work. She explained what a tunnel junction, quantum tunneling, coulomb island and coulomb blockade are. This concepts help to understand how a SET works.

She gave an example of SET using graphene where they have analyzed the conductance of a device with the central island as a function of Vg in the vicinity.

http://upload.wikimedia.org/wikipedia/commons/9/91/TyTunnelling.png

Tunneling

The presenter also introduced the concept of quantum computer as well as a comparison between a traditional bit and a qubit. She explain some of the features and potential applications of the quantum computer.

http://teleportationtravel.com/images/quantum_teleportation.gif

She stated the some criteria we have to consider to implement a quantum computer these are: scalability, initialization, control, stability, measurement. Also the physical requirements which are that the computer must operate in a Hilbert space, the space must be accessible using a finite set of control operations and it must be possible to extract the entropy of the computer to maintain the computer’s quantum state.

It was also presented the technologies that are currently use to test the concepts of quantum computing and implement some prototypes. They are using photons, trapped atoms, nuclear magnetic resonance, quantum dots and dopants in solids and superconductors. She explained how researchers are using these technology to fabricate quantum computers and gave some experimental examples.

The overall presentation was informative. However, I think that it would be more interesting if instead of a very shallow overview of quantum computing the presenter would have explain just one application or one device in detail. Some of the concepts were not well explained but this understandable due to the complexity of the topic.

Personally I find this topic very interesting specially because there is many things we do not fully understand, for example: why there is quantum entanglement?.

G2Review: Quantum mechanical devices

Alfredo Bobadilla

Single Electron Transistor Lecture Review

• Problems related with integration of single electron transistors (SET) in molecular circuits were not analyzed. These include the diffraction limit in optical lithography and the increase in thermal noise when integrating a much higher number of transistors. And it was not shown where SET research stands currently, what is needed or what is being tried to make this commercially available.

• Concepts related to quantum physics were not correctly clarified. The key idea was not simplified, i.e. how quantum phenomena is aimed to be used in quantum computer. I think some physics terminology (Hilbert’s space, decoherence time, etc) could have been explained in more friendly terms. Other fundamental physics concepts like qubits and entanglement needed a deeper analysis.

Alfredo D. Bobadilla

Single Electron Transistor Lecture Review

• The analysis of quantum computers was broad, being considered not only advantages but also disadvantages. Nevertheless suggestions were not given to further advance the area. The inherent problem is the environment perturbing the quantum states of the system. Other problems are the high cost and the complex fabrication process implied on the current alternatives for a quantum computer. I would suggest looking for a solution in biological systems. Biological phenomena such as photosynthesis is based on quantum effects (doi:10.1038/nature05678), and it seems the lipid bilayer is a good isolator from the environment. It has already been shown recently hybrid nanostructures with lipid layer covering tubular nanostructures such as microtubules (doi:10.1073/pnas.0502183102), carbon nanotubes (pubs.acs.org/doi/abs/10.1021/nl100499x) and silicon nanowires (doi:10.1073/pnas.0904850106).

Alfredo D. Bobadilla

REVIEW OF QUANTUM DEVICESNORMA RANGEL’S PRESENTATIONBy Mary Coan

G3

REVIEW

Discussed the basics of Transistors BJTs, FETs, SETs

Described the following in a fundamental way tunneling/tunnel junctions Coulomb blockade

Good for those who have not experienced this information before

Linked background information to the topic of the presentation in an organized manner

Gave examples of SETs Fabrication methods

Graphene SET

REVIEW

Reviewed Quantum Computers (QCs) Defined Quantum Computers

Light to laser Bit to Qubit

Examples of technologies for QCs Implementation of QCs

Scalability Initialization Control Measurement Decoherence

REVIEW Discussed current technologies researchers are

employing Current Status of QCs Future Work was also discussed Overall the presentation was put together very well

Supplied information in a organized manner Presentation was geared towards the majority of the class,

undergraduates This is appropriate

Used graphics to describe information and equations Very helpful

G4 Review (Quantum Devices)

Diego A Gómez-Gualdrón

A Tunnel JunctionA thin layer of insulator separating two electrodes is

know as ‘Tunnel Junction’

electrode

Insulator

electrode

Schematics of Tunnel JunctionPhysics of the Junction

• Classical mechanics says no electron can flow through the insulating barrier

• Quantum mechanics says one electron can flow through the barrier by ‘tunneling’

The barrier as a resistor

• The larger the bias voltage V1-V2, the more frequent the pass of electrons

• The thicker the barrier, the more resistant

V1 V2

The insulator barrier also has a finite capacitance C. When an electron tunnels, there is a voltage build up according to V= e/C

Coulomb BlockadeThe increase of the (differential) resistance at low bias

in a Tunnel Junction is known a ‘Coulomb Blockade’

Conditions

• Extremely low capacitance of the junction

• Low bias between electrodes

• Low thermal energy of the electrons

electrons

electrodeelectrode

electrons

electrodeelectrode

electrons

electrodeelectrode

Schematics of Coulomb Blockade

1)

2)

3)

V= e/CIf the C is low enough, then the entrance of just one electron (e) rises V so much as to refrain more electrons from passing

Single Electron TransistorThey take advantage of the coulomb blockade effect to

control the ‘current’ of electrons, and are composed by two tunnel junctions sharing a common electrode

common electrode

Insulator

electrode

Schematics of SET

V1 V2

electrode

V1

Insulator

• The common electrode is called ‘island’

sourcedrain

Gate

• The voltage of the gate affects the energy levels of the island

• One source electron tunnels through the island

• Coulomb blockade occurs until the electron tunnels to the drain

How

Quantum ComputingA different kind of computers taking advantage of

quantum entanglement of particles The Bloch sphere

• Uses qubits

• A qubit is a quantum state

• The total quantum state is a linear combination of particles states

• The state of each particle is represented by kets such as |0 > and |1>

• Instead of using 8 bits (0’s and 1’s)to represent 01001110 uses one qubit {|0 > + |1> + |0 > + |0 > + |1> + |1> + |1> + |0 > }

A qubit made out two states

REVIEW• The presentation was given in two parts: the first

one, the description, working principle and fabrication of single electron transistors; the second one, a review in the nascent area of quantum computing

• The featured paper (review) was very recent and potentially interesting to the audience. Although a bit unorganized, the slides had a fair amount of information and graphics. However, some references were missing or incomplete

REVIEW• I know the topic was hard, but the speaker

constantly apologized instead of focusing on giving her best effort, projecting confidence and credibility

• The speaker gave the impression of not having a good enough knowledge of the basic theory behind the presented technology, although might rather be lack of confidence handling this specific topic

• A friendlier outline of the presentation would have helped a lot. The sequence of slides was not optimal. For instance, after three slides talking about SET, there was one slide with the schematics of quantum tunneling, where actually the instructor had to intervene to explain it. It would have been better start with slide explaining quantum tunneling , and then follow with the device that uses that principle.

REVIEW

Review for G5

Jung Hwan Woo

• Generally, the subject was presented with ease of understanding, as this topic can be very hard to understand. However, this led to somewhat lacking depth in the subject.

• The connection between the introduction (SET) and the reviewed paper (Quantum Computer) was weak, interrupting the flow of the presentation. Choosing a paper with applications using SET might better induce the flow of the overall presentation.