Single Electron Tunneling Report

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Single Electron Tunneling

Introduction:

SET devices can be used to construct circuits which process information by manipulating individual

electrons. SET devices are small, dissipate little power, and can detect exquisitely small quantities ofcharge. The small size and low power dissipation of SET circuits makes them potentially useful for the

Information Technology industry. The electromagnetic environment in which a small tunnel junction

circuit is embedded plays a crucial role in its transport properties. Although the theory of single-electron

tunneling is well established, few analytical results are known.

THE FIRST BREAKTHROUGH COULOMB BLOCKADE:

Coulomb blockade was first suggested back in 1951 by Gorter. But, it remained largely unnoticed until,

almost 40 years later, Fulton and Dolan built a transistor based on single-electron tunneling.

Schematic representation of an

electron tunnelling through a barrier

WHAT IS COULOMB BLOCKADE:

A tunnel junction is, in its simplest form, a thin insulating barrier between two conducting electrode The

following reasoning is for the case of tunnel junctions with an insulating barrier between two normal

conducting electrodes (NIN junctions). According to the laws of classical electrodynamics, no current can

flow through an insulating barrier. According to the laws of quantum mechanics, however, there is a non

vanishing (larger than zero) probability for an electron on one side of the barrier to reach the other side

(see quantum tunnelling). When a bias voltage is applied, this means that there will be a current,

neglecting additional effects, the tunnelling current will be proportional to the bias voltage. In electrical

terms, the tunnel junction behaves as a resistor with a constant resistance, also known as an ohmic

Equivalent circuit and energy diagram of a single tunnel junction.The resistorRe represents the low-frequency impedance of the

environment.

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resistor. The resistance depends exponentially on the barrier thickness. Typical barrier thicknesses are on

the order of one to several nanometers.

Due to the discreteness of electrical charge, current through a tunnel junction is a series of events in

which exactly one electron passes (tunnels) through the tunnel barrier (we neglect cotunneling, in which

two electrons tunnel simultaneously). The tunnel junction capacitor is charged with one elementarycharge by the tunnelling electron, causing a voltage buildup U= e/C, where e is the elementary charge

of 1.61019 coulomb and Cthe capacitance of the junction. If the capacitance is very small, the voltage

buildup can be large enough to prevent another electron from tunnelling. The electrical current is then

suppressed at low bias voltages and the resistance of the device is no longer constant. The increase of the

differential resistance around zero bias is called the Coulombblockade.

CONDITIONS FOR COULOMB BLOCKADE:

1. the bias voltage can't exceed the charging energy divided by the capacitance Vbias2. the thermal energy kBTmust be below the charging energy EC or else the electron will be able to

pass the QD via thermal excitation

3. the tunneling resistance (Rt) should be greater than h/e2

, which is

derived from Heisenberg's Uncertainty principle.

4. Re >h/2e2

Evolution of theIVcharacteristic of a single tunnel junction

as the resistance of the environmentRe is increased

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Fig: Comparison of the change in Fermi energy for the addition of one electron in Si and Al.

Quantum Confinement Energies

With decreasing island size the energy level spacing of electron states increases indirectly proportional to

the square of the dot size. The energy levels is given by

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Fig: Comparison of the quantum confinement energy in Si and Al.

Helmholtz's Free Energy:

The energy that determines the transport of electrons through a single-electron device is Helmholtz's free

energy which is defined as difference between total energy stored in the device and work done by

power sources. The total energy stored includes all the before mentioned energy components that have to

be considered when charging an island with an electron.

Influence of the Electromagnetic Environment:The electromagnetic environment plays a crucial role in the observation of charging effects. For instance

in a single tunnel junction a high impedance environment is mandatory in order for current oscillations

to appear. In the case of a high impedance environment tunnel rates have to be calculated according to the

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local rule , where only the junction through which the electron tunnels is considered for the calculation of

the Coulomb energy. The high impedance kind of shields the rest of the environment from the junction. It

is difficult to provide a high impedance environment for a single junction, because stray capacitances

which are usually much bigger than the capacitance of the junction itself, cause the junction to be voltage

bias.

Single-electron box schematics

Double Junction Barrier:

Consider two tunnel junctions in series biased with an ideal voltage source. The charges on junction one,

junction two, and on the whole island can be written as

respectively, with n1 the number of electrons that tunneled through the first junction entering the island, n2

the number of electrons that tunneled through the second junction exiting the island, and n=n1-n2 the net

number of electrons on the island.

.

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Two tunnel junctions in series biased with an ideal voltage source. The background charge q0 is non-

integer, and n1 and n2 denote the number of tunneled electrons through junction one and junction two,

respectively

A double barrier structure attached to source (S) and drain (D). CSD denotes a residual capacitance

between the two leads.

A background charge q0 produces generally a non-integer charge offset. The background charge is

induced by stray capacitances that are not shown in the circuit diagram and impurities located near the

island, which are practically always present. Vb=V1+V2gives

With the electrostatic energy stored in the double junction is

IV-characteristic of a double tunnel junction. The solid line gives the characteristic for q0=0 and the

dashed line for q0=0.5e. The Coulomb blockade is a direct result of the additional Coulomb energy, e2/2C,

which must be expended by an electron in order to tunnel into or out of the island

.

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Energy diagram of a double tunnel junction without and with applied bias. The Coulomb blockade causes

an energy gap where no electrons can tunnel through either junction. A bias larger than e/C overcomes the

energy gap.

Single electron Transistor:

The tunnel junction consists of two pieces of metal separated by a very thin (~1nm) 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 the charge of electrons.

In the blocking state no accessible energy levels

are within tunneling range of the electron (red)on the source contact. All energy levels on the

island electrode with lower energies are

occupied. When a positive voltage is applied to

the gate electrode the energy levels of the islandelectrode are lowered. The electron (green 1.) can

tunnel onto the island (2.), occupying a

previously vacant energy level. From there it cantunnel onto the drain electrode (3.) where it

inelastically scatters and reaches the drain

electrode Fermi level (4.).

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Coulomb Blockade Thermometer:

A typical Coulomb Blockade Thermometer (CBT) is made from an array

of metallic islands, connected to each other through a thin insulating layer.

A tunnel junction forms between the islands, and as voltage is applied,

electrons may tunnel across this junction. The tunneling rates and hence

the conductance vary according to the charging energy of the islands as

well as the thermal energy of the system.

The Capacitance Model for single-electron tunneling circuits:

It is an arrangement of (n + m) conductors embedded in some insulating environment. Each conductor i is

at an electrostatic potential Vi, has a charge qi stored on it, and has a capacitance CiD to drain (ground).

Between each pair of conductors i andj, there is a mutual capacitance Cij. Some of these capacitances

may belong to tunnel junctions, which allow electron transfers between the corresponding conductors.

Furthermore, we assume that m conductors are connected to voltage sources, which we call electrodes,

while then remaining ones are islands. n islands are from 1 to n, and the m electrodes are from n + 1 to n

+ m. The charges and potentials of the islands can be written in terms of an island charge vector qI and

potential vector VI, respectively. Similarly, charge and potential vectors can be written down for the

electrodes, qE and VE. The state of the system can be specified by the total charge vector q= (qI,qE).

Equivalently, it can be characterized by the total potential vector defined as V= (VI,VE). Charge and

potential vectors are related via the capacitance matrix C:

q=CV

Energy levels of source, island anddrain (from left to right) in a single

electron transistor for both the

blocking state (upper part) and thetransmitting state (lower part).

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We write Cas C=( )This matrix model for double barrier is given by following:

( )with C11 = C1S + C1D and CSS = C1S+ CSD

Currentvoltage characteristics: Coulomb Island The Coulomb staircase:

Besides the Coulomb gap around V= 0, the Coulomb blockade generates under certain conditions a

staircase-like structure in the currentvoltage characteristic, known as a Coulomb staircase.

Stability of Single Electron transistor:

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Stability diagram of a single-electron transistor. Within the diamonds, Coulomb blockade is established,

while outside, a current flows between source and drain.

Capacitively-coupled single-electron transistor

The Coulomb gap is given by the onset of the same tunneling events as for the single island studied

above. Now, however, the Coulomb gap depends upon the gate voltage. Coulomb blockade is established

if all four energy differences are positive. For each n, this condition defines a stable, diamond-shaped

region in the (VG,V) plane. These stable regions are known as Coulomb diamonds and line up along the

VG-axis.

The single-electron pump:

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Via a tunnel junction, island 1 is coupled to source and island 2 to drain. The total capacitances C11 of

both islands are assumed to be equal. Furthermore, we neglect several capacitance matrix elements and

assume that electrode A (B) couples only to island 1 (2), with equal capacitances.

Single Electron Pump

Quantum Dot:

A quantum dot is a portion of matter (e.g. semiconductor) whose excitations are confined in all three

spatial dimensions. Consequently, such materials have electronic properties intermediate between those of

bulk semiconductors and those of discrete molecules.

Stated simply, quantum dots are semiconductors whose electronic characteristics are closely related to the

size and shape of the individual crystal. Generally, the smaller the size of the crystal, the larger the band

gap, the greater the difference in energy between the highest valence band and the lowest conduction

band becomes, therefore more energy is needed to excite the dot, and concurrently, more energy is

released when the crystal returns to its resting state.

Besides confinement in all three dimensions i.e. Quantum Dot - other quantum confined semiconductors

include:

Quantum wires, which confine electrons or holes in two spatial dimensions and allow freepropagation in the third.

Quantum wells, which confine electrons or holes in one dimension and allow free propagation intwo dimensions.

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Quantum Dots + Single Electron Structure- Information Processing:

Images of a single-electron quantum dot were obtained in the Coulomb blockade regime at liquid He

temperatures using a cooled scanning probe microscope (SPM). The charged SPM tip shifts the lowest

energy level in the dot and creates a ring in the image corresponding to a peak in the Coulomb-blockade

conductance. SPM manipulation of electrons in quantum dots promises to be useful in understanding,building and manipulating circuits for quantum information processing.

Single-electron quantum dots are promising candidates for quantum information processing. The electron

spin in each dot acts as a qubit, and tunneling is used to entangle spins on adjacent dots.13 To pursue

these ideas, quantum dots that contain only one electron are being developed, as individual single-electron

dots and as tunnel-coupled single-electron dots. A useful circuit for quantum information processing will

consist of many coupled quantum dots.

Schematic diagram of the experimental set-up used to image electrons in a single-electron quantum dot.

charged scanning probe microscope (SPM) tip is scanned at a fixed height above the surface of the

GaAs/AlGaAs heterostructure containing the dot. Images are obtained by recording the Coulomb

blockade conductance G vs. tip position.

SET & Artificial Atoms:

Natural atoms are studied by adding, removing or exciting electrons with light, these artificial atoms

typically have such small energy scales that they are best studied by measuring the voltage and current

resulting from tunneling between the artificial atom and nearby electrodes.charge quantization isobservable only at temperatures kT < U, which means that it is easier to see the effects in smaller artificial

atoms, which have larger U.

There are strong efforts around the world to make the artificial atoms in SETs smaller, in order to raisethe temperature at which charge quantization can be observed. These involve self-assembly techniques

and novel lithographic and oxidation methods whereby artificial atoms can be made nearly as small as

natural ones. This is, of course, driven by an interest in using SETs for practical applications. However, as

SETs get smaller, all of their energy scales can be larger, so it is very likely that new phenomena will

emerge.

Cotunneling:

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This effect was first predicted in 1989 and observed experimentally soon after . The essence of the effect

is that the tunneling of several (N>1) electrons through different barriers at the same time is possible as a

single coherent quantum-mechanical process. The rate of this process is crudely (RQ/R)N-1

times less than

that for the single-electron tunneling described by of the orthodox theory. Cotunneling can nevertheless

be clearly observed within the Coulomb blockade range where orthodox tunneling is suppressed.

SET &Analog Application:

Supersensitive Electrometry. Single-electron spectroscopy DC Current Standards Temperature Standards Resistance Standards Detection of Infrared Radiation

SET & Its Digital Application:

a) Voltage State Mode:The first opportunity is to use single-electron transistors in the "voltage state" mode. In this mode, the

input gate voltage Ucontrols the source-drain current of the transistor which is used in digital logic

circuits, similarly to the usual field-effect transistors (FETs). This means that the single-electron charging

effects are confined to the interior of the transistor, while externally it looks like the usual electronic

device switching multi-electron currents, with binary unity/zero presented with high/low dc voltage levels

(physically not quantized).

Problem: Static power Dissipation

b) Charge State Mode:The latter problem may be avoided by using another type of logic device in which single

bits of information are presented by the presence/absence of single electrons at certain conducting

islands throughout the whole circuit. In these circuits the static currents and power vanish, since

there is no dc current in any static state.

c) Problem With SET:1) The first big problem with all the known types of single-electron logic devices is the requirement

Ec ~ 100 kBT, which in practice means sub-nanometer island size for room temperature

operation. In VLSI circuits, this fabrication technology level is still nowhere in sight.

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2) The second major problem with single-electron logic circuits is the infamous randomness of thebackground charge.

The effect of a single charged impurity on the single-electron transistor.

Let a single charged impurity be trapped in the insulating environment, say on the substrate surface, at a

distance a from the island, comparable to its size. The impurity will polarize the island, creating on its

surface an image charge Q0 of the order ofe. This charge is effectively subtracted from the external

charge Qe which determines the Coulomb blockade thresholds Vt. One of 1,000 deviceswith 1-nm

islands will have a considerable background charge fluctuation (Q0> 0.1 e).Presumably, this isunacceptable for any VLSI application.

d) Other Applications:1) Background-Charge-Insensitive Memory2) Crested Tunnel Barriers3) NOVORAM4) Electrostatic Data Storage

SET & Logic Gates:

SET devices can be used to form number of gates, just like CMOS. Those are

given is following-

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Conclusion:

Single-electronic devices have already proved their value as tools in scientific research. Several

applications of these devices in metrology, including the fundamental standards of current, resistance, and

temperature also seem quite promising. Another prospective application field is terahertz radiation

detection and (possibly) imaging.

The situation with digital single-electronics is much more complex. The concepts of single electron logic

circuits suggested so far face tough challenges: either that of removing the random background charge or

alternatively that of providing continuous charge transfer in nanoscale resistors.

This still leaves us with the most important problem, the fabrication. Despite recent progress in the

fabrication ofsingle devices with a-few-nm minimum features, prospects for the fabrication of VLSI

circuits with the same resolution are still very distant. Indeed, the methods used in this research field

(mostly direct electron-beam writing and scanning probe manipulation) are hardly scalable to whole-

wafer or even whole-chip level, because of their very low speed. The development of VLSI

nanofabrication methods (e.g., multiple-electron-beam writing) will certainly require many years and

many billions of dollars.