Single Electron Tunneling and Coulomb Blockade.pptx

7/27/2019 Single Electron Tunneling and Coulomb Blockade.pptx

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Presented ByPrashant Kumar M.Tech , NST,

2nd Sem.


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ContentsTunnel Junctions and applications of tunneling

1. Tunneling through a potential barrier2. Potential Energy profiles of material interfaces

3. Applications of TunnelingCoulomb Blockade and Single ElectronTransistor

1. Coulomb Blockade2. Single Electron Transistor


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Tunneling through a potentialbarrier


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In classical mechanics, if E < V (the maximum height of thepotential barrier), the particle remains in the well forever

If E > V , the particle escapes

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Tunneling Classical Picture


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In Quantum Mechanics, the electron can escape even if its energy E

is below the height of the barrier V Quantum tunneling has no counterpart in classical physics

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Tunneling Quantum picture


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Potential Energy profile of metal vacuuminterfaces


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Metal- Semiconductor Junction


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Metal- Semiconductor Junction


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Applications of tunneling

Field EmissionGate Oxide Tunneling and Hot Electron Effects inMOSFETsScanning Tunneling MicroscopeDouble Barrier Tunneling and Resonant TunnelingDiode


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Field Emission


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Fowler-Nordheim Tunneling


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Scanning Tunneling Microscope


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Double Barrier Tunneling and ResonantTunneling Diode


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Double barrier junction under applied bias


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Coulomb Blockade and Single ElectronTransistor

Tunneling is the process by which current can flow from leadto lead through quantum dot.

Quantum dot which is merely a very small material region,is also called quantum island or coulomb island.

We will model the quantum dot and exterior leads using the classical concept of capacitance, and consider electron conduction via tunneling, and so we use a mixedclassical- quntum model.

As we will see the most fundamental effect in nanoelectronics is related to thesignificant change in energy when a single electron is transferred into a nanoscopicmaterial region , such as, a quantum dot is known as coulomb blockade.


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Coulomb blockade in a nano capacitor


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I-V characteristic in coulomb

blockade


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for air separating the plates at T= 293K.


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Equating the charging energy to the thermal energy we have

Assuming square capacitor plates of length L, and for convenience assume d= L/10Then to observe coulomb blockade we must have

L


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TUNNEL JUNCTIONS

The tunneling that occurs across can be accounted by

considering the capacitor to be a leaky capacitor modeling by anideal capacitance in parallel with a resistance

R t = V/I Where V is the DC voltage applied at the junction and I is the

resulting current due to tunneling.This tunneling resistance is not an ordinary resistance, butconceptually allows electrons to cross the insulation junction asdiscrete events.The parallel combination of capacitor and tunneling resistance is calleda tunneling junction .


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TUNNEL JUNCTIONS


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In order to see Coulomb Blockade, we need to limit tunneling somedegree, we can get an estimate of this by considering the uncertainty relation between time and energy,

E t /2 Time constant of parallel RC circuit is = RC

Then = R tC is a characteristic time associated with tunneling.This is not the time to tunnel through the junction, but, rather the timebetween the tunneling events. is considered to be the approximate lifetime of energy state of theelectron on one side of the barrier. Thus we have uncertainty in energy

E / (2RtC) To observe the Coulomb Blockade effect, the charging energy must bemuch larger than this uncertainty, such that

Rt >> /q 2

e 4.1 K Note that we have two effects to consider , capacitance value and the possibility of tunneling. In order to observe Coulomb blockade, we need very small values of capacitance to obtain large charging energy.


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Tunnel Junction Excited by a constant

current source


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Tunneling from the lower to the upper plate can occur (since Coulomb Blockade isthen thwarted) this results the decrease in the +ve charge on top plate

And the increase of ve charge on the bottom plate


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Coulomb Blockade in a quantum dot circuit


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Single electron transistor

HISTORY In 1985 Dmitri Averin and Konstantin Likharev proposed the idea of a new three-terminal devicecalled a single-electron tunneling (SET) transistor.Two years later Theodore Fulton and Gerald Dolan atBell Labs created SETSingle-electron transistors have been made with just afew nanometers using

1. Metals

2. Semiconductors3. Carbon nanotubes4. Individual molecules


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Single electron transistorUses Coulomb blockade for

functioningIt consists of two electrodesknown as the drain and thesource , connected through tunnel

junctions to one commonelectrode with a low self-capacitance known as the island .The electrical potential of the

island can be tuned by a thirdelectrode, known as the gate ,capacitively coupled to the island.


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Single electron transistor

-


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Single electron transistor -Fabrication


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A key point is that charge passesthrough the island in quantizedunits.For an electron to hop onto theisland, its energy must equal thecoulomb energy e 2/2C. When a positive voltage is appliedto the gate electrode the energy levels of the island electrode arelowered.

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Working


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When both the gate and the bias voltages are zero, electrons do nothave enough energy to enter theisland and current does not flow. As the bias voltage between the

source and drain is increased, anelectron can pass through theisland when the energy in thesystem reaches the coulomb energy.

The critical voltage needed totransfer an electron onto the islandequal to e/C, is called the coulombgap energy

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Working

Working


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(a)When a capacitor is charged

through a resistor, the charge onthe capacitor is proportional tothe applied voltage and shows nosign of quantization.(b) When a tunnel junction

replaces the resistor, a conductingisland is formed between the junction and the capacitor plate.In this case the average charge onthe island increases in steps as the voltage is increased(c) The steps are sharper for moreresistive barriers and at lowertemperatures.

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Working


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Here n 1 and n 2 are the number of electrons passed through the tunnelbarriers 1 and 2

n = n 1 n 2 Total island capacitance and energy

C = C G+C 1+C 2

I

V h t i ti f i g t lt g


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I V characteristics for various gate voltages


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Voltage transfer characteristics

V

d

vs

V

g


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Voltage transfer characteristics V d vs V g(Coulomb Diamond)

C d V i i


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Conductance Variation

I l d

M l i d


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For a SET made of metal all

diamonds would have identicalsize and there would be no variationsof conductance outside thediamonds.

Semiconductor SETs havediamonds of different sizesand peaks in differentialconductance outside thediamonds, corresponding toexcited states.

Ref : L.P. Kouwenhoven, T. H. Oosterkamp, M.W. S. Danoesastro, M. Eto, D. G. Austing,

T. Honda, and S. Tarucha, Scienc 278 (1997) 1788 69

Island - Metal or semiconductor


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Operations at Room temperature


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1

10

100

1000

0.1 1 10

Total island capacitance, CS (aF)

M a x

O p e r a t

i n g

T e m p a r a t u r e

( K )

0.1

1

10

100

Radiusof Island(n

Kiriharas criteria:

island capacitance


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Voltage gain in a SET is the ratio of the gatecapacitance to the junction capacitance Thus for every junction capacitance and temperature,there is a maximum voltage gain.

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Voltage gain of a SET

Noises in SET


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Johnson noise:

-electronic noise generated by the thermal agitation of the charge carriers- usually negligible (thanks to small kT)

Shot noise

-originates from the discrete nature of electric charge-but is lower in SET. Flicker noise

- also known as pink noise.

- dominant at low f, may shift the operational pointand totally break down the operationSolution : Avoid metal-oxide devices which has a lotof glassy amorphous material surrounding the

junctions 73

Noises in SET


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Advantage of SETHigh SpeedLow power dissipationHigh band width

Occupies less space on IC chip

Disadvantage of SET Noise


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AcknowledgementsDr A K V Sir for the guidanceMd. Rameez for the eBook

ReferencesFundamentals of nanoelectronics by George W.Hanson


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THANKS

Documents

Single Electron Tunneling and Coulomb Blockade.pptx