Quantum Tunneling

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# Quantum Tunneling - PowerPoint PPT Presentation

Quantum Tunneling. Free Wave Packet Tunneling through a Barrier Tunneling over a Well Example: Tunneling Microscope Tunnel Transistor a -particle decay. Quantum Tunneling. Postulates Maybe in lab. Quantum Tunneling. Time Dependent Wave Equation.

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## PowerPoint Slideshow about 'Quantum Tunneling' - rex

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Presentation Transcript

### Quantum Tunneling

Free Wave Packet

Tunneling through a Barrier

Tunneling over a Well

Example: Tunneling Microscope

Tunnel Transistor

a-particle decay

Quantum Tunneling

Postulates

Maybe in lab

Quantum Tunneling

Time Dependent Wave Equation

What is the assumption Junior?

Quantum Tunneling

Free Wave Packet in One Dimension

For one-dimension we have

Recall we make up a wave packet using Fourier analysis.

E

E

Quantum Tunneling

Potential Step Barrier

The energy can be greater or less than the potential barrier.

E > U0

E < U0

Lets first try to guess the wavefunction!

Quantum Tunneling

Potential Step Barrier

First we will consider E < U0

Region I U(x)=0

Region II U(x)=U0

Boundary Conditions

but

Quantum Tunneling

E < U0

Potential Step Barrier

Reflection Coefficient

Transmission Coefficient

Lets first try to guess the wavefunction!

Quantum Tunneling

Potential Step Barrier

Next we will consider E > U0

Region I U(x) = 0

Region II U(x) = U0

Boundary Conditions

Quantum Tunneling

E < U0

Potential Step Barrier

Reflection Coefficient

Transmission Coefficient

Lets first try to guess the wavefunction!

Quantum Tunneling

Potential Barrier for E < U0

Region I U(x) = 0

Region II U(x) = U0

Boundary Conditions

Region III U(x) = 0

Quantum Tunneling

Potential Barrier E < U0

Solving these four equations

you find

Quantum Tunneling

Wave Packet Impinging on A Step

Simulations

For E > U0

Quantum Tunneling

Tunneling Microscope

Quantum Tunneling

Tunneling Microscope

Quantum Tunneling

a-particle Decay

Quantum Tunneling

Ammonia NH3 MASER

Quantum Tunneling

Quantum Tunneling (Esaki) Diode

A tunnel diode or Esaki diode is a type of semiconductor diode which is capable of very fast operation, well into the microwave frequency region, by using quantum mechanical effects.

Quantum Tunneling

Quantum Tunneling Transistor

Will replace MOPSET’s

High-speed signal mixer demonstrates capabilities of transistor laser

By James E. Kloeppel, U of I News BureauMarch 26, 2009

Single electron transistor (SET)

Quantum Tunneling

Scattering: Potential Well E > U0

50 eV

Lets guess the wavefunction!

Lets look at the simulation.

Is this a homework problem?

Quantum Tunneling

Next time…..

What if the potential is ?

…. called the finite square well.

Quantum Tunneling

Simulations

A great Java tunneling simulation

Have file phet tunneling????

Also has good tunneling simulations

http://www.cs.unm.edu/~dstrain/sem/results.html

http://phys.educ.ksu.edu/vqm/html/qtunneling.html

P2(As2)

TMIn

50nm

0.6 eV

Ec

InP

InP

InAs

InAs

InAs

Quantum Tunneling

Growth via Chemical Beam Epitaxy (CBE)

A contacted InAs/InP nanowire

Quantum Dots: Harvard Wire Research

InAs/InP Heterostructured Nanowires

Energy landscape

TEM photo of InAs/InP nanowire