lecture 9

# Lecture 9 - EEE 352 Lecture 09 Tunneling Through a Potential Barrier Tunneling through a potential barrier Finite barrier length Scanning tunneling

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EEE 352: Lecture 09 Tunneling Through a Potential Barrier * Tunneling through a potential barrier Finite barrier length Scanning tunneling microscope

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Tunneling arises when we think about the particle as being a wave. That is, there is a classical phenomenon in optics known as total internal reflection. We see this in the swimming pool, where there is a critical angle beyond which we cannot see out of the water. This angle is given by the difference between the dielectric constant in water and that in air. However, there is an evanescent wave, and if we are close enough, we can couple to another high dielectric constant medium. This process is known as frustrated total internal reflection.

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There is total internal reflection of this light in this media, yet … we see some light coming out the back side.
The evanescent wave decays exponentially.

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In fact, we can use the evanescent wave to couple into another propagating media, such as a surface wave shown here.
This makes for wave couplers in optical fibers. How does this appear for quantum waves?

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Electron Motion in the Presence of a Barrier Let us first recall the solutions to the barrier problem * Which was solved by breaking the problem into TWO different regions ψ 2 ( x ) = C exp −γ x [ ] γ 2 = 2 m 2 ( V E ) 1 ( x ) = A exp ik 1 x [ ] + B exp ik 1 x [ ] k 1 2 = 2 mE 2 FREE ELECTRON PROPAGATION PROPAGATION IN THE BARRIER REGION (V>E)
Tunneling Through a Potential Barrier If the barrier EXCEEDS the total energy, motion in the barrier is FORBIDDEN classically, but quantum mechanics allows the electron to LEAK into the barrier Even though its energy remains

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## This note was uploaded on 09/28/2009 for the course EEE 352/333 taught by Professor Allee during the Fall '09 term at ASU.

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Lecture 9 - EEE 352 Lecture 09 Tunneling Through a Potential Barrier Tunneling through a potential barrier Finite barrier length Scanning tunneling

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