lecture14 - 2.57 Nano-to-Macro Transport Processes Fall...

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2.57 Fall 2004 – Lecture 14 1 2.57 Nano-to-Macro Transport Processes Fall 2004 Lecture 14 Review of last lecture In lecture 13, we talked about tunneling through a thin film, which can also happen to general EM waves and acoustic waves. If the second medium is very thin, a third medium attached to the second medium will have tunneling effects. The wave will be partly transmitted into the third medium before decaying off and the reflectivity R1 in this case. Define 0 2 cos / nd ϕ πθ λ = . For a thin film, the reflectivity is a periodic function of φ , as shown in the right figure. In the widely used coating technique, the color of a thin film will change periodically according to the thickness, which is used to estimate the film thickness by naked eyes. We also talked about the tunneling through an energy barrier presented in the following figure. The barrier region can be vacuum in this case. The transmissivity is approximated as () [] ( ) d k 2 2 o o o 2 o o 2 e U E U E 16 / d E U m 2 2 exp U E U E 16 = τ = Now let us estimate the d value for a 1eV energy barrier. The k 2 value is 2 2 2 9.1 31 1.6 19 ~~ 4 9 16 8 mu E ee ke e ×− = = m -1 , n 1 n 2 n 3 d φ R U o d U t 0 Ψ t (E) Ψ i (E)
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2.57 Fall 2004 – Lecture 14 2 and the characteristic length for d is 1/k~1 Å. Applications of tunneling 1) Scanning tunneling electron microscope (STM) The tunneling phenomena are the basis of several inventions that led to several Nobel prizes including the tunneling diode by Esaki (1958) and the scanning tunneling electron microscope (STM) (Binnig and Rhorer, 1982). As shown in the above figure, in a STM a sharp tip is brought in close proximity with a conducting surface but not contacting the surface. The piezoelectric stage can adjust the distance between the tip and sample with subatomic accuracy. Under an applied voltage, electrons tunnel through the vacuum gap and create a current in the loop. The current is extremely sensitive (sub-angstrom) to the separation between the tip and the contact because k 2 is on the order of ~1 Å -1 and the transmissivity changes exponentially according to d. As the tip is scanned over the sample, different region has different potential barrier or different heights. By using the current as a feedback signal, one can map the electronic wavefunction surrounding individual atoms or the surface roughness. 2) Other microscopes A) Photon scanning tunneling microscope In such a microscope, the incident angle on the scanned surface is larger than the critical angle and thus it will be totally reflected in normal cases. However, when a scanning probe approaches the other side of the surface, there will be tunneling between the surface and the probe and the topography is obtained as in a STM.
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This note was uploaded on 01/12/2011 for the course ME 305 taught by Professor Wright,j during the Spring '10 term at Birla Institute of Technology & Science, Pilani - Hyderabad.

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lecture14 - 2.57 Nano-to-Macro Transport Processes Fall...

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