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Fowler-Nordhiem tunneling

  1. Jun 30, 2011 #1
    1. The problem statement, all variables and given/known data

    For a project Im doing I have to use the concept of Fowler-Nordhiem tunneling to model a Scanning Tunneling Microscope. Basically we have to relate the current generated from the tip to the field to the tunneling probability. Then relate that current to the applied voltage and height of the tip from the sample. The project can be solved analytically or through approximating solutions using MATLAB (majority of the students usually use MATLAB) The prof suggested that we use a right angled triangular potential barrier and gave us the following equation for the tunneling. The use of this equation is however optional.

    2. Relevant equations

    [itex]\inte-(2*root(2))/hbar(V(x) - E)1/2dx[/itex]
    3. The attempt at a solution
    I decided the best way to do this question is to find and graph the transmission probability with respect to the potential barrier and the distance from between the tip and sample in the microscope (using planar waves). However, the concept of Fowler-Nordhiem tunneling is a little confusing to me because I dont know how using a triangular potential barrier will change anything or what the significance of it is. Is it supposed to resemble the sharp tip of the microscope? I think the analytical soln should be similar to that in this website


    http://ecee.colorado.edu/~bart/book/msfield.htm

    but to what level does the WKB (Wigner, Kramers, Brillouin) approximation hold? Please help me understand the significance of the triangular potential barrier and the WKB approximation.

    Thanks
     
  2. jcsd
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