1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Tip current in STM (fractional error problem)

  1. May 15, 2017 #1
    1. The problem statement, all variables and given/known data
    Suppose the STM tip current is given by

    [tex] i = aV e^{-A\phi^{1/2}s} [/tex]

    a) Derive an expression for the fractional change in tip current as function of fractional change in tip spacing s.

    b) If [tex]\phi = 4V[/tex] select a reasonable set of V values so that a 1Å increase in s will cause a factor of 10 decrease in i. (a and A are given)

    2. Relevant equations
    Given in problem

    3. The attempt at a solution

    It's probably very simple but I'm stuck. I'm simply using error formula to get that
    [tex] \delta i = \frac{\partial i}{\partial s} \delta s = -A\phi^{1/2} \cdot i \cdot \delta s[/tex]

    And then I move out i to the left side to get the fractional change in current.
    But that doesn't seem correct. Because then I don't understand how I am supposed to solve b), since the fractional change is independent of V.

    I tried other ways as well, but V seems to dissaperar out of the equation anytime I do that.
    If anyone has a good idea on how to proceed, it would be welcome.
    Thanks
    // John


     

    Attached Files:

  2. jcsd
  3. May 16, 2017 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    If the current changes by a factor 10, your linear approximation doesn't work any more - but then there is no formula relating a fractional change in s to a fractional change in i. There is a formula relating an absolute change in s to a fractional change in i, a more general version of the formula you derived (which only works for small changes in s).
     
  4. May 16, 2017 #3
    Yes I could simply divide the current at two different distances to get

    [tex]\frac{i(s+\delta s)}{i(s)} = \frac{aVe^{-A\psi^{1/2}(s+\delta s)}}{aVe^{-A\psi^{1/2}s}} = e^{-A\psi^{1/2}\delta s}[/tex]

    but then again, this is independent of the voltage V, so I don't see how I am supposed to solve the second question.

    The fractional change in current is the same regardless of the applied voltage (just like for exponential decay where the half life depends only on lambda).
     
  5. May 16, 2017 #4

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Not if ##\phi## (now ##\psi##?) depends on the voltage.
     
  6. May 16, 2017 #5
    Yes sorry about that, it was a typo. Phi is the work function
    Well I looked it up and the work function does depend on voltage, so I guess I have to assume that
    [tex] \phi = (V-4)\hspace{0.1cm}\mathrm{Volts}[/tex], and not just 4 Volts as one could think from the problem.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Tip current in STM (fractional error problem)
  1. Tips for problem (Replies: 6)

  2. Errors problem (Replies: 2)

Loading...