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Scanning Tunnelling Microscope

  • 17-12-2012 1:19pm
    #1
    Registered Users, Registered Users 2 Posts: 434 ✭✭



    The tip of a scanning tunnelling microscope is placed 1.0 nm away from a conducting surface and a potential of dV = 0.03 V is applied to the surface relative to the tip. When the tip is moved laterally to a new position on the surface the tunnelling current increases by 50%. What is the change in the tip to surface distance (in nm)? The work function of the tip and the surface are both 4.0 eV.

    (a) –0.15 (b) 0.0 (c) +0.15 (d) –0.02 (e) +0.02


    Relevant equations:
    Tunnelling probability P
    P ~ exp(-2αx)
    and
    α = { (2me(ϕ-dV))^0.5 } / (h-bar)


    I calculate α to be 1.025 x 10^10 which is correct.

    Then I use :

    |Below is x sub 2, and x sub 1|
    P2 / P1 = exp(-2αx2) / exp(-2αx1)

    1.5 below is due to 50% in question.
    1.5 = exp(2αdx)
    log(1.5) = 2αdx
    dx = 2.0 x 10^-11
    dx = 0.02nm

    So answer (e).

    However, the solution is given as answer (d).

    So either there is a problem in the signs I have attributed to the powers in the exp terms when calculating P2/P1. Or the given solution is incorrect and I have the correct answer.

    Was wondering if anyone could clarify?

    Thanks


Comments

  • Registered Users, Registered Users 2 Posts: 434 ✭✭Smythe


    I've got this sorted now.


  • Banned (with Prison Access) Posts: 3,455 ✭✭✭krd


    Have you had a chance to used one of those?

    I think they're common in colleges these days. It's amazing what you can see with them.


  • Registered Users, Registered Users 2 Posts: 434 ✭✭Smythe


    krd wrote: »
    Have you had a chance to used one of those?

    I think they're common in colleges these days. It's amazing what you can see with them.
    Unfortunately not as yet.


  • Banned (with Prison Access) Posts: 3,455 ✭✭✭krd


    Smythe wrote: »
    Unfortunately not as yet.


    Before you had to build them yourself. I've never seen one - I knew someone who was involved in building one. Not impossible to build one (it's a lot easier than building an electron microscope - which would be very expensive and very difficult) , but you'd need to be very handy - the thing, electronics, software.

    Commercial ones are common now because of so much nano-tech work being done. There are little desktop ones now.

    The pictures really are amazing.


  • Registered Users, Registered Users 2 Posts: 179 ✭✭Neodymium


    This guy built a scanning electron microcope.


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