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Homework Help: Nanoparticle dragged off a layer and tunnelling to a STM tip, equation

  1. Dec 5, 2013 #1
    Here we have a STM tip placing a potential V across a monolayer with a single electron on it.

    | STM (scanning tunneling microscope) Tip |
    | |

    (((((((((((( ELECTRON ))))))))))))))
    ------------------------ MONOLAYER ---------------------------

    it takes a potential V1 to get the electron away from the atom on the layer, it takes a potential V2 to get the electron to tunnel through the gap. So in effect we have 2 capacitors in series.

    the question wants V1 and V2, i.e. the potential across each 'capacitor' and gives the solution

    V1 = V (C1 / C1+ C2) - n (e / C1 + C2)

    V2 = V (C2 / C1+ C2) + n (e / C1 + C2)

    Obviously the second term of each equation is related to the charge e and the number of charges n which effect the potential. However when i treat the problem as a circuit diagram i get:

    V1 = V ( C1 / (C2 + C1))
    V2 = V ( C2 / (C2 + C1))

    Which is correct and would be correct if this were a normal circuit, however the solutions above each have that second term in.

    My question is, how do i introduce that second term? i understand why its there, but can i say there will be an additional term which relates to the number of particles and add it to my V1 and V2 terms? But one is negative? Do I just say the sum of the additional terms must be zero so haphazardly include one with a positive term and one with a negative term?
  2. jcsd
  3. Jan 9, 2014 #2
    currently revising, still havent been given the solutions back (even though ive asked for them) and it may come up in the exam :-///

    it's really an electronics question with two capacitors in series, but i still cant derive the solutions given, any ideas please?
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