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

1. Dec 5, 2013

### rwooduk

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. Jan 9, 2014

### rwooduk

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?