- #1
rwooduk
- 757
- 59
Here we have a STM tip placing a potential V across a monolayer with a single electron on it. | STM (scanning tunneling microscope) Tip |
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(((((((((((( 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?
| |
\\\\\\\\\\\\\\\\///////////////
(((((((((((( 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?