Scanning Tunnelling Microscope

Smythe

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

Smythe

I've got this sorted now.

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.

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.

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.

Neodymium

This guy built a scanning electron microcope.