I Quantum Tunneling in an STM: ELI5 Requested

[Jackissimus]

TL;DR Summary

I would like to understand the nature of the quantum tunneling effect. Also because I used to work with STMs.

In an STM, you image the surface topography by tunnelling electrons from the metallic tip to the conductive surface, while measuring the current. I have worked with these instruments before and I never understood why does one need a quantum explanation for this.

Wouldn't the electron jump to the surface under big enough voltage anyway? Lightning surely seems to travel through air. And even if operated in a vacuum, it's still not a complete dielectric, there is vacuum permittivity.

Could someone please ELI5? I would especially like it if someone could explain how would a quantum tunneling current behave differently from a classical electric arc, in this instrument or elsewhere. Thanks.

 

[andresB]

Wouldn't the electron jump to the surface under big enough voltage anyway? Lightning surely seems to travel through air.

No Idea how surface topography works, but qantum tunneling comes precisely when the voltage (the energy, really) is not enough to surpass a potential barrier. Classically, under such condition (you are not giving enough energy to the electron to travel to through the dielectric) you should see zero electrons crossing to the other side (in this case the conducting surface, I guess). Quantum mechanically, you will find some electrons on the other side.

 

[Jackissimus]

Classically, under such condition (you are not giving enough energy to the electron to travel to through the dielectric) you should see zero electrons crossing to the other side.

Right, that actually makes sense, the voltage used was not very high, just a couple of volts. The topography is reconstructed from the current map as the tip is raster scanned above the surface (about 50nm high) BTW.
Right, so the main difference is that classically the voltage would have to be much higher for the electrons to actually jump, ok.

 

[PeroK]

Right, that actually makes sense, the voltage used was not very high, just a couple of volts. The topography is reconstructed from the current map as the tip is raster scanned above the surface (about 50nm high) BTW.
Right, so the main difference is that classically the voltage would have to be much higher for the electrons to actually jump, ok.

I'm sorry you didn't get a good answer about how an STM works. I can't help you there I'm afraid. On the question of quantum tunneling there are two points:

If a quantum particle interacts with an infinite/large potential barrier, then there is a finite probability of its passing through the barrier. This results in reflection and transmission coefficients for a particle that are analagous to the same coefficients for light being reflected or transmitted at a surface. (As a sidenote, this idea leads via QED for the partial reflection of light at a barrier - between air and glass, say - to be described quantum mechanically. Classically, of course, it's described by Maxwell's equations and the classical wave model of light.)

The reflection and transmission coefficients for elecrons depend on the strength of the potential barrier. The higher the barrier, the fewer electrons pass through. This may be what an STM uses to map the surface. There seems to be plenty online if you want to read about it in more detail.

For a finite barrier, there are certain specific (low) energies for which the barrier becomes transparent. Clearly, if the energy is high enough, the particles will pass over the barrier, but there is a sequence of lower energies where perfect transmission occurs - and this is the basis of microelectronics. Again, the specific details must be available online.