Quantum Tunneling in an STM: ELI5 Requested

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• Jackissimus
In summary, an STM uses quantum tunneling to image the surface topography by measuring the current of electrons tunnelling from the metallic tip to the conductive surface. The voltage used in an STM is not high enough to surpass the potential barrier, resulting in a finite probability of electrons passing through. This results in different reflection and transmission coefficients for electrons, which can be used to map the surface. Additionally, there are specific energies for which the barrier becomes transparent, allowing for perfect transmission and the basis of microelectronics.
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.

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Jackissimus said:
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
andresB said:
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.

Jackissimus said:
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.

1. What is quantum tunneling in an STM?

Quantum tunneling in an STM (Scanning Tunneling Microscope) is a phenomenon in which electrons can pass through a potential barrier, even if they do not have enough energy to overcome it. This is made possible by the uncertainty principle in quantum mechanics.

2. How does an STM work?

An STM works by scanning a tiny probe tip over the surface of a material. As the tip gets closer to the surface, electrons can tunnel from the surface to the tip, creating a measurable current. This current is then used to create an image of the surface.

3. What is the significance of quantum tunneling in an STM?

Quantum tunneling in an STM allows scientists to study the properties of materials at a very small scale, down to the atomic level. It has also been used to manipulate individual atoms and molecules, leading to advancements in nanotechnology and materials science.

4. What are some real-world applications of quantum tunneling in an STM?

Some real-world applications of quantum tunneling in an STM include studying the surface properties of materials, creating nanoscale electronic devices, and manipulating individual atoms and molecules for various purposes such as data storage and drug delivery.

5. Are there any limitations to using quantum tunneling in an STM?

Yes, there are some limitations to using quantum tunneling in an STM. It is limited to studying conductive materials, as non-conductive materials do not allow for electron tunneling. Additionally, the process can be affected by external factors such as temperature and vibrations, which can impact the accuracy of the measurements.

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