# Quantum Tunneling in a Scanning Tunneling Microscope

## Main Question or Discussion Point

Hi! I have a physics presentation tomorrow where I have to explain how a scanning tunneling microscope works. I also have to explain what quantum tunneling is and how it is used in a scanning tunneling microscope. I've done some research on the internet and I think I have a basic grasp of quantum tunneling. However, I have no idea how it is applied in the scanning tunneling microscope. I would really appreciate it if someone could explain this to me.

I should probably also confirm whether my understanding of quantum tunneling is correct. I'll try to explain what I know in layman's terms, since that's how I'll be presenting it.
Quantum tunneling is the idea that an object, when colliding with a surface, has a very small chance of "tunneling" through the surface. For example, when throwing a tennis ball at a wall, there is a small chance that it will appear on the other side of the wall. This chance is VERY small (close to nil?) for large objects such as the tennis ball. However, for very small matter, such as electrons, quantum tunneling is realistic.

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f95toli
Gold Member
Yes, that is sort of correct. However, a more general way of thinking about it in this context to instead focus on potential barriers which do not necessarily have to be anything "physical"; in the most commons case this "barrier" is simply the energy difference between two stable configurations of a system (stable meaning it is an energy minimum).

An STM works by measuring the tunneling current as electrons tunnel between a scanning tip and the surface. Now, according to classical physics there shouldn't be any current flowing since the tip and surface are separated by a vacuum which creates a large barrier and blocks the current regardless of the applied voltage*.
However, the tunneling probability through this barrier is high enough to allow for a relatively large current which can quite easily be measured. The neat thing is that the magnitude of this current (which is proportional to the tunneling probability) depends upon the properties of the surface; you can also to some extent choose which energy scale you want to study by varying the voltage applied between the tip and the surface. Hence, an STM will give you more than just the topology the surface; you also get the density of states for "free".

Note that this kind of tunneling isn't very "exotic", one reason why it is so difficult to fabricate new microprocessors is that the distances in modern CMOS transistors are so small that the tunneling current becomes significant, it is effectively a leakage current which causes extra heating and Intel&co have to work hard to minimize the effects (by designing devices where the tunneling probability is as small as possible).
Hence, there quite a lot of tunneling going on inside your computer.

*the voltages involved are far too small to allow arcing

Thank you very much. I actually understood that, so it was a big help.

I don't understand why the discovery of quantum tunneling had to be made in order to make use of a concept such as the one that the scanning tunneling microscope uses.
For example, a STM scans surfaces and the electrons from the sample tunnel through the potential energy barrier of the space between the microscope's needle and the sample from the sample to the needle. Tunneling is needed because the potential energy of this "in between" space (between the analyzed sample and the needle) is greater than the energy that the electron obtains from the voltage between the needle and the sample (e.g. the potential of the in between space is 5eV and the energy the electron acquires is 2eV).
However, why can't the voltage simply be adjusted (e.g. by applying an external voltage to the needle) so that the electrons don't have to overcome any "barrier" but rather can enter the needle by classical theories (i.e. kinetic energy (e.g. 6eV) is greater than potential energy (e.g. 5eV))?
The needle would be held at a distance from the sample such that the current in the needle would remain constant and this would allow us to map out the surface of the sample.

What is the mistake I am making?

Thank you very much for your time.

Is the ETM recording the image of the surface over time? Like a camera with the shudder left open for an extended period of time.

ZapperZ
Staff Emeritus
2018 Award
I don't understand why the discovery of quantum tunneling had to be made in order to make use of a concept such as the one that the scanning tunneling microscope uses.
For example, a STM scans surfaces and the electrons from the sample tunnel through the potential energy barrier of the space between the microscope's needle and the sample from the sample to the needle. Tunneling is needed because the potential energy of this "in between" space (between the analyzed sample and the needle) is greater than the energy that the electron obtains from the voltage between the needle and the sample (e.g. the potential of the in between space is 5eV and the energy the electron acquires is 2eV).
However, why can't the voltage simply be adjusted (e.g. by applying an external voltage to the needle) so that the electrons don't have to overcome any "barrier" but rather can enter the needle by classical theories (i.e. kinetic energy (e.g. 6eV) is greater than potential energy (e.g. 5eV))?
The needle would be held at a distance from the sample such that the current in the needle would remain constant and this would allow us to map out the surface of the sample.

What is the mistake I am making?

Thank you very much for your time.
There is a difference between tunnel current, and ohmic current, which is basically what you tried to compare with. For one, ohmic current is nothing more than a simple "short",and you get your standard IV curve that you would get in a metal. However, a tunnel current is more sensitive than that and where you see a lot of features that would not happen. For example the potential barrier CAN be greater than the kinetic energy. In classical case, you see no current, but in a quantum mechanical tunneling, you can! Not only that, in cases where you have superconductor-insulator-superconductor tunnel junction, you may even get a very peculiar phenomenon of Josephson current, which occurs at ZERO potential difference! This effect is purely quantum mechanical with no classical analogue.

Zz.

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