# What actually are electron holes?

• I_am_learning
In summary, electron holes are the empty space that is left behind when an electron is missing in a crystal, and the movement of holes is due to adjacent electrons jumping into the holes. The Hall Effect is due to the fact that the magnetic force causes the electron drift towards negative direction due to its effective negative mass.
I_am_learning
What actually are electron holes?

I have come to read that electron holes are nothing but the blank space that is left behind when an electron is missing in a crystal where it ought to have been present. I have also learned that the movement of holes are due to adjacent electrons jumping into the holes (hence creating a hole in its former position). So a hole movement in one direction is created by electron movement in another direction.

But what bothers me is the Hall Effect. Hall Voltage in some metals like Zn are positive which is only possible if the charge carriers are positive.
Saying that holes are a kind of positive charge carrier doesn't answer the riddle because the holes movement are actually the electron movement in the other direction! so the magnetic force acts on these electron and hence negative Hall voltage should have been established?!.

Whats the point I am missing here?

The "effective mass" of an electron is given by the curvature of the band. Hence electrons near the top of a band have a negative mass and also the velocity is anti-parallel to the driving force. So you are right, the electrons really move in the other direction than what you would expect if they were free. The hole picture fits in here nicely. A missing electron of negative mass will behave like a particle with positive mass. The reason for the negative effective mass is that an increase in the crystal momentum of the electrons will lead to an increased Bragg scattering of the electrons. Near the top of the band, this increase in the backscattered wave outweights the increase in crystal momentum.

So, you mean that, when measuring Hall voltage, the magnetic force causes the electron drift towards negative direction due to its effective negative mass so that the hall voltage is +ve. Thank you, I understand that.
But, shouldn't it be emphasized that holes are not merely absent of electrons but absent of electrons with negative effective mass?

Yes, and I think any good book on solid state theory does that (try e.g. Ashcroft/ Mermin).

## 1. What are electron holes?

Electron holes are essentially the absence of an electron in an atom or molecule. They can also refer to the space or location where an electron is expected to be, but is not present.

## 2. How are electron holes created?

Electron holes can be created through various processes, such as thermal energy, photoexcitation, or ionization. They can also be created by the movement of electrons, leaving behind a positively charged hole.

## 3. What is the role of electron holes in semiconductors?

In semiconductors, electron holes play a crucial role in the flow of electricity. When an electron from a neighboring atom fills a hole, it creates a new hole in its place. This movement of holes and electrons allows for the conduction of electricity.

## 4. Can electron holes be observed?

Electron holes cannot be observed directly, as they are not physical particles. However, their effects can be observed through various experiments and technologies, such as in semiconductor devices.

## 5. How are electron holes different from positrons?

Electron holes and positrons are two different concepts. While electron holes refer to the absence of an electron, positrons are actual particles with a positive charge. They are the antiparticles of electrons and have the same mass but opposite charge.

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