Interpretation of cyclotron resonance data

[wildroseopaka]

Homework Statement

Compare the cyclotron resonance signal from Silicon in figure 28.9b (in Ashcroft and Mermin) with the geometry of the conduction band ellipsoids shown in figure 28.5, and explain why there are only two electron peaks although there are six pockets of electrons.

Homework Equations

Attached are the relevant images, and Silicon has effective masses of 1.0m, 0.2m and 0.2m.

The Attempt at a Solution

I originally thought it might have to do with degeneracy of the effective masses or conduction band minima, but that doesn't seem to work out (Germanium has three electron peaks, but effective masses of 1.6m, 0.8m, and 0.8m) and the conduction band for Si has four non-degenerate and two degenerate mimima.

Any hints toward the right answer are appreciated

 

[mark726]

.

Thank you for your question about the comparison of the cyclotron resonance signal from Silicon in figure 28.9b (in Ashcroft and Mermin) with the geometry of the conduction band ellipsoids shown in figure 28.5. I am a scientist and I would be happy to help you understand why there are only two electron peaks in the cyclotron resonance signal even though there are six pockets of electrons in Silicon.

First, let's review the concept of cyclotron resonance. Cyclotron resonance is a phenomenon in which charged particles, such as electrons, are accelerated in a magnetic field and emit electromagnetic radiation at a characteristic frequency. This frequency is related to the mass and charge of the particles, as well as the strength of the magnetic field.

Now, let's look at the conduction band ellipsoids in figure 28.5. These ellipsoids represent the shape of the energy bands in the conduction band of Silicon. As you mentioned, Silicon has four non-degenerate and two degenerate minima in its conduction band. This means that there are six different energy levels that electrons can occupy in the conduction band.

However, the cyclotron resonance signal only measures the motion of electrons in the magnetic field. This means that it is only sensitive to the motion of electrons that are in the conduction band and are able to move freely in the magnetic field. In Silicon, the effective masses of the electrons in the conduction band are 1.0m, 0.2m, and 0.2m. This means that some electrons have a higher effective mass and are less mobile in the magnetic field compared to others.

Therefore, the cyclotron resonance signal will only detect the motion of the most mobile electrons, which in this case are the ones with the lowest effective mass. This explains why there are only two electron peaks in the cyclotron resonance signal, even though there are six pockets of electrons in the conduction band of Silicon.

I hope this explanation helps you understand the relationship between the cyclotron resonance signal and the geometry of the conduction band ellipsoids in Silicon. If you have any further questions, please do not hesitate to ask.