Bandstructure and E-k diagrams

[Defennder]

I'm currently taking a microelectronics course and I missed a couple of lectures due to illness. As a result, I didn't understand the lecture notes fully. I hope someone would be able to help me on this. I consulted the recommended textbook for this course but it turns out that it didn't cover this part of the course. The textbook is SO Kasap's Principles of Electronic Materials and Devices 3rd Edn

I tried searching the Internet but I got a lot of links to upper level solid state physics courses, which covered this in far too much detail which is not required for my course and served to confuse me even further. For example, my lecturer omitted the concept of reciprocal lattice vectors, and just about every web page I came across had that concept embedded somewhere. This is just so frustrating.

1. Homework Statement and attempted solutions

http://img237.imageshack.us/img237/6853/ekdiagramzv1.th.jpg http://img153.imageshack.us/img153/9755/gebandstructurekl4.th.jpg

1st picture:
What exactly do heavy, light and split-off bands refer to? What is split-off energy?
I did some searching on google and found out that heavy, light bands are also termed heavy-hole and light hole bands, which suggests that somehow holes are divided into heavy and light holes and they then reside in these appropriate bands.

As for what exactly heavy and light refers, to, I'm guessing that these are the effective masses given by $$\frac{{\hbar}^2}{\frac{d^2E}{dk^2}}$$ and that 'heavy' holes reside in the less curved valence band because $${\frac{d^2E}{dk^2}}$$ is smaller there compared to the light band, meaning that the effective mass of the hole in the heavy band is higher than that of the light band. Is this correct?

But I have no idea what is split-off band and split-off energy.

2nd picture:
The picture shows that the lowest energy state for the conduction band is at L point. My notes also show that Si's lowest energy state for valence band is at X point. In general does this mean that the reason why X,L points are important is because they coincide with the lowest energy level of the conduction band for indirect bandgap semiconductors? If so, why is this the case?

Homework Equations

 

[jbsteele]

Not applicableThe Attempt at a Solution1st picture: Heavy and light bands refer to the effective masses of electrons or holes in the valence band. Heavy hole bands have a higher effective mass than light hole bands because the curvature of the valence band near the heavy hole band is much less than near the light hole band. Split-off bands are lower energy subbands that arise from the interaction between the spin-orbit interaction and the crystal field. The split-off energy is the energy difference between the heavy and light bands and the split-off band.2nd picture: Yes, the lowest energy state for the conduction band is typically at the L point and the lowest energy state for the valence band is typically at the X point in indirect bandgap semiconductors. This is as a result of the wave vector of the electrons and holes at these points being in opposite directions, which reduces the Coulomb attraction between the electrons and holes, leading to a lower energy state.

 

[Moetasim]

N/A



Bandstructure and E-k diagrams are important concepts in the study of electronic materials and devices. They help us understand the energy levels and momentum of electrons and holes in a material, which ultimately determine its electronic properties.

In regards to your questions, the terms heavy, light, and split-off bands refer to the different energy levels that electrons and holes can occupy in a material. In a solid, the energy levels form bands due to the overlapping of atomic energy levels. The heavy and light bands refer to the valence band, where the electrons reside, and the split-off band refers to the conduction band, where the holes reside. The split-off energy is the energy difference between the valence and conduction bands.

Your understanding of the effective mass of electrons and holes is correct. The effective mass is a measure of how easily an electron or hole can move in a material. In the valence band, the effective mass of the electron is smaller than that in the conduction band, leading to the division into heavy and light bands.

As for the X and L points, these are important points in the bandstructure because they represent the lowest energy states for the valence and conduction bands, respectively. In the case of indirect bandgap semiconductors, the lowest energy state for the conduction band is at the L point, while the lowest energy state for the valence band is at the X point. This is why these points are important in understanding the electronic properties of these materials.

I understand that missing lectures due to illness can be challenging, but I would suggest reaching out to your lecturer for clarification on any concepts that you may have missed. Additionally, there are many resources available online, such as video lectures and tutorials, that may help you better understand these concepts. I would also recommend consulting other textbooks or asking for recommendations from your lecturer for additional reading material. I hope this helps in your understanding of bandstructure and E-k diagrams.