# Kittel Chapter 7: Explaining Energy Gaps with First Brillioun Zone

• ehrenfest
In summary, the conversation discusses a confusion regarding the relationship between the first Brillioun zone and energy gaps in Kittel's solid-state physics book. The shape of the curve in Figure 2 is not clear, but Figure 3 provides a different explanation for energy gaps. The caption below Figure 2 mentions the energy gap being associated with the first Bragg reflection, which causes confusion as Bragg reflection is typically associated with light diffraction. However, it is clarified that Bragg reflection can be done with any wave, not just light waves. The use of standing waves in Figure 3 is also mentioned as a helpful tool in understanding this concept.
ehrenfest
[SOLVED] kittel chapter 7

## Homework Statement

This question relates to Kittel's solid-state physics book. I have edition 8.

I just do not understand how the first Brillioun zone relates to energy gaps. For example, in Figure 2, I do not understand the shape of the curve in Figure 2. I do understand what is going on in Figure 3, but it seems to me like that is a completely different way of explaining energy gaps.

In the caption below figure 2, what exactly does it that the "energy gap E_g is associated with the first Bragg reflection at ... " ? I thought Bragg reflection had to do with light getting diffracted when you send a beam of it into the crystal (e.g. x-ray diffraction). I have absolutely no idea why Bragg reflection is is being talked about here!

## The Attempt at a Solution

Last edited:
Bragg reflection can be done with ANY wave. So anything that have a k-vector can be bragg reflected.

remember that the section about light diffraction in ch 2, nothing was said what the wave was composed of.

And this is why you are lead to impose the standing waves, and fig 3.. as a helped you with earlier this week.

## 1. What is the First Brillouin Zone?

The First Brillouin Zone is a concept in solid state physics that describes the set of all possible wave vectors for electrons in a crystal lattice. It is the smallest repeating unit in the reciprocal lattice, and it is used to explain the energy gaps between different energy bands in a solid.

## 2. How does the First Brillouin Zone relate to energy gaps?

The First Brillouin Zone helps to explain energy gaps by showing the range of possible wave vectors for electrons in a crystal lattice. This allows us to understand how electrons can transition between energy bands and why certain energy gaps exist.

## 3. What is the relationship between the First Brillouin Zone and the crystal lattice?

The First Brillouin Zone is closely related to the crystal lattice, as it is a representation of the reciprocal lattice. It helps us understand the periodicity and symmetry of the crystal lattice, which in turn affects the energy levels and energy gaps in a solid.

## 4. How do we determine the size and shape of the First Brillouin Zone?

The size and shape of the First Brillouin Zone depend on the size and shape of the unit cell in a crystal lattice. The unit cell is the smallest repeating unit in the crystal lattice, and the First Brillouin Zone is a representation of the reciprocal lattice of the unit cell.

## 5. Can the First Brillouin Zone be used to explain energy gaps in all types of solids?

Yes, the First Brillouin Zone can be used to explain energy gaps in all types of solids, including metals, insulators, and semiconductors. However, the size and shape of the First Brillouin Zone may vary depending on the type of solid and its crystal structure.

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