Band Theory of Solids, Kittel CH 7

In summary, the conversation is about a problem in Kittel's book concerning band theory and the free electron bands of an fcc crystal lattice. The problem involves plotting the energies of all bands in the [111] direction and discussing why band edges may not necessarily be at the zone center. There is also mention of a potential degeneracy issue that may be resolved when considering the crystal potential. One person expresses confusion and another person offers a potential solution.
  • #1
KaiserSose`
2
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Homework Statement


I feel like I have a pretty good conceptual understanding of the origin of band theory, but these two problems were totally above my head.

Kittel Ch7 #2

Consider the free electron bands of an fcc crystal lattice in the approximation of an empty lattice, but in the reduced zone scheme in which all k's are transformed to lie in the first Brillouin zone. Plot roughly in the [111] direction the energies of all bands up to six times the lowest band energy at the zone boundary at k=2[tex]\pi[/tex]/a(1/2,1/2,1/2). Let this be the unit of energy. This problem shows why band edges need not necessarily be at the zone center. Several degeneracies will be removed when account is taken of the crystal potential.


Homework Equations


Wish I knew.


The Attempt at a Solution


Like I said, totally baffled.
 
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  • #2
Hi,

I realized that we're both concerned with the same problem in Kittel's book.
I'm not sure you're still interested, since your post dates back several months.
In case you are, you can have a look at this post.

I'm almost sure my last comment is the correct answer, but I'll appreciate some feedback.

Cheers

Franz
 

1. What is the Band Theory of Solids?

The Band Theory of Solids is a theory that describes the electronic structure of solids, specifically the energy levels of electrons within a solid material. It explains how the arrangement of atoms in a solid material affects the behavior of electrons and their ability to conduct electricity.

2. Who developed the Band Theory of Solids?

The Band Theory of Solids was developed by physicist Felix Bloch and chemist Rudolf Peierls in the late 1920s and early 1930s. However, it was further developed and expanded upon by many other scientists, including Charles Kittel, whose book "Introduction to Solid State Physics" is a widely used reference on the topic.

3. How does the Band Theory explain the difference between conductors, insulators, and semiconductors?

The Band Theory explains that the arrangement of atoms in a solid material creates energy levels for electrons to occupy. In conductors, there is significant overlap between the valence and conduction bands, allowing electrons to move freely and conduct electricity. In insulators, there is a large energy gap between the valence and conduction bands, making it difficult for electrons to move and conduct electricity. Semiconductors fall in between conductors and insulators, with a small energy gap that can be manipulated to allow for controlled conductivity.

4. How does temperature affect the Band Theory of Solids?

Temperature can affect the Band Theory of Solids in several ways. As temperature increases, the atoms in a solid material vibrate more, causing the energy levels to broaden and overlap. This can lead to a decrease in conductivity as electrons are less able to move freely. Additionally, at very low temperatures, quantum effects may come into play and alter the behavior of electrons in a solid material.

5. What are some practical applications of the Band Theory of Solids?

The Band Theory of Solids has many practical applications, including the development of electronic devices such as transistors, diodes, and integrated circuits. It is also used in the study of materials for renewable energy technologies, such as solar cells and thermoelectric materials. Additionally, the Band Theory is important in understanding the properties of materials used in everyday objects, such as metals, ceramics, and plastics.

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