Group Theory to Understand Band Gap Structure of Semiconductor Oxides

[drizzle]

ehim ehim...hello,
I wonder if anyone knows about “group theory” [= approximation method] which is helpful in describing band gap structure of semiconductor oxides, my main problem is the high symmetry points i.e. gama point which occur at k=0 [the first Brillion zone], how it varies from gama 1 to gama 7 when the bands splits -under the effect of crystal field and spin-orbit splitting- and what do these numbers represent, if anyone have a brief explanation of it please do. also any articles, books or sites that you recommend will be helpful. thanks.

 

[Dr Transport]

Group Theory describes the behavior of energy bands and their symmetry properties, it won't tell you any specifics about semiconductor oxides. If you know the symmetry of the crystal, you'll be able to determine specifics, i.e. if a transition will occur, which transitions are allowed, how bands split under crystal-fields etc. One thing everyone gets confused about is that group theory determines whether or not a transition is allowed, it will not determine the strength.

Look for Tinkham's text on group theory and quantum mechanics, it is terse but if you find a couple of others to help you, it'll be worth it.

 

[charng]

Group theory is a powerful mathematical tool used in many areas of physics, including the study of band gap structure in semiconductor oxides. It allows us to analyze the symmetry properties of a system and predict how it will behave under different conditions. In the case of semiconductor oxides, group theory can help us understand how the band gap structure changes as a result of crystal field and spin-orbit splitting.

The high symmetry points, such as the gamma point at k=0, are important in determining the electronic properties of a material. Group theory allows us to identify the different symmetries present at these points and how they interact with each other. This information can then be used to predict how the band structure will change as a result of external influences.

As for the numbers representing the different gamma points (gamma 1 to gamma 7), these refer to the different symmetry classes present at each point. Each symmetry class has its own set of properties that can be used to understand the electronic structure of the material.

In terms of resources, there are many articles and books available on the application of group theory in studying the band gap structure of semiconductor oxides. I would recommend starting with basic texts on group theory, such as "Symmetry and Spectroscopy: An Introduction to Vibrational and Electronic Spectroscopy" by Daniel C. Harris, and then moving on to more specialized texts on the topic. Additionally, there are many online resources and research papers available that may be helpful in understanding this concept.