# Discontinuous at horizontal axis, U and K points, in energy

• Tana-ami
In summary, the horizontal axis of the energy band in the band structure of FCC lattices, such as Si and GaAs, shows a discontinuity at the U and K points. However, in other regions, such as from Gamma to X or to L, it remains continuous. Some individuals may struggle to understand the reason for this discontinuity and are seeking clarification from someone who understands it. However, others may argue that there is no true discontinuity, but rather a discontinuity in the derivatives at the X point due to the sharp bend in the path in k space, as shown in the Brillouin zone diagram.
Tana-ami
I have a question about horizontal axis of energy band.
In band structure of FCC lattice, like Si, GaAs, the horizontal axis have discontinuous at U point and K point. But other region have continuous like from Gamma to X or to L.
Would anyone who understand the reason answer this question, please teach me.

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## 1. What does it mean for a function to be discontinuous at the horizontal axis?

Discontinuous at the horizontal axis means that the function has a break or gap in its graph at a specific point on the horizontal axis. This means that the value of the function at that point is undefined or not continuous with the rest of the function.

## 2. What is the significance of U and K points in energy in relation to discontinuity?

U and K points are specific points in the energy band diagram of a material, which represent the minimum and maximum energy levels of electrons in that material. The discontinuity at these points is significant because it can affect the behavior and properties of the material, such as its conductivity or optical properties.

## 3. How can we identify discontinuity at U and K points in energy?

The discontinuity at U and K points can be identified by analyzing the shape and behavior of the energy band diagram of a material. If there is a sudden change or break in the diagram at these points, it indicates a discontinuity.

## 4. What causes discontinuity at U and K points in energy?

Discontinuity at U and K points can be caused by various factors such as the band structure of the material, the presence of impurities or defects, or external influences such as temperature or pressure. These factors can affect the energy levels of electrons and lead to a break or gap in the energy band diagram.

## 5. How does discontinuity at U and K points affect the properties of a material?

The discontinuity at U and K points can have a significant impact on the properties of a material. It can affect the mobility of electrons, as well as the absorption and emission of light. It can also affect the overall electronic and optical properties of the material, making it an important factor to consider in the study and application of materials.

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