Understanding Valley Quantum Number in Si and Ge Band Structures

In summary, the article discusses the concept of valley quantum number in relation to crystal axes and electron waves. It then addresses a question about the symmetry of valleys in silicon and germanium and explains that while they have the same symmetry, the depth of their valleys differs due to the specific arrangement of their band gaps.
  • #1
hokhani
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According to "Nat. Nanotechnol., vol. 7, no. 8, pp. 488–489, 2012 (http://www.nature.com/nnano/journal/v7/n8/full/nnano.2012.117.html?WT.ec_id=NNANO-201208)":
Valley quantum number is associated with different crystal axes that differ only in their orientations. Such axes can support electron waves that are also identical apart from their direction (or, more precisely, their momentum),so an additional discrete index known as the valley quantum number is needed to fully describe these waves.

This argument raises a question:
Si and Ge have the same crystal structure. Therefore according to this statement they have to have the same valleys. However Si has 6 valleys in the ##\Gamma X## direction while Ge has 4 valleys in the ##\Gamma L## direction. I don'n know what goes wrong with my thought.
 
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Hi, I don’t really understand the question, but I wonder whether this might be any help.

Germanium and silicon both have valleys in their conduction bands along <100> direction and the <111> direction.

They both have valleys along both directions.

So the symmetry of their band structure is, in fact, the same – as it must be because it’s determined by the crystal lattice symmetry which as you point out is the same. In that sense, they do have the same valleys, at least the same symmetry, but in silicon the Γ-X valleys are a bit deeper than the Γ-L valleys whereas in germanium it’s the other way around.

So, when we talk about the silicon band gap, we’re referring to the indirect gap between Γ and the six X points. When we talk about the germanium band gap the shortest distance (in energy) between valence and conduction band just happens to be between Γ and the four L points.

Does that help at all?
 
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1. What is Valley's quantum number?

Valley's quantum number is a concept in solid state physics that describes the energy bands in a crystalline material. It represents the number of equivalent energy valleys in the material's band structure.

2. How is Valley's quantum number determined?

Valley's quantum number is determined by the crystal structure and symmetry of the material. It can also be influenced by external factors such as strain or electric fields.

3. What is the significance of Valley's quantum number?

Valley's quantum number plays a crucial role in understanding the electronic and optical properties of materials. It helps explain phenomena such as valley polarization and valley coherence in 2D materials.

4. How does Valley's quantum number affect electronic devices?

Valley's quantum number can impact the performance of electronic devices, especially in 2D materials. It can affect the speed, efficiency, and sensitivity of devices such as transistors and photodetectors.

5. Can Valley's quantum number be manipulated?

Yes, Valley's quantum number can be manipulated through external factors such as strain, electric fields, or optical excitation. This can lead to the control of electronic and optical properties of materials, making it a valuable tool in developing new technologies.

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