Can't find the effective mass of a 2-dimensional semiconductor

In summary, when the determinant of the 2x2 matrix for the band structure of a two-dimensional semiconductor is zero, the effective mass cannot be calculated. This may be due to an error in the expressions of the bands or the bands being too close together to differentiate between them.
  • #1
Feelingfine
3
1
This is the situation: you have the band structure of a two-dimensional semiconductor E=E(k). Both, valence band and condcution band. You use the definition of effective mass: (m)^(-1)=(d2E/dkidkj), but both bands are in such a way that the 2x2 matrix that you obtain has zero determinant. So that matrix has no inverse and therefore you can not get the effective mass. Is this possible? Should there be an error in the expressions of the bands? What does it mean?
 
Physics news on Phys.org
  • #2
Yes, this is possible. If the determinant of the matrix is zero, then the bands overlap in such a way that the effective mass cannot be obtained. This could be due to an error in the expressions of the bands, or it could mean that the bands are too close together for a meaningful distinction to be made between them.
 

1. How is the effective mass of a 2-dimensional semiconductor defined?

The effective mass of a 2-dimensional semiconductor is a measure of the mobility of charge carriers in the material. It is defined as the mass of an electron or hole in the material, taking into account the influence of the crystal lattice and other factors.

2. Why is it difficult to find the effective mass of a 2-dimensional semiconductor?

Finding the effective mass of a 2-dimensional semiconductor is difficult because it depends on several factors such as the crystal structure, temperature, and electric field. Additionally, the effective mass can vary in different directions within the material, making it a complex and challenging measurement.

3. What techniques are commonly used to determine the effective mass of a 2-dimensional semiconductor?

The most common techniques used to determine the effective mass of a 2-dimensional semiconductor include magneto-transport measurements, cyclotron resonance, and optical spectroscopy. These methods involve applying magnetic fields, measuring electrical conductivity, and analyzing light absorption to calculate the effective mass.

4. How does the effective mass of a 2-dimensional semiconductor affect its electronic properties?

The effective mass of a 2-dimensional semiconductor plays a crucial role in determining its electronic properties. A lower effective mass means that charge carriers can move more easily through the material, resulting in higher conductivity and faster electronic devices. On the other hand, a higher effective mass can lead to lower conductivity and slower devices.

5. Can the effective mass of a 2-dimensional semiconductor be tuned or controlled?

Yes, the effective mass of a 2-dimensional semiconductor can be tuned or controlled by changing the material's composition, crystal structure, or by applying external electric or magnetic fields. This can be useful in designing and optimizing electronic devices for specific applications.

Similar threads

  • Atomic and Condensed Matter
Replies
2
Views
1K
Replies
1
Views
2K
  • Atomic and Condensed Matter
Replies
3
Views
3K
  • Atomic and Condensed Matter
Replies
2
Views
3K
  • Atomic and Condensed Matter
Replies
3
Views
2K
  • Atomic and Condensed Matter
Replies
3
Views
4K
  • Advanced Physics Homework Help
Replies
1
Views
799
Replies
7
Views
3K
  • Advanced Physics Homework Help
Replies
2
Views
1K
  • Atomic and Condensed Matter
Replies
4
Views
2K
Back
Top