Exploring Effective Mass and Spin-Orbit Interactions in Semiconductor Physics

In summary, there is a common practice of using an effective mass model to describe electrons in the bottom of the conduction band, with spin orbit included as a perturbation. However, there is some debate over whether this is the correct approach, as some argue that starting from the full k dot p equation with spin orbit included and deriving an effective mass model may be more accurate. Additionally, it has been noted that external magnetic fields do not affect the effective mass in the k dot p method. There is also a discussion about the equivalence of writing the Hamiltonian in the form of p^2/2m* + SO + magnetic field and using second order perturbation theory to derive the effective mass Hamiltonian without the spin orbit and magnetic field
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Often I see people using an effective mass model to describe electrons in the bottom of the conduction band.
Spin orbit is then included as a perturbation in this effective mass model. But what is the justification for using this sort of model?
Would the correct way not be to start from the full k dot p equation with spin orbit included and then derive an effective mass model from this? My concern is due to the fact that I would expect the effective mass to be dependent on the spin orbit interaction, but maybe that is not true.
Also, what about external magnetic fields. Do these affect the effective mass?
 
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  • #2
no and no, spin orbit and the magnetic field do not affect the effective mass in [itex]\vec{k}\cdot\vec{p}[/itex]
 
  • #3
Okay so when I write a Hamiltonian on the form:

H = p2/2m* + SO + MAGNETIC FIELD

Is this equivalent to starting from the k dot p method and applying second order perturbation theory? (as you do in the case where you want to derive the effective mass hamiltonian without the SO and magnetic field terms).
 

1. What is the concept of effective mass in solid state physics?

Effective mass refers to the mass of an electron or hole in a solid that behaves as if it were free from the influence of other particles in the material. It takes into account the effects of the crystal lattice on the electron's motion, making it an important parameter in understanding the electronic properties of semiconductors and other materials.

2. How is effective mass related to the k dot p method?

The k dot p method is a mathematical approach used to calculate the effective mass of an electron or hole in a crystal. It involves expanding the energy bands of a crystal around a specific point in the Brillouin zone (k-point) and using the k dot p Hamiltonian to determine the effective mass at that point.

3. What is the significance of effective mass in electronic band structures?

Effective mass is a critical factor in determining the behavior of electrons and holes in a solid. It affects their mobility, optical and transport properties, and ultimately, the performance of electronic devices made from these materials. An accurate understanding of effective mass is crucial in designing and engineering new materials for technological applications.

4. Can effective mass have a negative value?

Yes, effective mass can have a negative value, which indicates that the electron or hole behaves as if it has a negative mass. This phenomenon is known as negative effective mass and is observed in materials with complex band structures, such as graphene, where electrons behave as if they are moving in a relativistic manner.

5. How does temperature affect the effective mass of electrons in a material?

At higher temperatures, the crystal lattice of a material experiences thermal vibrations, which can alter the effective mass of electrons. This effect is more significant in materials with heavier atoms and can lead to a decrease in the effective mass of carriers, resulting in changes in the material's electronic properties.

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