Effective mass of the electron for Si

In summary, the effective mass for holes in Si is a disputed topic and can have two values, 0.57 or 0.81, depending on whether the light or heavy hole band is being considered. This discrepancy is due to the fact that the heavy hole band does not have a spherical symmetry, leading to differences in calculating the effective mass through different methods.
  • #1
ZeroFunGame
93
5
TL;DR Summary
Which effective mass should I use?
https://ecee.colorado.edu/~bart/book/effmass.htm#short

Looks like the effective mass for holes in Si can either be 0.57 or 0.81, according to the link above.

Is there a temperature regime where one effective mass should be used instead of the other?

Is anyone able to explain in layman's terms why the effective mass is disputed?
 
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  • #2
There are two bands at [itex] \Gamma = 0[/itex], the light and heavy holes, each has their own band curvature which is related to the effective mass for each..
 
  • #3
Forgive my ignorance, but what is gamma? If there's a link on this topic that I could read more on, that would be great! Thank you!
 
  • #5
Effective mass depends on the shape of the band. So if in Si you have messy shaped bands you should expect the value of effective mass to change very much. But in the link you posted it is said that

  • 1 Due to the fact that the heavy hole band does not have a spherical symmetry there is a discrepancy between the actual effective mass for density of states and conductivity calculations (number on the right) and the calculated value (number on the left) which is based on spherical constant-energy surfaces. The actual constant-energy surfaces in the heavy hole band are "warped", resembling a cube with rounded corners and dented-in faces.

So basically I think they are telling you that the approximation they used to carry out the calculations about the structure of the band does not match with the other way of evaluating the effective mass (via the density of states, as I understood).
 

What is the effective mass of the electron for Si?

The effective mass of the electron for Si is a measure of the electron's mobility in a silicon crystal lattice. It is a quantity that describes how an electron behaves in a solid material, and is an important factor in determining the electrical and thermal properties of silicon.

How is the effective mass of the electron for Si calculated?

The effective mass of the electron for Si is calculated using mathematical models and experimental data. It is typically determined by analyzing the electron's behavior in a crystal lattice and comparing it to the behavior of a free electron in a vacuum. The effective mass can also be calculated using the band structure of silicon, which describes the energy levels of electrons in the material.

Why is the effective mass of the electron for Si important?

The effective mass of the electron for Si is important because it affects the electrical and thermal conductivity of silicon. It also plays a crucial role in the performance of electronic devices made from silicon, such as transistors and solar cells. Understanding the effective mass is essential for designing and optimizing these devices.

How does the effective mass of the electron for Si differ from other materials?

The effective mass of the electron for Si can vary depending on the crystal orientation and temperature. It is also different from other materials, such as metals or insulators, due to the unique structure and properties of silicon. The effective mass of the electron for Si is typically lower than that of metals, but higher than that of insulators.

Can the effective mass of the electron for Si be altered?

Yes, the effective mass of the electron for Si can be altered by changing the doping level or temperature of the silicon crystal. Doping refers to the intentional introduction of impurities into the crystal lattice, which can affect the behavior of electrons. Additionally, the effective mass can also be altered by applying external forces, such as an electric or magnetic field, to the silicon material.

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