Effective mass of the electron for Si

[ZeroFunGame]

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?

 

[Dr Transport]

There are two bands at $\Gamma = 0$, the light and heavy holes, each has their own band curvature which is related to the effective mass for each..

 

[ZeroFunGame]

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!

 

[Dr Transport]

Center of the Brillouin zone

 

[dRic2]

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).

 

[Dr Transport]

See this article...

https://aip.scitation.org/doi/abs/10.1063/1.329345