How to calculate the effective mass of silicon for the two cases: valence band maximum and valence band minimum (both at gamma point)? Any general procedure would be great to see.
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- 2$\begingroup$ Is this for a calculation? Because if it's experimental, it might be better to post this in the Physics or Chemistry SEs—chances are you're more likely to get an answer there. $\endgroup$isolated matrix– isolated matrix2024-08-27 07:19:08 +00:00Commented Aug 27, 2024 at 7:19
- 1$\begingroup$ It's for the general procedure to calculate it from an available bandstructure. For example, any workflow from silicon band structure would also work well. @isolatedmatrix $\endgroup$Sak– Sak2024-08-27 07:31:15 +00:00Commented Aug 27, 2024 at 7:31
- 1$\begingroup$ * "conduction" band minimum, not valence band minimum. $\endgroup$Steven– Steven2024-08-27 07:35:33 +00:00Commented Aug 27, 2024 at 7:35
- $\begingroup$ For my case, I would like to check it for valence band minimum as well. @Sha $\endgroup$Sak– Sak2024-08-29 09:45:10 +00:00Commented Aug 29, 2024 at 9:45
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1 Answer
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Mathematically speaking, calculating the effective mass corresponds to fitting a parabola $E(k)=a + bk^2$ to the electronic energy dispersion $E(k)$ of the band in question. Here, $a$ is the energy of the extremum at $k=0$ (band edge) and $b=\frac{\hbar^2}{2m^*}$. The resulting effective mass $m^*$ is then typically expressed in units of the free electron mass, e.g. $m^*=0.3m_e$.
If you don't want to code it yourself, have a look at the Effmass package.
