Effective mass of holes was measured using DFT

Question

Effective mass of holes was measured using DFT. The hole value is different for each band, is there a way to get the average or standard value of this value? It was calculated using the VASP program. Or what kind of band should I calculate the effective mass of holes with VASP?

Answer 1

The easier way to calculate the effective mass ($m^*$) is assuming the band as parabolic and calculate it from the equation below:

$$E(\vec{k}) = E_0 + \frac{\hbar^2\vec{k}^2}{2m^*}$$

This means that $m^*$, is dependent on the selected band and direction (i.e. $\vec{k}$ direction). This imply that, prior to do some calculations, you need to know what physical process you are interested in. Then, you need to identify which bands are involved in such process and then calculate the $m^*$ for them.

In Semiconductor Physics one processes of interested is the electron conductivity of the material. In such case, only the conduction band is used. Considering that the conduction band can be anisotropic (i.e. a different parabolicity for each direction), you can have a longitudinal ($m_l$) and two transversal (($m_t$)) effective mass. In such case, the electron conductivity mass can be calculated as the inverse sum of those mass:

$$m^*_{e,cond}=\frac{3}{\frac{1}{m_l} + \frac{1}{m_t} + \frac{1}{m_t}}$$

Other process of interested can be the semiconductor LED/laser physics where the transitions between the valence bands and conduction bands are important. In that cases, the corresponding effective mass for the valence bands (hole effective mass) are also calculated.

Always you are talking about holes, you have to use the valence bands to calculate the effective mass.