# Interpretation of effmass module

Currently, I am trying to figure out the effmass module. I'm newly into effective mass stuff and I'm able to run it and generate effective masses. However, I'm facing some trouble understanding it. Is there anyone in this community who could help me?

For example, I want to find the effective mass of $$\ce{WS2}$$ bulk system at VBM and CBM but this module generates so-called segments and I could not figure the logic behind that. What are these segments and what do these numbers in the square bracket mean?

In the following plot, it shows generated effmass plot for the $$\ce{WS2}$$ bulk system.

For example, effective mass values for segments 0 and 1 are:

0: $$-0.49$$

1: $$-0.37$$

Which one is the K point effective mass? It really confuses me.

I will give a quick answer, someone more experienced in this field may be able to elaborate better. You have two different effective masses because you have a different effective mass in the K->M and K->G directions in the valence band. I suspect the numbers in brackets represent the direction. M likely corresponds to [1 -2 0] for example.

You may find the tool sumo-bandstats to give you easier access to this information directly, I have never used effmass so I cannot advise if a similar tool exists within it. I have taken an example output from that page and included here so you can see how the output compares to what you see.

Direct band gap: 0.712 eV
k-point: [0.00, 0.00, 0.00]
k-point indexes: 0, 113
Band indexes: 34, 37

Valence band maximum:
Energy: 1.444 eV
k-point: [0.00, 0.00, 0.00]
k-point location: \Gamma
k-point indexes: 0, 113
Band indexes: 34, 35, 36

Conduction band minimum:
Energy: 2.155 eV
k-point: [0.00, 0.00, 0.00]
k-point location: \Gamma
k-point indexes: 0, 113
Band indexes: 37

Using parabolic fitting of the band edges

Hole effective masses:
m_h: -0.641 | band 34 | [0.00, 0.00, 0.00] (\Gamma) -> [0.50, 0.50, 0.50] (L)
m_h: -0.516 | band 34 | [0.00, 0.00, 0.00] (\Gamma) -> [0.50, 0.00, 0.50] (X)
m_h: -0.641 | band 35 | [0.00, 0.00, 0.00] (\Gamma) -> [0.50, 0.50, 0.50] (L)
m_h: -0.516 | band 35 | [0.00, 0.00, 0.00] (\Gamma) -> [0.50, 0.00, 0.50] (X)
m_h: -1.234 | band 36 | [0.00, 0.00, 0.00] (\Gamma) -> [0.50, 0.50, 0.50] (L)
m_h: -15.158 | band 36 | [0.00, 0.00, 0.00] (\Gamma) -> [0.50, 0.00, 0.50] (X)

Electron effective masses:
m_e: 0.207 | band 37 | [0.00, 0.00, 0.00] (\Gamma) -> [0.50, 0.50, 0.50] (L)
m_e: 0.211 | band 37 | [0.00, 0.00, 0.00] (\Gamma) -> [0.50, 0.00, 0.50] (X)

• Could you detail these directions or do you know any good paper, book or link which explains them? Aug 6 at 11:26

The effective mass ($$m^*$$) is one of the properties used in Solid State Physics, and specially in Semiconductor Physics. It is defined from the energy dispersion relationship as follow:

$$(\frac{1}{m^*})_{ij}=\frac{1}{\hbar^2}\frac{\partial^2E_n(\vec{k})}{\partial k_i \partial k_j},\;\;i,j=x,y,z$$

In case of parabolic bands, it can be calculated under the approximation:

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

So, in order to calculate it, you need to specify all the $$\vec{k}$$. As the k-path depends on the crystal symmetry, you can also "map" the k points with the crystal directions.

How $$m^*$$ is calculated, depend on how the program implements the first formula. In a full implementation, you will get one value for each pair $$(k_i,k_j)$$. From your question, looks like the software you are using do a linearization around the maxima/minimum, instead going through all the real k points.