# Calculation of effective mass from bandstructure

The effective mass is defined as $$\frac{1}{m_{ij}^*} = \frac{1}{\hbar^2} \frac{\partial^2\epsilon}{\partial k_i \partial k_j}$$

where, $$m_{ij}^*$$ is the effective mass, $$\hbar$$ is the Planck's constant, $$\epsilon$$ is the energy and $$k_i,\ k_j$$ are reciprocal latttice vectors.

Now let us consider that we have the values of energy corresponding to the points in a line connecting the center of Brillioun zone and a point in the reciprocal space (say $$k_x = 0.5$$, $$k_y = 0.5$$, $$k_z = 0.5$$). Now I would like to know if it is possible to get value of effective mass from this data. If yes how can I do that?

From your data, it seems like you can obtain the longitudinal effective mass in that direction. By the way, that line in the reciprocal space, the  direction, is often called the $$\Lambda$$ axis.
I suppose that if you represent the energy as a function of $$|\vec{k}|$$ in that direction there will be a minimum or a maximum. You could try then to fit the data around the minimum or maximum to a parabola $$\varepsilon(k)=Ak^2+Bk+C$$ and from there $$\frac{1}{m^*_l}=\frac{1}{\hbar^2}\frac{d^2\varepsilon}{dk^2}=\frac{2A}{\hbar^2}$$