I studied a materials which is optically anisotropic. Now, I want to know the effective mass in different direction to support the optical anisotropy.
The effective mass of electron is proportional to density of states. The formula can be expressed as,
g(E) = C*m^(3/2)*√(E-Ec)
If you consider the Fermi energy as a reference value, simply (E-Ec) becomes E (from Fermi level to selected point) for a specific k-value. From DOS curve, you have to find density of states g(E) at E. Then, you can calculate the effective mass of electron.
You should calculate the inverse of the effective mass tensor [1]. Upon diagonalising it, you will obtain the reciprocals of the effective masses along the principal axes (i.e. the eigenvectors) of the latter tensor. Note that it is assumed that the calculation is carried out around a k point where the energy dispersion under consideration is stationary.
[1] https://en.wikipedia.org/wiki/Effective_mass_(solid-state_physics)
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