I am trying to calculate the effective mass of electrons and holes manually from the band structure of a 2D system I am working on. I have only considered the maximum valence band and the minimum conduction band. At each "valley" whether maximum in the valence band or minimum in the conduction band, I have fitted the neighborhood with a parabolic function and calculated the effective mass there. I have got 4 values of the electron effective mass (at each valley) and 4 values of hole effective mass (at each maximum). What would the reported effective mass be? is it the geometric mean of all 4 values? How does the "degeneracy" (equivalent minima) come into play? Does anyone know?
The effective masses of different valleys should not be averaged. Physically, they are different charge carriers. The effective mass of each valley is the average geometric effective masses along each crystallographic axis in this valley.
Degeneracy does not affect the effective mass.
What does reported effective mass mean? Do you want to compare it with the experimental value?
Alexander N Titov ,
Thanks very much for your reply. I am trying to obtain electron and hole carrier concentrations at different Fermi levels (No comparison with experimental values are involved). These expressions contain the hole and electron effective masses. By "reported" I mean which effective mass in which valley shall I use? I guess it must be the one corresponding to the bandgap (which is indirect in my case). I also suppose there are different treatments for direct and indirect bandgaps.
What I have done in the last two days is the following: Suppose the minimum of the conduction band occurs at (kxmin,kymin,kzmin), then I am fitting the points in the neighborhood of this point by a function of the form : hbar^2/2 [(kx-kxmin)^2*1/mx+ (ky-kymin)^2/my+(kz-kzmin)^2/mz] to obtain mx and my and then apply the geometric average given by (mx.my.mz)^(1/3). Same thing goes for the valence band to compute the effective mass of the holes.
Am I on the right track?
Thanks once again.
If you consider the tempearture to be zero Kelvin, then in the presence of a gap, it makes sense to take into account only those minima or maxima that contain the Fermi level. If the temperature is not zero, then it makes sense to estimate the carrier concentration in each of the minima or maxima, considering the effective mass equal to m0. Then take into account only carriers whose concentration is significant.
In general, your way seems to me right.
I wish you success!
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