[Wien] effective masse

[Gavin Abo]

I haven't calculated the effective mass with WIEN2k, but my current 
understanding is as follows.

One method used to calculate the effective mass is the parabolic 
approximation method.

You can probably find this method described in semiconductor physics or 
solid state physics textbooks.  I find the description of the parabolic 
approximation method in section "3.2.3 Electron Effective Mass" of the 
book titled "Semiconductor Physics and Devices, 3rd Edition" by Donald 
Neamen useful.  Maybe others know of other good references.
*
**Summary of the parabolic approximation method*

1) Calculate the bandstructure (E-k: energy versus k) using WIEN2k.

2) Plot E-k

3) Using the E and k values from WIEN2k, fit the desired data points to 
the equation for a parabola [ 
http://www.mail-archive.com/wien%40zeus.theochem.tuwien.ac.at/msg04621.html 
].  For example, if fitting to the conduction band, the equation E = 
C1(k)^2 + Ec is used, which comes from equation 3.44 in the 
"Semiconductor Physics And Devices" book.

To fit the parabolic equation to the band, you should be able to use 
your favorite curve fit program like Matlab, Origin, or Octave to obtain 
the curve fitting parameters C1 and Ec.  The polyfit function might 
useful, if you use Matlab [ 
http://www.mathworks.com/matlabcentral/newsreader/view_thread/23793 ].

4) Plot the E equation (equation of the parabola) on the same E-k plot 
(of step 2) to visualize the wellness of the fit.

5) Substitute the E equation into the effective mass equation followed 
by taking the second derivative with respect to k to calculate the 
effective mass.  In other words, plug E (e.g., E = C1(k)^2 + Ec) into 
the equation 1/m* = 1/hbar*d^2E/dk^2 and solve for the effective mass m* 
(equation 3.47 in "Semiconductor Physics And Devices").

Another approach is the finite difference method.  Unfortunately, I 
don't know of any tools for WIEN2k that can currently do this. There is 
an Effective Mass Calculator (EMC) for VASP, but it does not support 
WIEN2k [ http://afonari.com/emc/ ].  However, you might trying 
contacting an author of the EMC to see if there are any future plans to 
support WIEN2k, and let us know what you find out.  Though, it might be 
a good project for someone in the WIEN2k community.  If a conversion 
program was made to convert the WIEN2k output to VASP format or reading 
of the needed WIEN2k output was implemented in the EMC source code, I 
think the EMC could be made to work.

On 11/18/2014 4:20 AM, ben amara imen wrote:
> Dear all,
>
> Can some one help me how I can calculate the effective masse of hole 
> and electron , from the structure bands ??
> Thanks in advance
> Best Regards
> Imen

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