hello everyone
can somebody tell me, how can we calculate effective mass of semiconductor from band structure.
Dear Rashmi, effective mass is an anisotropic quantity.So, the effective mass values at different k-points is different.If you are using VASP, then open band.txt file in origin software. From the electronic bandstructure, find double differentiate of E wrt k then use the relation m*= h cross square/ double derivative of E w.r.t k. If you do it at VBM you will get effective mass of hole and for effective mass of electron repeat all at CBM.You can also get the effective mass tensor using ELK code in which there is a script available for effective mass calculation.
Thank you Dimple, but i am not getting idea how take double differentiation of parabola (band diagram). can you please send me any example. if you need i can attach band st. file.
Hi Rashmi Khan,
I am attaching a link to a paper i recently published on this subject and its SI:
ftp://ftp.aip.org/epaps/journ_chem_phys/E-JCPSA6-144-045615
http://scitation.aip.org/content/aip/journal/jcp/144/16/10.1063/1.4946752
I have worked exactly on this issue and in the SI of the paper there is a Mathematica script package compatible with VASP outputs which directly calculates the effective mass tensor and average effective mass, and also DOS effective masses.
In general the idea is to plot the band diagram in different directions in k-space and perform a second derivative at extrema point, which can be calculated by finite difference schemes, or more accurately, as in the scripts above, by a fitting of general second order polynomial in 3D.
I hope the paper and scripts will help you, and if not directly by just using them on your outputs, then maybe just put you on the right track. there are some fine details to consider in such approximations like: partial occupancies, the location of the CBM and VBM, the k-grid density, the k-space integration method, the averaging technique, spin symmetry in the band structure, and some more issues, all of which are outlined and discussed in the paper and SI.
Do write me if you need some help setting things,
Ofer.
Hello Rashmi, As I mentioned to you. From band.txt file , you can open it in Origin.Select a column or band no. at which you want to calculate effective mass. Then in Origin , go to Analysis > Differentiate. Then a dialog box will open. There is option for derivative i.e. first , second and higher derivative. After it, there will be generation of new column of derivates of all the values of that column.
Hope so it will help you.
thank you very much ofer and Dimple.But ofer i did not find SI and script.
In the first link above you will be directed to scripts and a word file with information on them. if not you can just look for the words "Supplementary Material" in the paper, there is a link there. The scripts are .nb files that open in Mathematica.
Please look at the discussions of our paper, there are different ways to calculate:
https://www.researchgate.net/publication/257328883_Enhanced_Effective_Mass_in_Doped_SrTiO3_and_Related_Perovskites
Article Enhanced Effective Mass in Doped SrTiO3 and Related Perovskites
In case of band gap, we cannot calculate Fermi velocity anymore, as it is related to Fermi energy. We generally use an equation for parabolic band structure by taking double derivative of energy with respect to momentum space to calculate the effective mass of electron or hole. But in case of linear dispersion band, it is no any more valid. Could you please suggest any method to calculate the mobility of the material through its linear dispersion of band structure with band gap or mobility of carriers at Dirac point?
try these papers:
http://arxiv.org/pdf/1206.6100v2.pdf
http://arxiv.org/pdf/1205.3995v1.pdf
and possibly also check their references. i believe this is not a closed topic just yet, but there should be some theoretical papers out on this.
Hello, Dimple Sharma
Is effective mass calculated in reciprocal space or direct space?
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