[Wien] Deformation Potential

[Gavin Abo]

*Deformation Potential Calculation Process*

The goal of a deformation potential (DP) calculation is oftentimes to 
compute a relaxation time (𝜏).

The article at [1] contains an equation (4) for relaxation time:

/𝜏/ = /μm/*//e/

where /μ/ is the mobility, /m/* is the effective mass, and /e /is the 
electron charge.

One step in the DP calculation is to determine effective masses. In 
order to do that, a method of calculation for the effective masses has 
to be chosen.

One method could be to use the parabolic approximation [2].  This method 
is used in the WIEN2k article at [3].

Another method could be to use mstar [4].  This method is used in the 
WIEN2k article at [5].

There may be other methods published in literature that you could select.

Another step in the DP calculation is to calculate the mobility. First, 
you must chose an appropriate mobility equation for your structure.

A few mobility equation examples follow.

The article at [6] has an equation (7) for an isotropic 2D semiconductor:

/μ/ = 2*/e/*/ħ/^3*C11/[kB*T*(/m/*)^2*(E1)^2]

The article at [7] has an equation (1) for a 1D structure:

/μ /=///e//*//ħ/^/2//*/C1D_c/[(2*π*kB*T)^(1/2)*|/m/_c*|^(3/2)*(E1c)^2]

The article at [8] has an equation (7) for a 3D structure:

/μ /= 2*(2*π)^(1/2)*/e/*/ħ/^4*Cii/[3*(kB*T)^(3/2)*(m*)^(5/2)*(E1_β)^2]

There are additional mobility equations published online that you may 
find as a better selection for your structure.

The above mobility equations have in common the electron charge /e/, the 
reduced Planck constant /ħ/, the Boltzmann constant kB, the temperature 
/T/, the effective masses m*, the DP constants E1, and the elastic 
constants C.

WIEN2k has different internal and external programs you may select from 
for calculating elastic constants.  There is Elast, ElaStic, and IRelast 
[9].  There is also ElaTools as seen on the WIEN2k unsupported page 
[10].  It looks like the WIEN2k article at [11] used IRelast for their 
DP calculation.

The conduction and valance band constants for E1 can be extracted from 
curving fitting the conduction band minimum (CBM) and valance band 
maximum (VBM) energy versus strain data computed from multiple WIEN2k 
calculations, respectively.  I think Fig. 9 in the article at [12] could 
be a good example of that.

Hopefully, the above helps.  Unfortunately, I don't have a procedure 
from beginning to end with all the commands used for a DP calculation 
and have yet come across a document or video online for that. If a 
person in the list as done an entire DP calculation, perhaps they will 
be able to share additional information with you.

[1] https://doi.org/10.1039/C7RA08828K
[2] 
https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg11446.html
[3] https://doi.org/10.1016/j.mtcomm.2025.114321
[4] https://github.com/rubel75/mstar/wiki
[5] https://doi.org/10.1103/PhysRevMaterials.7.104602
[6] https://doi.org/10.1088/1757-899X/231/1/012116
[7] https://doi.org/10.1021/acsomega.1c03728
[8] https://doi.org/10.1038/srep22778
[9] 
https://wien2k-algerien1970.blogspot.com/2016/09/summarization-of-calculation-of-elastic.html
[10] http://susi.theochem.tuwien.ac.at/reg_user/unsupported/
[11] https://doi.org/10.1088/1361-648X/ac431d
[12] https://doi.org/10.1016/j.rinp.2025.108312

Kind Regards,

Gavin
WIEN2k user

On 2/8/2026 5:08 AM, uchit chaudhary wrote:
> Dear experts,
>
> How to calculate the deformation potential in Wien2k?
>
> Best Regards,
> Wien2k user
> uchit
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