Germanium Bandstructure

[Dhirendra]

Hi,

Bandstructure calculation of Ge shows bandgap of 0eV with LDA and GGA, however with MGGA its overestimated to ~0.85-1 eV. Moreover the bandgap is direct bandgap. Can anyone comment on how to get correct "bandstructure" (indirect bandgap of 0.66 eV) for Ge?

[Shan]

Hello...

Well, i checked ur comments... u r correct....
I too faced some similar problems in calculating Bandstructure, TE optimization etc...
It is upto the atk team.. they need to answer what the problem is...

[Anders Blom]

Ge is tricky. We are working on it ourselves. Will report results when we have them!

[Umberto Martinez]

You can get a good description of Ge electronic structure (indirect band gap) with MGGA with the parameters below for different basis sets. Check Meta-GGA and 2D confined InAs tutorial for the optimization of the c (tb09) parameter in MGGA. a = 5.6574 Å at least 11x11x11 k-points With FHI you need the DoubleZetaPolarized basis set and c = 1.0070 giving: Γ-L: 0.663 eV Γ-Γ: 0.694 eV With HGH you need to use the GGA.PBE Tier 4 basis set which you can specify with the following lines:

Code

basis_set = [
    BasisGGAPBEHGH.Germanium_4_Tier_4,
    ]

incresing the number of k-points to 21x21x21 and with c=0.955 you get: Γ-L: 0.630 eV Γ-Γ: 0.846 eV Finally, you can use OMX basis set and spin-orbit MGGA. You will need to specify explicitely the basis set through the atomic_species keyword to include d functions (from the Script Generator you can only specify contracted basis, Tier type):

Code

GermaniumBasis = OpenMXBasisSet(
    element=PeriodicTable.Germanium,
    filename="openmx/pao/Ge8.0.pao.zip",
    #tier=0,
    atomic_species='s4p4d3',
    pseudopotential=NormConservingPseudoPotential("openmx/vps/Ge_CA13.vps.zip"),
    )

basis_set = [
    GermaniumBasis,
    ]

in this case c = 1.0571 an you will get the BS attached with: Γ-L: 0.65 eV Γ-Γ: 0.71 eV ESO: 0.27 eV

[Anders Blom]

The HGH version is my favorite, because it gives a clear separation of G and L at zero strain, and gives good strain behavior compared to HSE calculation (article coming out soon!).

[Dhirendra]

Hi,

Is it recommended to play around with the parameters of the confined orbitals to get the MGGA bandstructure accurately? Meaning some trial and error over the radii in the confined orbitals are able to give me the reasonably accurate bandstructure of Ge. (Significant distinction between Eg_direct and Eg_indirect)

[Jess Wellendorff]

I guess this depends on what you are going to do afterwards. If effective mass, then I guess it's ok, since that quantity depends on the band structure. If geometry optimization , it may or may not have a negative impact on the forces and stress.

[Dhirendra]

Jess, I am not much interested in the geometry optimization there. Or I can optimize the geometry using the predefined basis set that is shipped with ATK. The parameter tuning is to only get the expected bandstructure with MGGA.

[Anders Blom]

I think Umberto has provided a very comprehensive answer above. But to address your specific question: no, I don't think it's a good idea to try to optimize the basis set, because there are quite many parameters that could be tuned, so it becomes a big exercise.