[Wien] Slab dielectric function vs. bulk dielectric function
Peter Blaha
pblaha at theochem.tuwien.ac.at
Tue Nov 26 07:54:53 CET 2013
Of course, in principle slabs should converge to bulk epsilon. But:
In your slabs with a k-mesh of 69x69x1 you are using "effectively" a k-mesh
of 69x69x39 instead of a 69x69x69 mesh.
In addition, in the z direction you use "root-sampling" instead of tetrahedra
method. It is like integration with the rectangular-rule instead of a trapezoidal rule.
Try fcc-Al with a small tetragonal distortion during setup, so that you get only 16 sym.ops.
then change c/a back to 1 and use a kmesh of 69x69x39 and compare the dielectric function
to the 2 times 69-mesh. (This mimics the k-mesh problem, but still there s the
integration method !!).
You probably need even more layers ....
Am 26.11.2013 04:51, schrieb phlhj phlhj:
> Dear Prof. Blaha,
>
> Thanks so much for your suggestion.
>
> I tried bulk Al supercell with 39ML without vacuum with the same k-mesh as used in 39 ML thin film supercell. In fact I get the same results for plasma frequency and
> dielectric function as those from Al unit cell with only one Al atom. I think the k-mesh of 61x61x1 I used in my calculation is dense enough to give a precise result.
>
> The main difference for the dielectric function between thin film geometry and bulk geometry is at the low energy range (<1.2eV). I researched some paper for studying the
> anisotropic surface reflectance in semiconductor surface, say, GaAs(110). Even 15 atomic layers are used in the LDA calculation but still some difference around the band
> gap regime for the dielectric function is found between surface calculation and bulk calculation. I think the difference I encountered for teh dielectric function between
> slab Al(111) and bulk Al might be similar to the case in semiconductor system. However, from the physical point of view, it's hard to understand why there is still
> appreciable difference out there even though very thick film is used. Physically the dielectric function of the very thick slab should converge to that in the bulk counterpart.
>
> Thank you so much for sharing any understanding about this,
>
> Wenmei
>
>
> 2013/11/24 Peter Blaha <pblaha at theochem.tuwien.ac.at <mailto:pblaha at theochem.tuwien.ac.at>>
>
> As you probably know, the dielectric function of Al converges VERY slowly
> with respect to the k-mesh.
>
> When you do slab calculations, you include the surface effect, but you also replace
> the periodicity in k-z (and thus the k-mesh in k-z) to a backfoldung according to
> your slab. Even a 39 ML slab corresponds probably not to a very large k-z mesh and
> in addition the integration over k-z is limited to a "root"-sampling instead of the
> tetrahedron method. I could even imagine large numerical problems in this 2-D integration
> using a 3-D algorithm in joint due to large degeneracy of the tetrahedra.
>
> At least you could differentiate between "integration problems" and surface effects
> by using a 39-layer bulk structure (i.e. remove the vacuum in your supercell, so that
> you get 3D-Al again, but restrict yourself to 1-k point in k-z) and compare the
> resulting eps to bulk Al (with 1 atom/cell and good k-meshes.
>
> Am 23.11.2013 16:54, schrieb phlhj phlhj:
>
> Dear all,
>
> I was trying to calculate the optical properties of Al(111) slab. For the bulk FCC Al, I can reproduce the dielectric functions and plasma frequency very precisely
> reported
> in literature before. However, I did find some difference between the slab dielectric functions and the corresponding bulk values.
>
> Especially even though I used very thick slab, say 39MLs, in the low photo energy range (<1eV), the imaginary part is much larger than the bulk. I doubt this may be
> related
> to the band-folding and symmetry reduction in the direction normal to the surface.
>
> Also, I found the plasma frequency of the slab is smaller than the bulk plasma frequency.
>
> Mathematically, this behavior of the imaginary parts of the interband and intraband transitions contributions seems to be able to be understood from the f-sum rule.
>
> 1) However, physically it's hard to believe, because when the slab thickness is very thick for example the 39MLs used in my test calculation, the slab wavefunctions
> should
> be very very close to the bulk wavefunction except in the very thin slab/vacuum interface region. This should give us the dielectric functions for the slab which
> are very
> very close to the bulk values. This argument should be also true for the slab plasma frequency.
>
> 2) If the different values are because of the surface slab structure we used in the calculation, which indeed breaks the translational symmetry in the normal direction.
> Then the question is that in real experiment because the sample always is finite with the boundary surface, how can we get the dielectric information really for the
> ideal
> bulk rather than the slab similar as that mentioned above. Or in calculating dielectric function, when should we use bulk geometry? when should we use slab geometry?
>
> Thanks a lot for any idea.
>
> Wenmei
>
>
>
>
>
>
>
>
> _________________________________________________
> Wien mailing list
> Wien at zeus.theochem.tuwien.ac.__at <mailto:Wien at zeus.theochem.tuwien.ac.at>
> http://zeus.theochem.tuwien.__ac.at/mailman/listinfo/wien <http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien>
> SEARCH the MAILING-LIST at: http://www.mail-archive.com/__wien@zeus.theochem.tuwien.ac.__at/index.html
> <http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html>
>
>
> --
> ------------------------------__-----------
> Peter Blaha
> Inst. Materials Chemistry, TU Vienna
> Getreidemarkt 9, A-1060 Vienna, Austria
> Tel: +43-1-5880115671 <tel:%2B43-1-5880115671>
> Fax: +43-1-5880115698 <tel:%2B43-1-5880115698>
> email: pblaha at theochem.tuwien.ac.at <mailto:pblaha at theochem.tuwien.ac.at>
> ------------------------------__-----------
> _________________________________________________
> Wien mailing list
> Wien at zeus.theochem.tuwien.ac.__at <mailto:Wien at zeus.theochem.tuwien.ac.at>
> http://zeus.theochem.tuwien.__ac.at/mailman/listinfo/wien <http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien>
> SEARCH the MAILING-LIST at: http://www.mail-archive.com/__wien@zeus.theochem.tuwien.ac.__at/index.html
> <http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html>
>
>
>
>
> _______________________________________________
> Wien mailing list
> Wien at zeus.theochem.tuwien.ac.at
> http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien
> SEARCH the MAILING-LIST at: http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html
>
--
-----------------------------------------
Peter Blaha
Inst. Materials Chemistry, TU Vienna
Getreidemarkt 9, A-1060 Vienna, Austria
Tel: +43-1-5880115671
Fax: +43-1-5880115698
email: pblaha at theochem.tuwien.ac.at
-----------------------------------------
More information about the Wien
mailing list