[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
>
>
>
>
>
>
>
>
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>     --
>     ------------------------------__-----------
>     Peter Blaha
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-- 
-----------------------------------------
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
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