[Wien] Slab dielectric function vs. bulk dielectric function

[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>

> 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
> 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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