Dear Prof. Blaha,

Thank you for your suggestion. I tried using hexagonal structure of bulk Al
with 39 MLs and 61x61x1 k-mesh. Actually I can reproduce plasma frequency
and dielectric function compared to the results from one Al atom unit cell
calculations.

I plotted the calculated slab plasma frequency as a function of Al(111)
film thickness and find the value is approaching converged, even though the
converged value is 2eV smaller the plasma frequency from bulk geometry
calculation.

For the thickness dependence of dielectric function, I also get the similar
converged results. The sizable difference lies at the low energy
range(<1.2eV). it converges to bulk value at large energy range, say, of
>2.5eV.

I am trying to do a very dense k-mesh calculation, (e.g. 99x99x1). However
this dense mesh does not sound practical.

Thank you again,
Wenmei


2013/11/25 Peter Blaha <pbl...@theochem.tuwien.ac.at>

> 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 <pbl...@theochem.tuwien.ac.at <mailto:
>> pbl...@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 <tel:%2B43-1-5880115671>
>>     Fax: +43-1-5880115698 <tel:%2B43-1-5880115698>
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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: pbl...@theochem.tuwien.ac.at
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