<div dir="ltr">Dear Prof. Blaha,<div><br></div><div>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.</div>
<div><br></div><div>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.</div>
<div><br></div><div>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. </div>
<div><br></div><div>I am trying to do a very dense k-mesh calculation, (e.g. 99x99x1). However this dense mesh does not sound practical.</div><div><br></div><div>Thank you again,</div><div>Wenmei</div></div><div class="gmail_extra">
<br><br><div class="gmail_quote">2013/11/25 Peter Blaha <span dir="ltr"><<a href="mailto:pblaha@theochem.tuwien.ac.at" target="_blank">pblaha@theochem.tuwien.ac.at</a>></span><br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Of course, in principle slabs should converge to bulk epsilon. But:<br>
<br>
In your slabs with a k-mesh of 69x69x1 you are using "effectively" a k-mesh<br>
of 69x69x39 instead of a 69x69x69 mesh.<br>
In addition, in the z direction you use "root-sampling" instead of tetrahedra<br>
method. It is like integration with the rectangular-rule instead of a trapezoidal rule.<br>
<br>
Try fcc-Al with a small tetragonal distortion during setup, so that you get only 16 sym.ops.<br>
then change c/a back to 1 and use a kmesh of 69x69x39 and compare the dielectric function<br>
to the 2 times 69-mesh. (This mimics the k-mesh problem, but still there s the<br>
integration method !!).<br>
<br>
You probably need even more layers ....<br>
<br>
Am 26.11.2013 04:51, schrieb phlhj phlhj:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div class="im">
Dear Prof. Blaha,<br>
<br>
Thanks so much for your suggestion.<br>
<br>
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<br>
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.<br>
<br>
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<br>
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<br>
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<br>
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<br>
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.<br>
<br>
Thank you so much for sharing any understanding about this,<br>
<br>
Wenmei<br>
<br>
<br></div>
2013/11/24 Peter Blaha <<a href="mailto:pblaha@theochem.tuwien.ac.at" target="_blank">pblaha@theochem.tuwien.ac.at</a> <mailto:<a href="mailto:pblaha@theochem.tuwien.ac.at" target="_blank">pblaha@theochem.<u></u>tuwien.ac.at</a>>><div>
<div class="h5"><br>
<br>
As you probably know, the dielectric function of Al converges VERY slowly<br>
with respect to the k-mesh.<br>
<br>
When you do slab calculations, you include the surface effect, but you also replace<br>
the periodicity in k-z (and thus the k-mesh in k-z) to a backfoldung according to<br>
your slab. Even a 39 ML slab corresponds probably not to a very large k-z mesh and<br>
in addition the integration over k-z is limited to a "root"-sampling instead of the<br>
tetrahedron method. I could even imagine large numerical problems in this 2-D integration<br>
using a 3-D algorithm in joint due to large degeneracy of the tetrahedra.<br>
<br>
At least you could differentiate between "integration problems" and surface effects<br>
by using a 39-layer bulk structure (i.e. remove the vacuum in your supercell, so that<br>
you get 3D-Al again, but restrict yourself to 1-k point in k-z) and compare the<br>
resulting eps to bulk Al (with 1 atom/cell and good k-meshes.<br>
<br>
Am 23.11.2013 16:54, schrieb phlhj phlhj:<br>
<br>
Dear all,<br>
<br>
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<br>
reported<br>
in literature before. However, I did find some difference between the slab dielectric functions and the corresponding bulk values.<br>
<br>
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<br>
related<br>
to the band-folding and symmetry reduction in the direction normal to the surface.<br>
<br>
Also, I found the plasma frequency of the slab is smaller than the bulk plasma frequency.<br>
<br>
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.<br>
<br>
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<br>
should<br>
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<br>
are very<br>
very close to the bulk values. This argument should be also true for the slab plasma frequency.<br>
<br>
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.<br>
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<br>
ideal<br>
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?<br>
<br>
Thanks a lot for any idea.<br>
<br>
Wenmei<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br></div></div>
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-- <br>
------------------------------<u></u>-----------<br>
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Inst. Materials Chemistry, TU Vienna<br>
Getreidemarkt 9, A-1060 Vienna, Austria<br>
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