[Pw_forum] Energy window in STM simulation
David Pullman
dpullman at mail.sdsu.edu
Tue Dec 11 11:33:39 CET 2012
Dear Gabriele,
Thanks very much. I understand better now the
idea behind including states that are outside the
energy window defined by Ef and
Ef+sample_bias. I'm still confused about
something, though. Let's say we're simulating a
room temperature STM image of a metal or
semimetal. Here's my logic-- please correct me
if I'm wrong. Typical smearing widths of the
order of 0.01 Ry correspond to non-negligible
populations of excited states (for Fermi-Dirac
smearing, 0.01 is equivalent to ~1500K). It
seems to me that when you add in states to the
LDOS that are, say, above the Tersoff-Hamann
energy window, then you could very well be adding
in charge density from states composed of
higher-index periodic functions [psi=planewave *
periodic function] that really shouldn't
contribute much to the LDOS at 300K. The shapes
of these higher-index periodic functions could
distort the STM image. So, to minimize the
distortion, you'd want to run the PW calculation
at a rather low smearing width (~0.002 Ry), which
of course would require a finer k-point mesh. Does this argument make sense?
Thanks,
David
At 08:31 AM 12/10/2012, you wrote:
>Dear David,
>
> I don't think the algorithm is wrong, it is
> (more or less) consistent with the way the
> charge density is computed in presence of a
> smearing of the electronic occupations.
>The energy window for the integral of the local
>density of states is the one prescribed by the
>Tersoff-Hamann method, but one also needs to
>consider the "tails" of the electronic levels
>just above and below that window. The code does
>this by including extra states outside the
>window, but their charge is weighted with a
>"smeared" delta function w0gauss( ) that falls off exponentially or so.
>The extend range is defined to spare time by
>considering only eigenvalues not too far from the window edges.
>
>This is not so bad, but in my opinion one should
>instead use the wgauss functions (integral of
>the smeared delta, or generalized step function,
>if you prefer), in order to be consistent with
>the charge integration in the rest of the code. Something like:
>wg(ibnd,ik) = wgauss(up-et(ibnd,ik)) - wgauss(down-et(ibnd,ik))
>would do the job, consistently with the weights
>wg computed in PW/src/gweights.f90, and used in
>sum_band.f90 (I am correct, Paolo?).
>Probably this solution would give similar results
>
>HTH
>
>GS
>
>
>>I have a question about QE's implementation of the the Tersoff-Hamann
>>formalism for simulating STM images. If I understand the stm.f90
>>code correctly, the energy sampling window does not range from Ef to
>>Ef+sample_bias (which is what Tersoff-Hamann says it should
>>be). Rather, the code increases the upper limit by 3*degauss
>>(degauss=smearing width) and also decreases the lower limit by
>>3*degauss. In the case of metals, the value of degauss is taken from
>>the prior PW run. I believe the subsequent lines of code modify the
>>weights of the states that are outside the Tersoff-Hamann window.
>>
>>So, as an example, if a metal has a bias of -0.1 eV and the smearing
>>width from the prior PW run was 0.01 Ry (or 0.136 eV), then states
>>from -0.5 eV to +0.4 eV (with respect to Ef) are included in
>>calculating the LDOS. This strikes me as a rather broad range, even
>>if temperature and energy linewidths are considered, and could alter
>>the appearance of the computed images.
>>
>>Why do the STM energy limits take into account the smearing width
>>from the PW output? And is it best to use as small a width as
>>possible if you intend to run STM simulations?
>>
>>Thanks,
>>
>>David Pullman
>>Department of Chemistry and Biochemistry
>>San Diego State University
>>San Diego, CA 92182-1030
>
>
>§ Gabriele Sclauzero, EPFL SB ITP CSEA
> PH H2 462, Station 3, CH-1015 Lausanne
>
>
>
>
>
>
>
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