[Ifeffit] DWF's for amorphous InP

[Claudia Schnohr]

Hey Bruce,

thanks a lot for your e-mail. The correlation between the coordination
numbers and the DWF’s is exactly the problem. It is made worse by the
overlap of the two peaks (In-P and In-In), allowing less free parameters
for the fit to be physically reasonable. I was probably not specific
enough with my question (apologies for that) so here some more
information:

Crystalline InP has a zinc blende structure with In tetrahedrally bonded
to four P atoms and vice versa. However, this does not apply for the
amorphous phase. The amorphous structure of compound semiconductors such
as InP is characterized by structural as well as chemical disorder, i.e.
the presence of “wrong” homopolar (In-In) bonds. The information we like
to get from the EXAFS measurements (taken at the In K-edge) of the
amorphous system are:

(1) The total coordination number (though the total coordination number is
around four, it is not yet clear whether it is exactly four, slightly over
or slightly under coordinated.)

(2) The percentage of the wrong (In-In) bonds. Due to the correlation
between coordination number and DWF, varying ratios of the In-In and In-P
DWS’s give varying In-In percentages even with the total coordination
number being the same. Thus we need to apply constraints (as you said)

We think that restraining the DWF’s might be a good approach.
Unfortunately, the crystalline and amorphous systems do not have similar
DWF’s due to the large amount of disorder in the amorphous phase. From
previous studies it is known, that the DWF of an amorphous semiconductor
is roughly (!) twice the DWF of the crystalline phase. Hence, fixing the
In-P DWF to twice the crystalline value (from a standard we also measured)
would be a a first approach. My question is whether there maybe is a
better way of relating/restraining the DWFs, as for example suggested by
Crozier, Rehr and Ingalls (X-ray Absorption, Koningsberger and Prins,
Wiley & Sons, 1988). They derive a formula for the DWF that contains the
reduced mass and an integral over the projected density of states. If one
could make a reasonable assumption about the integral (which is the
problem) it would be possible to correlate the two DWF’s. Or maybe there
is another way to make an educated guess (by computing with FEFF or so).

Hope that’s a bit more clear now.

Many thanks, Claudia


> On Thursday 29 March 2007 02:57, Claudia Schnohr wrote:
>> Hello everyone.
>>
>> I am a PhD student and I have encountered a problem with analysing the
>> EXAFS of amorphous InP.
>>
>> For amorphous InP the first shell around an In atom is comprised of both
>> P
>> and In atoms. The In leads to a small peak in the R-spectrum that
>> strongly
>> overlaps with the bigger peak due to scattering from P. If I use two
>> different Debye-Waller-factors, one for each scatterer, and let them
>> both
>> float during the fit I get weird values since the coordination numbers
>> for
>> both peaks have to be floated as well. Therefore, some restraint is
>> needed
>> for the DWF's.
>>
>> Is there any correlation between the two DWF's following from theory or
>> experiment that I could use to restrain my fitting parameters ?
>> Are there other possibilities to handle such a situation ?
>>
>> Many thanks in advance for your help,
>
> Hi Claudia,
>
> If I understand your explanation, I suspect that the problem is that
> your fit has more freedom in its parameters than the data can
> support.  It is always the case that coordination number and sigma^2
> are highly correlated.  They are both terms that affect the amplitude
> of chi.
>
> I doubt that the solution is somehow to constrain the sigma^2 values.
> Without doing some serious theory to figure out how those two values
> might be related, I would not know what constraint to apply.  What
> would be a lot more reasonable would be to constrain the total number
> of atoms in the coordination shell.  I don't know what kind of crystal
> InP forms, but I would assume that the In is either 4- or
> 6-coordinated with P in the crystal.  It seems reasonable to enforce
> that coordination in the amorphous material.  That is, require that
> the sum of In and P atoms in the first coordination shell be 4 (or 6
> or whatever).
>
> Make a guess parameter that describes the amount of the In:
>
>     set   n    = 4       # (or 6 or whatever)
>     guess x_in = 0.1
>     def   x_p  = n - x_in
>
> then define you sigma^2 parameters as before:
>
>     guess ss_in = 0.003
>     guess ss_p  = 0.003
>
> That reduces the number of parameters in the fit by one, enforces a
> physically reasonable constraint on the total number of parameters,
> and -- hopefully -- helps to stabilize your fit by removing one of the
> highly correlated guess parameters.
>
>
> As I re-read what I wrote, it occurs to me that another reasonable
> constraint might be to require that sigma^2 for the In-P bond be the
> same in the amorphous material as in the crystal.  Did you measure
> crystalline InP as well?
>
> Hope that helps,
> B
>
>
> --
>  Bruce Ravel  ----------------------------------------------
> bravel at anl.gov
>
>  Molecular Environmental Science Group, Building 203, Room E-165
>  MRCAT, Sector 10, Advanced Photon Source, Building 433, Room B007
>
>  Argonne National Laboratory         phone and voice mail: (1) 630 252
> 5033
>  Argonne IL 60439, USA                                fax: (1) 630 252
> 9793
>
>  My homepage:    http://cars9.uchicago.edu/~ravel
>  EXAFS software: http://cars9.uchicago.edu/~ravel/software/exafs/
>
>
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-- 
Claudia S. Schnohr
Department of Electronic Materials Engineering
Research School of Physical Sciences and Engineering
The Australian National University
Canberra, ACT 0200
AUSTRALIA