software to fit optical spectra - Quantum Materials Group

that time. The later development of RefFIT was to a great extent governed by a desire to
combine the best OPTPAL features with a user-friendly interface. The creative science
atmosphere of Dirk’s group is very stimulating for me. I must specially acknowledge Patricio
Mena, who helped me a lot to improve RefFIT by using it extensively in his PhD study and
even writing several subroutines. And, of course, I want to thank all my colleagues who elected
to use RefFIT as their computational tool and thus furthered its evolution.
1.2. What is RefFIT for?
One can generally say that RefFIT is designed to analyze the optical spectra of solids.
Clearly, this statement has to be a bit specified, because there are myriads of thinkable optical
experiments and, correspondingly, very different ways to analyze them. So which sort of data
are we going to deal with and what for ‘analysis’ we are going to apply?
First of all, by optical spectra, we mean frequency-dependent optical quantities. An
example of an optical spectrum is the frequency-dependent reflectivity R (ω)
, which can be
directly measured. Another example is given by the optical conductivity σ (ω)
, which is
usually not measured directly but derived from experimental data after some analysis (or,
alternatively, it can be taken from articles of other groups, which is also a sort of measurement
☺). Of course, in addition to the light frequency there might be other experimental parameters,
such as the angle of incidence, a sample thickness etc. Secondly, we put a common dogma, that
the optical properties we deal with are determined solely by the complex dielectric function
ε ( ω)
= ε1
( ω)
+ iε
2 ( ω)
of the studied material. Thus, we assume that the measurable optical
quantities, such as reflection, transmission, ellipsometry outputs etc., are described by the
textbook Fresnel equations [2].
The primary goal of spectra analysis, that RefFIT does, is to get information about the
material dielectric function on the base of optical spectra. It is done by the fitting of these
spectra using a model of the dielectric function with a set of adjustable parameters. These
parameters are varied in order to obtain the best match between the experimental and calculated
data points.
There are two ways to model the dielectric function. It might be either a mathematical (or
physical, if you like) formula with a limited number of parameters, or a variational (also called
a ‘free-shape’) dielectric function, which is ‘allowed’ to vary independently at every frequency
point [4] (see sections 2.2.4 and 2.2.5). The first possibility is very familiar to many (e.g., the
Drude-Lorentz modeling of reflectivity). Although the second one might look uncommon, it is
often implicitly present in the data analysis. For example, in spectroscopic ellipsometry ε 1 and
ε 2 are extracted independently at every frequency from the two measured ellipsometric angles
- ψ and ∆ . The same thing can be done in RefFIT by the fitting of ε (ω)
with a not-Kramers-
Kronig-constrained variational dielectric function (section 2.2.5). Another example is the
conventional Kramers-Kronig transformation of reflectivity [6] (used, by the way, in about
90% of papers on infrared spectroscopy of solids), which can be substituted in RefFIT by the
fitting of R (ω)
by a Kramers-Kronig-constrained variational dielectric function (section 2.2.4).
To make a long story short: every analysis that RefFIT does is a fitting!
Guide to RefFIT Page 5