Tag Archives: oscillator

Model selection

How do I select the right model for the optical constants?

Selecting appropriate optical constant models with the right number of parameters is difficult and requires some experience. The choice depends – first of all – on the material and also on the spectral range of interest.

In the infrared the choice is rather easy: Use a constant refractive index, and add for each clearly visible vibrational mode a Kim oscillator. If you have free charge carriers (i.e. you deal with a metal or a doped semiconductor) you should add a simple Drude model (in case of highly doped semiconductors use an enhanced Drude model instead).

In the NIR, visible or UV the right choice is not so simple. Here you can be guided by the following rules of thumb:

Use a constant to represent high energy interband transitiions. For every interband transition causing structure in the wanted spectral range use a Tauc-Lorentz or an OJL term. Take a Drude model for the free electrons.

Semiconductors (crystalline):
Combine a constant and Tauc-Lorentz terms for interband transitions. Add a Drude model for low doped materials. In the case of high doping levels use an extended Drude model.

Semiconductors (amorphous):
Setup a model like for crystalline semiconductors (see above) but replace the Tauc-Lorentz terms by OJL terms.

Oxides and Nitrides:
Combine a constant and an OJL term. If the OJL term alone cannot generate the right absorption and dispersion, you should add a harmonic oscillator in the far UV (resonance frequency 60000 1/cm, oscillator strength in the range 10000 … 100000 1/cm, damping 1 1/cm). In the fitting procedure the harmonic oscillator parameters should be kept fixed with the exception of the oscillator strength.

Organic materials:
Combine a constant, an OJL model and Kim oscillators. Whereas the OJL model is used to describe the ‘fundamental absorption’ in the UV, the Kim oscillators should represent absorption bands in the visible and NIR.

!!! Please note that OJL and Tauc-Lorentz terms may not be inserted in the susceptibility list as the other models. Instead, they have to be used within a KKR susceptibility object. !!!

Improvement of Gervais oscillators

Certain parameter combinations of Gervais oscillators may lead to unphysical optical constants (i.e. negative imaginary part of the dielectric function). Physical meaningful solutions satisfy a sum rule for the damping constants which may be used to steer the fit into the direction of ‘good’ solutions.

The “check sum” (sum of the difference of LO damping and TO damping for all oscillators) can now be obtained as optical function. Use the optical function “my_material (Gervais_condition)” to retrieve the current value of the check sum.

In order to make use of this number in a fit you can proceed like this(this hint will work in CODE only): Generate an integral quantity of type ‘function of int. quant.’ and call it ‘Gervais check sum’. As formula to compute the value use the term “of(1)” (here it is assumed that the check sum is the first optical function). So the integral quantity is the check sum itself.

Now define a penalty shape function for this integral quantity. It should be 0 if the check sum is positive, and get large for large negative values of the check sum. An expression like “abs(y)*step(-y)y)” will do the job (in penalty shape functions for integral quantities the symbol “y” refers to the current value of the integral quantity). This way large negative values of the check sum are severely punished whereas positive values do not contribute to the fit deviation at all.

Finally activate the option “Combine fit deviations of integral quantities and spectra” in the fit options dialog (File/Options/Fit). This lets CODE simultaneously minimize the difference of measured and simulated spectra and the fit deviation of the integral quantities (which is in this case the penalty for an unphysical check sum). Eventually you have to experiment a little bit with the weight of the ‘Gervais check sum’ in the list of integral quantities in order to get a good fit.