Category Archives: FAQ

Store to database

How do I store optical constants in the database?

Make sure that the material object you want to store to the database is in good shape: It will appear in the database like it is formatted at this time. Select a proper name and color for the object.

In the treeview, open the subbranches of ‘Materials’ by clicking on the small ‘+’ sign. The materials in your configuration are now visible as treeview items, including the one you want to enter into the database.

Now right-click the treeview item ‘Optical constant database’ so that the content of the database appears on the right side.

Finally, drag the treeview line of the wanted material to the area on the right which displays the database items, and drop it there. You will have to answer a few questions about the object generation (i.e. program version) of the database item (select a version that every potential user of the database can read), your name and a database comment. Once you have answered all questions the new database item is available for future use.

Absorption

How does the software compute the absorption coefficient?

When the software re-computes optical constants, the so-called dielectric function is computed first. This material quantity (a complex number with real and imaginary part) connects the electric field of the light wave to the polarization that is caused in the material.

In order to compute the reflection and transmission properties of interfaces between two adjacent materials, the complex square root of the dielectric function is needed. This is called the refractive index. The real part is usually denoted as n, the imaginary part as k. Whereas the real part contains information about the speed of light in the material, the imaginary part is responsible for absorption.

The absorption coefficient alpha, finally, is the exponent of the intensity decay of a light wave traveling through the material, i.e. the intensity decays proportional to exp(-alpha*x) where alpha = 4*pi*k*wavenumber. The wavenumber is the inverse of the wavelength, usually measured in cm.

Master model

The list of materials offers the object type ‘Master model’. What’s that?

Master models are based on the object type ‘Dielectric function model’, i.e. they are used to compute optical constants using a user-defined set of susceptibility terms. In addition, master models have built-in so-called master parameters (you can use up to 6 of them) which can be used to compute selected parameters of the optical constant model as ‘slave parameters’.

A typical application of a master model is this: Suppose you are producing an oxide by a deposition process which can end up in various oxygen concentrations in a layer. If you describe the optical constants with an OJL model, the OJL parameters like bandgap or strength will then depend on the oxygen content of your material. In such a case you can define a master parameter ‘Oxygen content’ and compute the values for the bandgap and strength based on the oxygen content of a particular sample. In order to do this you must know the relations, of course. You can apply user-defined formulas (bandgap vs. oxygen content, for example) or lookup tables which you can generate after a batch analysis of several samples with different oxygen content.
Sometimes it is convenient to apply master parameters just to re-scale parameters. For example, if you do not like to enter bandgaps in wavenumbers, you can define a master parameter that gives the bandgap in eV, and then re-compute the OJL bandgap (which must be specified in wavenumbers for historical reasons) as a slave parameter (like OJL_bandgap = bandgap_eV* 8065).

Warning:
The SCOUT and CODE software contain a list of global master parameters in their treeview which are used to connect and control any parameter of the optical model in these programs. Please try not to mix up global master parameters and the individual master parameters of master models.

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:

Metals:
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. !!!

Import n and k data

How can I import tables of n and k data and use them in SCOUT or CODE?

Open the list of materials and generate a new object of type ‘Imported dielectric function’.

If you have a text file with 3 columns (like wavelength, n, k or energy, n, k) open the new object and execute the local command ‘Import’. In the file dialog you should set the file type to ‘n and k from data table (x,n,k)’. You will be asked to specify the spectral unit (nm, eV, 1/cm, …). After the data import you should use the menu command ‘Property/Refractive index’ to visulize the imported data.
If you have an Excel table of the data (a data block with columns of the spectral position, n and k), you can import the Excel table into the workbook. In the object tree view, right-click the workbook and use the ‘File/Open’ command of the workbook (or copy & paste from Excel directly). Select the cell in the workbook where you want to start reading the data – this should be the first spectral position (usually the first wavelength, wavenumber or energy value). Go back in the treeview to the material object that wants to read the data (right click on the corresponding treeview line) and execute the lcoal menu command ‘Workbook/ Import x,n,k’ of the material object.

When you are finished importing the data and you have adjusted the graphics of the object (set an appropriate title, …) you can enter the new material into the database. First right-click the treeview item ‘Optical constant database’ and then drag&drop the material from the treeview into the database window on the right side.

Gradient?

How do I describe a gradient of optical constants?

A gradient of optical constants can be implemented in an optical model using the layer type ‘concentration gradient’.

The strategy is this:
Define an effective medium, i.e. a mixture of 2 materials, using one of the simple effective medium objects Bruggeman, Maxwell-Garnett or Looyenga. The best choice for gradients is Bruggeman, also known as EMA. The only parameter to describe the topology of the mixture is the volume fraction.
In the next step, insert a concentration gradient layer into the layer stack and assign the effective medium material to it. The gradient will be described by a user-defined function that defines the depth dependence of the volume fraction from the top of the layer to the bottom. Select the layer and use the Edit command to access the formula definition window.
Finally, you go back to the layer stack definition window and specify how many sublayers should be used to sample the gradient. Be careful not to take too many sublayers – this could increase the computational times a lot. On the other hand, be careful not too ‘undersample’ the gradient – if you increase the number of sublayers by 1 the spectra should not change significantly.

Please consult the manual for further details …

Roughness

How do I describe surface roughness?

Roughness can be taken into account in different ways in optical models for thin films.

The easiest way is to replace the sharp interface between two materials by a thin layer with mixed optical constants. This is a good approach for roughness dimensions clearly below the light wavelength. Mixed optical constants can be computed using an effective medium model. The Bruggeman formula (also known as EMA – effective medium approximation) is a good choice (please read the remarks below). Start with a very thin intermediate layer (e.g. 2 nm) and select its thickness as fit parameter. The volume fraction of the effective medium model should be an adjustable fit parameter as well.
An advanced version of this kind of roughness modeling is to use a concentration gradient layer. This type of layer can describe a smooth transition between adjacent materials. The depth dependence of the volume fraction can be expressed by a user-defined formula with up to 6 parameters that can be fitted.
A warning must be raised using effective medium models to describe roughness effects. All effective medim models in our software are made for two phase composites which are isotropic in three dimensions. They are not valid for surface roughness effects. To apply these concepts anyway can be justified by saying that there is no reasonable alternative and that it is very common to do so …
Describing rough metal surfaces with an effective medium model may be a little tricky. This is especially true for silver. Inhomogeneous metal layers can be efficient absorbers with very special optical properties, and effective medium approaches can be very wrong – please read SCOUT tutorial 2 about this.

The roughness described by effective medium layers does not lead to light scattering but modifies the reflectance and transmittance properties of the interface between the adjacent materials. Light scattering at heavily rough interfaces can be taken into account in a phenomenological way in cases where the detection mechanism of the spectrometer system does not collect all the scattered radiation. You can introduce a layer of type ‘Rough interface’ which scales down the reflection and transmission coefficients for the electric field amplitude of the light wave. The loss function is a user- defined function which may contain 2 parameters C1 and C2 which are fit parameters. In addition, the symbol x in the formula represents the wavenumber.
The expression C1*EXP(-(X/C2)^2), for example, would describe an overall loss by a factor C1 and an additional frequency dependent loss which is large for small wavelengths and small for large wavelengths. This kind of approach has turned out to be satisfying in several cases.

How accurate?

How accurate are the results when I use optical modeling?

This is hard to tell, and it depends on many details. So there is no general answer to this question.
A good optical model should use the lowest possible number of parameters. If you have too many parameters in the model they may be correlated in a way that raising one parameter value and decreasing another leads to the same optical spectra. In this case the parameter values are more or less arbitrary, and the accuracy is very low.
The result of a parameter fit depends very much on the information contained in the measured data. If you want to determine a layer thickness, for example, you must have measured contributions of radiation which has seen the bottom of the layer, i.e. which has travelled through the layer at least once. If that is not the case in the spectral range that is accessible to you, you will never be able to get the thickness of the layer.

Any real result?

Can I get anything real out of a model?

Yes, of course. If your model is good, and your spectra do contain enough information, the parameter values reflect the real values as good as they can.
Please have in mind that in many cases talking about ‘real values’ is using a model in itself. If you ask for the real value of a layer thickness, for example, your question implies that there is something like a layer with a top and a bottom end. You ignore the atomic structure and surface roughness effects, or, if not, you apply (at least in your mind) a certain roughness averaging procedure.