1.    How do I tell if my fit results are good?

  • To determine if your results are good, you should look at several different criteria.  You should check the χ2 value first to determine how well the model fits the data.  You should then compare the results visually, check if the fit is reasonable and physical, check the error bars on the resulting values, and examine the correlation matrix.  If the error bars are large or the correlation matrix shows strong correlations, for example, there may be an issue with your model.  One other indicator of a good fit is quick convergence of the fitting algorithm, which suggests the fit is unique.   

2.    What is a good value for χ2?

  • Typically, for a simple single layered thin film, a χ2 value of around 1 is very good. As the samples get more complex, the χ2  values will start to rise.  For a complex sample, an χ2 of up to 10 or more is acceptable, as long as all other results are physical and reasonable.  Keep in mind that even if the χ2 value is small, the results may not always be physical or reasonable, so be sure to check the other goodness of fit criteria as well.  

3.    What if I see strong correlations in the correlation matrix?    

  • If you see strong correlations, you should add any additional data that you might have, whether it is data taken at different angles of incidence, or reflectance/transmittance data.  You can also identify the parameters which are correlated and check if they both need to be fit at the same time.  If not, it might be possible to fix one, if this makes sense to the model.  

4.    Which dispersion function do I choose for my sample?

  • Each dispersion function is used for a certain type of material.  For example, a Drude dispersion function is commonly used for metallic films and a Lorentz dispersion functions is commonly used for transparent or weakly absorbing films.  For a list of all of the dispersion functions used in the DP2 software, as well as what types of materials they are used for, please email us at ellipsometry.us@horiba.com.  You can also find more information about dispersion functions by reading the technical notes contained in the DeltaPsi2 folder on your hard drive.  

5.    What are the most commonly used dispersion functions?

  • The most commonly used dispersion functions include Cauchy and Lorentz (Classical) for transparent or weakly absorbing films, amorphous, new amorphous, and Tauc-Lorentz for semi-transparent materials (dielectrics, polymers, semiconductors absorbing in the VIS/FUV), and Drude for metals.  

6.    What is an EMA?

  • An EMA (Effective Medium Approximation) allows for the mixture of two or three components in the same layer that form an effectively “mixed” layer.  The physical interpretation of the EMA theory involves small particles of one material suspended within a host material.  Under the EMA, the optical constants can be mixed to satisfy the electromagnetic equations.  EMA’s are typically used to represent surface roughness, interfaces, porous layers, and polycrystalline materials.

7.    What types of EMA’s exist?

  • There are various types of EMA’s available. The two most common are: Bruggeman and Maxwell-Garnett.  The Maxwell-Garnett EMA represents heterogeneous mixtures in which small amounts of one (or two) material are in a matrix of the other material. The Bruggeman approximation, which is the most commonly used, extends to represent materials which span the entire range of composition.    

8.    How do I determine grading in my films?

  • The Delta Psi 2 software has a built in graded layer function which allows you to vary optical properties throughout the thickness of the film in order to obtain a graded layer profile.  For more information please visit our Software page or email us at ellipsometry.us@horiba.com

9.    How do I determine an optical band gap?

  • To determine an optical band gap, you will need to measure below, near and above the estimated optical band gap of the material.  In some cases, this will require the use of the NIR extension which allows for measurements up to 2100 nm.  The band gap can then be obtained from the dispersion formula parameters which describe the extinction coefficient (k) or by utilizing the Tauc plot, which is included in the DP2 software.  For additional information, please contact us at ellipsometry.us@horiba.com.

10.    How do I determine crystallinity?

  • The crystallinity of your sample can be determined by using an EMA to represent volume percent of the different types of crystallinity within one single layer.  The features in the optical properties can also suggest what the crystallinity of the sample looks like.  For example, sharp features represent a more crystalline material, whereas broader features represent a more amorphous material.  Please see the FAQ’s, “What is an EMA?” and “What types of EMA’s exist?” and email us at ellipsometry.us@horiba.com if you have further questions.  

11.    How do I determine surface roughness?

  • Generally, you can include a surface roughness layer as a part of your model.  This layer is comprised of 50% void and 50% of the underlying layer, and fitting for the thickness of this layer will give you the surface roughness thickness.  It is important to keep in mind that the surface roughness thickness value given by ellipsometry is typically over a large area (size of measurement spot), as opposed to roughness given by AFM which is on the microscale.
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