M.Theiss Hard- and Software for Optical Spectroscopy
Dr.-Bernhard-Klein-Str. 110, D-52078 Aachen
Phone: (49) 241 5661390
Fax: (49) 241 9529100
E-mail: theiss@mtheiss.com
Web: www.mtheiss.com

CODE
Analysis, design, production controlof thin films
by Wolfgang Theiss

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indirectly by this document.
Printed: 10.03.2004, 23:52 in Aachen, Germany

Developing optical production control methods for SCOUT

Contents

I

Table of ContentsForeword

2Part I Overview

3

1 The company................................................................................................................................... 3
2 The talk................................................................................................................................... 3

3 The software................................................................................................................................... 4

Part II Customized views

4Part III Optical model

5

1 Material constants................................................................................................................................... 5
Optical constants:.........................................................................................................................................................
Overview
5Interband transitions......................................................................................................................................................... 6
Vibrational.........................................................................................................................................................
modes
8
Charge carriers......................................................................................................................................................... 9Master model......................................................................................................................................................... 10

2 Layer stacks................................................................................................................................... 11Computation.........................................................................................................................................................
of reflectance and transmittance11
Coherent/incoherent.........................................................................................................................................................
superposition
12
What is the.........................................................................................................................................................
correct layer stack?
13

3 Spectrum...................................................................................................................................
types
17

Part IV Computation of technical data

18

Part V Remote control by OLEautomation

20

Part VI Batch processing

20

Part VII Analysis and design22

1 Fit strategy................................................................................................................................... 22
2 Examples................................................................................................................................... 24
3 Design ................................................................................................................................... 25

Part VIII Production control schemes

27Part IX Program development, training,consultance work

29

Index

0

Foreword
This document gives a short summary of several talks and documents about
spectrum simulation.
All the pictures are just screen shots, not prepared explicitly for this document.
In between the pictures there are comments that should guide you from slide toslide.
Most of the slides in the talks are interactive pictures: You can vary slider
positions and see what happens to the spectra. Unfortunately, in this static
document these dynamical impressions cannot be reproduced.
In the graphs displaying optical constants the real part is drawn blue, theimaginary one is given in red.
In the case of spectrum fits, the measured spectra are always in red, thesimulated spectra in blue.
All simulations have been performed with our SCOUT, CODE and SPRAY
software products which are commercially available.

Aachen, March 2004

SCOUT methods

1Overview

1.1

The company

1.2

The talkOverview

3© 2003 Wolfgang Theiss

SCOUT methods

1.3

The software

2

Customized views

Overview

4

The appearance of the main window is defined by so-called views (user-defined):© 2003 Wolfgang Theiss

SCOUT methods

3

Optical model

3.1

Material constants

3.1.1

Optical constants: Overview

Optical model

5

Three basic types of excitations determine the optical constants of almost all materials:© 2003 Wolfgang Theiss

SCOUT methods

3.1.2

Optical model

6Interband transitions
Interband transitions of cystalline materials can be descibed using the Tauc-Lorentz model:

Here is a typical example using the superposition of 8 interband transitions:

Amorphous materials have less rich featured, broad interband transitions which can often be
described in good quality using a single OJL model:© 2003 Wolfgang Theiss

SCOUT methods

Optical model

7

The theory behind the OJL model is summarized in the following page:

Here is an example of a succesful application of the OJL model:© 2003 Wolfgang Theiss

SCOUT methods

3.1.3

Optical model

8

Vibrational modes
Vibrational modes and some electronic interband transitions can be modeled using oscillator
terms. The simplest approach is the harmonic oscillator which leads to a Lorentzian line shape of
the absorption band:

However, in most cases a Gaussian line shape is more realistic. In SCOUT and CODE this can beobtained using Kim oscillators:© 2003 Wolfgang Theiss

SCOUT methods

3.1.4

Optical model

9Charge carriers
The interaction of free charge carriers like electrons or holes can be described with the Drude
model. This model has two parameters only: The plasma frequency is proportional to the squareroot of the carrier density, the damping constant to the inverse of the mobility.
Characteristic for the presence of many charge carriers (like in metals) is the large imaginary partof the refractive index. If it is larger than the real part, no wave propagation is possible in thematerial. This leads to a 'rejection' of incoming waves, i.e. to a high reflectance. Radiation
penetrating a metal is absorbed very efficiently in a very thin film.

The following example shows that the simple Drude model does not always perform excellently:© 2003 Wolfgang Theiss

SCOUT methods

Optical model

10In cases like this you can try an extension of the Drude model which features a frequencydependent damping constant. Electron scattering at charged donor or acceptor atoms may lead toa characteristic frequency dependence of the damping constant in the Drude model:

3.1.5

Master model
Sometimes the optical constants of a material vary systematically with a compositional parameter
like oxygen content in a non-stochiometric oxide or the concentration of an atomic species in aternary system. This can be described conveniently in SCOUT and CODE using so-called mastermodels which provide for every parameter a user-defined formula to express its dependence on
the master quantity:© 2003 Wolfgang Theiss

SCOUT methods

3.2

Layer stacks

3.2.1

Computation of reflectance and transmittance

Optical model

11

Single layer treatment using geometric series:

Multilayers are processed applying the single layer expressions many times:© 2003 Wolfgang Theiss

SCOUT methods

3.2.2

Optical model

12

Coherent/incoherent superposition
CODE has a very efficient algorithm to compute R and T of partially coherent superposition ofwaves:

For thick layers the incoherent contributions to R and T can be computed individually. Red curve inthe following graph: All reflection orders superimposed. Blue curve: Backside reflection only:© 2003 Wolfgang Theiss

SCOUT methods

3.2.3

Optical model

13

What is the correct layer stack?

Example: The next graphs show the influence of the introduction of a surface layer to the results ofa `single layer analysis´. It is not easy to decide if the differences are significant if the roughness isalways the same. However, if the roughness changes from sample to sample it should definitely bepart of the model and part of the exported results.

© 2003 Wolfgang Theiss

SCOUT methods

Optical model14© 2003 Wolfgang Theiss

SCOUT methods

Optical model

15

Here is another example: A customer asked for the optical constants of a single layer deposited on
glass with a sputtering device. It turned out that even advanced optical constant models could notdescribe the optical properties of the layer properly.

Only introducing a depth inhomogeneity (and a surface layer) could solve the problem:© 2003 Wolfgang Theiss

SCOUT methods

Optical model

16

Communication with the producer finally verified the assumptions made in the successful fit:

© 2003 Wolfgang Theiss

SCOUT methods

3.3

Optical model

17

Spectrum types© 2003 Wolfgang Theiss

SCOUT methods

4

Computation of technical data

18

Computation of technical data

© 2003 Wolfgang Theiss

SCOUT methods

Computation of technical data

19

© 2003 Wolfgang Theiss

SCOUT methods

5

Remote control by OLE automation

20

Remote control by OLE automation

The Excel example shows how spectra can be sent to SCOUT which are then automatically fitted.
The results are passed back to an Excel worksheet.

6

Batch processing

CODE can analyze series of input spectra automatically in a batch process. Enter the filenames
and the import filter to be used and start the batch fit operation in the batch control window:© 2003 Wolfgang Theiss

SCOUT methods

Batch processing

21

The results can be displayed directly in a view:© 2003 Wolfgang Theiss

SCOUT methods

7

Analysis and design

7.1

Fit strategy

Analysis and design

22

Once the optical model is ready, one must be decide which parameters may vary from sample tosample. These parameters must be determined following a fit strategy that leads to stable andreproducible results in the specified time frame.

Multiple parameter optimization is a common problem of numerical mathematics. One of the main
issues is to avoid that algorithms get stuck in local minima of the fit deviation. Methods likesimulated annealing or genetic algorithms which overcome the local minimum problem are much
too slow to be used for production control.
Here is an example of a SCOUT fit running into a local fit deviation minimum: A start value of thelayer thickness far away from the correct value drove the model into the wrong interference fringeorder.

© 2003 Wolfgang Theiss

SCOUT methods

Analysis and design

23

Using the 'grid fit' feature of SCOUT this problem can be overcome very efficiently: Before themultiple parameter fit is started, the right fringe order is found by trying several thickness values(equally spaced in a user-defined thickness range) and taking the best result as starting value forthe thickness.

In many cases advanced fit strategies using so-called fit parameter sets are successful: Separate
the fit parameters into groups which are optimized one after the other. You can, for example, fit thethickness and the refractive index of a material in a spectral region where the layer is transparent.
Then freeze the parameters, and determine bandgap and other interband parameters in a spectral
range with strong absorption. Then, in a final step, all parameters are optimized using the full widthof the spectral data. Separating the problem into smaller pieces can speed up the optimization
procedure significantly.

© 2003 Wolfgang Theiss

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7.2Analysis and design

24

ExamplesFitting three ellipsometry and a reflectance spectrum. Since the investigated sample spot is notexactly the same in both experiments two different layer stacks are used in the model:

Here 8 spectra are fitted simultaneously:

Quantitative description of a solar control coating:© 2003 Wolfgang Theiss

SCOUT methods

7.3

Analysis and design

25

DesignInvestigate the influence of the variation of a model parameter (e.g. a film thickness) on the coating
properties using the parameter variation feature. Here the angle of incidence is varied and thecolor of a coating in reflection is inspected:© 2003 Wolfgang Theiss

SCOUT methods

Analysis and design

26

The parameter fluctuation feature computes the variation of technical data and spectra in thepresence of random parameter fluctuations. This can be used to simulate the effect of production
tolerances, for example:© 2003 Wolfgang Theiss

SCOUT methods

8

Production control schemes

27

Production control schemes
Now the method must be brought to the factory. The first question is how the various programs
involved in the problem should be connected:

With SCOUT, several options are possible. The following example shows a configuration whereboth SCOUT and the data acquisition are controlled by the process control software. SCOUT canbe accessed as OLE server or by TCP/IP communication.

The optical analysis can also be completely independent of the process control software:© 2003 Wolfgang Theiss

SCOUT methods

Production control schemes

28

SCOUT can also be used to control spectroscopic hardware and display results. In this case anappropriate user interface must be developed.

Once the decision concerning the factory configuration is made, the required hardware andsoftware installations are to be done and the proper data exchange between all involved programs
and computers must be established and verified.

© 2003 Wolfgang Theiss

SCOUT methods

9

Program development, training, consultance work29

Program development, training, consultance work

© 2003 Wolfgang Theiss