M.Theiss Hard- and Software for Optical Spectroscopy
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Phone: (49) 241 5661390
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E-mail: theiss@mtheiss.com
Web: www.mtheiss.com

Developing optical production
control methods for SCOUT
by Wolfgang Theiss

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indirectly by this document.
Printed: 04.11.2003, 15:36 in Aachen, Germany

Developing optical production control methods for SCOUT

Contents

ITable of ContentsForeword

2Part I Overview
1 Title3................................................................................................................................... 3

2 Introduction................................................................................................................................... 4

Part II Preliminary actions

5

1 Gathering ...................................................................................................................................
information
5
2 Selecting the...................................................................................................................................
appropriate method
6
3 First test measurements...................................................................................................................................
and rough optical modelling6
4 Systematic...................................................................................................................................
test measurements
9Part III Development of the optical model

9

1 Optical constants................................................................................................................................... 9Interband.........................................................................................................................................................
transitions
11
Vibrational.........................................................................................................................................................
modes
13
Charge carriers......................................................................................................................................................... 14Master model......................................................................................................................................................... 16'Rules of thumb'......................................................................................................................................................... 18
Substance.........................................................................................................................................................
A: Test oxide model
19
Substance.........................................................................................................................................................
B: Develop a new model
19

2 Layer structure................................................................................................................................... 23
3 Fit strategy................................................................................................................................... 28

Part IV Final actions30

1 Integration...................................................................................................................................
into the customer's environment30
2 Company...................................................................................................................................
tests and long-time support
32

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 software which iscommercially available.

Aachen, October 2003

SCOUT methods

1

Overview

1.1

Title

Overview3© 2003 Wolfgang Theiss

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1.2

Overview

4Introduction
A short introductory rush through the three main steps of the presentation:© 2003 Wolfgang Theiss

SCOUT methods

2Preliminary actions

2.1

Gathering information

Overview

5

Get information about the problem to be solved and the circumstances of the development:© 2003 Wolfgang Theiss

SCOUT methods

2.2

Preliminary actions

6

Selecting the appropriate method
Considering the goal of the method and the external conditions, the appropriate experimental
technique is selected:

2.3First test measurements and rough optical modellingDo first test measurements: Investigate a blank substrate, and - if possible - a seris of thin film
spectra covering the expected variety of cases in the production.
Verify that measured substrate spectra agree with simulated ones. This is an important check of
the spectrometer hardware and the measurement procedure.
Can we successfully describe the thin film test measurements with preliminary, simple opticalmodels?
Identify the type of material by comparison to known cases: Metal, semiconductor, oxide or nitride?

© 2003 Wolfgang Theiss

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Preliminary actions

7

The following graphs show spectra of typical metal, semiconductor and oxide thin films on a siliconwafer substrate. The top pictures display the reflectance, the bottom ones show ellipsometry
spectra:We now load measured ellipsometry data for an unknown substance on silicon. A roughcomparison shows that the material behaves like a typical oxide. Very likely an adjustable ´oxide© 2003 Wolfgang Theiss

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Preliminary actions

8model´ will lead to a succesful simulation (this will be verified later on):For another test material there is no convincing agreement with any of the typical cases. In thiscase a new type of optical constant model has to be developed:© 2003 Wolfgang Theiss

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2.4

Preliminary actions

9

Systematic test measurements
In case of succesful pre-liminary tests: Decide to realize the method and continue with systematic
test measurements.

3

Development of the optical model

3.1

Optical constants
Having gathered enough information and data the optical model for the given analytical problem
can be developed.
The basis of any spectrum simulation method are correct optical constants. In most cases of
optical process control models with adjustable parameters are required.

© 2003 Wolfgang Theiss

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Development of the optical model

10

With these models we can successfully treat the three basic excitations: Interband transitions,vibrational modes and the acceleration of free charge carriers (electrons, holes).

Models for the individual excitation types are suggested in the following sections.

© 2003 Wolfgang Theiss

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3.1.1

Development of the optical model

11

Interband 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:© 2003 Wolfgang Theiss

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Development of the optical model

12

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

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

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3.1.2

Development of the optical model

13

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 ofthe absorption band:© 2003 Wolfgang Theiss

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Development of the optical model

14

However, in most cases a Gaussian line shape is more realistic. In SCOUT this can be obtainedusing Kim oscillators:

3.1.3

Charge 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.

© 2003 Wolfgang Theiss

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Development of the optical model

15

The following example shows that the simple Drude model does not always perform excellently:

In 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:© 2003 Wolfgang Theiss

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3.1.4

Development of the optical model

16

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 using so-called master models
which provide for every parameter a user-defined formula to express its dependence on the masterquantity:© 2003 Wolfgang Theiss

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Development of the optical model17© 2003 Wolfgang Theiss

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3.1.5

Development of the optical model

18'Rules of thumb'Use the following rules of thumb to find appropriate models for optical constants:© 2003 Wolfgang Theiss

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3.1.6

Development of the optical model

19

Substance A: Test oxide model
The optical properties of the unknown substance A (see above) can be described easily using thesuggested oxide model:

3.1.7

Substance B: Develop a new model
None of the standard cases seemed to be applicable for substance B (see above). Hence we haveto develop a new model from scratch. In the following we assume that the layer thickness is about
40 nm (let's assume that we have got this rough number from the producer).
The simplest model would be just a constant. Varying the constant and the layer thickness thefollowing 'agreement' of model and measurement is found:© 2003 Wolfgang Theiss

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Development of the optical model20The spectral features do not look like interference fringes, so a rather strong dispersion of therefractive index and a strong absorption may be responsible for the observed structures.
Test a strong Kim oscillator (combined with a constant):

This looks promising. However, there are more structures in the measurement. Let's see if asecond oscillator can help to improve the model. Although the second oscillator has been© 2003 Wolfgang Theiss

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Development of the optical model

21

positioned around 750 nm initially, the fit algorithm moved it into the infrared in order to reduce thedifference of model and measurement above 800 nm wavelength:

Still there is a large structural mismatch between 650 and 750 nm wavelength. Again, another Kimoscillator is introduced in order to fix this problem:© 2003 Wolfgang Theiss

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Development of the optical model

22

This is a real breakthrough. Only minor differences have to be removed. A Kim oscillator placed in
the blue is now added which is going to improve the model for small wavelengths:

It's not easy to stop now because every additional oscillator turned out to be useful (and it seems tobe a nice game). Let's do it one more time in the spectral range around 650 nm:© 2003 Wolfgang Theiss

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Development of the optical model

23

This seems to be good enough now. It would be important to check the obtained optical constantsin other situtations. Other thicknesses could be prepared, and other substrates or different opticalmethods like reflectance or transmittance could be used in order to verify the validity of the result ofthe analysis.

3.2

Layer structure
In addition to the setup of optical constant models (see above) the structure of the layer stack must
be questioned in some cases. Often layers additional to the ones reported by the producer must
be introduced.

© 2003 Wolfgang Theiss

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Development of the optical model

24

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

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Development of the optical model

25

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

© 2003 Wolfgang Theiss

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Development of the optical model

26

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

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Development of the optical model27Communication with the producer finally verified the assumptions made in the successful fit:

© 2003 Wolfgang Theiss

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3.3

Development of the optical model28

Fit strategy
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

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Development of the optical model

29

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© 2003 Wolfgang Theiss

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Development of the optical model30

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.

4Final actions

4.1

Integration into the customer's environment
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.

© 2003 Wolfgang Theiss

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Final actions

31

The optical analysis can also be completely independent of the process control software:

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

© 2003 Wolfgang Theiss

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Final actions

32

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.

4.2

Company tests and long-time support
Finally, the method must be tested and optimized in the plant during production. The long-time
support contains the processing of error reports (bug fixing) and updates of the model and theuser-interface.

© 2003 Wolfgang Theiss

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Final actions

33© 2003 Wolfgang Theiss