**Optical Spectroscopy with
dispersive Spectrometers
Basics - Building Blocks - Systems - Applications**

**This page
summarizes chapter 2 of the book
"Applications of Dispersive Optical
Spectroscopy Systems",
ISBN 9781628413724, SPIE monographs, Bellingham, WA, USA **

**Application E1
Spectroscopic Ellipsometry and Polarisation Measurement**

**This page
presents the directory, the signs and symbols, conversions, and equations
of the book, while the details are an exclusive part of the book**.

**E1.0 Introduction**

This page differs remarkably from others of the Spectra-Magic Basics.

The page on Ellipsometry is the only one, not specially written for Spectra-Magic.
The German version is based on the paper 02 "Spektroskopische
Ellipsometrie; Grundlagen, Stand der Technik und Anwendungen (D)". Another difference is the endorsement of a company name, which is not the
case in all other Basics pages. But, in order to stay compatible with
the other
Basics and Application pages, the list of formulas and equations is maintained.
In comparison to the German version, the English one appears summarized.

**E1.0.1 Applications of
spectroscopic Ellipsometry (SE)**

If the wavelength of the instrument is correct, angle of incidence, polarization,
and collimation of the light are perfect, an SE system needs no further
calibration to measure the refractive index **n**, and the absorption
coefficient **k** correctly. Both are basic parameters
for the characterization of
materials. In the case of measuring unknown samples, but based on knowlegde of the
structure system, SE software is able to define the real structure. That in turn
needs the
precise
n & k values of the materials involved in the reduction and fit library. Theoretically
there are no calibration samples required. In practice, they are needed to
check the above mentioned parameters, and for day-to-day comparison. But that
does not diminish the application power of the method.

**E1.0.2 SE System for Research,
Material, and Product
Definition
**

Graph E1.1A

Graph E1.1B demonstrates the behaviour of a polarized light beam after the rotating polarizer.

Suggestion: an excellent tutorial on the topic of polarization is found in the homepage of András Szilágyi: http://www.enzim.hu/~szia/emanim/emanim.htm. It is available in Hungarian, English, and German, and can be loaded down.

**E1.2 Basics of SE and relevant data:**

SE data are based on the Fresnel equations:

**F43**:
also represented as

with

r** _{p}** and r

The illumination angle at the sample is marked by

The complex value of **
r**, in a system
with polarizer - sample -
compensator - analyzer, is created by

**F44**:

Whereas A, C, P are the angles of polarizer, compensator, and analyzer. For all standard SE measurements, it is satisfying to recover the real part only, which needs no algebraic sign. That in turn needs no compensator.

In an SE system with rotating polarizer, programmed analyzer, but no compensator, the measured data are created by:

**F45**:

where the coefficients **
a** and **
b** are recovered by Hadamard
reduction, that leads to tg **Y**,
and cos **D.**

**F46:
**

Data, acquired with optimum working instruments, and well suited samples, can be reduced to absolute thicknesses of 0.1 nm, and values of 0.0005 in n and k.

**E1.3 When is SE required in favour of single
wavelength ellipsometry (SWE)?**

**E1.4 Components of an SE system
E1.5 SE with parallel detection
**

with

**S _{0}** through

One more important parameter is the

**F48: **

**E1.8 SE examples:
**

Graph E1.8.1 Ellipsometric data

Graph E1.8.2 Ellipsometric data

Graph E1.8.3 Ellipsometric data

**E1.11 A Selection of References on SE:
E1.12 Extensions to the
instrumentation for spectroscopic ellipsometry (SE)
E1.13 SE system for the deep UV
**

Graph E1.13: UV SE system

**E1.14 SE system for the IR range
**

Graph E1.14: IR SE System

All copyrights on "spectra-magic.de" and "Optical
Spectroscopy with dispersive Spectrometers
Basics - Building Blocks - Systems - Applications " are reserved by
Wilfried **Neumann, D-88171 Weiler-Simmerberg.
Status April 2012**