measurement of optical constants of thin film using delta psi software

1. VIJITHA. I.
JRF, CSIR-NIIST

2. For the 1st time Paul DRUDE use ellipsometry in 1888
In our LAB

3. Alexandre Rothen Published in 1945 a paper where
the word «Ellipsometer» appears for the 1st time
film thickness within ±0.3A

4. What is Ellipsometry?
A method of probing surfaces with light.
ELLIPSOMETRY is a method based on measurement of the
change of the polarisation state of light after reflection at non
normal incidence on the surface to study.
Why we use
Ellipsometry?
Very sensitive
Highly accurate &reproducible
Non-destructive
Easy and quick measurement
No reference material
necessary

5. What Ellipsometry measures: What we are interested in:
Desired information must
be extracted through a
model based analysis
using equations to
describe interaction of
light and materials

6. Principle Of Ellipsometry
Φ0 : angle of incidence
Δ: relative phase change
Ψ: relative amplitude change
s-plane stands perpendicularly
to the plane of incidence
p-plane stands parallel to the
plane of incidence

7. The Fresnel equations
Ellipsometry measures the complex reflectance ratio
With n0 being air, n0 =1, so n1 is directly related to ellipsometric
angles

8. Experimental Setup

9. Null Ellipsometry
By rotating the polarizer it is possible to change the phase
shift between the p- and s-component of the incident light.
The trick is to compensate for the phase shift that will occur at
the surface so that the p- and s-component of the reflected
wave will be again in phase and thus linearly polarized.

10. Spectroscopic Phase-Modulated
Ellipsometry (SPME)
Fused silica bar
MgF2 Rochon prism
Xenon lamp /
spectral range = 190 to
2100 nm
Photomultiplier:
UV-Visible
Photodiode: NIR

11. Advantages of PEM
Wide spectral range coverage
Wide spectral range from the FUV to the NIR is covered without
the need for several hardware configurations, and without
moving any optical elements
Large acceptance angle
The photoelastic modulator optical element has a large
tolerance of the incident angle allowing more simple alignment
of the system.
High Accuracy Measurements for all Values of Psi and
Delta
The phase modulated ellipsometer delivers optimum accuracy
for all values of Ψ and Δ

12. Ellipsometry Data Analysis
n, k, d, adjustment
Instead of
Ψ and Δ,
intensity
is
measured
Dispersion
relations are
used for the
representation
of sample
Minimizing the
Mean-square
deviation Χ2
Thickness
of the film,
Refractive
index,
Extinction
coefficient
Delta Psi software

13. Literature Discussed

14. The modulated signal to detector takes the general form as
follows:
I(t) = Io + Is sinΔ(t) + Ic cosΔ(t)
Jones formalism equation
The measurement configuration is chosen for the purpose of
simplifying the calculation of trigonometry functions. In the
present set of measurement,
M = 0°, P = 45°, A = 45°, so that,
Io = 1
Is = sin2ΨsinΔ
Ic = sin2ΨcosΔ

15. Each optical element of the system is represented by a (2x2)
matrix.
Sample Polarizer/Analyzer
Modulator
Rotation matrix to
adjust to proper basis

16. Ellipsometer spectra Is(λ), Ic(λ) of a ZnO film analyzed by
Delta Psi software (Jobin – Yvon Co.)

17. Model contains initial estimates of the parameters
which are then varied to generate a set of calculated
Ψcalc and Δcalc that fits best the measured data.
.
Transparent Materials: Classical, Lorentz, Cauchy
Transparent, Conrady, Hartmann, Schott, Sellmeier
Transparent.
Absorbing, Non Metallic Materials: Cauchy Absorbant,
Sellmeier Absorbant, Tauc-Lorentz, Cody-Lorentz.
Absorbing Semiconductors: Adachi, Afromovitz, Excitonic.
Metals: Drude.

18. Backside reflexion is collected but not interfering with front
side due to loss of coherency
Backside reflexion is not collected because diffusion on rough
side or beam is masked
Model should be in agreement with the experiment

19. Thin film
Substrate
Thin film 50% Void 50% Roughness
Bruggeman Effective
Medium Approximation
(EMA) Model
Thin film
Substrate
Void
Thin film
Substrate
Void

20. Data fitting consists in minimizing the mean-square deviation
Χ2 between calculated and measured ellipsometric parameters
(Ψ and Δ) using different algorithm, e.g. Marquardt –
Levenberg algorithm.
The Mean Square Error (MSE) Χ2 is used to qualify the
difference between the experimental and predicted data.
where σi is the standard deviation of the ith data point
N is the number of data points
Mesi is the ith experimental data point
Thi is the ith calculated data point from assumed theoretical
model

21. Model 1

22. Model 2

24. References
P. Drude, Ann. d. Physik u. Chemie 39, 481 (1890).
Alexandre Rothen, The Review of Scientific Instruments, Vol. 16, No. 2
(1945).
Nguyen Nang Dinh , Tran Quang Trung,Le Khac Binh, Nguyen Dang
Khoa, Vo Thi Mai Thuan, VNU Journal of Science, Mathematics - Physics 24
16-23 (2008) .
Harland G. Tompkins & Eugene A. Irene, Handbook Of Ellipsometry
(2005).
R.M. A Azzam, N.M. Bashara, Ellipsometry and Polarized Light (1999).
Rudolf Holze, Surface and Interface Analysis: An Electrochemists Toolbox
(2009).
Horiba Scientific, Spectroscopic Ellipsometry Manual.
Gaertner Scientific Corporation, Ellipsometry Manual.
Ramdane Benferhat, Basic Principles of Spectroscopic Ellipsometry and
Photo-Elastic Modulator.
Dietrich R. T. Zahn, Optical Spectroscopies of Thin Films and Interfaces.
J.Ph.PIEL, Introduction to Ellipsometry.
G.E Jellison Jr., Ellipsometry Data Analysis: a Tutorial.