ELLIPSOMETRY

VIJITHA. I.

JRF, CSIR-NIIST

For the 1st time Paul DRUDE use ellipsometry in 1888

In our LAB

Alexandre Rothen Published in 1945 a paper where the word «Ellipsometer» appears for the 1st time

film thickness within ±0.3A

What is Ellipsometry?

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.

Very sensitiveHighly accurate &reproducible

Non-destructiveEasy and quick measurement

No reference material necessary

Why we use Ellipsometry?

A method of probing surfaces with light.

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

Film ThicknessRefractive Index

Extension Coefficient

Surface RoughnessAnisotropy

CompositionUniformity

Psi (Ψ)Delta (∆)

Principle Of Ellipsometry

Φ0 : angle of incidence∆: relative phase changeΨ: relative amplitude change

s-plane stands perpendicularly to the plane of incidencep-plane stands parallel to the plane of incidence

Ellipsometry measures the complex reflectance ratio

The Fresnel equations

With n0 being air, n0 =1, so n1 is directly related to ellipsometric angles

Experimental Setup

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.

Null Ellipsometry

Spectroscopic Phase-Modulated Ellipsometry (SPME)

Fused silica bar

Xenon lamp /spectral range = 190 to 2100 nm

MgF2 Rochon prism

Photomultiplier:UV-VisiblePhotodiode: NIR

Advantages of PEM

Wide spectral range coverageWide spectral range from the FUV to the NIR is covered without the need for several hardware configurations, and without moving any optical elementsLarge acceptance angleThe 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 DeltaThe phase modulated ellipsometer delivers optimum accuracy for all values of Ψ and Δ 

Ellipsometry Data Analysis

1Measureme

nt

2Model

3Fit

4Result

n, k, d, adjustment

Instead of Ψ and ∆, 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

Literature Discussed

1Measurement

The modulated signal to detector takes the general form as follows:

I(t) = Io + Is sin∆(t) + Ic cos∆(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 = sin2Ψsin∆

Ic = sin2Ψcos∆

Each optical element of the system is represented by a (2x2) matrix.

Sample Polarizer/Analyzer

ModulatorRotation matrix to adjust to proper basis

Ellipsometer spectra Is(λ), Ic(λ) of a ZnO film analyzed by

Delta Psi software (Jobin – Yvon Co.)

2Model

.

Model contains initial estimates of the parameters which are then varied to generate a set of calculated Ψcalc and ∆calc 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.

Some dispersion relations used in our software

Model should be in agreement with the experiment

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

Bruggeman Effective Medium Approximation (EMA) Model

LAYER STACK MODEL

SubstrateThin film

VoidSubstrateThin film

VoidSubstrateThin film

Void 50%Thin film 50% Roughness

3Fit

Data fitting consists in minimizing the mean-square deviation Χ2 between calculated and measured ellipsometric parameters (Ψ and ∆) 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 pointN is the number of data pointsMesi is the ith experimental data pointThi is the ith calculated data point from assumed theoretical model

Model 1

Model 2

4Result

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.

References

Thank You