introduction to ellipsometry - epfl 2008
TRANSCRIPT
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
1/57
EPFL October 7th 2008 1
Introduction to ellipsometry
J.Ph.PIEL (PhD)Application Lab ManagerSOPRALAB
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
2/57
EPFL October 7th 2008 2
OUTLINE :
- Basic Theory
- GES5 description
- Data Analysis
- Conclusion
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
3/57
EPFL October 7th 2008 3
I - BASIC THEORY
- Brief history of Ellipsometry
- Principle
- Physical meaning of and
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
4/57
EPFL October 7th 2008 4
Phase measurement
For the 1st time Paul DRUDE use ellipsometry in 1888
2000
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
5/57
EPFL October 7th 2008 5
Alexandre Rothen Published in 1945
a paper where the word Ellipsometer appears for the 1st time
Thickness sensitivity : 0.3 A
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
6/57
EPFL October 7th 2008 6
Bref Historique
Schematic representation of the mounting from Alexandre Rothen(Rev. of scientifique instruments Feb 1945)
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
7/57
EPFL October 7th 2008 7
Malus in 1808 : discovery of the polarisation of light by reflexion.
Fresnel in 1823 : Wave theory of the light.
Maxwell in 1873 : developpment of the Electrogmagnetic field theory.
Drude in 1888 : Use of the extreme sensitivity of the ellipsometry to detectultra thin layers (monolayer).
Abeles in 1947: Developpment of matrix formalism applied to thin layersstack.
Rothe in 1945 : Introduction of the word : Ellipsometer
Hauge, Azzam, Bashara in 1970 : description and developpement ofdifferent ellipsometer settings.
1980 : development of Personal Computer , automatisation of thetechnique. Industrial development of tools.
Few key people in ellipsometry area
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
8/57
EPFL October 7th 2008 8
INTRODUCTION
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
-The measurement gives two independent angles: and
- I t i s an absolute measurement: do not need any reference
- I t i s a non-direct technique: does not give directly the physicalparameters of the sample (thickness and index)- It is necessary to always use a model to describe the sample
SPECTROSCOPIC ELLIPSOMETRY (SE) gives more comprehensive resultssince it studies material on a wide spectral range
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
9/57
EPFL October 7th 2008 9
PRINCIPLE OF SPECTROSCOPIC ELLIPSOMETRY
=
rp
rs = tan.e
j= f( ni, ki, Ti )
Substrate (ns, ks)
Thin Film 1 (n1, k1, T1)
Thin Film 2 (n2, k2, T2)Thin Film i (ni, ki, Ti)
Ambient (n0, k0)
ES
EiEP
rs
rp
Erlinear polarisation
EiEpEs
Er Ep.rp
Es. rs
elliptical polarisation
0
Ellipsometry measures the complex reflectance ratio :
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
10/57
EPFL October 7th 2008 10
- After reflection on the sample, the extremity of the electric field vector describes anellipse
0
rp
rs
p
s
- This ellipse is characterised by
*the ellipticity Tan which is the ratio of the large axis to the small axis
*the angle of rotation between the main axis and the P axis:
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
11/57
EPFL October 7th 2008 11
Extremity of the electric field vector descrives an ellipse
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
12/57
EPFL October 7th 2008 12
Physical meaning of and .Those parameters give all relevant information about the polarization state of the light ata given wavelength.
- Tan gives exactly the angle of the first diagonal of the rectangle in which theellipse is enclosed.
- Cos gives roughly how fat is going to be the ellipse (shape).
Its mathematically linked to the ratio of short axis to long axis of the ellipse in its fundamentalframe.
However, and are not straightforwardly linked to the easiest geometrical features ofthe ellipse.
: angle of rotation of the long axis of the ellipseversus axis p
= CosTanTan )2()2( - 1 - 0.5 0.5 1
- 1
- 0.5
0.5
1
40 .
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
13/57
EPFL October 7th 2008 13
- 1 - 0.5 0.5 1
- 1
- 0.5
0.5
10
- 1 - 0.5 0.5 1
- 1
- 0.5
0.5
120.
- 1 - 0.5 0.5 1
- 1
- 0.5
0.5
140.
- 1 - 0.5 0.5 1
- 1
- 0.5
0.5
1
60 .
- 1 - 0.5 0.5 1
- 1
- 0.5
0.5
1
80.
- 1 - 0.5 0.5 1
- 1
- 0.5
0.5
1
90.
Example of some different phase shift () for a given value. On those graphics, the long axis is the ellipse is represented and it has to be compared with the
diagonal of the rectangle.
Because is fixed, the ellipse is enclosed in the same rectangle for each graphic.
Modification of change both angle of inclination and ellipticity.
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
14/57
EPFL October 7th 2008 14
II - GES5 DESCRIPTION
- Physical description
- Jones Formalism
- Mathematical treatment of the signal
- Example
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
15/57
EPFL October 7th 2008 15
Goniometer
Analyser Arm
Polariser Arm
Sample
Mapping
rho/theta
Microspots
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
16/57
EPFL October 7th 2008 16
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
17/57
EPFL October 7th 2008 17
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
18/57
EPFL October 7th 2008 18
SPECTROSCOPIC ELLIPSOMETER
Scanninig
channelC.C.D.
channel
Xe Lamp
PA
Optical Fiber
Goniometer
PhotoMultiplier
Tube
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
19/57
EPFL October 7th 2008 19
Spectrometer
Spectrograph
Schematics of dispersion elements
Grating : rotating
Prism : rotating
NIR detector
PMT
Entrance Fiber
Grating : fixed
Multichannel
Detector
Entrance Fiber
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
20/57
EPFL October 7th 2008 20
GENERAL GES5 DESCRIPTION:
- Xenon Lamp:75 W, Short arc, High brilliance- MgF2 Rotating Polarizer MgF2 : 6 Hz- Adjustable Analyzer
- Goniometer from 7 up to 90- Microspots : spot size : 400 m
- High resolution way :
-Spectral range : 190 nm up to 2000 nm- resolution < 0.5 nm- double monochromator: prism + grating- Photon counting PMT
-High speed way :- Spectral range : 190 nm up to 1700 nm- Measurement duration : few seconds- Fixed grating spectrograph
- CCD (1024x64 pixels)and OMA NIR (256 pixels) detectors
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
21/57
EPFL October 7th 2008 21
Jones Formalism
BUT : Jones formalism can only workif there is no depolarisation effects induced by the material
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
22/57
EPFL October 7th 2008 22
Optical system with no depolarisation effectsis characterized by this following Jones Matrix :
2X2 complex Matrix
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
23/57
EPFL October 7th 2008 23
If the material is isotrope :
Ellipsometric Angles and measured simultaneously
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
24/57
EPFL October 7th 2008 24
P =R(-).Px.R()
Jones Matrix for a Linear Polarizer : Px = 00 01
P =
cossin
sincos
Rotation Matix :
General expression for a polarizerwhere the main axis is oriented with an angle
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
25/57
EPFL October 7th 2008 25
I = Edp . Edp* + Eds . Eds*
I (t) = I0 . ( 1 + Cos 2 (t) + Sin 2 (t) )
A : Angle between Analyser and plane of Incidence.(t) : Angle between Polariseur and plane of Incidence.
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
26/57
EPFL October 7th 2008 26
Edp 1 0 Cos A Sin A rp 0 Cos P - Sin P 1 0 Ep
Eds 0 0 -Sin A Cos A 0 rs Sin P Cos P 0 0 Es=
Detector Analyser Rotation Sample Rotation Polariser Lamp
A : Angle between Analyser axis and Plane of Incidence.P(t) : Angle between Polarizer axis and Plane of Incidence.
I = Edp . Edp*
+ Eds . Eds*
I = I0 . ( 1 + Cos 2 P(t) + Sin 2 P(t) )
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
27/57
EPFL October 7th 2008 27
S1 S4S2 S3 S1
Time
Intensity
S I P dP10
4
= ( )
S I P dP2
4
2
=
( )
S I P dP32
34
= ( )
S I P dP43
4
= ( )
[S1 - S2 -S3 + S4 ]
2 I0 =[S1 + S2 - S3 - S4 ]
2 I0 =[S1 + S2 + S3 + S4 ]
0 =
HADAMART TRANSFORM
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
28/57
EPFL October 7th 2008 28
CALCULATION OF THE ELLIPSOMETRIC PARAMETERS
Cos 2 ATan 2 + Tan 2 A
0 =
Tan 2 - Tan 2 ATan 2 + Tan 2 A
= 2 Cos . Tan . Tan ATan 2 + Tan 2 A
=
1 + 1 -
Tan = Tan A .
1 - 2
Cos =
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
29/57
EPFL October 7th 2008 29
DUV UV VISIBLE NIR
ELLIPSOMETRIC MEASUREMENT
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
30/57
EPFL October 7th 2008 30
RESULTS ANALYSIS
Ti , ni , ki
Experimental Measurement
=Model Simulation ?
No
Yes
Cos
Tan
Experimental
Measurement
Physical ModelEstimated sample structure
- Film Stack and structure- Material n, k, dispersion- Composition Fraction of Mixture
REAL SAMPLE STRUCTURE
Non direct technique.
Need the use of modelsto interpret the measurementsand to get physical parameters of thelayers
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
31/57
EPFL October 7th 2008 31
III - DATA ANALYSIS
- Which physical parameters can we get ?
- Sensisitivy of the technique
- Description of the main models used
- How to describe optical properties of thematerials.
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
32/57
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
33/57
EPFL October 7th 2008 33
Spectroscopic ellipsometry sensitiviy
Phase variation : isextremelly sensitive to ultra
thin layers
Angle of incidence: 75
S t i lli t iti i
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
34/57
EPFL October 7th 2008 34
0nm
10 A
Spectroscopic ellipsometry sensitiviy
Angle of incidence: 75
Sensitivity could reach
0.01 A
or 1 picometer
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
35/57
EPFL October 7th 2008 35
Description of the main models used
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
36/57
EPFL October 7th 2008 36
2 media model : Substrat alone
1
0Ambiant : air
Substratns = s - i.ks
rp = (ns.cos0 n0.coss)/(ns.cos0 + ns.cos1)
and
rs= (n0.cos0 - ns.coss)/(ns.cos0 + ns.cos1)
with = r
p/ r
s= Tan.exp(i.)
Fresnel equation and Snell-Descartes law:
ns = sin0.(1 + ((1-)/(1+))2.Tan20)1/2Direct inversion of the ellipsometric parameters to get substrate indices
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
37/57
EPFL October 7th 2008 37Silicium Angle of incidence 75
2 media model : Substrat alone
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
38/57
EPFL October 7th 2008 38
3 media model : one layeron known substrate
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
39/57
EPFL October 7th 2008 39
Native oxide (SiO2) on SiliconSicr
SiO2 30.8
3 media model : one layer on known substrate
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
40/57
EPFL October 7th 2008 40
SicrSiO2 1200 SiO2 layer on silicon
3 media model : one layer on known substrate
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
41/57
EPFL October 7th 2008 41
3 media model : one layer on known substrate
Thick SiO2 layer on Silicon SicrSiO2 1,9838m
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
42/57
EPFL October 7th 2008 42
Rp et Rs are periodic functionSame periods Idem for Tan and Cos
If a =75Period=/(nb2-0.93)0.5
For SiO2 filmnb =1.5 Period = /2.3
At =450 nm, period = 200 nm
Sensitivity to :In this case variation de 360 for a period = 200 nm
sensitivity given by instrument: 5.10-2
Thickness sensitivity : 0.01 A
3 media model : one layer on known substrate
M l il k
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
43/57
EPFL October 7th 2008 43
Multilayer stack
Multilayer stack
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
44/57
EPFL October 7th 2008 44
Interface relations : FresnelPropagation inside the layer :Interferences
-
Multilayer stack
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
45/57
EPFL October 7th 2008 45
How to describe optical properties of thematerials
Index library Effective medium mixing laws Dispersion law Harmonic oscillators laws
Drude laws
Index Library
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
46/57
EPFL October 7th 2008 46
Index Library
3 main type of materials:
Dielectric : transparent in the visible range but absorbing in the UV and haveabsorbing band in the IR.Transparent materials : Oxides (SiO2, TiO2) Fluorides (MgF2)
Optical filters, Anti reflective coatings, dielectric mirror (lasers).
Semi-conductors dispersives laws extremelly rich in the visible range linkedto the band structures. Could be metallic in the IR.Silicon : Si; Germanium : Ge; Gallium arsenide : GaAs;
Gallium nitride: GaN;
Carbon Silicon SiC (blue diode);
Metal highly absorbing in the visible.Infrared mirrors :Au, Al, Cu
Magnetic Materials : Co, Ni, Fe, Gd
Handbook of Optical Constants from Palick
SOPRA library Direct measurements on bulk materials
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
47/57
EPFL October 7th 2008 47
Effective medium model
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
48/57
EPFL October 7th 2008 48
Popular effective medium model
I t f d S f h
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
49/57
EPFL October 7th 2008 49
Interface and Surface roughnesstreated by Effective medium Model
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
50/57
EPFL October 7th 2008 50
- Model is convenient for physical or mechanical mixing.Ex : Porous material with inclusion of void.
- Model is not convenient for chemical mixingEx : Inclusion of atom in elementary cellsor variable atomic concentrationEx : Si(1-x)Gex.
- Model is not applicable when the size of inhomogeneitiesexceed few hundredth (1/100) of the wavelenght of the beam.
Limits of the effective medium model
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
51/57
EPFL October 7th 2008 51
Dispersion Law
Sellmeier law :
42
CBAn ++= 53
FEDk ++=
Cauchy law :
k =0 for transparent materials
)(
)1(1)(
2
22
B
Ar
+=
53)(
EDCi
++=
1
3
32
1
4
2
2
3
2
2
2
1
0 ).(.)()(..
)(
++=++=
BB
BnkA
A
A
A
AnSiNx example
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
52/57
EPFL October 7th 2008 52
4 absorption peaks
SiO2 in the Infrared range2222
0
2
3
2222
0
2
2
0
22
.)(
..
.)(
)(..
+
=+
=L
A
L
LAir
Harmonic Oscillators
Absorption band in the measured spectral rangeLorentz oscillators
A: Intensity.
L0: Middle wavelength.
: Oscillator width.
Harmonic Oscillators
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
53/57
EPFL October 7th 2008 53
100 nm of an absorbing layer on Silicon substrate
Spectroscopic Ellipsometry data Indices of the layer
Harmonic Oscillators
Drude Law
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
54/57
EPFL October 7th 2008 54
Wavelength ( m)
2 4 6 8 10 12 14 16
n, k
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Measure and Drude law
fit on doped silicon
undoped silicon
( )
1
2
2 2= p
( )
2
2
2 2=
p
( )
Indices are fitted
using Drude law :
p : Plama frequency : diffusion frequency
Semi conductors indices are sensitive to the doping level in the IR range
Drude Law
N() doped Silicon N()
k() doped Siliconk() undoped Silicon
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
55/57
EPFL October 7th 2008 55
=e
m*
Spectroscopic ellipsometry fit gives :
Plasma frequency p and Diffusion Frequency
Material Conductivity
Carrier Density
Carrier Mobility
= 0
2p
N m e
p
=
* 0
2
2
For the sample correspondingto the previous measurement :
N =1.6 1019 at./cm3
= 104 cm2 V-1 s-1
= 264 -1 cm-1
Drude Law
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
56/57
EPFL October 7th 2008 56
Conclusion
-
8/2/2019 Introduction to Ellipsometry - EPFL 2008
57/57
EPFL O t b 7th 2008 57
The measurement gives two independent angles: and
-Absolute measurement: do not need any reference.
-Extremely sensitive to very thin layers (less than a monolayer).-fast : get the full spectrum (190 nm up 1700 nm) in few seconds
-Non-direct technique: does not give directly the physical
parameters of the sample (thickness and index)-Need to use a modelto describe the sample.
Determination of : but also :
Thickness PorosityRefractive index : n Resistivity
Extinction coefficient : k
Molecular bounds