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Ellipsometric Analysis of Thin Films. Alexander Couzis ChE 5535. Principles of Ellipsometry. Linear Polarization vs. Elliptical Polarization. If E=2m p m=0, ±1, ±2, ±3 … ---> waves are in phase. This wave has a fixed amplitude ie it is linearly polarized.
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Ellipsometric Analysis of Thin Films Alexander Couzis ChE 5535
Linear Polarization vs. Elliptical Polarization If E=2mp m=0, ±1, ±2, ±3 … ---> waves are in phase This wave has a fixed amplitude ie it is linearly polarized If E=(2m+1)p m=0, ±1, ±2, ±3 … ---> waves are out of phase
Circular Polarization Scalar amplitude, but direction varies with time. Amplitude is not restricted to a single plane as before, but instead rotates so that the axis of rotation is opposite to the direction of motion
Detector Laser P q A Q Surface Ellipsometer An ellipsometer measures the changes in the polarization state of light when it is reflected from a sample. If the sample undergoes a change, for example a thin film on the surface changes its thickness, then its reflection properties will also change. Measuring these changes in the reflection properties can allow us to deduce the actual change in the film's thickness.
Null Ellipsometry • Ellipsometry is a sensitive optical technique for determining properties of surfaces and thin films. • If linearly polarized light of a known orientation is reflected at oblique incidence from a surface then the reflected light is elliptically polarized. The shape and orientation of the ellipse depend on the angle of incidence, the direction of the polarization of the incident light, and the reflection properties of the surface. We can measure the polarization of the reflected light with a quarter-wave plate followed by an analyzer; the orientations of the quarter-wave plate and the analyzer are varied until no light passes though the analyzer. From these orientations and the direction of polarization of the incident light we can calculate the relative phase change, , and the relative amplitude change, , introduced by reflection from the surface.
Polarization of Light To simplify reflection and transmission calculations, the incident electric field is broken into two plane polarized components. The plane of incidence is denoted by the "wheel" in the pictures below. The normal to the surface and all propagation vectors (ki,kr,kt) lie in this plane.
Ellipsometry • The ellipsometry is an optical technique devoted to the analysis of surfaces. It is based on the measurement of the variation of the polarization state of the light after reflection on a plane surface. The technique of ellipsometry has been discovered one hundred years ago but it is only fifteen years ago, thanks to the development of electronic and computers that the technique expand largely in numerous fields. • The strong advantages of ellipsometry are its non destructive character, its high sensitivity due to the measurement of the phase of the reflected light, its large measurement range (from fractions of monolayers to micrometers ), and the possibilities to control in real time complex processes.
Ellispometry After reflection on a sample surface, a linearly polarized light beam is generally elliptically polarized. The reflected light has phase changes that are different for electric field components polarized parallel (p) and perpendicular (s) to the plane of incidence. Ellipsometry measures this state of polarization or more precisely the complex ratio r written as: where and are the amplitude ratio and phase shift, respectively, of the p and s components and are the ellipsometric parameters (often given as tan, cos) measured as described in the Signal treatment and calibration section. The reflectance coefficients are directly related to the optical constants of the surface by assuming the ambient is air (Fresnel relations ): where n is the complex refractive index n = N -iK of the surface.
Ellipsometry • The angle of refraction may be obtained using Snell-Descartes's Law: • Thus if the sample is an ideal bulk, the real and imaginary parts of the complex refractive index may be calculated from the measured tan and cos parameters with the knowledge of the incidence angle. The optical index and thickness of a transparent layer on known substrate can also be deduced in the same way. This kind of analysis is characteristic of a single wavelength ellipsometric measurement.
MEASUREMENT TECHNIQUES • Different measurement techniques of the polarization after reflection exist. They all use the same optical components: a source, a polarizer, an analyzer and a detector. At these basic elements different other components like modulators or compensators can be added.
Extinction method The method uses the extinction of the signal to make an angular measurement. The optical setup is constituted by a monochromatic source (laser or lamp + spectrograph ), a polarizer, a compensator (a quarter wavelength plate for example), an analyzer and a photomultiplier tube. The polarization is linear after the polarizer. It is elliptical after the compensator which is orientated to obtain a linear polarization after reflection on the sample. The analyzer is then orientated to extinguish the beam. The orientation of the polarizer P, of the compensator C and of the analyzer A allow to obtain the ellipsometric parameters of the sample from:
Theory of the Rotating Polarizer Technique The field amplitude is splitted into the S and P components perpendicular and parallel to the plane of incidence respectively. The effect of each element is represented by a complex matrix On the Detector the field amplitude is: Finally the intensity, I, seen by the detector:
Extraction of Physical Parameters Ellipsometry is not a direct deductive method except in one simple case: the case of a bulk material. It is generally necessary to build a priori multilayer models to extract physical informations after numerical adjustement. Case of a substrate In the ideal case of a substrate without native oxide and surface roughness the ellipsometric parameters depend only on the angle of incidence and on the indices of the substrate. The following expression can be obtained: ni+jkiis the refractive index of the substrate F0 is the angle of incidence, n0 is the refractive index of the medium
Multilayer System • Field Continuity • Propagation across one layer
Multilayer System We define the field amplitude E+ and E- of the wave propagating in the positive and in the negative direction respectively. At the depth z, the field is represented by the vector: The field continuity at the interface between the layer i and the layer i+1 is represented by: • E(zi-) is the value of the electric field in the layer i at the interface with the layer i+1. • E(zi+) is the value of the electric field in the layer i+1 at the interface with the layer i. • ri,i+1 and ti,i+1 and the reflection and transmission coefficients at the interface between layer i and i+1.
Multilayer System Propagation across one layer is represented by a transfert matrix Li following: where: The angle phi is deduced from the Snell-Descartes relation. At the surface the expression of the field amplitudes is finally expressed by an iterative formula: At the interface between substrat and layer N, we assume that E+=1 and E-=0. Finally the reflection coefficients are obtained making the amplitude ratio of the incident and reflected waves.
Polymer Adsorption Isotherms(Takahashi A. and Kawagushi M., Advances in Polymer Science, 1982, 46, 1.)
Polymer Adsorption Kinetics “Time dependent studies have mainly been reported using ellipsometry for the measurement of the amount adsorbed and the thickness of the layer. They state that the equilibrium thickness was reached within several hours while the equilibrium adsorbance was attained only after one day. “
Adsorption of Surfactants at the Air-Liquid InterfaceLangmuir 1999, 15, 1400-1409
Multilayer Growth and Wetting ofC2Cl2F4 Physisorbed on GraphiteLangmuir 1998, 14, 4904-4907 Vapor Pressure Below Saturation
