Ellipsometry
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Ellipsometry Han Haitjema Mitutoyo RCE, Best, The Netherlands
Definition Collective name for a number of techniques dealing with the measurement and interpretation of the change in the polarization state of a polarized beam of radiation which is reflected from a surface. From this change, optical properties of the reflecting surface can be derived.
Theory and Application Basic Theory for Reflection and Transmission at an Interface and the Basic Ellipsometry Equation In Fig. 1 the beam trajectories are sketched for a wave incident on a plane interface between two media having a real refractive index n1 and n2, respectively. The incoming beam with amplitude E1 is reflected by the interface, giving a reflected beam with amplitude E2 and a transmitted beam with amplitude E3. The condition that the phase of the three waves must be the same at the interface gives Y1 = Y2 and sin(Y1)/sin(Y3) = n1/n2 which is Snell’s law. The ratio between the incident amplitude E1 and
the reflected amplitude E2 will be different between light that is polarized parallel to the interface (p-direction) and the direction perpendicular to this (s-direction, as the arrows in Fig. 1). In general it can be written that r ðl, yÞ ¼
r p ðl, yÞ r s ðl, yÞ
¼ tan ðcðl, yÞÞ expðiDðl, yÞÞ
(1)
where rP and rS are the amplitude reflectances for light polarized in the p- and s-directions, respectively. This equation defines the ellipsometric angles C and D that can be determined in an ellipsometric measurement as shown below. Equation 1 states that the ratio between the reflectances, and with that the ellipsometric angles C and D, will depend on the angle of incidence # and the wavelength l for a given interface, whether it consists of a single homogeneous material or is a complicated system consisting of several absorbing and nonabsorbing thin films. Considering Eq. 1, ellipsometry consists of: 1. Measurement of the angles C and D An instrument that enables the determination of these quantities is called an ellipsometer. 2. Give a physical interpretation to the measured angles C and D Using the Fresnel coefficients of stratified surfaces, the theoretical angles C and D can be
# CIRP 2016 The International Academy for Production Engineering et al. (eds.), CIRP Encyclopedia of Production Engineering, DOI 10.1007/978-3-642-35950-7_16705-3
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Ellipsometry
Ellipsometry, Fig. 1 Reflection and refraction at a plane interface
Ellipsometry, Fig. 2 Schematic of an ellipsometer according to the PCSA arrangement
calculated of a surface, whether it consists of a single homogeneous material, a birefringent material, or a combination of absorbing and transparent coatings on a surface.
Measurement of C and D: The Ellipsometer Static Null Ellipsometer
An example of an ellipsometer arrangement is given in Fig. 2. It is one of the most elaborate arrangements but it well illustrates the key points of ellipsometry.
Ellipsometry
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Figure 2 depicts an ellipsometer in the PCSA (polarizer-compensator-sample-analyzer) arrangement. The polarizer, compensator, and analyzer c
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