1 December 1999 Ž . Optics Communications 171 1999 195–204 www.elsevier.comrlocateroptcom Vectorial diffraction patterns and limits of Brewster ellipsometry L. Froehly a,b, ) , I. Verrier b , C. Froehly c,1 , G. Brun b , C. Veillas b a Angenieux SA, BouleÕard RaÕel de MalÕal, 42570 Saint Heand, France ´ ´ b Laboratoire TSI, Faculte des Sciences, 23 rue du Dr. Paul Michelon, 42023 Saint Etienne Cedex 2, France ´ c IRCOM, 123 aÕenue Albert Thomas, 87060 Limoges Cedex, France Received 18 June 1999; received in revised form 6 September 1999; accepted 22 September 1999 Abstract A vectorial modulation transfer function approach of diffraction patterns observable around Brewster’s incidence is proposed. The good agreement between experimental results and vectorial model will allow the correlation of refractive index measurement accuracy with the average magnitude of surface defects. Consequences in the metrology of refractive index gradients will then be briefly discussed. q 1999 Elsevier Science B.V. All rights reserved. PACS: 42.25.Ja; 42.30.Kq; 42.30.Lr; 42.87.yd Keywords: Ellipsometry; Vectorial modulation transfer function; Refractive index measurement accuracy 1. Introduction Ellipsometers have been widely used for decades in order to study layers thicknesses, Langmuir films metrology, refractive index measurement, etc. Ellipsometry will often be performed around Brewster incidence rather than under normal illumi- nation for the sake of optimum photometric sensitiv- ity. The incident probe beam used for refractive index determination is then assumed to be a ‘rectilin- early polarized plane wave’. In fact the beam paral- lelism and the degree of rectilinear polarization state Ž are limited by diffraction Fourier uncertainties rela- . tions: DÕD x s 1. ) Corresponding author. Tel.: q33-4-7748-1571; fax: q33-4- 7748-5120; e-mail: froehly@univ-st-etienne.fr 1 Tel.: q33-05-55-45-74-16; fax: q33-05-55-45-74-16. These vectorial diffraction effects have been, for the first time, recently described qualitatively by wx Hosoda et al. 1 but, to our knowledge, conse- quences on ellipsometric measurement accuracy have never been computed quantitatively. In this article we propose a quantitative and quali- tative description of polarization and diffraction phe- nomena encountered during Brewster ellipsometry measurements. The vectorial modulation transfer Ž . function VMTF of the whole ellipsometric system Ž . polarizer and plane interface is calculated. This VMTF characterizes all the distortions that an inci- dent polarized monochromatic beam, with moderated angular aperture, undergoes after propagation through the whole system. Finally this calculation allows a better understanding of the ellipsometric refractive index measurement limits due to the interface inho- mogeneities: polish defects, scattering light sources and flatness defects, etc. 0030-4018r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. Ž . PII: S0030-4018 99 00540-4