, "Combined reflection and transmission thin-film ellipsometry: a unified linear analysis," Appl. Opt. 14, 1652Opt. 14, -1663Opt. 14, (1975 http://www.opticsinfobase.org/ao/abstract.cfm? URI=ao-14-7-1652 Combined reflection and transmission thin-film ellipsometry: a unified linear analysis R. M. A. Azzam, M. Elshazly-Zaghloul, and N. M. Bashara A scheme of combined reflection and transmission ellipsometry on light-transmitting ambient-film-substrate systems is proposed and the required sample design and instrument operation are investigated. A comparative study of the sensitivity of external and internal reflection and transmission ellipsometry is carried out based on unified linear approximations of the exact equations. These approximations are general in that an arbitrary initial film thickness is assumed. They are simple, because a complex sensitivity function is introduced whose real and imaginary projections determine the psi (@) and delta (A) sensitivity factors. Among the conclusions of this paper are the following. (1) External reflection ellipsometry near the Brewster angle of a transparent ambient-substrate system is extremely sensitive to the presence of very thin interfacial films. For example, films as thin as 10-5 A of gold are readily detectable on glass substrates at an angle of incidence 0.30 below the Brewster angle, assuming a measuring wavelength of 5461 A with an ellipsometer of 0.05° precision. (2) The formation of thin nonabsorbing films at the interface between transparent ambient and substrate media is not detectable, to first order, as a change in the ellipsometric angle Q by either internal or external reflection or transmission ellipsometry.

M. Elshazly-Zaghloul and R. M. A. Azzam, "Brewster and pseudo-Brewster angles of uniaxial crystal surfaces and their use for determination of optical properties," J. Opt. Soc. Am. 72, 657-661 (1982) Brewster and pseudo-Brewster angles are defined for surfaces of transparent and absorbing uniaxial crystals parallel and perpendicular to the optic axis. Two Brewster angles of a transparent uniaxial crystal surface parallel to the optic axis, measured when the optic axis is oriented perpendicular and parallel to the plane of incidence, readily determine the ordinary and extraordinary indices No and Ne. N 0 and Ne can also be obtained from two Brewster angles measured on a surface perpendicular to the optic axis in contact with two media of different refractive indices. Conditions for the existence of two Brewster angles are discussed. The complex No and Ne of an absorbing uniaxial crystal can be derived from pseudo-Brewster-angle and minimum-reflectance data obtained in two symmetrical orientations of a surface parallel to the optic axis. An approximate, but accurate, explicit inversion procedure is presented for this purpose.

The transmission ellipsometric function (TEF) of a film-substrate system relates the polarization change, upon transmission, of an electromagnetic wave obliquely incident on, and transmitted through, a film-substrate system. The behavior of the TEF depends on the category of the film-substrate system: negative, zero, or positive. The category is determined by the sign of [equation in text]: negative for a negative film-substrate system, zero for a zero system, and positive for a positive system. We discuss the behavior of the TEFs of the two transparent nonnegative film-substrate systems, zero and positive. We describe the TEF as two successive transformations and analyze its behavior as the angle of incidence and film thickness of the film-substrate system are changed. We use the constant-angle-of-incidence contours and constant- thickness contours to analyze and utilize that behavior. From the analysis and understanding of the behavior of the TEF, and from the definition of a polarization device as a film-substrate system that introduces prescribed polarization changes, we discuss the design of all possible types of polarization devices using either of the two systems. We present a design formula for each. We also present a general formula that is used for the design of any of the devices. Thin-film coatings are treated as polarization devices for the purposes of our discussion. We conclude with a brief discussion of suggested practical modifications to, and simplifications of, ellipsometric memory, which is an interesting application of polarization devices for which there is a patent pending.

No abstract

A closed-form inversion expression for obtaining the optical constant (complex refractive index) of the substrate of an absorbing-film-absorbing-substrate system from one reflection ellipsometry measurement is derived. If, in addition, the film thickness is to be determined, a second measurement at another angle of incidence may or may not be used. The derived formula does not introduce errors itself, and tolerates errors in input variables very well. Random and systematic errors in the measured ellipsometric parameters do not affect the value obtained for the optical constant of the substrate: it is always the true value to two decimal places. Two examples in ellipsometry and in the design of reflection-type optical devices, one each, are presented and discussed. In addition, experimental results for a commercially available wafer are also presented. Two other closed-form inversion expressions for obtaining the optical constant of the substrate from two and three measurements are also presented and briefly discussed.