Photometric methods for determining the optical constants and the thicknesses of thin absorbing films: selection of a combination of photometric quantities on the basis of error analysis

Abstract

We select the best combinations of spectrophotometric quantities for the most accurate determination of the optical constants, n (refractive index), k (absorption coefficient), and the thicknesses of thin absorbing films. The basic comparative criteria used are the maximum absolute errors in the determination of n, k, and d that result from experimental errors in photometric measurements and in the optical constants of the substrates. We studied all possible combinations of photometric quantities T, T(s)(theta), T(p)(theta), R, R(s)(theta), R(p)(theta), R(m), R(ms)(theta), and R(mp)(theta) at 0 degrees < theta < or = 70 degrees, where T denotes transmission; R, reflection; the subscripts s and p, s- and p-polarized light; m, reflection from a thin film coated upon an opaque substrate; and superscript theta, the angle of incidence of light. The absence of the subscripts s and p implies nonpolarized light; that of the subscript m, a nonabsorbing substrate; and that of superscript theta, normally incident light. The error analysis that is made admits the following conclusions: (1) The best double combinations are (TR), (TR(m)), (TR(p)(70)), and (TR(mp)(70)); (2) the best triple combinations are (TRR(m)), (TRR(p)(70)), (TRR(mp)(70)), (TR(m)R(p)(70)), and (TR(m)R(mp)(70)); (3) the methods indicated above, suitably combined, are quite sufficient to provide the maximum accuracy and reliability of n, k, and d for all practical situations; (4) TRR methods based on measurements with obliquely polarized light are more suitable for thin films with n < 1, such as some metal films; (5) the regions of n, k, and d/lambda with the highest and the lowest accuracies do not overlap in either the TR or the TRR methods. Hence more combinations, preferably all, should be applied for the most accurate determination of n, k (and d), and the errors should be evaluated as a criterion for the best combination.

Thin Chalcogenide Films for Photonic Applications

“…We have demonstrated that the spectrophotometric and ellipsomeric methods offer a good accuracy for determination of the optical parameters of thin chalcogenide films from /30 to 2 ( is working wavelength) (Konstantinov et al 1998, Babeva et al 2001, Todorov et al 2010a. Results on the reflectance response of photonic crystals from chalcogenide glass/polymer (DeCorby et al, 2005;Kohoutek et al, 2007a) or chalcogenide glass/chalcogenide glass, e.g.…”

“…8. The Swanepoel's method (Swanepoel, 1983) was used for optical constants determination of the thin films with d > 300 nm and a combination of double (T, R) and triple (T, R, R) methods was applied in calculations for thinner layers (d < 300 nm) (Konstantinov et al, 1998;Babeva et al 2001). The calculated values for optical parameters of thin films show that their refractive index is independent on the layer's thickness for d > 50 -70 nm (Fig.…”

Optical methods for microstructure determination of doped samples

“…Such treated samples show a "layer-like" structure [17]. Then an averaging method [18,19] to analyse effective optical properties of modified materials can be justified. Such method allows for characterisation of the bulk and the surface when the samples are not too thick and absorbing.…”

Ellipsometric studies on rough Zn and Cd polycrystalline samples

“…These include the principal angle of incidence / principal azimuthal angle method [1,2], reflectance of plane polarized light at non-normal incidence [3] pseudo-polarizing angle method [4] and ellipsometric measurements [5,6]. Other techniques include interferometric, reflectance, photometric and other methods [7][8][9].…”