Azimuthal alignments in ellipsometry: a high-precision method using a polarization modulator

Abstract

An original (to the best of our knowledge) method to achieve azimuthal alignments of all polarizing components in ellipsometry is presented. It is an accurate nulling method, and it is easy to implement and can be used with any isotropic reflecting layer. It also allows one to check the eventual presence of surface anisotropy. The ferrofluid modulator used in this setup is briefly described. Measurements made for three reflecting surfaces (fused silica, silicon, and germanium) are presented.

Magnetic properties and magneto-birefringence of magnetic fluids

“…Birefringence. The birefringence measurements, performed by using the null ellipsometry principle [20], are taken over from paper [21]. The samples analyzed were DOS-based samples 6 and 9.…”

10.1007/s10786-008-2020-6

“…Expanding cosδ i and sinδ i (i = 1, 2) into series in Bessel functions as (10) (11) and substituting these expressions into Eq. (9), we can represent the measured signal intensity I(t) as a sum of the constant and variable components.…”

“…In the case where the phase shift δ in modulator M 1 varies with time according to the harmonic law (8), let us expand (similar to the case of two modulators considered above) cosδ i and sinδ i (i = 1, 2) into series using formulas (10) and (11) and set the modulation index δ 0 = 2.404 rad. Restricting the expansion to the principal terms, we obtain the following expression for the intensity (in I 0 units):…”

“…M [1] M [2] M [3] M [4] M [5] M [6] M [7] M [8] M [9] M [10] M [11] M [12] a constant factor). It should be noted that, owing to the small capacitance of modulators (<25 pF) and low frequency of the control signals, the output transformers operate virtually in an idle mode.…”

“…Polarimeters (ellipsometers) intended for the measurement of elements of the Mueller matrix employ polarization modulators (converters) representing combinations of phase plates (quarter-or half-wave plates) [2,3] or phase modulators (e.g., electro-optical modulators [4][5][6], including those based on liquid crystals [7] and elasto-optical [8][9][10] and magneto-optical [11] media). It is expedient to perform spectropolarimetric measurements using phase modulators, which allow exact adjustment of the phase shift (phase modulation depth) at every wavelength and exhibit a higher operation speed compared to that of the polarization converters based on rotary phase plates.…”