44 CHAPTER 2. EXPERIMENTAL METHODS25210 [deg]20180 [deg]1515010400800 [nm]12001600Figure 2.5: Spectroscopic Ψ <strong>and</strong> ∆ spectra, acquired at incidence <strong>of</strong> θ = 50 ◦ on a ≈ 6 nmfilm <strong>of</strong> gold supported on a nanopatterned LiF(110) substrate (fig. 2.10(b)).2.2.2 Spectroscopic Reflectometry <strong>and</strong> TransmittanceWe now briefly introduce the other optical methods employed in this thesis for the opticalcharacterizations, namely reflectivity <strong>and</strong> transmissivity. Compared to ellipsometry, spectroscopicreflectivity (SR) <strong>and</strong> transmissivity (ST) are much simpler techniques, requiringa less elaborated experimental apparatus <strong>and</strong> allowing a more direct interpretation <strong>of</strong>the data; however, these measurements are also more affected by systematic errors <strong>and</strong>provide less informations on the optical <strong>properties</strong> <strong>of</strong> the samples.I 0θI R100I 01.0I TTa.Intensity [a.u.]500.80.6TransmittanceI TI 0θb. c.0400800 [nm]120016000.4Figure 2.6: Panels a, b: sketches <strong>of</strong> reflectivity (a) <strong>and</strong> transmissivity (b) experiments,at incidence θ. Panel c: example <strong>of</strong> baseline (red curve) <strong>and</strong> transmitted intensity (blackcurve) at normal incidence, <strong>and</strong> the corresponding transmittance obtained from their ratio(blue curve). The light source was the Xe lamp <strong>of</strong> the M2000-U ellipsometer; the samplewas a ≈ 6 nm Au film deposited on a nanopatterned Lif(110) substrate (fig. 2.10(b)).The basic principle behind SR <strong>and</strong> ST experiments is quite straightforward. Theintensity <strong>of</strong> a light beam is measured, as a function <strong>of</strong> the wavelength or energy, before(I 0 , called baseline) <strong>and</strong> after the interaction with the sample under scrutiny; in case <strong>of</strong>SR, the intensity I R <strong>of</strong> the reflected beam is measured (fig. 2.6(a)), while in case <strong>of</strong> STthe intensity I T <strong>of</strong> the transmitted beam is acquired (fig. 2.6(b)). The ratios betweenthe intensities <strong>of</strong> the reflected or transmitted beam <strong>and</strong> the incident beam are called theabsolute reflectance R or transmittance T:
2.2. OPTICAL CHARACTERIZATION 45R(ω) = I R(ω)I 0 (ω) ,T(ω) = I T(ω)I 0 (ω)(2.2)An example <strong>of</strong> baseline <strong>and</strong> transmitted intensity, measured during a ST experiment, isreported in fig. 2.6(c), along with the computed transmittance T.In general, a rudimentary SR/ST setup would require a source <strong>of</strong> light, a sample holder<strong>and</strong>adetector. Inour case, theSR/ST measurements were performedemploying thesameM2000-U instrument used for spectroscopic ellipsometry, implying that the polarization<strong>of</strong> the light beam can be selected between s or p. First, the baseline I 0 is acquired bymeasuring the beam emitted by the lamp directly on the detector, then, after inserting thesample, the reflected or transmitted beam is acquired, <strong>and</strong> R or T is computed accordingto (2.2).SR/ST measurements present several advantages <strong>and</strong> disadvantages with respect tospectroscopic ellipsometry. SR/ST require the acquisition <strong>of</strong> plain constant intensities,in contrast to ellipsometry where Ψ <strong>and</strong> ∆ are computed from a time-dependent signalgenerated by the rotating element (polarizer, analyser or compensator); therefore, theexperimental apparatus is much simpler, <strong>and</strong> custom setups can be easily implemented(see fig. 2.3 for example). In addition, since the beam has a fixed s or p polarization, themeasured reflectance <strong>and</strong> transmittance are related to only one reflection or transmissioncoefficient 1 , thus it is possible to separately investigate the effects <strong>of</strong> the two states <strong>of</strong>polarization. In contrast, the individual measurements provide less informations thanellipsometry, because the phases <strong>of</strong> the EM fields is lost by acquiring the intensity <strong>of</strong> light.Moreover, the baseline <strong>and</strong> the reflected/transmitted beams are acquired separately atdifferent times, so the measurements are affected by the fluctuations in the lamp intensity,unlike in ellipsometry where the ratio ρ = r p /r s is directly measured, so no baseline isrequired.1.00.140.12R SR P0.0150.90.8R S0.100.080.0100.005RPT0.70.60.5T ST P400 800 1200 1600a. [nm]b.0.44008001200 [nm]1600Figure 2.7: Panel a: s- <strong>and</strong> p-polarized light reflectivity, at θ = 50 ◦ <strong>of</strong> incidence, measuredon a ≈ 6 nm Au film deposited on a nanopatterned Lif(110) substrate (fig. 2.10(b)).Panel b: s- <strong>and</strong> p-polarized light transmissivity measured on the same sample at normalincidence.Some examples <strong>of</strong> SR/ST spectra are reported in fig. 2.7, corresponding to the ellipsometricspectra in fig. 2.5. Each curve in fig. 2.7 represents a different measurement,in contrast to fig. 2.5 where Ψ <strong>and</strong> ∆ are acquired at the same time. We postpone theinterpretation <strong>of</strong> the data to the next chapters. Here we just notice that from the SR/ST1 I.e. R s,p = |r s,p| 2 <strong>and</strong> T s,p = |t s,p| 2 , where |...| 2 is the square magnitude <strong>of</strong> the complex value.