Evanescent-Wave Cavity Ring-Down Ellipsometry - American

LETTER pubs.acs.org/JPCL

Evanescent-Wave Cavity Ring-Down Ellipsometry Michael A. Everest,†,‡ Vassilis M. Papadakis,† Katerina Stamataki,†,§ Stelios Tzortzakis,† Benoit Loppinet,† and T. Peter Rakitzis*,†,|| †

Institute of Electronic Structure and Laser, Foundation for Research and Technology-Hellas, 71110 Heraklion-Crete, Greece Department of Chemistry, George Fox University, Newberg, Oregon 97132, United States § Department of Chemistry and Department of Physics, University of Crete, 71003 Heraklion-Crete, Greece )

‡

ABSTRACT: We introduce the new technique of evanescent-wave cavity ring-down ellipsometry (EW-CRDE), used for the measurement of ellipsometric angles of samples at a solid
gas or solid
liquid interface, and achieve phase-shift measurements with precision of ∼0.01°. We demonstrate the technique by measuring the time-dependent refractive index of methanol
water mixtures and thin films at the liquid/fused-silica interface, showing that the monitoring of monolayers on microsecond time scales using EW-CRDE should be achievable. SECTION: Kinetics, Spectroscopy

E

vanescent wave (EW) spectroscopies are commonly used for probing properties near and at interfaces.1 Through total internal reflection (TIR), an optical probe with spatial dimensions on the order of the wavelength of light is simply produced. EW or TIR variants have been adapted to FTIR, UV
vis, Raman, and other spectroscopies as well as cavity ring-down (CRD)2 and ellipsometry.3 Cavity ring-down spectroscopy (CRDS) measures absorbance based on the lifetime of a pulsed beam in a (Fabry
Perot) optical cavity, and EW-CRDS allows the extension of the technique to liquid
solid or gas
solid interfaces; both are now well-established techniques.4
12 CRDS techniques are immune to fluctuations in the light-source intensity, and because of the long path lengths involved, CRDS is one of the most sensitive techniques available for absorption measurements. Under TIR conditions, reflection coefficients are very close to unity for all polarizations. However, the reflection introduces an s
p phase-shift between the out-of-plane s and the in-plane p polarization states. EW-ellipsometry measures this phase shift, which relates to the refractive index profile perpendicular to the reflecting surface. The technique is able to probe nonabsorbing (dielectric) interfaces and thin films. Recently, Karaiskou et al. have introduced cavity ring-down ellipsometry (CRDE),13 which is a form of polarization-dependent CRDS,14
17 in which the s
p phase shift, in addition to the absorption, is measured. This is accomplished by injecting simultaneously both s- and p-polarized light into the cavity and placing an analyzing polarizer before the detector. In this configuration, the experimental signal is an exponentially decaying sinusoidal signal in which the decay time is the result of cavity losses and the frequency of the oscillation is proportional to the s
p phase shift. r 2011 American Chemical Society

Karaiskou et al. used a four-mirror cavity geometry in which the entire cavity was contained within a vacuum chamber, and they detected the adsorption of approximately a monolayer of gas-phase fenchone onto the surface of the mirrors, determined by the large change in the s
p phase shift. Although very effective for certain applications (such as measuring the adsorption of gases or the study of thin films), this technique is limited to lowloss samples that do not degrade significantly the high reflectivity of the mirrors In this Article, we demonstrate EW-CRDE using a two-mirror cavity that encloses a prism within which the beam undergoes total-internal reflection (as in EW-CRDS) but with input and output polarizers used as in ellipsometry. EW-CRDE thus combines the advantages of EW-CRDS and ellipsometry and provides phase-shift measurements at the interface of the totally internally reflecting surfaces with sensitivity comparable to that of standard ellipsometric techniques; the main advantage of EW-CRDE is the potential of microsecond time resolution, which is orders of magnitude faster than commercial ellipsometers. A schematic for the experimental set up is shown in Figure 1. The cavity plane is arranged vertically, and the totally internally reflecting surface is horizontal in the laboratory to facilitate handling of liquids. The input polarization and detection polarization directions are both set to 45° (with equal projections on the s and p axes). The 740 nm laser pulses were generated from an excimerpumped dye laser (Lambda Physik LPX300 and LPD3000), operating at 10 Hz, with pulse widths of ∼30 ns. The entrance Received: April 15, 2011 Accepted: May 12, 2011 Published: May 17, 2011 1324

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The Journal of Physical Chemistry Letters

LETTER

Figure 1. EW-CRDE experimental apparatus.

Figure 3. Series of measurements made in succession of water on fused silica to show stability and noise.

angle as pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi nsample ¼ sin θ 1
tan2 ðΔ=2Þ tan2 θ nprism

Figure 2. Typical experimental EW-CRDE traces for samples of (a) air and (b) water, showing large changes in the beat frequency, ω, and s
p phase shift, Δ.

and exit surfaces of the prism were antireflection-coated for light between ∼740 and 850 nm at normal incidence, with reflection losses 0.9997 and f = 1 m between 761 and 867 nm. The cavity length was 1.6 m, with the prism placed symmetrically in the center. Typical ring-down traces are shown in Figure 2. For samples of (a) air and (b) water, from which one can see both the exponential envelope of the signal, and the polarization beating frequency, described by an equation of the form IðtÞ ¼ I 0 e
t=τ ½cos2 ðωt=2 þ jÞ þ B

ð1Þ

where τ is the ring-down time and ω is the polarization beat frequency. (Note that eq 1 is a special case of eq 3 from Karaiskou et al., for τs = τp = τ, Rs = Rp, and θi = θo = 45°.) The constant B is added to account for experimental imperfections that reduce the modulation depth of the polarization beating, and j accounts for the phase of the polarization beating with respect to the input laser pulse. For our geometrical arrangement, the beat frequency ω ¼ cΔ=d

ð2Þ

where d is the cavity length, Δ is the s
p phase shift caused by a single reflection in the prism, and c is the speed of light. It is possible to determine τ and ω for each laser shot using a fast fitting procedure based on the Fourier transform of the signal (ref 18 and unpublished results). The large differences in ω for air and water (due to the large differences in refractive index and thus Δ) are immediately apparent upon inspection of the traces in Figure 2. Assuming a simple refractive index step profile (Fresnel interface), the s
p phase shift Δ is directly related to the refractive index ratio between the two media and the incidence

ð3Þ

where θ is the incidence angle of the laser beam with the surface. Figure 3 shows a series of measurements acquired in immediate succession of a water drop on fused silica. Each displayed point is the result of fitting the time-domain average of 10 laser shots. There is a slight downward drift in the data in Figure 3 of ∼4 kHz/s. This small drift is possibly owing to thermal drift or evaporative cooling because no effort was taken to control the temperature. After the linear drift is removed from the data, the standard deviation of 100 points in Figure 3 is 24.86 kHz, which corresponds to 0.01° per pass. We believe that the major source of this random error is due to the large shot-to-shot fluctuations in the beam shape of the laser beam, which causes fluctuations in the mode-excitation of the cavity, and can thus be significantly improved with the use of a laser with a more stable shot-to-shot beam profile. We further demonstrate the use of EW-CRDE by measuring the time-dependent refractive indices of water/methanol mixtures at the interface of a fused silica prism. Measurements were performed on 11 mixtures with water molar fraction x ranging from 0 to 100% (measured every 10%) from drops that were placed on the prism in open air. The time dependence of the beat frequency for these mixtures is shown in Figure 4a. The timedomain signals of 10 laser shots were averaged before fitting to obtain the beat frequency. The beat frequency ω shows marked differences depending on x: for samples with x = 0
50%, ω decreases monotonically with time; for those with x = 70
90%, ω increases with time; for those with 50
60%, ω first decreases then increases, whereas for the 100% water sample, ω remains constant. The change of beat-frequency is related to the change of the refractive index of the samples. Such changes can be caused by two coupled effects: the preferential evaporation of methanol, which changes the composition x, and the change of temperature induced by the evaporative cooling. For pure methanol, dn/dT is about
0.4  10
3 K
1,19 so that an increase in refractive index of ∼10
2 corresponds to a temperature change of 25 K. The other relevant coefficient dn/dx is not constant because it is positive at low x and becomes negative at larger x. (See Figure 4b.) Quantitatively modeling this complex process,20 which includes mass and thermal diffusion, is beyond the scope of the current work. Nonetheless, we believe that the combination of temperature and 1325

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Figure 5. (a) Beating frequency ω of methanol/water mixtures as they are added and removed. (b) Expanding the y axis from (a) about the baseline. (See the text.)

Figure 4. (a) Time evolution of several methanol/water mixtures on fused silica. The indicated initial concentration is the mole fraction of water. The curves are placed on the same graph only for comparison and were not acquired in the order or at the exact times indicated. (b) Measurement of beating frequency and refractive indices of methanol/water mixtures using EW-CRDS (points) and calibrated literature values (line, see the text). EW-CRDS measurements are determined from the first data points of each mixture from Figure 4a. Error bars are 95% confidence intervals for three measurements at each point.

concentration changes described above capture the major features of the data in Figure 4a. The first time point for each mixture shown from Figure 4a is plotted in Figure 4b. The relationship between ω and nsample is deduced from eqs 2 and 3 and used to relate the two ordinate axes in Figure 4b; in the narrow range plotted, the relationship between ω and nsample is almost linear. The measurements of EW-CRDE are shown with points and 95% confidence intervals for three repeated measurements of each solution. We compare these measurements to an independent determination of the refractive indices of the mixtures using literature values (solid line in Figure 4b); the agreement with the characteristic curve of the change of refractive index with mixture concentration shows that relative (not absolute) changes in refractive index can be measured. To determine the expected beat frequency of the EW-CRDE signals for each solution sample, we used the experimental frequencies of air/prism (86.134 MHz) and water/prism (28.667 MHz) interfaces along with the literature values of the refractive indices of air (1.0003) and water (1.32933) at 740 nm,21 along with eqs 2 and 3 to determine the effective angle of incidence and effective prism refractive index. These were determined to be 70.442° and 1.4469, which are close to the nominal values of 70° and 1.45445. With the angle of incidence and the refractive index of the prism determined, these values were held fixed, and the effective index of refraction for methanol was adjusted to fit the data. The refractive indices of the mixtures at 740 nm were determined after Herraez and Belda.22 The resultant value for the refractive index of methanol used to

calculate the line in Figure 4b is 1.3254, which is higher (by ∼7σ) than the literature value of 1.3178.19 The discrepancy between the literature and best-fit effective values for the refractive index of methanol could be due to several factors, including contamination of the liquids, the cleanliness of the surface, uncertainties in the geometry of the cavity, birefringence in the prism, and the rapid time evolution of the frequency for these samples described above. Absolute measurements of refractive index will require all of the parameters mentioned to be controlled or calibrated. The pooled standard deviation of all 33 experiments in Figure 4b is 0.133 MHz. This corresponds to an error in the s
p phase shift of 0.1° per pass, which is ∼10 times larger than the error shown in Figure 3. This precision reflects the reproducibility of the measurement when the sample is removed, and a new sample is replaced for each experiment. The reproducibility is much improved if subsequent experiments are performed without removing the sample. We further study the evaporation of trace amounts left after the water/methanol samples are wiped-off the prism. In Figure 5a, we show the time-dependent beat frequency as water/methanol samples are added and wiped-off from the prism. In Figure 5b, we expand the y axis about the baseline by a factor of ∼100 and see that the value of ω does not recover exactly to the original baseline value but is ∼100 kHz smaller. This shift is consistent with thin films of sample that are no larger than a few monolayers (or else the baseline shift would be larger). In the substrate/film/ambient configuration, the phase angle variation is primarily related to the change of optical thickness (product of nsample with film thickness). In the present experiments, the change should originate mostly from the thickness change due to sample evaporation (although the effect of dn/dT may also be significant). Numerical simulation assuming a simple uniform film with refractive index of 1.33 leads to a phase shift variation of 0.04°/nm. The measured phase variations of ∼0.02° are therefore attributed to thickness variations of ∼0.5 nm, which is on the order of the molecular size of the solvents. Although noisy, similar trends in the time dependence of ω can be seen as that for the bulk samples (Figure 4a), indicating that the dynamics of processes involving monolayers (such as thin-film evaporation) can be monitored if the sensitivity is improved. One way that the sensitivity of EW-ellipsometry can be increased is by using a layered structure at the interface.23,24 Indeed, such high sensitivity was achieved in Karaiskou et al. through the use of high-reflectivity multilayered mirrors. EW-CRDE 1326

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The Journal of Physical Chemistry Letters combines the sensitivity and ease of EW-ellipsometry with the fast and precise detection of CRD. EW-CRDE permits the measurement of the s
p phase shift in a single laser shot, and the precision mentioned above can be attainable continuously (over ∼1 s) using miniaturized cavities with submicrosecond ring-down times and using commercially available fast-repetition rate (e.g., MHz) laser sources and oscilloscopes.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT We thank the EU for partial support through the European Research Council grant TRICEPS (GA no. 207542), the Marie Curie Excellence Grant MULTIRAD MEXT-CT-2006-042683, the Marie Curie ITN Programme ICONIC (grant no. PITN-GA2009-238671) and the FP7 IAPP Programme SOFORT (PIAPGA-2009-251598). We also thank SopraLab for kindly supplying their ellipsometry software package.

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