1. Introduction

Unlike conventional oxides which are deposited or grown with limited flexibility in the processing, silica sol-gel materials are synthesized using an acid or base catalyzed hydrolysis and condensation reaction [1,2]. The optical and mechanical properties of the final sol-gel layer are governed by the specific chemicals used as well as the temperature, pH and annealing conditions [3]. Additionally, as a result of the liquid synthesis method, it is possible to directly incorporate dopants into the sol-gel. Therefore, silica sol-gel materials have found numerous applications in integrated photonics. For example, by judicious selection of reactants, it is possible to tune the refractive index by over 40%, enabling the fabrication of silica-on-silicon waveguides for quantum computing applications [4]. By adding rare earth elements, such as Erbium and Ytterbium, low threshold microlasers have been demonstrated [5]. However, while it is straightforward to characterize the refractive index of a material using methods like ellipsometry, it is more challenging to characterize the more subtle thermal non-linear properties of these sol-gel materials. One approach is to fabricate a device from the material, and use the device as a sensor to probe its material properties [6]. Clearly, it is critical that the device is sufficiently sensitive. Because silica sol-gel materials have very low optical loss and negligible thermo-optic coefficients, this requirement is very challenging to satisfy.

Recently, an approach based on hybrid high quality (Q) factor whispering gallery mode microcavities was used to characterize the material loss and thermo-optic coefficient of polymer thin films [6]. High Q optical microcavities confine light of a specific wavelength, also known as the resonant wavelength of the cavity, which is governed by the cavity geometry and material [7]. Because the circulating optical field interacts with the entire material system, the resonant wavelength can be used to characterize the material properties and optical response.

In the present work, ultra-high-Q microcavities are conformally coated with high refractive index silica sol-gel materials synthesized using either tetraethyl orthosilicate (TEOS) or methyltriethoxysilane (MTES) (Fig. 1 ). Sol-gel synthesis represents a simple yet versatile method for tuning the optical properties of a deposited thin film suitable for use in waveguide applications [8]. In addition to characterizing the basic material properties of the films using Fourier Transform Infrared Spectroscopy (FTIR) and spectroscopic ellipsometry, the transmission loss of the sol-gel layer and the thermo-optic behavior of the material are determined using the optical resonant cavity and complementary Finite Element Method (FEM) simulations.

 

Fig. 1 (a) SEM image of silica microtoroid, (b) SEM image of TEOS sol-gel spin-coated on a silica microtoroid.

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2. Theory

2.1 Calculation of material loss

The quality factor (Q) of a resonant cavity is determined by both the intrinsic losses and the extrinsic losses of the cavity [7]. In silica hybrid cavities, the intrinsic loss is dominated by the material loss (Q_mat) while the extrinsic loss is dominated by the coupling loss (Q_coupl) [9]. The analytical form for Q_mat is Q_mat = 2πn_eff/λα_eff, where n_eff is the effective refractive index, λ is the wavelength, and α_eff is the effective material absorption. While Q_mat or the intrinsic Q of a given resonant cavity is constant, Q_coupl is dependent on the amount of power coupled into the cavity. Therefore, by judicious experimental design, it is possible to isolate this loss mechanism.

To determine the material loss of a cavity, this equation can be re-arranged:

2.2 Calculation of thermo-optic coefficient

The thermo-optic coefficient (dn/dT) of a material is the change in the refractive index per unit change in temperature. It is a result of the competition between a material’s polarizability and thermal expansion. In dielectric materials, the polarizability term is typically dominant, resulting in positive values of dn/dT [11]. In the context of an optical cavity, the dn/dT of the cavity material results in a change in the resonant frequency (Δλ) when the cavity is exposed to a change in temperature according to the following relation: Δλ/ΔT = (dn_eff/dT)(λ/n_eff), where Δλ/ΔT is an experimentally measured value and dn_eff/dT is the effective thermo-optic coefficient. To calculate the dn/dT of the material (dn_film/dT), dn_eff/dT is expanded [12]:

By combining this expression with the values for χ, γ, δ determined from the FEM simulations, it is possible to determine the dn/dT of the sol-gel film.

2.3 Finite element method modeling and results

In order to determine the material loss of the sol-gel thin film, the optical field distribution was modeled using COMSOL Multiphysics FEM. The field distribution was determined using the measured major (98-115μm) and minor (9-11μm) diameters of the toroidal cavities. The sol-gel film thickness and refractive index values were determined using spectroscopic ellipsometry and are in Table 1 . With the defined geometry and optical properties of the thin films, we were able to model the distribution of the optical field in our devices by controlling the azimuthal mode order (M) in the cavity. The mesh size used in the simulations was 0.021 μm². All constants, such as refractive index and film thickness, used in the simulations are either included in Table 1 or were taken from the COMSOL Library.

Table 1. Thermo-Optic Coefficient and Material Loss Measurements

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Representative simulations are shown in Fig. 2 for 633 nm wavelength. The optical field distribution was calculated by measuring the magnitude of the electric field squared in the toroid, the film, and the air; therefore the units of the optical intensity are V²/μm². The optical field distribution in the toroid, sol-gel film, and air was then found by dividing the optical field intensity of each section by the total optical field intensity in all three sections. From these simulations, the precise values for χ, γ, δ are determined.

 

Fig. 2 Finite element modeling of optical field distribution of 633 nm wavelength in microtoroid coated with (a) TEOS sol-gel (n = 1.454 at 633 nm), (b) MTES R = 0.1 sol-gel (n = 1.518 at 633 nm), and (c) MTES R = 0.3 sol-gel (n = 1.618 at 633 nm). The optical field distribution was determined by finding the magnitude of the electric field squared, thus the units of the scale bar are in V²/μm². As the refractive index of the sol-gel coating increased, the optical mode shifted to the coating, resulting in a higher percentage of the optical field being contained in the sol-gel film.

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Several important conclusions can be drawn from these simulations. The most immediately apparent is the shift in the location and shape of the optical field. As the refractive index of the film increases, the optical mode transitions from only slightly interacting with the film to being completely confined within the film. This provides one mechanism for increasing the mode confinement in and interaction with the film.

3. Material synthesis and characterization methods

Two distinctly different types of sol-gel composite thin films were synthesized. A titanium precursor, titanium butoxide (Ti(OBu)₄) (Aldrich, 97%), was added in order to increase the refractive index of the material. In the high refractive index composite sol-gel, methyltriethoxysilane (MTES) (Alfa Aesar, 98%) and Ti(OBu)₄ were used as precursors. In the second sol-gel, tetraethyl orthosilicate (TEOS) (Alfa Aesar, 99.999 + %) was used as the silica sol-gel precursor. Both sol-gel silica materials were prepared in an ethanol solvent and catalyzed by hydrochloric acid (HCl) (EMD, 36.5-38.0%). The sol-gels were prepared holding molar ratios between solvent, precursor, catalyst and water constant.

MTES R = 0.3 sol-gels held a constant molar ratio of 0.3:1 Ti(OBu)₄ to MTES precursor, in 16 moles anhydrous ethanol with 0.1 grams HCl. Similarly, MTES R = 0.1 sol-gels were prepared using a 0.1:1 molar ratio of Ti(OBu)₄ to MTES precursor in 16 moles ethanol and 0.10 grams HCl. Both MTES sol-gels were prepared without any added water to avoid forming a precipitate. The composite solutions were prepared by adding the MTES precursor to the solvent, then adding HCl to hydrolyze the MTES, stirring for 20 minutes, and finally adding the Ti(OBu)₄ to the pre-hydrolyzed silica precursor. The titanium precursor hydrolyzes much more rapidly, so in order to avoid an irreversible precipitate the silica precursor must be allowed to hydrolyze first. Adding Ti(OBu)₄ before adding the catalyst formed solid white precipitate. After mixing for 2 hours, the sol-gels were aged for 24 hours to allow propagation of polymer matrix.

TEOS sol-gels were prepared using 1:4:0.1:2 molar ratios between TEOS silica precursor, ethanol solvent, HCl catalyst, and deionized water. Similar to the MTES sol gel materials, the sol gel was prepared by adding the TEOS precursor to the solvent, followed by H₂O, then HCl to hydrolyze the TEOS, and stirring for 5 minutes between each addition. After mixing for 2 hours, the sol-gels were aged for 24 hours to allow propagation of polymer matrix. Synthesis procedures for both the TEOS and MTES-Ti(OBu)₄ sol-gels were performed at room temperature and atmospheric pressure in a chemical fumehood.

The method used for depositing and annealing the sol-gel thin films was the same for TEOS sol-gels, MTES R = 0.1, and MTES R = 0.3 sol-gels. After sol-gels were properly aged, the solutions were applied to the control wafers and the toroid devices by spin coating. The films were spun at 7000 rpm for 30 seconds to apply a homogeneous thin film. The remaining solvent was removed by heating on a hot plate at 75 degrees Celsius for 5 minutes. Then the deposited TEOS films, MTES R = 0.1 films, and MTES R = 0.3 films were annealed using a Lindberg/Blue M Tube Furnace from Thermo Scientific. All samples were heated from 25 °C at a constant ramp rate of 5 °C per minute up to 1000 °C and held at this temperature for 1 hour to remove any remaining organic components and complete densification through thermal sintering. After 1 hour of annealing at 1000 °C, samples were then cooled down to 25 °C at a ramp rate of −5 °C per minute. No further annealing or reflowing steps are used.

Several different methods were used to characterize the material properties. Scanning electron microscopy (SEM) was used to image the material surface for porosity. Colorimetric analysis was performed to determine the thermal expansion coefficient [13]. FTIR spectroscopy confirmed the removal of solvent and organic components, and spectroscopic ellipsometry was used to measure film thickness and refractive index of the material. The SEM images showed no evidence of porosity, although sub-nanometer pores are beyond the resolution of the SEM. The colorimetric analysis was performed over a temperature range from room temperature to 100 °C, and no color change was observed. Therefore, the assumption that the polarizability term in the dn/dT equation is dominant is valid for these materials. The FTIR spectroscopy and spectroscopic ellipsometry results are discussed in more detail in subsequent sections.

4. Device fabrication and characterization methods

By spin coating the TEOS and MTES sol-gels onto silica toroids, we can further characterize the material loss and thermo-optic coefficient of these unique materials. The silica toroids are fabricated as follows. First, 160 µm diameter circular silica pads are defined on silicon wafers using standard photolithography and BOE etching procedures. Next, XeF₂ is used to isotropically etch silicon underneath the silica pads, forming elevated silica microdisks. Finally, the silica microdisks are reflowed using a CO₂ laser to form ultra-high Q toroids [14]. A uniform coating of sol-gel is subsequently applied to the finished toroids by spin coating at 7000rpm and annealed, as described in the previous section.

As mentioned, the material loss α_eff and thermo-optic coefficient dn/dT of the TEOS and MTES coatings can be determined by experimentally measuring the intrinsic quality factor and the Δλ/ΔT values of the coated toroids. All measurements were performed on multiple toroidal devices. Additionally, it is important to note that all measurements were taken in an ambient environment.

To determine the material loss of the sol-gel coated toroids, it is necessary to measure the quality factor of the devices. In the present series of experiments, the linewidth measurement method is chosen. In this approach, the linewidth (Δλ) of the cavity is measured by scanning a tunable laser across a series of wavelengths until a resonant wavelength is identified. The quality factor can then be calculated from the simple expression Q = λ/Δλ. However, to determine the intrinsic quality factor, it is necessary to isolate and remove the coupling losses from the measurement. When using tapered fiber waveguides, this process is straightforward, and requires performing the linewidth measurement under a range of coupling conditions. This is accomplished by tuning the gap between the toroid and the tapered fiber. If there are only two loss mechanisms (Q_mat and Q_coupl), the quality factor will vary linearly with the percentage of power coupled into the device, allowing a linear fit to be applied to the Q versus coupling data. The quality factor at zero percent coupling is the intrinsic Q and is used to calculate the material loss.

To measure the linewidth of the sol gel coated toroid, a nanopositioning stage and top/side view microscope cameras were used to align the sol-gel coated toroid with a tapered optical fiber (Fig. 3 ). The tapered optical fiber evanescently couples light from a tunable 633nm or 1300nm laser (New Focus) into the sol-gel coated toroid samples with high efficiency and low loss [15]. Transmission data from the tapered optical fiber is recorded in real-time on a computer for analysis. The linewidth is then determined from a Lorentzian fit to the spectra. The error in a given material loss measurement is proportional to the error in the related quality factor measurement and is approximately ± 0.01m⁻¹. However, the overall error of the measurement method is larger, as it includes the error due to variations between the Q factors of the different devices.

 

Fig. 3 The characterization set-up. a) A schematic of the optical device characterization set-up. A tunable laser (Laser input) is used to couple light into the cavity using a tapered fiber, and the output light is detected on a photodetector (PD). The initial alignment is imaged with a machine vision system. The signal is recorded using a high speed oscilloscope/digitizer (PCI card). The laser is controlled using a function generator (FG) and a GPIB PCI card. b) An optical image of the toroid coupled to a tapered optical fiber.

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To determine the thermo-optic coefficient, it is necessary to measure the value of Δλ/ΔT experimentally. This is done by recording the change in resonant wavelength with temperature. Using a custom-built temperature control stage which included a heater and thermo-couple (Omega), the resonant wavelength λ₀ was recorded at constant coupling as the coated samples were incrementally heated from approximately 20 to 60°C in ~1°C steps [16]. All of these measurements were performed in the under-coupled regime at low input powers to eliminate additional contributions from thermal non-linear effects inherent to high-Q cavities, such as thermal bistability.

5. Experimental results

5.1 Material characterization

Thin film characterization was performed using a Bruker Optik ALPHA-P FTIR spectrometer in combination in order to confirm the removal of solvent and additional organic groups (Fig. 4 ). The Bruker Opik ALPHA-P measurement module uses attenuated total reflection (ATR) to measure the absorption intensity spectra. The ALPHA-P module uses an anvil to place sufficient pressure on the sample in order to make contact with the ATR diamond used for reflectance measurements. At each reflectance point of the ATR diamond, the sample, in contact with the diamond, absorbs IR light according to its signature chemical bond vibrations. The IR light absorbed by the sample is then missing in the reflected beam. The reflected beam changes in intensity depending on the wavenumber, allowing us to record an absorption spectrum for the sample. The absorption intensity spectra are then compared to literature values to determine the identity of the chemical bonds in the thin film.

 

Fig. 4 FTIR spectroscopy comparison of thermally grown silicon oxide, TEOS sol-gel thin films, MTES R = 0.1, and MTES R = 0.3. The arrow on the graph highlights the peak at 905 cm⁻¹ that confirms to the presence of Si-O-Ti bond vibrations.

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All thermal silicon dioxide films show strong characteristic peaks between 1110 and 1080 cm⁻¹. Additionally, we were able to identify peaks characteristic of the Si-O-Ti vibrational mode. The Si-O-Ti characteristic peak occurs around 905 cm⁻¹ and is seen in the composite films prepared with the Ti(OBu)₄ precursor [8]. After annealing at higher temperatures, it was seen in our composite films (Fig. 4, arrow). This peak is indicative that titania is coordinating with four oxygen atoms, forming TiO₄ [17].

Additionally, the sol-gel films identified broad peaks near 1130 cm⁻¹ corresponding to Si-O-Si siloxanes bonds [18]. As siloxane bonds increase throughout the polymer network, it is common to see these peaks broaden and become more complex. This may be due to two or more overlapping bands in this range. A broader, weaker band around 810-800 cm⁻¹ corresponds to absorption by amorphous silica, rather than the α-Quartz crystalline form of SiO₂, which would have been indicated by a sharp doublet at 800 cm⁻¹ and 780 cm⁻¹. As expected, the TEOS thin films were absent of peaks around 905 cm⁻¹ due to the lack of the titania precursor. Peaks in the range of 1030 cm⁻¹ and 1160 cm⁻¹ were indicative of silica bond vibrations. Similarly, thermally grown oxide contained peaks very similar to that of the TEOS silica thin films except for a specific peak occurring around 460 cm⁻¹. This peak is attributed to the rocking motion of the bridging oxygen atom perpendicular to the Si-O-Si plane commonly seen as a result of silica gel preparation [19]. As sol-gel films are heat treated at temperatures as high as 1000 °C the peak at 460 cm⁻¹ gradually shifts up in frequency, suggesting a strengthening of the silicate network due to densification of the porous thin film [18].

Spectroscopic ellipsometry was performed to measure the thickness of the deposited thin film, in addition to determining the refractive index of the material. Using a V-VASE (J.A. Woollam Co.) variable wavelength and angle of incidence ellipsometer, psi and delta measurements were gathered for three angles of incidence (64°, 69°, and 74°) scanning from 550 nm to 1350 nm. The measured values, psi (ψ) and delta (Δ), are related to the ratio of the Fresnel reflection coefficients R_p and R_s for p- and s- polarized light respectively. The Fresnel reflection relationship is related to psi and delta by:

The psi and delta parameters were fit using regression analysis by WVASE32 Ellipsometry Analysis Software to determine layer thickness and refractive index. The measured experimental data acquired from the V-VASE Ellipsometer is first compared with a generated model. The model can be adjusted to minimize the difference between the generated data and measured data through series of iterations. The WVASE32 software fits the thickness and refractive index by defining a quantity called the maximum likelihood estimator, which represents the quality of the match between the data calculated from the model and the experimental data. WVASE32 determines the maximum likelihood estimator by the method of Mean-Squared Error (MSE), which reduces the fitting problem to finding a set of values for the variable model parameters and which gives a single unique minimum of the MSE corresponding to a single set of variable parameters. The MSE was minimized using the Levenberg-Marquardt algorithm to evaluate the desired parameters, thickness and refractive index. A representative measurement of the psi and delta parameters is shown in Fig. 5 , and the determined values of thickness and refractive index are in Table 1. Because the same synthesis, spin-coating and annealing conditions were used, the film thickness is nearly constant across the different sol-gel materials.

 

Fig. 5 Spectroscopic ellipsometry measurements for MTES R = 0.3 thin films. (a) Ψ with WVASE32 parameter fitting, and (b) Δ with WVASE32 parameter fitting.

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5.2 Quality factor and material loss

The quality factor of all three materials was determined at 633nm and at 1300nm to study the dependence of the material loss on wavelength. Example spectra are shown in Fig. 6 and the material loss values are summarized in Table 1. As can be observed in Fig. 6, there is no lineshape distortion because low input powers were used [12]. However, occasionally, linewidth splitting occurred (Fig. 6a). This behavior is commonly observed in ultra-high-Q cavities and is the result of coupling into the clockwise and counterclockwise modes of the cavity simultaneously.

 

Fig. 6 Representative transmission spectra of toroids coated with a) TEOS, b) MTES R = 0.1. and c) MTES R = 0.3 films. By fitting a Lorentzian curve to the spectra, the quality factor can be measured. The presence of titanium in the coating increases the film’s material loss, therefore reducing the quality factor of the coated toroids from over 10⁷ (TEOS film) to 10⁵ (0.3 MTES film).

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The TEOS films have significantly lower material loss than the titanium butoxide MTES films. Additionally, the loss of the TEOS films was nearly identical at both wavelengths studied, whereas the loss of the MTES films was strongly dependent on the wavelength and the concentration of titanium butoxide. This dependence is the result of the strong absorption of titanium butoxide [17].

5.3 Thermo-optic coefficient

Representative results from the series of thermo-optic characterization measurements are shown in Fig. 7 . As detailed previously, the change in refractive index (Δn) is directly related to Δλ. Over the entire temperature range, the change in refractive index (dλ/dT or dn_eff/dT) is extremely linear, indicating that there are no additional material or optical effects present, such as solvent evaporation or electro-optic effects. Using these results, the calculated thermo-optic coefficients of the three different material systems are summarized in Table 1.

 

Fig. 7 Representative Δλ versus ΔT data for toroids coated with a) TEOS, b) MTES R = 0.1, and c) MTES R = 0.3 films.

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As is clearly observable in Table 1, the three sol-gel materials have distinctly different thermo-optic coefficients. This result is somewhat surprising given the extremely similar responses observed in Fig. 7. Namely, the dn/dT of TEOS is twice that of both MTES R = 0.1 and MTES R = 0.3 films. However, as expressed by Eq. (4), the total shift (dλ/dT) is related to the dn/dT of the film (dn_film/dT) times the amount of the optical field located in the film. As observed in the FEM simulations in Fig. 2, the optical field confinement in the film increases with increasing refractive index. Therefore, a decrease in the dn_film/dT can be compensated by an increasing optical field overlap.

6. Conclusion

Silica sol-gel thin films spun-coat on silicon were synthesized and characterized using FTIR and spectroscopic ellipsometry. The presence of titanium in the sol-gel films changed the FTIR spectra and substantially increased the refractive index. Subsequently, the films were deposited on high Q optical resonant cavities, and the material loss and thermo-optic coefficient of the silica sol-gel glasses were determined. The material loss of the film increased with refractive index and the thermo-optic coefficient decreased with refractive index. However, because the optical field overlap increased with refractive index, the resonant wavelength dependence on temperature (Δλ/ΔT) was nearly constant. Recent applications of sol-gel materials in thermo-optic switches have increased interest in integrating these materials with photonic devices to improve the stability of optical switches and filters as well as aid in the development of tunable optical delay lines [22,23].