## Abstract

We fabricated waveguide resonators with high thermal stability using tantalum pentoxide thin film covered with PECVD silicon dioxide cladding. Without complex athermal design, low temperature dependence of 7.4 pm/°C and 8.15 pm/°C were measured in waveguide Bragg gratings (WBG) and Fabry-Perot resonator sandwiched by a pair of identical WBG mirrors, respectively. Suggested by semi-analytical perturbation calculations, the athermal properties of tantalum pentoxide waveguide grating are attributed not only to the low thermo-optical coefficient in tantalum pentoxide thin film but also to the strong chromatic dispersion of the guided modes. Guidelines are proposed to design waveguide-based frequency devices of low thermo-optical effect without complex athermal design.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

Waveguide resonators are important devices for integrated optics and silicon photonics. Their sensitive spectral response to the environments makes waveguide resonators applicable to sensor devices for detections of refractive indices [1,2], temperatures [3] and strains [4] the shifts in resonant wavelength. Such high sensitivity to environments also enables simultaneous retrieval of many environmental parameters such as temperature and refractive index [5] or temperature and strain [6]. However, such high sensitivity turns out to be a major drawback as spectral selective devices or optical filters embedded in communication systems for example arrayed waveguide grating (AWG) for wavelength division multiplexing (WDM). In particular, silicon or silica waveguides suffer from large thermo-optical effect so that standard AWG can only achieve temperature sensitivity as low as tens of pm/°C without athermal designs [7]. For even lower temperature sensitivity, complicated resonator structures were proposed that can improve the temperature dependence down to 1 pm/°C at the expanse of not being compatible to silicon photonics fabrication routes [1]. The idea of athermal design originated from compensated temperature diode laser using externally coupled cavity with negative thermo-optical effect [8]. This concept has been adopted to waveguide devices by using polymer (MMA) cladding with negative thermo-optical coefficient so the effective refractive index of guiding mode is insensitive to temperature dependence [9]. Several reports on athermal waveguide design using cladding material with negative thermo-optical coefficient have been proposed [10] and is also applied to optical add-drop multiplexers down to within 1 pm/°C for TM polarized mode at C band [11]; yet the athermal property holds only for a specific temperature range [12]. Recently high quality waveguide devices based on a large band gap (~5 eV.) material, Tantalum Pentoxide (Ta_{2}O_{5}) which has very low linear and nonlinear absorption in visible to infrared wavelength are reported [13]. By virtue of large band gap, Ta_{2}O_{5} is free from free carrier absorption and two photon absorptions in near infrared wavelengths which are widely utilized in optical communications. Its large nonlinear coefficient (10^{−14} W/cm^{2}), high refractive index (2.08 at 1550 nm) and CMOS-compatible property make Ta_{2}O_{5} a promising material for developing integrated optoelectronic devices [13]. Moreover the thermo-optical effect of Ta_{2}O_{5} is 2.3 $\times $ 10^{−6} K^{−1} [14], which is an order of magnitude smaller than that of silica (1.3 $\times $ 10^{−5} K^{−1} [15]) and is almost two order of magnitude smaller than that of silicon (1.8 $\times $ 10^{−4}K^{−1} [15]). Without a doubt, Ta_{2}O_{5} should be better core material for fabricating athermal integrated optical devices. In this work, we report the fabrication and characterization of athermal Ta_{2}O_{5} waveguide Bragg grating (WBG) resonator for silicon photonics. In addition, guidelines based on semi-analytical approaches are proposed to design the waveguide-based device of low thermo-optical effects. We believe the athermal Ta_{2}O_{5} WBG resonator should be of significant contribution in extending the frequency selection functionality for silicon photonics.

## 2. Device design and fabrication

Schematic of the WBG is shown in Fig. 1(a). The WBG fabrication follows the routes described below. First a 400 nm-thick Ta_{2}O_{5} thin film was sputtered on 3 μm-thick thermal oxide grown over silicon substrate using home-made radio-frequency magnetron sputter equipped with a 2-inch magnetron gun. In the sputtering process, the RF power level was 100 W and mixture of Ar and O_{2} gases at a composition of 4:1 was given at 2 mtorr. On the thin film, a 200 μm-long distributed Bragg reflector (DBR) mirror made of surface corrugated gratings was fabricated using e-beam lithography with Inspect F50 thermal field emission scanning electron microscope system. The acceleration voltage and dose of e-beam for photoresist patterning were 30 keV and 20 μC cm^{−2}, respectively. The period of the gratings was designed to be 470 nm with 50% duty cycle and the surface corrugation is 30 nm and 20 nm in depth for the DBR mirror and Fabry-Perot (FP) resonator. It was then dry etched in CHF_{3} plasma at 80W and 2 mtorr using the Oxford Plasmalab 80 + RIE etcher. After the grating is defined, waveguide core of 700 nm in width is patterned also by e-beam lithography route. Finally, the Ta_{2}O_{5} core was covered with commercially available organic spin on glass (SOG) or PECVD oxide as cladding. The PECVD oxide claddings were prepared by Oxford Plasmalab 100 PECVD system at 13.56 MHz and 1.2 torr with a substrate temperature of 350 °C and an RF power of 250 W.

In Fig. 1(b), the top view of scanning electron microscopy (SEM) image covers the WBG region and straight waveguide regions. Details of the fabricated WBG and waveguides are shown in Fig. 1(c) and Fig. 1(d), respectively to reveal the periodic corrugation of the WBG and good quality of the sidewalls of the waveguide. The period of the fabricated WBG is determined to be 473 nm at 45% duty cycle, which slightly deviates from the designed values. Taking an SEM image from the polished end surface of the fabricated sample, the core region of the waveguide has a trapezoidal cross section with a base angle of 85°.

To get the knowledge of the optical property of the fabricated WBG device, we calculate the transverse electric (TE) polarized mode and their corresponding effective index by solving eigenvalue equation for the guided modes without gratings. At the wavelength of 1533.6 nm, which matches the WBG resonance condition to be revealed later, the intensity profile of fundamental mode of the trapezoidal waveguide in TE polarization is shown in Fig. 2(a). The waveguide core shown in Fig. 2(a) is 700 nm in base width and 400 nm in thickness and cladding is PECVD oxide. Taking into the material dispersion characterized by Wu *et al.* [13], the effective indices of the fundamental modes as a function of wavelength are plotted in Fig. 2(b) for waveguides of core thickness of 400 nm and 370 nm, respectively with two different cladding materials, i.e. PECVD SiO_{2} and SOG accordingly. It is clear that smaller core thickness results in smaller effective index because of evanescent wave penetrate deeper in the cladding region from the interface. Moreover, with SOG cladding, the change in waveguide thickness results in greater effective index contrast than that with PECVD SiO_{2} cladding. It is also interesting to see that the group indices of these guided modes are very large when compared to their effective indices. This infers strong dispersion in waveguides of Tantalum-Pentoxide core.

The WBG with surface corrugation can then be modeled by effective index method and coupled mode equation [16], in which the effective index of thicker and thinner straight waveguide represent the thicker and thinner portion of the WBG, respective. The stacking of high effective index in thicker portion and of low effective index in thinner portion of WBG forms almost periodic variation in the refractive index for electromagnetic waves guided in WBG as shown in Fig. 3(a). For small index change, coupled mode theory can be applied and yields analytical expressions to the transmitted and reflected fields of the WBG working as DBR mirror [16].

*γ*is the loss in the DBR region. Λ is the grating period and ${\beta}_{1}=\frac{2\pi}{\lambda}{n}_{1}$ and ${\beta}_{2}=\frac{2\pi}{\lambda}{n}_{2}$ are the propagation constant of guided waves in the high and low index region, respectively and ${n}_{1}$, ${n}_{2}$ are their effective index accordingly. The coupling coefficient of the forward and backward waves is $\text{\kappa}=\frac{2\left({\beta}_{1}-{\beta}_{2}\right)}{\text{\Lambda}\left({\beta}_{1}-{\beta}_{2}\right)}$ standing for the amount of field reflected per unit length as waves incidents the interface along normal direction twice in a one grating period. The resonance wavelength,

*λ*of the DBR mirror is determined by applying Bragg condition ${\beta}_{1}\left(\lambda ,T\right)+{\beta}_{2}\left(\lambda ,T\right)=2\pi /\text{\Lambda}$ where

_{DBF }*T*refers to the waveguide temperature and

*λ*is the wavelength. When temperature drifts, the resonance wavelength can easily be obtained by perturbation approach. To the first order, it writes,

In Fig. 3(b), effective indices of guided wave are shown for the temperature ranging from 40 to 100 degree Celsius for waveguide with PECVD SiO_{2} cladding (in blue) and SOG cladding (in red). ${n}_{1}$ is the effective index of waveguide device of 400 nm in core thickness and corresponds to the propagation constant ${\beta}_{1}$ marked in Fig. 3(a). ${n}_{2}$ is the effective index of waveguide device of 370 nm in core thickness and corresponds to the propagation constant ${\beta}_{2}$ marked in Fig. 3(a). The fitted slope of each line in Fig. 3(b) gives the thermo-optical coefficients of the guided wave in each structure and can be used together with the dispersion relation given in Fig. 2(b) to calculate according to Eq. (3) the temperature sensitivity. Table 1 lists the temperature dependence and dispersion relations near the designed resonance wavelength at 1533.5 nm and 1526 nm for the two devices. For WBG with PECVD SiO_{2} cladding, the resonance wavelength shifts at a rate of 6.134 pm/°C. But the WBG with SOG cladding experiences blue shift of −7.221 pm/°C. It is seen from Table 1 that the two WBG have commensurate dispersion but SOG cladded WBG suffers from large negative thermo-optical effect due to the intrinsic thermo-optical coefficient of SOG is in magnitude much larger than that of Ta_{2}O_{5}. In this case the size-dependent athermal design [10–12] will conflict with desired single mode operation for the WBG. Moreover, the organic contents in SOG might also bring issues related to long-term reliability and not being CMOS compatible in fabrication processes [17].

The calculation listed in Table 1 utilizes the structure parameter described in Fig. 1(a). The resonant wavelengths are λ = 1533nm and λ = 1526nm when Ta_{2}O_{5} core is cladded by PECVD SiO_{2} and SOG, respectively. Refractive index of Ta_{2}O_{5} follows the dispersion relation in REF [13] and its thermo-optical coefficient is 2.3$\times $10^{−6} K^{−1} [14]; the refractive index of PECVD SiO_{2}.follows the reported dispersion-equation [18]; the refractive indices and thermo-optical coefficient of SOG are 1.4 and −60$\times $10^{−6} K^{−1}, respectively [19]; the thermal expansion coefficient of Ta_{2}O_{5}*,*$\alpha =3.6\times {10}^{-6}$ K^{−1} is adopted [20].

Next we examine a FP resonator made of a 200-*μ*m straight waveguide sandwiched by PECVD-SiO_{2} cladded WBG as DBR mirrors. Each DBR mirror has a physical length of 200 *μ*m as shown in Fig. 4(a), which is capable of reflecting 97.18% of incident power at resonance wavelength and the full width half maximum (FWHM) spans over 4.54 nm according to the calculation using Eq. (1) and Eq. (2). The transmission and reflection spectrum of the WBG are plotted in Fig. 4(b) using solid line and dashed line in red, respectively. The transmission of FP resonator with DBR mirrors can be described by a standard mathematical expression [21],

$\begin{array}{l}\frac{\partial {L}_{eff}}{\partial \lambda}=\frac{\partial {L}_{eff}}{\partial \kappa}\frac{\partial \kappa}{\partial \lambda}\\ \\ \frac{\partial {L}_{eff}}{\partial T}=\frac{\partial {L}_{eff}}{\partial \kappa}\frac{\partial \kappa}{\partial T}+\alpha {L}_{WBG}\frac{{\text{sech}}^{2}\left(\kappa {L}_{WBG}\right)}{2}\\ \\ \frac{\partial {L}_{eff}}{\partial \kappa}=-\frac{\mathrm{tan}\mathrm{h}\left(\kappa {L}_{WBG}\right)}{2{\kappa}^{2}}+{L}_{WBG}\frac{{\text{sech}}^{2}\left(\kappa {L}_{WBG}\right)}{2\kappa}\\ \\ \frac{\partial \kappa}{\partial \lambda}=\frac{\Lambda}{2}\left[\frac{\frac{d{\beta}_{1}}{d\lambda}-\frac{d{\beta}_{2}}{d\lambda}}{{\beta}_{1}+{\beta}_{2}}-\frac{{\beta}_{1}-{\beta}_{2}}{{\left({\beta}_{1}+{\beta}_{2}\right)}^{2}}\left(\frac{d{\beta}_{1}}{d\lambda}+\frac{d{\beta}_{2}}{d\lambda}\right)\right]\\ \\ \frac{\partial \kappa}{\partial T}=\frac{\text{\Lambda}}{2}\left[\frac{\frac{d{\beta}_{1}}{dT}-\frac{d{\beta}_{2}}{dT}}{{\beta}_{1}+{\beta}_{2}}-\frac{{\beta}_{1}-{\beta}_{2}}{{\left({\beta}_{1}+{\beta}_{2}\right)}^{2}}\left(\frac{d{\beta}_{1}}{dT}+\frac{d{\beta}_{2}}{dT}\right)+\alpha \left(\frac{{\beta}_{1}-{\beta}_{2}}{{\beta}_{1}+{\beta}_{2}}\right)\right]\end{array}$Given the parameters described in Fig. 4 and Table 1, a shift of 4.952 pm/°C in resonant wavelength is calculated.

## 3. Experimental measurement and discussion

To characterize the fabricated WBG and FP resonator devices, experimental setup for the test bed is implemented following the schematics in Fig. 5. Our light source is a tunable laser modeled Agilent HP 8164A Mainframe equipped with 81642A and 81689A laser modules. It spans radiation wavelength from 1510 nm to 1640 nm from amplified spontaneous emission. A set of polarization controller is installed before a tapered fiber that couples tunable laser into the WBG and FP resonator devices. The device samples are placed on a temperature-controlled plate driven by thermoelectric cooler. Varying temperature from 20 to 80 degrees Celsius, output laser transmitting through the device is received by a tapered fiber that connects to either an Optical Spectral Analyzer (OSA) or a power meter to take the transmission spectrum and to evaluate the insertion loss accordingly.

The insertion loss of the 700-μm WBG device that includes 200μm WBG section sandwiched by two 200μm-long straight waveguides is 10.6 dB including the coupling loss and propagation loss. Employing the same fabrication route for the waveguides [13], low propagation loss of 1.5 dB/cm in our waveguide is expected and the contribution of propagation loss is as low as 0.105 dB corresponding to power loss of 3.4%. Yet without the inverse-taper design, large coupling loss should be responsible for the insertion loss of the fabricated WBG device. Notably the loss in the surface corrugated grating appears to be small as it will be discussed later. The measured transmission spectrum is plotted in Fig. 6(a) together with the theoretical calculation using Eq. (1). The calculation is in good agreement with the measurement in the stop band near the DBR resonance. In the experiments, however, oscillation fringes are recorded particularly at the high transmission region. By taking the Fourier transform of the measured spectrum as shown in Fig. 6(b), one clearly sees a peak at 1.17 nm^{−1}, which is confirmed to result from a low finesse FP resonant fringes of a cavity length of 700 μm that matches the length of our device length. Assuming the FWHM bandwidth of the DBR structure remain unchanged, which is confirmed by experiments, we plot in Fig. 7(a) the variations in resonance frequency as a function of device temperature and a linear function that best fit experimental data. The slope${\scriptscriptstyle \frac{dn}{d\lambda}}=7.4$ pm/°C refers to the temperature stability of the WBG device with PECVD SiO_{2} cladding. It is slightly greater than theoretical value of 6.134 pm/°C calculated by a semi-analytical approach discussed in Sec. II. When this value is compared to standard WBG device with silicon core, our device has a better temperature stability that is greater an order of magnitude improved [22]. For the WBG device with SOG claddings, ${\scriptscriptstyle \frac{dn}{d\lambda}}=-19.4$ pm/°C can be retrieved from the experiments shown in Fig. 7(b). It is also comparable to the theoretical calculated value of −7.221 pm/°C when the athermal design is not adopted. Athermal design requires a larger core size of the waveguide and may conflict to single mode operation for the WBG with SOG cladding. Moreover, a discrepancy of 10 nm in the resonating wavelength is observed in Fig. 6(a) and Fig. 7(a) because the measurements are taken by two distinct fabricated WBG devices with PECVD SiO_{2} cladding. We believe such a discrepancy lies in the possible fabrication error of the e-beam lithography. The change in DBR resonance approximates to the expression,

In Fig. 8(b), the resonance wavelength of the FP resonator is recorded as a function of device temperature controlled by thermo-electric cooler. The resonance wavelength experiences a red shift as the temperature increases shown in the inset of Fig. 8(b) and temperature stability ${\scriptscriptstyle \frac{dn}{d\lambda}}=8$ $\text{pm}{/}^{\text{o}}\text{C}$ can be fitted which is slightly higher than ${\scriptscriptstyle \frac{dn}{d\lambda}}=5.12$ $\text{pm}{/}^{\text{o}}\text{C}$ obtained by semi-analytical calculation adopting the grating corrugation of 15.5 nm obtained from experiment. Nevertheless, the fabricated FP resonator of low temperature depending drift in resonance wavelength already match the industrial requirement using fabrication process that is completely CMOS compatible [11,17].

Without any athermal design using material compensation or complicated structure, WBG device using Ta_{2}O_{5} as core material enjoys not only the smaller thermo-optic coefficient but also stronger chromatic dispersion in the waveguide. As can be perceived from Eq. (3) and Eq. (8), strong chromatic dispersion makes the denominator large and consequently the temperature stability of the device is enhanced. It infers that the athermal design of a spectral device might not necessarily resort to low thermo-optic effect solely. Either by strong materials dispersion or design of waveguide to high dispersion configuration may improve the temperature stability of frequency device. In contrast, frequency devices designed near the zero dispersion point could suffer from severe frequency shift as the device temperature varies subject to absorption or environmental effects. Regarding to large chromatic dispersion, issues like pulse broadening and bandwidth limitation might degrade the performance and limit the propagation range of some optical communication system. Such application is apparently not suitable to apply our design scenario for temperature stability. However, for frequency devices such as AWG for WDM, add-drop filters, add-drop multiplexors, FP resonators and the like, large chromatic dispersion is essential for them to function properly. Enhancing their temperature stability by adopting large chromatic dispersion is straightforward and significantly effective. In particular, the desired functionality and performance of these frequency devices are not sacrificed.

## 4. Conclusion

To conclude, we reported the fabrication and characterization of frequency devices including WBG and FP resonator using Ta_{2}O_{5} as core material to achieve high thermal stability. The reflectivity of WBG of greater than 90% was obtained and the insertion loss of the 700 $\mu $m-long WBG was 10.6 dB at 1550 nm. The center wavelength-to-temperature shifts of the WBG with the SiO_{2} and SOG cladding were 7.4 $\text{pm}{/}^{\text{o}}\text{C}$ and −16.8 $\text{pm}{/}^{\text{o}}\text{C}$, respectively and were both with high thermal stability. The fabricated FP resonator has a quality factor greater than 9,000 and a WBG corrugation of 15.5 nm can be fitted by semi-analytical calculations. The resonance wavelength of the FP resonator experiences red shifts by 8 $\text{pm}{/}^{\text{o}}\text{C}$. Such thermal stability in resonant wavelength are attributed to not only low thermo-optical coefficient of Ta_{2}O_{5} thin film but also its large chromatic dispersion supported by the semi-analytical calculations. The semi-analytical expressions utilized in this work further provide guidelines to design waveguide-based frequency device of low thermo-optical effect without complex athermal configuration.

## Funding

Ministry of Science and Technology, Tawaiin (MOST) (107-2112-M-110-004).

## Acknowledgments

The authors thank Prof. Chao-Kuei Lee, Prof. Yung-Jr Hung, Prof. Yu-Ju Hung, and Dr. Chung-Lun Wu for their technical supports and valuable suggestions.

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