1. Introduction

Over the last decades, polymeric optical waveguide devices have been studied with keen interests, because of the simple processes, flexibility of integration with different material systems, and potential low cost of polymers [1,2]. In particular, benzocyclobutene (BCB) is an organic polymer with high thermal stability (glass transition temperature > 350 °C), excellent planarization, high chemical resistance, and low moisture uptake [3]. It has been widely used as an optical waveguide material [4–6]. Thermal cure of BCB is usually performed in nitrogen atmosphere [7]. Due to the three-dimensional thermoset structure, it is generally considered as completely isotropic. Nevertheless, BCB film on a substrate frequently exhibits anisotropy in refractive indices (in-plane/out-of-plane birefringence), known to be due to the residual stress (i.e., stress-optic effect). Indeed, this is a common issue for most optical polymers. However, such stress-induced effects are not generally considered in the design of waveguide devices, possibly due to the substantial lack of accurate data that can be used in the optical design. In consequence, discrepancies are often found between the theoretical design and the fabricated device performance [5,8]. In such cases, researchers usually follow the trial and error process to achieve the desired performance of the devices, which cost substantial resources and time. Thus, the design of quality (i.e., independent of polarization and/or temperature) optical devices highly depends on the precise knowledge and characterization of the material optical properties, such as the refractive index n and its temperature dependence [i.e., thermo-optic (TO) coefficient $dn/dT$].

Recently, we have investigated the stress-induced birefringence in BCB waveguides at room temperature and thus demonstrated an accurate design of nonbirefringent devices taking such stress-effects into account [9]. However, due to the large TO effect of polymer, an understanding of thermal behavior of polymer waveguides is also crucial; whether one is designing a device where this behavior provides device functionality [10] or whether it is a problem to be managed [11]. Moreover, several factors including the residual stress may also cause anisotropy (polarization dependence) in the $dn/dT$ of polymer thin films [12,13]. For the precise thermal design of the waveguide devices using BCB, therefore, the anisotropies in $dn/dT$ of the BCB films should be quantitatively examined.

Furthermore, the refractive index of BCB is often controlled by oxidizing the films through several ways, such as oxygen-ion implantation [14], UV irradiation [15,16] and curing under partial oxygen environment [5]. These techniques offer the flexibility of controlling the refractive index by a large value, and/or allow the fabrication of buried waveguides which have potential for integration of optoelectronic devices. While the correlation of the refractive index change with the oxidization parameters (i.e., UV dose) has been widely studied [14–16], there has been no report on the optical anisotropies of the oxidized BCB films.

In this work, we employed a simple and accurate prism coupler technique to systematically investigate the anisotropies in refractive indices and in TO coefficients for both nonoxidized and oxidized BCB films. To facilitate the measurement using prism waveguide coupler, the BCB thin film waveguides formed on silica-on-silicon substrates were investigated. The dependence of the anisotropies on thermal stress and oxidation was determined and discussed individually. Despite the successful development of many optical devices using BCB, designers will surely benefit from having access to such data.

2. Experimental details

2.1 Sample preparation

The BCB material used was the commercially available Cyclotene 3022 from Dow Chemical. The resin was spin-coated onto a number of silica-on-silicon substrates (1.5 × 1.5 cm²) and then thermally cured at 250 °C for 1 hour. Different samples were cured under different flow rates [0-10 liter per minute (LPM)] of nitrogen (N₂). The flow of N₂ at 10 LPM was sufficient to provide a complete N₂ atmosphere, resulting nonoxidized films. However, due to partial oxygen atmosphere at lower flow rate of N₂, the process results different degree of oxidation in the different BCB films. To check the repeatability of the process, three samples were prepared at different time (i.e., one after another) in each flow rate of nitrogen. The average film thickness was 5 µm, as measured by the stylus profiler (Ambios XP2).

2.2 System calibration and refractive index measurement

A prism coupler system (Metricon 2010/M) equipped with a heat pump [17] was used to measure the refractive indices of the films as a function of temperature. Among other conventional techniques such as ellipsometry or interferometry [18], the prism coupling method is preferred in the thin film measurement due to its higher accuracy, ease in use, and capability to measure in-plane and out-of-plane optical anisotropy (birefringence). A number of works have been carried out using prism waveguide coupler to investigate the temperature dependence of the refractive index of thin film waveguides [12,13,19,20]. However, the proper calibration of the prism coupler system is very important for the accurate index measurement, in particular, at elevated temperature.

Before starting the measurement, our prism coupler system was properly calibrated at different temperature using a 0.5 mm thick fused quartz (HOQ 310) from Heraeus. The refractive index of this standard quartz is 1.4443 at 20 °C for the wavelength of 1536 nm with its temperature dependence of 10.5 ppm/°C as provided by Heraeus [21]. Since the prism use in our system is a precision one, which prism angle is provided by the manufacturer with higher accuracy, we needed to calibrate the prism refractive index only. As explained in the user manual of Metricon, the standard sample was used with the prism coupler and the prism index was simply adjusted to obtain the expected index for the standard. In this way, the prism index was calibrated at different temperature in the range of 20-60 °C with the corresponding standard index. The prism index at any measurement temperature was then obtained by interpolating the calibrated index as a function of temperature. In this calibration, the refractive index at a certain temperature was assumed constant (i.e., no spatial variation) for both prism and sample. The prism used was of lower refractive index (<1.935) which provided low index contrast between the prism and the film, and thus helped to achieve better accuracy. A typical error in the refractive index measurement was found to be less than ± 0.0002 over the measurement temperature range. When the temperature is changed, the air gap between the prism and the film (i.e., coupling pressure) may also change due to the thermal expansion of the sample. However, the influence of such change of air gap was not noticeable in our measurement. This was confirmed by varying the coupling pressure within a certain range in which all the measurements were conducted.

After calibrating the system, the refractive indices of the thin film samples were measured at a wavelength of 1536 nm for both transverse-electric (TE) and transverse-magnetic (TM) polarization. These represent the in-plane $n_{TE}$ and the out-of-plane $n_{TM}$ refractive indices, respectively. The measurements were carried out over the temperature range of 20-60 °C, which was monitored by a K-type thermocouple located on the sample surface.

3. Results and discussions

In the refractive index measurement, 4-5 numbers of guided modes were obtained in our sample structures. All samples were measured with high calculation accuracy ( ± 0.00002) in the modal solution of thin film waveguide. This indicates a good precision among the repeated measurement for every individual sample. Averages were made in the measurements within each set (three samples corresponding to each flow rate) of samples. Figure 1 shows the averages of refractive indices ($n_{TE}$ and $n_{TM}$) measured at room temperature (21 ± 1 °C) and their corresponding birefringence ($\Delta n=n_{TE}-n_{TM}$) for different flow rate of N₂. The error margins in the Figs. are the differences between the measured values and averages among the samples in each set. The refractive index increases when the flow of N₂ decreases. As we know, the refractive indices of BCB increase due to the oxidation [14–16]. This was verified again in this work through analyzing the IR spectra of the BCB films. Similar phenomena (increase in carbonyl (C = O) and hydroxyl (O-H) groups) were observed as described in Ref [15,16]. when the flow rate of N₂ decreased. Thus, it was confirmed that lower flow rate of nitrogen produced higher oxidation and so, higher index in our BCB films. The refractive index obtained for 0 LPM (no flow) of N₂ was the maximum available index in our measured wavelength, which corresponds to the fully oxidized film. The condition of complete oxidation was confirmed by comparing the measured index with that of the BCB films prepared under sufficient flow of oxygen. Results show that the errors (differences between averages and measured values) are smaller than ± 0.0005, which is comparable to the measurement accuracy. This implies a good repeatability in the preparation of BCB film with a desired index by controlling the flow of N₂. As shown in Fig. 1(b), the birefringence also increases following the increase in refractive index [Fig. 1(a)].

 

Fig. 1 (a) Refractive indices (n) for the TE and TM polarizations and (b) their birefringence ($\Delta n$) versus flow rate of nitrogen measured at room temperature.

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Figure 2 shows the temperature dependence of the refractive indices and their birefringence measured for a typical sample corresponding to the N₂ flow of 1 LPM. The temperature dependence of the substrate refractive index (11.9 ppm/°C) was considered in the measurements. Based on Fig. 2(a), the refractive indices decrease linearly with the rise of temperature with a correlation coefficient $r\ge$0.998, and show significant anisotropy over the measurement temperature range. Figure 2(b) shows that the values of $\Delta n$ also exhibit linear temperature dependence with $r\ge$0.985, implying the anisotropy in TO coefficient ($dn/dT$) as well. The $dn/dT$ values were obtained from the linear regression analysis of the measured indices as a function of temperature. The measurement results for all other samples also followed the similar trends (Fig. 2) of linear temperature dependence but with different values. The measured optical properties are summarized and discussed in the following sections.

 

Fig. 2 (a) Measured refractive indices (n) for the TE and TM polarizations and (b) their birefringence ($\Delta n$) as a function of temperature for a typical sample corresponding to the nitrogen flow of 1 LPM.

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3.1 Anisotropy in refractive index

Table 1 lists the averages of the refractive indices ($n_{TE}$ and $n_{TM}$) and their anisotropies (i.e., birefringence $\Delta n$) measured at room temperature for 4 sets of samples corresponding to different flow rate of N₂ (10, 3, 1 and 0 LPM). The values of the obtained birefringence, as listed in Table 1, lie in the range of 0.0029 to 0.0065 with the repeatability of better than ± 0.0002 among the samples in each set.

Table 1. Measured film refractive indices (n) at room temperature, and in- plane/out-of-plane anisotropy ($\Delta n$) at a wavelength of 1536 nm*.

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3.1.1 Refractive index anisotropy of nonoxidized film

Being an isotropic material, the birefringence $\Delta n$ in the nonoxidized BCB film (sample set 1) mainly caused by the residual stress, which can be verified by [22]:

3.1.2 Effects of oxidation on the refractive index anisotropy

As seen in Table 1, the refractive indices of the BCB films increase gradually from sample set 1 to 4. As previously explained, this is due to the different degree of oxidation of the BCB. However, the values of $\Delta n$ also increased with the increase in refractive indices (i.e., set 1 to 4). Since the material refractive index is the primary concern in the design of optical devices, it is worth to discuss the anisotropy as a function of the refractive index rather than the flow rate of N2 or degree of oxidation. Figure 3 shows the birefringence ($\Delta n$) versus average refractive index ($n_{av}$), where $n_{av}^{}$ is calculated by [12]: $n_{av}^2=(2n_{TE}^2+n_{TM}^2)/3$. While the $n_{av}$ increased by 2% (i.e., 1.5364 to 1.5701) due to oxidation, the values of $\Delta n$ increased by 120% than that of nonoxidized film (i.e., 0.0029 to 0.0065).

 

Fig. 3 Measured refractive index anisotropy $\Delta n$ versus the oxidation induced change of average refractive index $n_{av}$. The numbers in the figure correspond to those of sample sets.

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In the first assumption, this increase in birefringence may be attributed to the increase in the stress-induced effects. To investigate the influence of oxidation on the stress-induced birefringence, the stress was also measured for the oxidized BCB film. However, the film stress was not found to be dependent on the oxidation. Moreover, the relative stress-optic coefficient ($C_1-C_2$) of the BCB also did not change significantly due to oxidation; this will be explained in the next section. According to Eq. (1), thus, the stress-induced anisotropy remains unchanged in all samples. It implies that the oxidation caused some intrinsic birefringence, and the value of which increased with the degree of oxidation (Fig. 3). This additional anisotropy can be attributed to the anisotropic properties of the chemical structure of oxidized BCB film. For instance, the polarizability of the oxygen containing polymer structure along the main chain (i.e., parallel to the polymer backbone) can be different from that of the side chain (i.e., perpendicular to the backbone) [24]. This may cause differences between the in-plane and out-of-plane refractive indices. However, the designer should carefully consider such optical anisotropy in designing with oxidized BCB film.

3.2 Anisotropy in thermo-optic (TO) coefficient

The averages of the measured temperature dependence of the refractive indices ($d{n}_{TE}/dT$ and $d{n}_{TM}/dT$) and the corresponding anisotropies ($d(\Delta n)/dT$) are summarized in Table 2 . The values of $d(\Delta n)/dT$ are in the range of 15.4 to 21.8 ppm/°C, which were obtained with the repeatability of better than 1.5 ppm/°C among the samples in each individual sets. The absolute values of $d{n}_{TE}/dT$ (polarization parallel to the film plane) were always higher than the $d{n}_{TM}/dT$values (perpendicular to the film plane). The errors (differences between averages and measured values) in the $dn/dT$ values were found to be less than 5% ( ± 4-7 ppm/°C) within the sets, which are also comparable to the measurement accuracy.

Table 2. Measured temperature dependence of the film refractive indices for TE ($d{n}_{TE}/dT$) and TM ($d{n}_{TM}/dT$) polarizations, and their corresponding anisotropy ($d(\Delta n)/dT$) at a wavelength of 1536 nm*.

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3.2.1 Anisotropy in TO coefficient of nonoxidized film

The TO coefficient of a polymeric material is generally expressed by the derivative of Lorentz-Lorentz equation [12,20]:

The effects of thermal stress on the measured $dn/dT$ values of the thin films of isotropic material can be explained using the following relations [17]:

To verify the experimental results, the value of $d\sigma /dT$ was determined using the material constants of $E_f$ = 2.9 GPa, ${\nu }_f$ = 0.34, and ${\alpha }_s$ = 2.6 ppm/ °C [9]. The value of ${\alpha }_f$ can be directly obtained from Eq. (2) to be β = 3α [20]. However, the measured values of $dn/dT$ are perturbed by the stress-optic effects as explained by Eq. (3). To determine the α accurately, the value of $dn/dT$ considered in Eq. (2) should be, theoretically, same as the original (stress-free) TO coefficient $d{n}_{sf}/dT$ in Eq. (3). Therefore, the value of ${\alpha }_f$ was determined, in this work, by solving Eqs. (2), (3), and (5) numerically satisfying $d{n}_{sf}/dT$ and $d{n}_{av}/dT$ are equal. Here, the $d{n}_{av}/dT$ was calculated for an average refractive index $n_{av}$ (listed in Table 1) using Eq. (2). The determined values of ${\alpha }_f$ and $d\sigma /dT$ are given in Table 3 , which are 49.8 ± 3 ppm/ °C and −0.207 ± 0.013 MPa/°C, respectively for sample set 1. The values are consistent with the corresponding values of 53.8 ± 13.6 ppm/ °C and −0.204 ± 0.019 MPa/°C, respectively, reported in the literature [23]. This agreement partially verifies the material constant used in this work.

Table 3. Calculated values of thermal expansion coefficients of BCB films (${\alpha }_f$), temperature dependence of the film stress ($d\sigma /dT$) and birefrigence ($d(\Delta n)/dT$), and stress-free thermo-optic coefficient ($d{n}_{sf}/dT$) at a wavelength of 1536 nm*.

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Since the material properties are independent of temperature in our analysis range [23], the stress-temperature slope is linear. The negative slope indicates that the in-plane tensile stress (σ) is reduced when the temperature increases for $dn/dT$ measurements. As the value of $C_1+C_2$ is larger than the value of $2C_2$ for BCB films, according to Eq. (3), the effect of stress on the measured $dn/dT$ is higher for TE polarization compared to that for TM polarization. This is why the $d{n}_{TE}/dT$ is always higher than the corresponding $d{n}_{TM}/dT$ in our measurement results. The value of $d(\Delta n)/dT$ calculated using Eq. (4) is −13.9 ± 0.9 ppm/°C (Table 3), which is very close to the measurement value of −15.4 ppm/°C (Table 2). Based on this agreement, it can be concluded that the anisotropies in the measured $dn/dT$ values are mainly caused by the thermal stress.

Substituting all the values into Eq. (3), the TO coefficient ($d{n}_{sf}/dT$), which is free from stress-optic effects, was decoupled from the measurement results ($d{n}_{TE}/dT$and$d{n}_{TM}/dT$). The calculated values of $d{n}_{sf}/dT$ are given in Table 3. For nonoxidized film (sample set 1), the value of $d{n}_{sf}/dT$ is −96 ± 5 ppm/°C, which differs (less) by as large as 23% in magnitude than the measured values of $d{n}_{TE}/dT$ and $d{n}_{TM}/dT$ (−124.1 and −108.7 ppm/°C, respectively). This implies that the conventional approach which considers the measured $dn/dT$ values as the thermo-optic coefficient [12,13] may be rendered inaccurate in this (higher film stress) situation. Such large difference in the $dn/dT$ values can easily mislead the thermal design of optical devices. For instance, in the design of an athermal arrayed waveguide grating (AWG) according to Ref [11], the use of the TO coefficient of a waveguide material that differs with the actual value by 23% may result in a temperature sensitivity of about 0.03 nm/°C. Thus, the total wavelength shift can be 1.2 nm when the temperature changes from 20°C to 60°C, which is already large enough for misfunctioning most of the practical AWGs. It should be noted that $d{n}_{sf}/dT$ of thin films may not necessarily be the same as $dn/dT$ of bulk materials because expansion or shrinkage on the film plane are constrained by the substrate [12].

3.2.2 Effects of oxidation on the TO coefficient

As seen in Table 2, the temperature dependence of the refractive indices increases gradually from sample set 1 to 4. This trend is similar to the oxidation-induced increase in refractive index (Table 1). The $d{n}_{sf}/dT$ values as well as the corresponding values of β ( = 3α) were determined for the oxidized films (sample sets 2-4) following the same way as explained before. The obtained values are given in Table 3. Similar to the nonoxidized film, the values of $d{n}_{sf}/dT$ (−118 to −166 ppm/°C) are also isotropic and significantly different (12 - 23% less in magnitude) from the measured values of $d{n}_{TE}/dT$ and $d{n}_{TM}/dT$ (−134.5 to −210.0 ppm/°C). Such significant difference in the results indicates that the effect of thermal stress on the TO coefficient of BCB cannot be neglected.

Figure 4 plots these values of $d{n}_{sf}/dT$ (Table 3) as a function of the average refractive index $n_{av}$ (Table 1). While $n_{av}$ increases by 2% (i.e., 1.5364 to 1.5701) due to oxidation, the magnitude of $d{n}_{sf}/dT$increases by about 73% (i.e., −96 ppm/°C to −166 ppm/°C) compared with that of nonoxidized film. This increase in $dn/dT$ can be explained by Eq. (2), which is due to a large n and/or a large β. By calculation, we verified that the influence of increasing $n_{av}$ on the $dn/dT$ is relatively much smaller than the total change in $d{n}_{sf}/dT$. This indicates that the oxidized BCB films should have larger β than the nonoxidized film, and its value increases with the degree of oxidation (i.e., from sample set 1 to 4). This is exactly what we obtained for β (= 3α) as listed in Table 3. The relation between the TEC and the average refractive index (i.e., oxidation) were obtained as ${\alpha }_f=885.96n_{av}-1312.424$.

 

Fig. 4 Relationship between the thermo-optic coefficient $dn/dT$ and the oxidation-induced change of average refractive index$n_{av}$. The numbers in the figure correspond to those of the samples.

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Unlike the increase in birefringence $\Delta n$ (Table 1), the anisotropies in $dn/dT$ values ($d(\Delta n)/dT$) are less affected by the oxidation of the BCB films (Table 2). According to Eq. (4), the small change in $d(\Delta n)/dT$ can be attributed to the change of the ($C_1-C_2$) and/or $d\sigma /dT$ value. We verified, using Eqs. (1) and (4), that the change in the value of $C_1-C_2$ cannot satisfy the measurements results of $\Delta n$and $d(\Delta n)/dT$ simultaneously. And, also the effect of the change of $C_1-C_2$ value on the anisotropies is relatively smaller than the large anisotropies measured due to oxidation. On the other hand, the calculated values of $d(\Delta n)/dT$ in Table (3), which considered the influence of thermal expansion β (i.e., $d\sigma /dT$) of the BCB film, are in well agreement with the corresponding measured values as given in Table 2. Thus, it was reasonable to consider that the value of $C_1-C_2$ of the BCB film did not change significantly with the oxidation. Since the stress-optic effects due to change in β (i.e., change in $d(\Delta n)/dT$) is very small, however, its large TO effects can be useful to change the $dn/dT$ value by oxidation. Such tuning of the TO coefficients of BCB can provide the flexibility of choosing the suitable substrate material in the optical design that [11] requires the use of the substrate with proper TEC.

4. Conclusions

This work presented a quantitative study on the anisotropy in refractive index and in TO coefficient of the BCB thin film waveguides. Discussions were made for the dependence of anisotropies on the film stress and oxidation. Aside from the stress-induced effects, oxidation caused significant intrinsic birefringence in the BCB films, suggesting that the design with oxidized BCB films requires careful consideration for such anisotropic behavior. On the other hand, the anisotropies in the TO coefficients were mainly due to the thermal stress, and independent of oxidation. However, the original (free of stress-optic effect) TO coefficients were obtained as isotropic and significantly different (10-23% less in magnitude) from the measured values. Such large difference between the conventional measurement result and the actual value of TO coefficient can easily mislead the thermal design of optical devices. This indicates that our findings can be useful for the efficient design of polarization- and/or temperature-insensitive integrated optical devices using BCB.