1. Introduction

Recent progress in silicon photonics [1–6] has been accompanied by several new technologies, such as a ring-resonator-based modulator [2], a hybrid silicon laser [5], and a slot waveguide [7–11].

A slot waveguide attracts scientific attention with its peculiar property of guiding light within a narrow low-index slot between high-index materials [7–11]. The slot waveguide is very attractive because various materials can be inserted within the slot to change the optical property of the waveguide. The slot waveguide is useful for optical waveguide devices requiring the effects of low-index materials within the slot [10].

One of the applications requiring the effects of low-index materials is one that results in the reduction of the temperature dependence of a silicon waveguide device using a polymeric upper cladding. The amount of temperature-dependent wavelength shift (TDWS) of a silicon waveguide ring resonator was shown in our previous report to be reduced by using a polymer over-layer, easily done for the transverse magnetic (TM) mode, but not as simply done for the TE mode [12].

Using a slot, we expect that the TDWS of the TE mode can be controlled more efficiently. In this regard, we apply a slot structure filled with a polymer material to a silicon waveguide ring resonator in order to reduce the TDWS for the TE mode.

2. Experimental scheme and simulation

Figures 1(a) and 1(b) show the scanning electron microscope (SEM) images of a slot waveguide ring resonator. Figure 1(c) shows the cross-sectional structure of Fig. 1(a), and Fig. 1(d) shows the schematic diagram for Fig. 1(b). The silicon slot waveguide is fabricated using electron beam lithography and dry etching on a silicon-on-insulator (SOI) wafer having a 220 nm-thick top silicon layer on a 3000 nm-thick buried oxide (BOX) layer. The slot is located asymmetrically between silicon wires that are 210 nm wide (Wo in the figure) and 290 nm wide (Wi in the figure) to reduce bending loss [10]. The radius of the slot waveguide ring resonator is 12 µm. The slot waveguide is connected to a normal 500 nm-wide silicon waveguide through a 10 µm-long lateral taper (Lt in the figure) as in Fig. 1(d) [11]. The width of the slot (Ws in the figure) is varied from 90 nm to 120 nm in order to control the temperature dependence of the ring resonator.

The waveguide is covered with a polymeric material to compensate for the temperature dependence of the waveguide. A UV-curable resin based on perfluorinated acrylate, WIR30-490, and a thermally curable polymer based on highly fluorinated polyethers, ZP49, are used separately for a comparison. The polymer materials are supplied by ChemOptics, Inc. The refractive index for both materials is the same as 1.49, but the thermo-optic coefficient (TOC) is different. The TOC of WIR30-490 is about -1.8×10^-4/°C, which is opposite to the silicon, and the TOC of ZP49 is about -0.8×10^-4/°C.

The polarization of the TE mode is considered in this experiment and calculation, because the TE mode is more popularly used in silicon photonics than the TM mode with the merits of low bending loss and low leakage to the silicon substrate under the thin BOX layer of the SOI wafer [6, 13].

 

Fig. 1. SEM images of silicon slot waveguide ring resonator in (a) and (b); cross-sectional view of (a) in (c); and schematic diagram of (b) in (d) [not to scale for (c) and (d)].

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The TDWS of a WDM waveguide device is caused both by the thermo-optic effect of the material forming the waveguide and by the thermal expansion of the substrate. The TDWS can be calculated as follows [13, 14]:

where T is the temperature, λ ₀ is the resonant wavelength, Neff is the effective index of the waveguide, α is the coefficient of thermal expansion, and Ng is the group index of the waveguide. Ng is calculated as follows:

There have been some reports [15, 16], including our previous report [12], which have used Neff instead of Ng in Eq. (1). But a rigorous derivation in [13] and [14] and the experimental data in [12–14] show that Eq. (1) is more accurate than the previous equation using Neff instead of Ng. The difference between Neff and Ng can be negligible for a low-index contrast waveguide, but it is not negligible for a subwavelength-scale, high-index contrast waveguide. In the case of silicon, the TDWS mainly originates from the thermo-optic effect because the coefficient of thermal expansion is as low as 2.5×10^-6/°C, resulting in a TDWS of only several pm/°C. So, we ignore the influence of the thermal expansion through the following simulation.

 

Fig. 2. Theoretically calculated TDWS in ring resonators, depending on the width of the slot; in case of total width of silicon-wires of 500 nm covered by oxide (Oxide_500), air (Air_500), ZP49 (ZP49_500), and WIR30-490 (WIR_500); 550 nm covered by WIR30-490 (WIR_550); and 600 nm covered by WIR30-490 (WIR_600), respectively.

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Fig. 3. Theoretically calculated TDWS in ring resonators depending on the height of the slab of a rib-type slot waveguide covered by WIR30-490; with the total width of silicon-wires of 500 nm; and with the width of the slot of 50 nm (WIR_500_s50), 80 nm (WIR_500_s80), and 100 nm (WIR_500_s100), respectively.

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We used a commercial program, FEMSIM, to calculate the effective index Neff for various slot waveguide structures with various widths of slots. Then, the variation of the TDWS in a WDM device such as a ring resonator composed of slot waveguides was calculated using Eq. (1). The calculated result is in Fig. 2, which shows that the TDWS of the slot waveguide is reduced as the width of the slot increases. Figure 2 shows the TDWS for the total widths of silicon wires (Wi+Wo in Fig. 1) of 500 nm covered by oxide (Oxide_500), air (Air_500), ZP49 (ZP49_500), and WIR30-490 (WIR_500); 550 nm covered by WIR30-490 (WIR_550), and 600 nm covered by WIR30-490 (WIR_600), respectively. In Fig. 2, the TDWS is not reduced enough with the oxide or the air cladding, but it is reduced even to a negative value in the case of the 500 nm-wide waveguide with WIR30-490. It means that we can control the TDWS by adjusting the width of the slot filled with the polymer cladding.

There is another parameter used to control the TDWS. The waveguide can be fabricated as a rib-type with a thin silicon slab, and we can adjust the TDWS by controlling the height of the slab. Figure 3 shows the calculated variation of the TDWS of a rib-type slot waveguide depending on the height of the slab and for the slot widths of 50 nm (WIR_500_s50), 80 nm (WIR_500_s80), and 100 nm (WIR_500_s100). The upper cladding is WIR30-490 and the total width of silicon wires is 500 nm in this calculation. We can see in Fig. 3 that the TDWS can be reduced to zero by adjusting the height of the slab.

3. Experimental results

Figure 4 shows the variation of the measured transmission spectra of the ring resonator as the temperature increases from 25 to 65°C [up to 75°C for Fig. 4(d)]. 25T means a through-port signal at 25°C, and 25D means a drop-port signal at 25°C. The resonant wavelengths are shifted about +3.0 nm without a slot, +0.5 nm with a 120 nm-wide slot filled with ZP49, -1.3 nm with 110 nm-wide slot, and -0.9 nm with 90 nm-wide slot filled with WIR30-490. These results show that it is possible for the TDWS to be controlled by optimizing the structure of a slot properly for the composition of materials. We have not measured the loss of the slot waveguide yet, but the loss of a waveguide without a slot was measured at about 0.3 dB/mm regardless of the polymer over-layer. It shows that the polymer fills the waveguide structures without a serious void and does not degrade the waveguide loss.

 

Fig. 4. Measured transmission spectra of ring resonators; (a) for a waveguide without a slot covered by ZP49; (b) for a 120 nm-wide slot waveguide covered by ZP49; (c) for a 110 nm-wide slot waveguide covered by WIR30-490; and (d) for a 90 nm-wide slot waveguide covered by WIR30-490.

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Figure 5 shows the TDWS for various cases of ring resonators. In Fig. 5, S0_Air, S0_ZP, and S0_WIR are for normal waveguides without a slot but with different upper claddings such as air, ZP49, and WIR30-490, respectively. The TDWS of the ring resonators without a slot are about +77 pm/°C for S0_Air, +73 pm/°C for S0_ZP, and +66 pm/°C for S0_WIR. These results show that the polymer over-layer without a slot does not effectively compensate for the TDWS of the TE mode.

 

Fig. 5. Measured temperature-dependent wavelength shifts of ring resonators. S0_Air, S0_ZP, and S0_WIR are for waveguides without a slot but with different upper claddings: air, ZP49 and WIR30-490, respectively. S90_ZP and S120_ZP are for 90 nm-wide and 120 nm-wide slot waveguides, respectively, with a ZP49 upper cladding. S90_WIR and S110_WIR are for 90 nm-wide and 110 nm-wide slot waveguides, respectively, with a WIR30-490 upper cladding. SR90_WIR is for a rib-type 90 nm-wide slot waveguide with a WIR30-490 upper cladding.

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S90_ZP and S120_ZP are for 90 nm-wide and 120 nm-wide slot waveguides, respectively, with ZP49 upper cladding. The TDWS of ring resonators with the ZP49 over-layer are about +25 pm/°C for S90_ZP and +13 pm/°C for S120_ZP. These results show that the TDWS is reduced a lot with the slots, but not enough by the insufficient TOC of the ZP49 polymer.

S90_WIR and S110_WIR are for 90 nm and 110 nm slot waveguides, respectively, with the WIR30-490 upper cladding. The TDWS of ring resonators with the WIR30-490 upper cladding are about -25 pm/°C for S90_WIR and -32 pm/°C for S110_WIR. These results show that it is possible to compensate for the TDWS by the highly negative TOC of the WIR30-490 polymer.

SR90_WIR is another 90 nm-wide slot waveguide with a WIR30-490 upper cladding, but with a rib-type waveguide with about a 20 nm silicon slab on the BOX. The TDWS for SR90_WIR is about -2 pm/°C in Fig. 5. This result shows that the use of a properly designed slot structure filled with a polymer material can fully compensate for the TDWS.

Figure 6 shows the transmission spectra for a ring resonator with a rib-type slot waveguide in which the polymer almost completely compensates for the wavelength shift. The transmission spectra of the ring resonator in Fig. 6 are not as sharp as the spectra in Fig. 4(d). We guess the low quality of the spectra can be improved by optimizing the fabrication. In addition, it is possible to control the TDWS of the slot waveguide more efficiently by adjusting the width of the silicon wires without the slab, as shown in the simulation in Fig. 2.

Figure 7 shows the measured TDWS data in comparison with the calculation in Figs. 2 and 3. We can see that the experimental result is very well in accord with the calculation. These results show that TDWS can be fully controlled by adjusting the variables of a slot waveguide filled with a proper polymer.

A strong merit of this method is that it can be applied to general waveguide devices by inserting the slot structure within a phase section of the devices. For example, we can compensate for the temperature dependence of the AWGs by inserting the polymer-filled slots within the phase arms of arrayed waveguide gratings (AWGs). In addition, these results can be applied in the fabrication of temperature-insensitive silicon ring add-drop filters, multichannel ring WDM devices, and ring modulators.

 

Fig. 6. Measured transmission spectra of a ring resonator composed of a rib-type 90 nm-wide slot waveguide covered by WIR30-490.

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Fig. 7. Comparison of measured data with theoretically calculated TDWS of ring resonators, depending on the width of the slot. ZP49_500_Exp represents measured data for slots covered by ZP49, WIR_500_Exp for slots covered by WIR30-490, and WIR_500_s20_Exp for a rib-type slot with a 20 nm slab covered by WIR30-490.

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4. Conclusion

We showed, theoretically and experimentally, that temperature sensitivity of a silicon slot waveguide ring resonator can be fully compensated by adjusting the structure of the slot filled with a polymer material. We can control the temperature dependence by adjusting several variables of the slot structure, such as the width of the slot between the walls of the silicon wires, the width of silicon-wires, and the height of a silicon slab, in addition to the proper selection of polymer material. These results are expected to be applied in the fabrication of temperature-insensitive silicon ring add-drop filters, AWGs, and ring modulators.