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Abstract
Germanium-on-silicon (GOS) represents the leading platform for foundry-based long-wave infrared photonic integrated circuits (LWIR PICs), due to its CMOS compatibility and absence of oxides. We describe ring resonance (Q-factors between 2×103 and 1×104) and thermo-optic tunability in germanium-on-silicon waveguides throughout the long-wave-infrared. The ring resonances are characterized by Q-factors and couplings that agree with measurements of propagation loss (as low as 6 dB/cm) and simulations and are enabled by broadband edge coupling (12dB/facet over a 3 dB bandwidth of over 4 microns). We demonstrate the furthest into the infrared that ring resonators have been measured and show the potential of this platform for photonic integration and waveguide spectroscopy at wavelengths from 7 microns to beyond 11 microns.
1. Introduction
The long-wave infrared (LWIR, wavelengths of approximately 6-12 $\mu$m) is important for defense and commercial technologies such as chemical agent detection [1,2], environmental monitoring [3], and hyperspectral imaging [4]. At present, these systems are all based on traditional bulk optics. Photonic integrated circuits, on the other hand, promise low-cost, low-size optical systems fully integrated onto a single die using wafer-scale semiconductor fabrication. In particular, low-loss, evanescent waveguides in the LWIR can be used in place of benchtop attenuated total reflection Fourier-transform spectrometers (ATR-FTIR) for materials characterization [5] and biochemical detection [6].
The waveguide platforms available in the LWIR are more limited than those in the near-infrared and mid-wave infrared due to the strong absorption of many amorphous and crystalline thin films. Even silicon begins to show absorption at wavelengths above 9 $\mu$m due to multi-phonon resonances. To compensate, low-loss silicon/germanium-based platforms [7] utilizing thick germanium cores [8], suspended germanium [9], or germanium-rich SiGe [10–15] have all been reported in the LWIR. While these platforms all have advantages (for example, reduced overlap with the silicon substrate), they also suffer from the need for deep etches and more complicated growth (for thicker germanium cores and graded silicon-germanium cores) or from increased fragility (for suspended waveguides). Indeed, many applications require only modest losses and benefit more from simpler, foundry-compatible fabrication. For example, waveguide spectroscopy requires an increased evanescent field outside of the germanium core to enhance interactions with a target analyte. For these reasons we focus here on epitaxially-grown Ge-on-Si.
In this work, we describe our LWIR measurements of thermo-optic tuning and ring resonance for both the TE$_{00}$ and TM$_{00}$ waveguide modes in germanium-on-silicon (GOS) waveguides [8,16–18]. We demonstrate the furthest into the IR that ring resonators have been measured, and show excellent agreement between the ring resonances and the measured waveguide loss and calculated coupling. In addition, we show how ring resonators can be used to measure the thermo-optic coefficients of the germanium core and silicon cladding, and demonstrate extremely wide-band edge coupling. Ring resonators in this waveguide platform are of particular importance for trace-gas absorption spectroscopy [19] and numerous signal processing techniques.
2. Fabrication, experimental setup, and modeling
The waveguides comprise a 1.5 $\mu$m thick germanium core layer grown by molecular beam epitaxy on a silicon substrate [17]. Deep ultraviolet (DUV) contact photolithography was used to pattern photoresist to define s-bend waveguides as well as ring resonators coupled to straight bus waveguides. The s-bend waveguides have a bend radius of 500 $\mu$m and lengths that vary from 4.8 mm to 14.6 mm in order to accurately measure propagation loss. The ring resonators are racetracks with a 200 $\mu$m long coupling region and bend radius of 500 $\mu$m. A 1.3 $\mu$m deep fluorine-based inductively coupled plasma reactive ion etch (ICP-RIE) was then used to laterally define the waveguides. The die was laser scribed and cleaved resulting in facets for free-space coupling, as shown in Fig. 1(a). The waveguide is slightly trapezoidal, as shown in Fig. 1(a), with an etch angle of 12 deg. from vertical. We report below nominal widths for these waveguides, corresponding to an actual width at the top that is narrower by approximately 250 nm, and wider at the bottom by approximately 400 nm.
Fig. 1. (a): A scanning-electron microscope image of a nominally 5 $\mu$m wide waveguide facet. (b): A microscope image of a ring-resonator coupled to a bus waveguide with a nominally 1.0 $\mu$m gap.
The waveguides are measured using similar methods as described previously [17]. Briefly, Schwarzschild reflective microscope objectives (focal length = 8 mm) are used to couple tunable laser light (a Daylight MIRcat quantum cascade laser, QCL) into and out of the waveguide facets. The transmitted light is spatially filtered through a 25 $\mu$m pinhole and measured by a cooled mercury cadium telluride (MCT) detector. The propagation loss measurements are carried out with s-bend waveguides with the laser in pulsed mode using a lock-in amplifier referenced to the 100 kHz repetition rate. Ring resonators are measured with the laser in continuous wave (CW) mode and modulated by a mechanical chopper and detected by the lock-in amplifier.
Finite-element modeling (FEM, Comsol Multiphysics) is used for modal analysis of the waveguide properties. In addition to calculating the effective index ($n_{\mathrm {eff}}$) as shown in Fig. 2(a), the analysis is also used to calculate group index, bend loss, and ring-bus coupling. The wavelength at which $n_{Si}=n_{\mathrm {eff}}$ corresponds to phase-matched propagation between the waveguide mode and the substrate, resulting in substrate loss beyond this cutoff wavelength. The dispersion calculations predict this substrate cutoff for the TM modes for wavelengths between 9 $\mu$m and 10 $\mu$m, and a cutoff of 10.5 $\mu$m for the TE$_{00}$ mode in the 4 $\mu$m wide waveguide. All wavelengths beyond this cutoff are no longer guided by the germanium waveguides. In addition, for bent waveguides, weak confinement results in bend loss for wavelengths to the blue of this cutoff, as shown in Fig. 2(b) for our 500 $\mu$m bend radius.
Fig. 2. (a): The modal effective index ($n_{\mathrm {eff}}$) dispersion calculated by finite-element modeling for the fundamental TE and TM modes for waveguides with widths of 4 $\mu$m, 5 $\mu$m, and 6 $\mu$m. (b): The calculated bend loss for a 500 $\mu$m radius of curvature. (c) and (d) show the mode electric field intensity at a wavelength of 8.4 $\mu$m and a width of 5 $\mu$m..
3. Propagation loss and facet coupling
Transmission spectra were acquired from the s-bend waveguides with widths of 4 $\mu$m, 5 $\mu$m, and $6~\mu$m. The spectra are normalized by transmission spectra acquired with the same optics and laser polarization, but with the sample removed. The spectra are then used in an automated linear regression to extract propagation loss (slope) and facet coupling (y-intercept) spectra [20]. Figure 3 shows the resulting loss obtained, along with the error found from the uncertainty in the fit. The plotted facet coupling loss corresponds to one-half the total (input plus output) coupling loss, indicating an extremely broadband edge coupling with a per-facet loss of between 10 dB and 12 dB for both the TE$_{00}$ and TM$_{00}$ modes. For the TE$_{00}$ mode in the 5 $\mu$m and 6 $\mu$m wide waveguides, the per-facet coupling varies by less than 3 dB over the whole 7 $\mu$m to 11 $\mu$m wavelength range.
Fig. 3. Measured propagation loss and coupling loss (for a single waveguide facet) for waveguides nominally 4 $\mu$m, 5 $\mu$m, and 6 $\mu$m wide.
The facet loss is dominated by mode-mismatch between the waveguide and the focused spot: Here the focused spot 1/e$^2$ diameter is estimated to be 30 $\mu$m at a wavelength of 9 $\mu$m, corresponding to a numerical aperture (NA) of 0.20. As the wavelength approaches the substrate cutoff, the waveguide mode size increases, which decreases this mismatch and thus decreases the facet loss. Our modal overlap simulations indicate that the facet coupling loss can be decreased by using a smaller focused spot, and a wider waveguide [18]. For example, at a wavelength of 9 $\mu$m, a focusing NA of 0.40 and a waveguide width tapered to 14 $\mu$m at the facet would result in a coupling loss of approximately 6 dB for the TE$_{00}$ mode and 5 dB for the TM$_{00}$ mode.
As discussed above, for wavelengths redder than the n$_{\mathrm {eff}}$/n$_{\mathrm {Si}}$ degeneracy, the mode couples to the silicon substrate, as shown by the width-dependent cutoffs of the the modes in Fig. 2(a), and by the large increase in measured loss shown in Fig. 3. For the TE$_{00}$ mode, propagation is observed at wavelengths as long as 11.2 $\mu$m for waveguides as narrow as 5 $\mu$m, consistent with our modal simulations. For the TM$_{00}$ mode, the substrate cutoff is observed for wavelengths between 8.5 $\mu$m and 9.5 $\mu$m, also consistent with calculations. The increase in loss prior to cutoff (e. g. above 9.5 $\mu$m for the TM$_{00}$ mode in the 6 $\mu$m wide waveguide) is likely due to the weakly confined mode suffering significant bend loss. The bends are a small fraction of the overall waveguide length, so scaling the calculated bend loss in Fig. 2(b) by this fraction results in loss approximately consistent with that measured below cutoff.
While these propagation loss measurements are generally consistent with those reported by us previously [17], they differ in a number of substantial ways. This sample was etched more deeply and was subject to different photolithography conditions leading to lower sidewall roughness and waveguide width offsets. Since we hope to compare ring Q-factors (discussed below) to waveguide loss, it is important to accurately measure the loss in this sample. In addition, the use of s-bend waveguides has enabled the measurement of the TE$_{00}$ loss across the whole spectral range (6.8 $\mu$m to 11.2 $\mu$m), and has resulted in significantly improved accuracy for both the TE$_{00}$ and TM$_{00}$ modes.
The absorption peak observed in the spectra at 9.05 $\mu$m is consistent with the Si-O impurity absorption [21] that arises from oxygen incorporation into the silicon substrate during Czochralski (Cz) boule growth. The other dominant feature of these spectra is the baseline loss that increases with wavelength. Though this loss is lower than that in recent reports of GOS propagation loss [8], it is higher than that recently measured in lightly n-doped germanium [18]. Our observed baseline loss is inconsistent with sidewall scattering, which increases as the wavelength decreases. In addition, as shown in Fig. 2(b), our models indicate insignificant bend loss (< 1dB/cm) for these modes 1 $\mu$m bluer than the substrate cutoff. Though lattice absorption due to multi-phonon resonances in silicon is expected to increase with wavelength, modal simulations [18] based on bulk absorption values [21] indicate the waveguide absorption would be <3 dB/cm at wavelengths <11 $\mu$m. However, recent measurements of similar GOS waveguides [18] suggest that the epitaxial germanium may be unintentially p-doped, potentially resulting in waveguide propagation loss $\sim$10dB/cm (for a p-doping of approximately 3$\times 10 ^{15}$ cm$^{-3}$) that increases with wavelength. Epitaxial germanium instead grown with light n-doping has resulted in waveguide losses of approximately 1 dB/cm at wavelengths between 10 $\mu$m and 11 $\mu$m [18].
4. Ring resonance
Since the laser employed does not sweep with sufficient stability to accurately measure the narrow bandwidth features such as ring resonators, the samples were thermally tuned using a resistive heater. The temperature of the sample mount was simultaneously monitored with a thermistor. Typical bus transmission thermal sweeps are shown in Fig. 4 for both modes for 5 $\mu$m wide bus and ring waveguides. Clear ring resonances due to the thermo-optic effect are observed despite thermal drift that results in misalignment between the facet and focused spot. The TE$_{00}$ mode shows ring resonances at wavelengths as red as 11.0 $\mu$m, which is to our knowledge the furthest into the IR ring resonances have been observed. Previous studies reported ring resonators at a wavelength of 5.3 $\mu$m [22] (in germanium-on-silicon-on-insulator) and at 8.4 $\mu$m [23] and 8.0 $\mu$m [24] (in graded silicon-germanium). We measure both heating and cooling, showing that the observed temperatures correspond to the actual sample temperature since there is no lag between the temperature and observed transmission features.
Fig. 4. Measured thermo-optic tuning showing TM$_{00}$ and TE$_{00}$ ring resonances in 5 $\mu$m wide waveguides. The lines are nonlinear least-square curve fits as described in the text.
To analyze the thermal sweeps, we fit the bus transmission data to a model that includes a drifting bus transmission with Fabry-Perot facet oscillations in addition to the ring resonance. These fits are shown with the data in Fig. 4. The ring resonance component of the fit is [25]
where $t$ is the “through” field fraction in the bus-ring coupling region, $a$ is the fractional field loss once around the ring, $T$ is the ring temperature, $T_0$ is the resonant temperature, and $\mathrm {FTR}$ is the “free-thermal-range”, i. e. the spacing between adjacent resonances analogous to the free-spectral-range in frequency tuning. These fits provide a measurement of the propagation loss in the ring ($=-20\log (a)/L$), where $L$ is the ring perimeter, the power coupling between the bus and the ring ($K=1-t^2$), and $\mathrm {FTR}$, which will be discussed in the next section. The extracted propagation losses can be compared to those measured in the s-bend waveguides, and the coupling can be compared to our calculations.To calculate the coupling for a given waveguide width, we find the even and odd modes as a function of the coupling gap ($g$) and wavelength from our mode solver, use the relationship $\kappa (\lambda ,g) = \pi [n_{\mathrm {even}}(\lambda ,g)-n_{\mathrm {odd}}(\lambda ,g)]/\lambda$, and numerically integrate this coupling across the whole coupling region:
The results of the calculation are shown in Fig. 5 along with the extracted coupling from the rings with high-confidence fits. The agreement is quite good, and indicates that the resonances observed in the thermal tuning can be accurately modeled using this method. It should be noted that the extracted propagation losses for the rings plotted in Fig. 5 are consistent with the values given in Fig. 3 to within 40%. These losses (between 25 dB/cm and 3.5 dB/cm) correspond to Q-factors between 2$\times 10^{3}$ and 1$\times 10^{4}$. These Q-factors are likely limited by the same factors as discussed in Section 3.: free-carrier absorption and bend loss. For comparison, recently measured SiGe ring resonators at a wavelength of 8.0 $\mu$m [24] and diamond microdisk resonators at a wavelength of 9.5 $\mu$m [26] were shown to have Q-factors of 3.2$\times 10^{3}$ and 3.6$\times 10^{3}$, respectively.
Fig. 5. Measured and calculated ring-bus coupling for the TM$_{00}$ and TE$_{00}$ modes in 5 $\mu$m wide waveguides vs. wavelength.
5. Thermo-optic coefficients
The measured free-thermal-range (FTR) from the ring resonances can also be used to measure the thermo-optic coefficient in the LWIR. The optical phase for light propagating in a waveguide a distance $L$ is given by
For a ring resonator with perimeter $L$ that is heated by $\Delta T$, the phase change for a full revolution around the ring is
The data shown in Fig. 6 provide a measurement of $\mathrm {FTR}$ and thus ${\mathrm d n_{\mathrm {eff}} \over \mathrm d T}$ for both the TE$_{00}$ and TM$_{00}$ modes at $\lambda$= 8.40 $\mu$m:
As discussed above, the measurement of both the heating and cooling of the ring ensures that the measured temperature is the actual temperature of the ring, with an error given by the shift between the two data sets. These $\mathrm {FTR}$ values can then be used to calculate the material thermo-optic coefficients of Ge and Si at this wavelength.
Fig. 6. Measured thermo-optic tuning showing TE$_{00}$ and TM$_{00}$ ring resonances in 5 $\mu$m wide waveguides at a wavelength of 8.40 $\mu$m. The FTR is indicated by the arrows and is found from a fit to the data.
The temperature dependence of $n_{\mathrm {eff}}$ is related to the material thermo-optic coefficients:
The four coefficients ${\mathrm d n_{\mathrm {eff}}^{TE} \over \mathrm d n_{Ge}}$, ${\mathrm d n_{\mathrm {eff}}^{TE} \over \mathrm d n_{Si}}$, ${\mathrm d n_{\mathrm {eff}}^{TM} \over \mathrm d n_{Ge}}$, and ${\mathrm d n_{\mathrm {eff}}^{TM} \over \mathrm d n_{Si}}$ are related to the modal confinement factors and can be found using our finite-element mode solver. We obtain 0.826, 0.228, 0.549, and 0.521, respectively for the waveguide under investigation at $\lambda$= 8.40 $\mu$m. Equation (7) can then be rearranged to solve for ${\mathrm d n_{Ge} \over \mathrm d T}$ and ${\mathrm d n_{Si} \over \mathrm d T}$:
The measured thermo-optic coefficient for Ge is consistent with values reported in the mid-wave and long-wave IR [27,28]: 4.16 $\times 10^{-4}$ K$^{-1}$ at 5.5 $\mu$m, decreasing with wavelength. However, the measured value for Si is significantly larger than that reported in the IR [27,28]: 1.7 $\times 10^{-4}$ K$^{-1}$. The reason for this discrepancy remains under investigation, but could be due to the presence of a thin graded buffer layer or other intermixing present beneath the Ge layer used for high-quality epitaxy. Thin oxide layers could also be present on the waveguide, potentially reducing the accuracy of this analysis. Our measurements highlight the need for in-situ thermo-optic material characterization for accurate thermal-tuning performance of long-wave IR GOS photonic components.
6. Conclusions
We have demonstrated the measurement of ring resonances and thermo-optic tuning in the long-wave infrared in germanium-on-silicon waveguides. The results show wide-bandwidth edge coupling of over 4 $\mu$m, propagation of the TE$_{00}$ mode to beyond 11.2 $\mu$m, accurate measurement of material thermo-optic properties, and the observation of ring resonances at wavelengths as red as 11.0 $\mu$m. This is, to our knowledge, the furthest into the IR that ring resonance has been observed in integrated waveguides. GOS ring resonators are of particular importance in the LWIR for the detection and identification of trace levels of chemical analytes using IR spectroscopy. Ongoing work is focusing on understanding and decreasing losses for the GOS platform and demonstrating feasibility for high-fidelity integrated IR spectroscopy.
Funding
Office of Naval Research (NRL Base Program WU 1P84).
Acknowledgments
The authors acknowledge funding from the Office of Naval Research via NRL Base Program WU 1P84.
Disclosures
The authors declare no conflicts of interest.
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