We report a photonic temperature sensor with enhanced performance in both broad- and narrow-bandwidth optical measurements. The device consists of a heterogeneously integrated Mach–Zehnder interferometer with arms composed of silicon and silicon nitride waveguides whose thermo-optic coefficients differ by an order of magnitude. The waveguides are fabricated in distinct layers of a monolithic device and guide light in a single transverse-electric mode. The resulting small bend radii enable compact sensing of temperatures local to integrated photonic components with a device footprint of 580 × 410 μm2. Furthermore, the dual layers of the sensor enable overlaying of the spiral arms of the interferometer over each other or other photonic circuit components. We measure a sensitivity of 324 pm/K, an over threefold enhancement compared to the measurement of an asymmetric Mach–Zehnder constructed of silicon waveguides on the same device. We additionally define a useful figure of merit for the side-of-fringe measurement regime, which uses direct detection of a narrow linewidth laser and show that the reported device is also competitive on this metric.

Common integrated photonic components, such as ring resonators and asymmetric interferometers, are sensitive to local temperatures, with wavelength shifts per temperature determined by the sensitivity, S, typically 60–90 pm/K for silicon-on-insulator depending on the waveguide geometry used. This thermal sensitivity has allowed such devices to be used as optical temperature sensors1,2 as well as providing for thermo-optic control through on-chip heating elements, such as resistive metal strips3,4 or doped junctions.5,6 Stabilization to ambient temperature changes is crucial to ensure that the response of photonic components does not drift over time. However, increasing circuit complexity and component density of photonic integrated circuits (PICs) can result in significant crosstalk between components.

In recent years, integrated photonic temperature sensors have received significant attention due to their small form factor and lack of electromagnetic interference that affects comparable electrical components.7 These sensors are typically used in either a wavelength scanning or a side-of-fringe regime.8,9 Previous demonstrations using ring resonators and Mach–Zehnder interferometers (MZI) have achieved high performance in sensitivity, a key figure of merit (FOM), using techniques that include adding polymer cladding materials with large thermo-optic coefficients,10–12 exploiting the optical Vernier effect,13,14 or engineering the thermo-optic and dispersive properties of waveguides.2,12 However, each of these methods have significant downsides. Footprints of devices using polymer cladding are typically on scales of tens of millimeters.10,11 Using the optical Vernier effect places stringent requirements on the wavelength resolution of the measurement apparatus to avoid aliasing effects. Finally, waveguide engineering requires a combination of wide multimode and narrow single-mode waveguides, resulting in a trade-off between device footprint and loss.

Both silicon and silicon nitride components have reached a mature stage of development.15,16 In particular, recent advances in fabrication methods have led to the heterogeneous implementation of silicon nitride waveguides,17–20 III/V lasers,19,20 and germanium photodiodes21,22 onto the same wafer as high-quality silicon-on-insulator waveguides, permitting circuits with increasingly small footprints and complex circuitry for which temperature fluctuations play a key role.

In this Letter, we report a temperature sensor using a compact heterogeneous Mach–Zehnder interferometer (HIMZI) as a component-level temperature sensor. The device could be stand-alone or integrated with more complex heterogeneous photonic integrated circuits. The sensor utilizes silicon and silicon nitride waveguides in each path of the interferometer, such that high temperature sensitivity is achieved via the order-of-magnitude difference between the thermo-optic coefficients (TOCs) of silicon and silicon nitride while simultaneously ensuring good path length matching between the paths formed by the waveguides to achieve a large free spectral range (FSR). The sensor is highly CMOS compatible, and the light propagates in a single transverse-electric mode in each waveguide, which results in minimal loss even for compact bend radii of 30 and 10 μm for the silicon nitride and silicon waveguides. Furthermore, the dual layer nature of the platform allows local sensing of otherwise topologically isolated components such as ring resonators. We measure a sensitivity of SHIMZI= 324 pm/K from the device, an over threefold improvement over a silicon asymmetric MZI (AMZI) we measure on the same die (SSiAMZI= 88.3 pm/K). Improved path length matching could increase this further.

We now describe the two common modes of operation for temperature sensors. In the wavelength scanning mode, broadband light is directed to a temperature sensitive optical component, such as a ring resonator, AMZI, or Bragg grating. As the temperature changes, the phase of the optical paths change via the thermo-optic coefficient, resulting in a shift in the wavelength of the phase-dependent resonant features. Through this mechanism, the temperature of the device can be inferred by measuring the spectrum of the transmitted light. The key FOM in this scheme is the sensitivity S, which is defined as the wavelength shift of a resonance or other spectral feature per degree change in temperature.

For an interferometer with two arms of different lengths L1, L2, the difference in the accumulated optical phase between the arms changes with both temperature and wavelength. To first order the output intensity varies sinusoidally with temperature and wavelength, with periods given by the temperature period (TP) and free spectral range (FSR), respectively. These can be defined as

TP=λ0(neff,1TL1neff,2TL2)1
(1)

and

FSR=λ02ng,1L1ng,2L2,
(2)

where ng,i=neff,ineff,iλ is the group index and neff,iT is the thermo-optic coefficient of each path at the operational wavelength λ0 of the device. The sensitivity is the ratio of these two values

S=FSRTP=λ0(neff,1TL1neff,2TL2)(ng,1L1ng,2L2)1.
(3)

Thus, a device for which the phase difference between the two arms varies significantly with temperature but not with wavelength will result in a high sensitivity, with large resonance wavelength shifts as temperature changes. The output intensity varies with a periodicity equal to the temperature period which gives the dynamic temperature range of the sensor for direct readout. Therefore, the sensitivity can be improved by increasing the FSR of the device to avoid reducing dynamic range.

In the case of an AMZI or ring resonator constructed from a waveguide of a single material and of constant dimensions, the sensitivity is given simply by

S(ng,1=ng,2=ng)=λ0ngneffT,
(4)

which is independent of the size of the sensor and is only dependent on the thermal and dispersive properties of the waveguide. For a typical silicon waveguide, the sensitivity is limited to less than 100 pm/K.8,9,30

The second “side-of-fringe” method for temperature measurement sacrifices the precision of the wavelength scanning technique for a simpler set-up and direct detection.8 A narrow linewidth source is directed to the most dispersive wavelength of the sensor. Changes in temperature alter the light transmitted by the sensor which can be detected by a photodiode at the output. If the frequency noise of the laser is dominant, as is likely for low-cost implementations, the signal-to-noise ratio (SNR) is given by

SNR=1σT(IT)T=1σλ(λT)(IT)TSσλ1TP=FSRσλ,
(5)

where I is the output light intensity of the sensor and σT,λ are the standard deviations of temperature and wavelength, respectively. Thus, maximizing the FSR of the device decreases the impact of frequency noise from the input.

The response of the detector in the side-of-fringe mode can be increased by increasing the incident laser power or electronically amplifying the output power measured by a photodiode, but the additional power requirements for each of these could limit the scalability of photonic circuits. Alternatively, the temperature response can be increased by reducing the temperature period of the sensor, at the cost of simultaneously reducing the dynamic range of the sensor in a single-shot measurement. Due to the direct detection of the signal in side-of-fringe mode, it is a natural choice for closing a negative feedback loop. Provided a sufficiently large bandwidth of the loop response, the temperature can then be stabilized before a deviation from the set point exceeds the temperature period.

One method of reducing the temperature period is to increase the optical path lengths of the interferometer, at the cost of the device footprint. Therefore, we define a new figure-of-merit (FOM), which we call the temperature responsivity RT, that has particular relevance for the stabilization of large-scale photonic integrated circuits using the side-of-fringe mode, where both the footprint and power draw of the sensor should be minimized. We define it as the maximum intensity response of the device normalized by the maximum path length in the interferometer, such that

RT=λ0πI0max{L1,L2}max{|I(λ)T|}=λ0TP×max{L1,L2},
(6)

where I is the output intensity from a narrow-band input source of intensity I0. The wavelength λ0 is chosen to maximize I/T, which corresponds to an output intensity I(λ0)=I0/2 (see the supplementary material). As the temperature period scales inversely with the interferometer arm lengths L1, L2 for a given heterogeneous AMZI, the temperature responsivity gives a FOM to compare the performance of different designs in the side-of-fringe mode which is normalized to the size of the device.

For a wavelength insensitive device with perfect path length matching such that ng,1L1=ng,2L2, and thus S,FSR=, we can further state that

RT(FSR=)=|n1Tng,1ng,2n2T|,
(7)

where ng,1>ng,2. Therefore, for a perfectly wavelength-insensitive device, the limit of temperature responsivity is given by the waveguide mode properties alone.

The temperature sensor is shown in Fig. 1. It consists of a MZI containing silicon grating couplers for coupling light into and out of the circuit, and silicon multimode interferometers for splitting and recombining the light into and out of each arm of the interferometer. Silicon waveguides with a dimension of 500 × 220 nm2 are used to guide light between these components and the arms of the interferometer. The key aspect of the design is the transition in one arm of the interferometer from the silicon waveguides to a 1.2 mm length of silicon nitride waveguide via adiabatic tapers, which have a nominal loss of less than 0.25 dB per transition.17,18 The silicon nitride was deposited with a thickness of 400 nm using a CMOS-compatible plasma-enhanced chemical vapor deposition method with a gap of 250 nm from the silicon lithography layer. We chose a waveguide width of 1000 nm for the silicon nitride waveguides to ensure single-mode, low-loss propagation. The two waveguide modes are shown in Fig. 1(a). The results of simulations in Lumerical of their dispersive and thermo-optic characteristics are shown in Table I. We confirmed the accuracy of the calculated ng values by measuring the free spectral range of AMZIs in both silicon (ng=4.22) and silicon nitride (ng=2.07).

FIG. 1.

Modes and device schematic. (a) The E field intensities of the modes in the silicon and silicon nitride waveguides. (b) Micrograph of the device. Full details in text. The thermo-optic phase shifter (TOPM) was not used. (c) Simplified schematic of the device. For compactness the LSi arm of the MZI could be placed below silicon nitride photonic components, while the LSi3N4 arm of the MZI could sit above silicon photonic components.

FIG. 1.

Modes and device schematic. (a) The E field intensities of the modes in the silicon and silicon nitride waveguides. (b) Micrograph of the device. Full details in text. The thermo-optic phase shifter (TOPM) was not used. (c) Simplified schematic of the device. For compactness the LSi arm of the MZI could be placed below silicon nitride photonic components, while the LSi3N4 arm of the MZI could sit above silicon photonic components.

Close modal
TABLE I.

Simulated and experimental waveguide properties at 1540 nm. Data were simulated using Lumerical FDE solver from the waveguide geometries and average values of bulk thermo-optic coefficients from Refs. 23–28. The discrepancy between the measured and simulated silicon nitride coefficient may be due to differences in stoichiometry.29 

SiliconSilicon nitride
Dimensions (nm) 500 × 220 1000 × 400 
neff 2.46 1.62 
Simulated ng 4.24 2.01 
Measured ng 4.24 2.07 
Simulated dneffdT (×105 1/K) 19.6 2.1 
Measured dneffdT (×105 1/K) 24.2 3.2 
SiliconSilicon nitride
Dimensions (nm) 500 × 220 1000 × 400 
neff 2.46 1.62 
Simulated ng 4.24 2.01 
Measured ng 4.24 2.07 
Simulated dneffdT (×105 1/K) 19.6 2.1 
Measured dneffdT (×105 1/K) 24.2 3.2 

To measure the response of the sensor to temperature variations, we glued the chip to a printed circuit board (PCB). A thermistor (ERTJ0ER103H, Panasonic) was soldered adjacent to the chip to measure the local temperature. We confirmed the calibration of temperature-resistance relation of the thermistor by comparing measurements of its resistance, Rth, to ambient temperature measurements from an independent calibrated thermometer as well as measurements from a forward-looking infrared (FLIR) camera at each temperature. The temperature of the chip and the PCB was adjusted using a thermo-electric cooler (TEC), and stabilized by a proportional-integral-derivative temperature controller (Arroyo 5240). A homemade copper block acted as a heat sink for the TEC. High thermal conductivity paste (ARCTIC MX-4) was used to ensure good thermal contact between the surfaces of the heat-sink, the TEC, and the PCB. Such an experimental setup is common for thermal stabilization of PICs and is only required for initial calibration of the sensor, after which the sensor can operate independently.

First we describe our measurements in the wavelength scanning mode. We transmitted a superluminescent diode (SLED, OSICS SLD) through the interferometer and measured the wavelength fringes of the output spectrum using an Anritsu MS9740A optical spectrum analyzer (OSA), with a nominal resolution bandwidth of 36 pm. The temperature of the sensor was varied using the temperature controller, and the temperature was calculated from thermistor resistance measurements which were verified by the FLIR camera. The accumulated phase difference between the silicon and silicon nitride arms of the sensor varies with temperature, resulting in a shift in the interference spectrum measured by the OSA, as shown in Fig. 2(a).

FIG. 2.

Sensitivity measurements of the reported device and comparisons to single-material AMZIs. (a) Wavelength shift of interference fringes of the HIMZI to higher wavelengths as the temperature of the device increases. The temperature of the device is measured from the resistance Rth of the thermistor. (b) Average wavelength change of the minima in the output spectra of the HIMZI temperature sensor compared to measurements from silicon and silicon nitride AMZIs. Temperature errors result from a nominal 3% thermistor calibration error. For the HIMZI and silicon AMZI, wavelength resolution bandwidth of the OSA dominates the wavelength error which is negligible. Silicon nitride demonstrates greater wavelength shift error due to increased variation between the tracked resonances. From these data, we measured sensitivities of SHIMZI=324.0±7, SSi,AMZI=88.3±5, and SSiN,AMZI=23.5±7 pm/K. (c) Simulated sensitivity as a function of the path length of each arm of the HIMZI. The white lines show where TP=0 (resulting in athermalization) and FSR=0 (resulting in maximum sensitivity). In (b) and (c), the arrows marked 1 and 2 show how the sensitivity of the device to temperature can be tailored by changing the path lengths of the two arms of the interferometer.

FIG. 2.

Sensitivity measurements of the reported device and comparisons to single-material AMZIs. (a) Wavelength shift of interference fringes of the HIMZI to higher wavelengths as the temperature of the device increases. The temperature of the device is measured from the resistance Rth of the thermistor. (b) Average wavelength change of the minima in the output spectra of the HIMZI temperature sensor compared to measurements from silicon and silicon nitride AMZIs. Temperature errors result from a nominal 3% thermistor calibration error. For the HIMZI and silicon AMZI, wavelength resolution bandwidth of the OSA dominates the wavelength error which is negligible. Silicon nitride demonstrates greater wavelength shift error due to increased variation between the tracked resonances. From these data, we measured sensitivities of SHIMZI=324.0±7, SSi,AMZI=88.3±5, and SSiN,AMZI=23.5±7 pm/K. (c) Simulated sensitivity as a function of the path length of each arm of the HIMZI. The white lines show where TP=0 (resulting in athermalization) and FSR=0 (resulting in maximum sensitivity). In (b) and (c), the arrows marked 1 and 2 show how the sensitivity of the device to temperature can be tailored by changing the path lengths of the two arms of the interferometer.

Close modal

The sensitivity of the device is given by the rate of wavelength shift per degree of temperature change. We tracked the wavelength of minima in the output spectrum as the temperature varied in a 50 nm bandwidth centered on λ0 = 1541 nm for the reported device, and a silicon AMZI and a silicon nitride AMZI, all on the same die. An example resonance near 1541 nm is shown in Fig. 2(a). The combined wavelength shift of the resonances of the reported HIMZI, a silicon AMZI, and a silicon nitride AMZI are shown in Fig. 2(b). At each measurement temperature, the wavelength changes of each minimum in a 50 nm bandwidth were averaged, and a standard deviation was calculated and combined with the resolution bandwidth of the OSA to give the wavelength change error seen in Fig. 2(b). The small wavelength change error observed for our device indicates that the sensitivity of our device varies minimally over at least 50 nm. We measure sensitivities of 324.0±7, 88.0±5, and 23.5±7 pm/K for the HIMZI, silicon AMZI, and silicon nitride AMZI, respectively. The measured sensitivities are greater than predicted by simulation as shown by dashed lines on the sensitivity scale of Fig. 2(c). This discrepancy could be due in part to the position of the thermistor being offset from the center of the TEC, resulting in a measured temperature range that is lower than the true temperature range imparted to the optical sensor. Using an oven to calibrate the temperature sensor would ensure a more even temperature distribution between the optical sensor and the thermistor and would reduce this inaccuracy. Nevertheless, the ratio of the sensitivity of the HIMZI to the sensitivity of the silicon AMZI is in good agreement between the simulations and measured value.

The sensitivity of the device can be increased further by increasing the FSR of the HIMZI. In particular, our analysis has treated the transitions as a step change between the two waveguides (see the supplementary material). A full characterization of the dispersive and thermo-optic properties of the silicon to silicon nitride waveguide transitions could allow for improved path matching. The expected sensitivity based on the measured parameters given in Table I is shown in Fig. 2(c). Also shown by the white dashed lines in Fig. 2 is the minimum sensitivity measured by the device, which corresponds to neff,1TL1=neff,2TL2 and an infinite temperature period. Choosing path lengths that satisfy this condition results in athermalization of the AMZI, while the FSR of the device is given by

FSR=λ02L2Cathermal,Cathermal=ng,1Tneff,1neff,2Tng,2,
(8)

where Cathermal is constant and the FSR can be varied by changing L2. In this case, the change in optical path length with temperature for each arm of the interferometer is equal, resulting in no wavelength shift in the interference fringes of the interferometer under ambient temperature changes which affect both arms equally. Thus, the techniques used here also can be used to create AMZIs that are protected against thermal crosstalk, which could allow for the creation of highly temperature-stable components for wavelength filtering.

From the sensitivity and the 3.15 nm FSR of our device, we infer a temperature period of 9.7 K for the device. While this is a limited dynamic range, it results in a high temperature responsivity of 12×105/K. Using the waveguide properties in Table I and Eq. (7), we note that a perfectly path length matched device would achieve an even higher temperature responsivity of 38×105/K. The performance of the reported device in both sensitivity and temperature responsivity is compared to several previous results using MZIs in Table II. Our sensor can provide a significant wavelength-independent temperature response thanks to the very large thermo-refractive coefficients between the cores of the silicon and silicon nitride waveguides, where the optical field intensity is greatest. We also simulated the effect of fabrication error on our device, as shown in Fig. 3. We observe less than 10% deviation in the sensitivity over a fabrication error of ±10% in each waveguide, and this is dominated by the larger absolute error in the material parameters of the silicon waveguides.

TABLE II.

Comparison of other MZI-based temperature sensors with high CMOS-compatibility.

ReferenceMethodSTemperature Period [K]RT (×105 K)RT(FSR) (×105 K)
31  Si MZI with TiO2 cladding 340 16.6 21.3 ⋯ 
2  Waveguide-width engineered silicon MZI 438 46 0.17 1.0 
32  Waveguide-width engineered silicon AMZI 445 84 3.7 5.5 
This work Silicon and silicon nitride HIMZI 324 9.8 12 39.0 
ReferenceMethodSTemperature Period [K]RT (×105 K)RT(FSR) (×105 K)
31  Si MZI with TiO2 cladding 340 16.6 21.3 ⋯ 
2  Waveguide-width engineered silicon MZI 438 46 0.17 1.0 
32  Waveguide-width engineered silicon AMZI 445 84 3.7 5.5 
This work Silicon and silicon nitride HIMZI 324 9.8 12 39.0 
FIG. 3.

Simulated tolerance to fabrication error of our device. (a) Deviation of simulated dispersive and thermo-optic material parameters as a function of waveguide width deviation. (b) Resulting variation in S for our device for fabrication errors in silicon or silicon nitride waveguides.

FIG. 3.

Simulated tolerance to fabrication error of our device. (a) Deviation of simulated dispersive and thermo-optic material parameters as a function of waveguide width deviation. (b) Resulting variation in S for our device for fabrication errors in silicon or silicon nitride waveguides.

Close modal

The dual-layer structure of the device permits localized temperature sensing in otherwise hard-to-reach areas of a chip. For example, the silicon spiral could be placed inside silicon nitride ring resonators, which have been used extensively to generate quantum and classical light through four-wave mixing,33–35 or the silicon nitride waveguide of the interferometer could be placed vertically above complex silicon photonics circuits to reduce the overall footprint.36 Alternatively, overlaying the spirals perpendicularly to each other would significantly reduce the footprint of the device, limited by the converter lengths to a footprint of 250×50μm2. Additionally, further heterogeneous electro-optic integration could be implemented. Hetero-epitaxial Germanium photodiodes are already available on the fabrication platform used in this experiment,18 and III–V lasers could additionally be integrated.19,20

In conclusion, we have demonstrated a temperature sensor, which uses a heterogeneous Mach–Zehnder interferometer to achieve high temperature sensitivity. The sensitivity could be significantly improved with better path length matching, or altered to produce an athermal AMZI filter by matching the thermal responses of the two paths. The sensor also exhibits good performance in the “side-of-fringe” regime, for which we have described a figure of merit which is relevant to compact temperature sensing of complex photonic integrated circuits. The sensor is highly CMOS compatible and the use of dual-layer single-moded waveguides allows for compact and versatile footprints. Further integration of epitaxial germanium photodiodes18 and integration of flip-chip bonded semiconductor optical amplifiers, potentially combined with low-loss silicon nitride microring resonators for narrow linewidth operation in side-of-fringe mode,15,20 could produce a contained temperature sensor with purely electronic inputs and outputs. In addition, an on-chip arrayed waveguide grating could be used to replace the requirement for an optical spectrum analyzer in the wavelength scanning measurement scheme, at the cost of additional device footprint.37 Designing the device for a TM mode instead of the TE mode used here could facilitate temperature independent sensing of biological or chemical samples.38,39 Furthermore, with the continued development of heterogeneous integration, the techniques to tailor thermal sensitivity that we have demonstrated here could be used with other materials, such as Indium Phosphide40,41 or Lithium Niobate,42 for potential applications requiring non-linearities or electro-optic modulation.

See the supplementary material for derivation of the temperature responsivity and modeling of the silicon-to-silicon nitride transitions.

D.A.P. acknowledges support from the EPSRC Grant No. EP/S023607/1. J.C.F.M. acknowledges support from the ERC starting Grant No. ERC-2018-STG 803665. The authors thank L. Kling for technical assistance.

The authors have no conflicts to disclose.

David A. Payne: Conceptualization (equal); Data curation (equal); Formal analysis (lead); Investigation (lead); Methodology (lead); Visualization (lead); Writing – original draft (lead). Jonathan C. F. Matthews: Funding acquisition (lead); Project administration (lead); Resources (lead); Supervision (lead); Writing – review & editing (lead).

The data that support the findings of this study are openly available in the University of Bristol's repository at https://doi.org/10.5523/bris.1kg2xnkc0lvqw2gpti5bsfhybz, Ref. 43.

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