Temperature sensor with enhanced sensitivity based on silicon Mach-Zehnder interferometer with waveguide group index engineering

Yang Zhang; Jun Zou; Jian-Jun He

doi:10.1364/OE.26.026057

1. Introduction

Temperature sensors have been widely used in many fields. Resistance thermometers are mature but sensitive to environmental variables. A number of fiber-optical temperature sensor structures have been reported, including fiber Bragg gratings (FBGs) [1–3], fiber ring lasers [4], Sagnac interferometer [5], bent micro fibers [6], etc. However, these fiber based temperature sensors have relatively low sensitivity, due to low thermo-optic coefficient (TOC) of silica and they also have relatively large sizes.

Recently, temperature sensors based on SOI platform have received much attention because of the large TOC of silicon (~1.86 × 10⁻⁴/°C [7]) and the high refractive index contrast. Ring resonators [8], Fabry-Perrot (FP) cavities [9] and waveguide Bragg gratings [10] based on silicon show the sensitivity of about 80pm/°C. Kim et al [11] improved the temperature sensitivity of SOI ring resonators to 293.9pm/°C by using the Vernier effect of cascaded ring resonators, at the expense of reduced resolution because of its error on envelope peak fitting. Zhang et al [12] presented a temperature sensor based on cascaded silicon photonic crystal nanobeam cavities. One of the two cavities has a red shift in its wavelength in response to rising temperature while the other has a blue shift, increasing the total sensitivity to 162.9pm/°C.

Mach-Zehnder Interferometer (MZI) is another robust structure of choice for temperature sensing. To obtain higher sensitivity than conventional MZI, Lee [13] used titania (TiO₂) material with a large negative TOC as the waveguide cladding, and the sensitivity was improved to −340pm/°C by appropriately choosing design parameters. Guan et al [14] reported a MZI sensor employing silicon/polymer hybrid waveguides, giving an experimentally measured sensitivity of 172pm/°C. However, these two approaches either increase the complexity of fabrication process or introduce polymer materials, which are not CMOS-compatible.

In this paper, we propose a highly-sensitive SOI-based MZI temperature sensor employing group refractive index engineering. The waveguide widths in the two MZI arms are tailored to have different temperature sensitivities but nearly the same group refractive indices. It can be fabricated in a single etch step with a single mask, without any polymer or titania cladding. The process is therefore compatible with CMOS technology and can realize mass-production with low-cost. More importantly, temperature sensitivity of the proposed sensor was measured to be 438pm/°C, which is about seven times larger than that of a conventional silicon MZI and is higher than all previously reported values.

2. Principle and analysis

The proposed temperature sensor is schematically shown in Fig. 1. It has two arms with the same physical length, each containing a sensing waveguide segment of length $L$ (ignoring the length of tapers) with a specially designed width. The waveguide widths of the differential sensing segments in the two MZI arms are denoted as $W_{1}$ and $W_{2}$ , respectively.

Fig. 1 Schematic diagram of the proposed temperature sensor.

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Assuming $W_{1} \geq W_{2}$ , the transmission peak condition of the MZI is given as:

m λ = [n_{e f f} (W_{1}) - n_{e f f} (W_{2})] \cdot L

where

m

is the interference order (being an integer for constructive interference or a half-integer for destructive interference),

λ

is the wavelength in vacuum and

n_{e f f} (W_{1})

and

n_{e f f} (W_{2})

are effective indices of the waveguide with widths of

W_{1}

and

W_{2}

, respectively. Taking into account the wavelength dispersion effect, the interference order

m

should be modified as [15]:

M = a b s (m - [\frac{\partial n_{e f f} (W_{1})}{\partial λ} - \frac{\partial n_{e f f} (W_{2})}{\partial λ}] \cdot L)

The environmental temperature induced wavelength shift of MZI is related to the thermal expansion coefficient of silicon and the TOC of silicon, however the former has the value of 3.57 × 10⁻⁶/K [16], much smaller than the latter ~1.86 × 10⁻⁴/K. Thus we only consider the effect of the TOC of silicon in the following analysis. Temperature sensitivity of the proposed MZI sensor is determined by the following Eq.

\frac{\partial λ}{\partial T} = \frac{L}{M} \cdot [\frac{\partial n_{e f f} (W_{1})}{\partial T} - \frac{\partial n_{e f f} (W_{2})}{\partial T}]

Substituting Eqs. (1) and (2) into Eq. (3), we obtain the sensitivity:

\frac{\partial λ}{\partial T} = \frac{λ}{| n_{g} (W_{1}) - n_{g} (W_{2}) |} \cdot [\frac{\partial n_{e f f} (W_{1})}{\partial T} - \frac{\partial n_{e f f} (W_{2})}{\partial T}]

Here

n_{g} (W_{i}) = n_{e f f} (W_{i}) - λ \frac{\partial n_{e f f} (W_{i})}{\partial λ} (i = 1, 2)

is the group index of the fundamental mode with waveguide width

W_{i}

. Equation (4) shows that the temperature sensitivity is determined by both the difference between the group indices of the waveguides in the two MZI arms and the difference between their temperature sensitivities of their effective indices.

Considering a SOI wafer with a top silicon layer of 250nm and a buried oxide (BOX) layer of 3μm, and assuming the waveguide upper-cladding to be silica with a thickness of 1.5μm, we simulated the effective index $n_{e f f} (W_{i})$ of quasi-TM mode and its dispersion coefficient $\frac{\partial n_{e f f} (W_{i})}{\partial λ}$ for a waveguide with the width ranging from 400 nm to 1000 nm by using finite-difference eigenmode solver. The wavelength and initial temperature are set to 1560nm and 300K, respectively, in the simulation. The results are shown in Fig. 2(a). One can see that the effective index $n_{e f f} (W_{i})$ increases with increasing $W_{i}$ , while the second item in the expression of group index, i.e. $- λ \frac{\partial n_{e f f} (W_{i})}{\partial λ}$ , has a maximum value at the $W_{i}$ of around 520nm, and then begins to decrease as the waveguide width further increases. Therefore, $n_{g} (W_{i})$ reaches a local maximum value where the derivatives of these two terms, i.e. $n_{e f f} (W_{i})$ and $- λ \frac{\partial n_{e f f} (W_{i})}{\partial λ}$ , with respect to $W_{i}$ are equal in value but opposite in sign. We find that the maximal $n_{g} (W_{i})$ appears when the waveguide width is about 680nm by calculation. Nevertheless, temperature sensitivity of the waveguide, being expressed by $\frac{\partial n_{e f f} (W_{i})}{\partial T}$ , rises monotonically with increasing waveguide width. Figure 2(b) shows $n_{g} (W_{i})$ and $\frac{\partial n_{e f f} (W_{i})}{\partial T}$ as a function of waveguide width. One can see that there exist two waveguide widths for the same values of $n_{g}$ , when $n_{g}$ is slightly smaller than the maximum value. According to Eq. (4), high temperature sensitivity can be realized by reducing the denominator and increasing the numerator. Therefore, we can set the values of $n_{g} (W_{1})$ and $n_{g} (W_{2})$ to be very close while keeping a large difference between their temperature sensitivities to improve the temperature sensitivity of the MZI.

Fig. 2 (a) $n_{e f f} (W_{i})$ and $- λ \partial n_{e f f} (W_{i}) / \partial λ$ as a function of the waveguide width, respectively. (b) The group index and temperature sensitivity of the waveguide as a function of the waveguide width. Here the wavelength, initial temperature and the thickness of core Si layer is 1560nm, 300K and 250nm, respectively, with silica cladding.

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Figure 3 shows how the sensitivity changes when the waveguide width of one arm is fixed and the other varies at the wavelength of 1560nm. The fixed $W_{1}$ and $W_{2}$ are chosen to be 900nm and 520nm, respectively. As can be seen in Fig. 3, a proper combination of $W_{1}$ and $W_{2}$ can improve the sensitivity up to more than hundreds of picometers per centi-degree. A comparison of Figs. 3(a) and 3(b) indicates that the sensitivity is more susceptible to the width of arm 2 (the narrower one) than that of arm 1 (the wider one). It is easy to understand because the group index and temperature sensitivity of the waveguide will level off when $W_{i}$ gets large enough. It is worth noticing that the sensitivity may reach an ultrahigh value when $n_{g} (W_{1}) - n_{g} (W_{2})$ approaches to zero. However, this kind of combination is not recommended due to its low fabrication tolerance and high wavelength dependence, which will be discussed later. Therefore, we chose $W_{1}$ to be 900nm and $W_{2}$ to be 520nm (corresponding to group indices of 4.4883 and 4.4618, respectively), with the calculated sensitivity of ~500pm/°C and good tolerance. Similar characteristics can also be seen in TE mode. However, the proper waveguide widths for TE mode are much narrower than those for TM mode, and thus have lower fabrication tolerances. Therefore, TM mode waveguides are chosen in this work, and the input/output grating couplers are also designed for TM mode.

Fig. 3 (a) Temperature sensitivity of the MZI sensor as a function of $W_{2}$ when $W_{1}$ is fixed at 900nm. (b) Temperature sensitivity as a function of $W_{1}$ when $W_{2}$ is fixed at 520nm.

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The dynamic range of the sensor is determined by the free spectral range (FSR) and the sensitivity. The FSR can be calculated by $F S R = \frac{λ^{2}}{L \cdot | n_{g} (W_{1}) - n_{g} (W_{2}) |}$ [14], thus the dynamic range $Δ T_{D R}$ can be expressed as:

Δ T_{D R} = \frac{F S R}{S e n s i t i v i t y} = \frac{λ}{L \cdot [\frac{\partial n_{e f f} (W_{1})}{\partial T} - \frac{\partial n_{e f f} (W_{2})}{\partial T}]}

While

W_{1}

and

W_{2}

are fixed, the

Δ T_{D R}

mainly depends on the length

L

of the differential sensing waveguide segments, which can be adjusted to meet different performance requirements. However, there is a tradeoff between the dynamic range and the resolution because of the squared cosine shape of the response spectrum of the MZI [17]. Larger FSR will lead to greater errors when tracing the trough wavelength of the spectrum. Therefore, the length

L

should be chosen appropriately.

3. Fabrication and results

The proposed sensor was fabricated on the SOI platform with a 250nm Si core layer and a 3μm silica buried layer. First a negative e-beam resist ma-N 2403, was spin coated on the wafer. Then it was patterned by an e-beam lithography system Raith150 TWO and developed by a specific developer ma-D 525. Subsequently, the chip was etched by the inductively coupled plasma (ICP) using a gas mixture of SF₆ and C₄F₈ chemistry. A 1.5μm silica upper cladding was deposited on the chip by Plasma Enhanced Chemical Vapor Deposition (PECVD), after the residual resist was removed. Optical micrograph of the fabricated sensor is shown in Fig. 4(a). The widths of waveguides on the input and output sides were both 450nm, in order to satisfy the single mode condition. The widths of the two arms are designed to be 520nm and 900nm, respectively. The length $L$ of the differential sensing segments is 2mm in each arm. Linear tapers are used to connect the 450nm-wide waveguide to the 520nm- and 900nm-wide waveguides, with 5μm and 9μm taper lengths, respectively. The radius of curvature of the bent waveguide used in the Y-branch is 120μm. Figures 4(b) and 4(c) are scanning electron microscopy (SEM) images of the waveguides in arm 1 and arm 2, respectively. The widths of the two arms were measured to be 902.5nm and 521.8nm, within an error range of about 0.4%. The quasi-TM mode light was coupled in and out by grating couplers on the input and output sides of the sensor.

Fig. 4 (a) Optical microscope image of the fabricated MZI sensor. (b)-(c) The SEM images of two arms.

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The Agilent lightwave measurement system (8164B), with a tunable Laser source (81606A) and a power sensor (81634A), was utilized to test the sensor. The highest wavelength resolution of this system was 1 pm. The chip was placed on a sample holder made of red copper, with a thermistor placed inside for the temperature feedback. A thermal electric cooler (TEC) beneath the holder was used for heating and cooling. Errors between the actual chip temperature and the set value were measured to be less than 0.3°C.

The transmission spectra were measured and shown in Fig. 5(a). The ambient temperature was tuned from 16°C to 32°C, with a step of 2°C. Figure 5(c) gives the dip wavelength shift with respect to temperature for data shown in Fig. 5(a). We can see that it has an approximately linear shift with increasing ambient temperature. The slope was found to be 438pm/°C by linear fitting, which was slightly lower than the simulated value, as shown in Fig. 3, due to the fabrication errors and thickness variation of the silicon core layer. For comparison, we also measured the temperature response for a conventional silicon MZI with the same waveguide width. The length difference between the two arms is set to 50μm, in order to obtain a large FSR similar to the proposed sensor. Note that the sensitivity of a conventional MZI can be expressed by $\frac{\partial λ}{\partial T} = \frac{λ}{n_{g}} \cdot \frac{\partial n_{e f f}}{\partial T}$ , which is not dependent on the length difference. The results are plotted in Figs. 5(b) and 5(c). It can be seen that the sensitivity is significantly enhanced by about seven times using the proposed design. As we have mentioned before, a larger FSR results in blunter troughs that lead to greater errors when tracing the dip wavelengths of the MZI spectra. The relative accuracy of the power sensor used in this system is 0.015dB. It corresponds to a wavelength uncertainty of about 13pm near the dip in the spectra of the proposed sensor. From the measured sensitivity of 438pm/°C, we can derive the temperature sensitivity of about 0.03°C.

Fig. 5 (a)-(b) Transmission spectra of the proposed sensor and conventional MZI at different temperature, respectively. (c) The wavelength shifts of interference spectrum with respect to the temperature variation. Slopes are obtained by linear fitting.

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Additionally, several sensors with other parameters are fabricated and tested, in order to find out how the performance changes with respect to fabrication errors. As mentioned above, $W_{1}$ has larger tolerance than $W_{2}$ . Thus we tuned $W_{1}$ from 850nm to 950nm, and $W_{2}$ from 500nm to 540nm on the graphs. The results are shown in Fig. 6. The sensitivity of each width-combination was also obtained by linear fitting. We can find that in the $W_{1}$ range of 900nm $\pm$ 50nm and $W_{2}$ range of 520nm $\pm$ 20nm, variation of the sensitivity is less than 6%, which indicates that the proposed sensor has a large fabrication tolerance.

Fig. 6 Dip-wavelength shift with respect to temperature variation. Five width-combinations were fabricated and measured, indicating a good tolerance for the proposed sensor.

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As we discussed in Eq. (5), the dynamic range of the proposed sensor, $Δ T_{D R}$ , is related to FSR of the MZI, which is mainly determined by the differential sensing segment length $L$ when the waveguide widths are fixed. However, the actual measurement range is also limited by wavelength dependence of the sensitivity. Figure 5(a) experimentally proves that the sensitivity at wavelength of about 1578nm is lower than that at wavelength of 1560nm. As we can see in Fig. 3, the high-sensitivity condition changes with different operating wavelengths, which mainly results from the large dispersion characteristics of silicon material. Therefore, Eq. (4) needs to be recalculated when the operating wavelength has a large variation. In general, higher sensitivity is more rigorous in Eq. (4), which means it is more dependent on wavelength. Here we recommend two designing schemes of the proposed sensor. One is the scheme for high precision and small range detection. The sensitivity can reach more than 400pm/°C by utilizing a proper combination of $W_{1}$ and $W_{2}$ , as we demonstrated experimentally. The dynamic range is estimated to be around 20°C. The differential sensing segment length $L$ can be larger to improve the resolution because the main major limiting factor for the sensing range is wavelength dependence of the sensitivity, instead of the FSR. The other scheme, at the cost of reducing the sensitivity, can be used for wide range detection. We experimentally confirmed that when $W_{1}$ and $W_{2}$ are designed to be 900nm and 460nm, respectively, the average sensitivity becomes about 220pm/°C at the wavelength range from 1560nm to 1590nm, with the variation less than 8%, amounting to a sensing range of more than 130°C, as shown in Fig. 7. Here $L$ should be moderately reduced because the dynamic range is mainly confined by FSR of the transmission spectrum.

Fig. 7 Transmission spectra of the proposed sensor at different temperature when $W_{1} = 900 n m$ and $W_{2} = 460 n m$ . The temperature sensitivities at different wavelength from 1560nm to 1590nm are labeled respectively.

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Conclusion

In summary, we reported a sensitivity-enhanced temperature sensor on SOI platform. The sensor utilizes a MZI with different waveguide widths in its two arms. In this work we experimentally presented the MZI with 900nm and 520nm waveguide width in two arms, respectively. Its sensitivity reached 438pm/°C, over seven times more than that of a conventional silicon MZI. Moreover, when we slightly tuned the widths to 900nm $\pm$ 50nm and 520nm $\pm$ 20nm, the sensitivity changed no more than 6%, which showed a good fabrication tolerance. Larger dynamic range detection can be realized by properly reducing the sensitivity and differential sensing segment length $L$ . Besides the high temperature sensitivity, the proposed sensor has a significant advantage that it can be fabricated by a single mask, without any overlay processes and polymer cladding. This makes it easy to be integrated with other structures in a lab-on-chip system.

Funding

National Natural Science Foundations of China (61535010, 61605172); Public Project of Zhejiang Province (2016C33074).

References

1. Y. J. Rao, D. J. Webb, D. A. Jackson, L. Zhang, and I. Bennion, “In-fiber bragg-grating temperature sensor system for medical applications,” J. Lightwave Technol. 15(5), 779–785 (1997). [CrossRef]

2. S. Bandyopadhyay, J. Canning, M. Stevenson, and K. Cook, “Ultrahigh-temperature regenerated gratings in boron-codoped germanosilicate optical fiber using 193 nm,” Opt. Lett. 33(16), 1917–1919 (2008). [CrossRef] [PubMed]

3. J. L. Kou, S. J. Qiu, F. Xu, and Y. Q. Lu, “Demonstration of a compact temperature sensor based on first-order Bragg grating in a tapered fiber probe,” Opt. Express 19(19), 18452–18457 (2011). [CrossRef] [PubMed]

4. J. Shi, Y. Wang, D. Xu, H. Zhang, G. Su, L. Duan, C. Yan, D. Yan, S. Fu, and J. Yao, “Temperature sensor based on fiber ring laser with sagnac loop,” IEEE Photonics Technol. Lett. 28(7), 794–797 (2016). [CrossRef]

5. L.-Y. Shao, Y. Luo, Z. Zhang, X. Zou, B. Luo, W. Pan, and L. Yan, “Sensitivity-enhanced temperature sensor with cascaded fiber optic Sagnac interferometers based on Vernier-effect,” Opt. Commun. 336, 73–76 (2015). [CrossRef]

6. P. Munendhar, L. Zhang, L. Tong, and S. Yu, “Highly sensitive temperature sensor using intrinsic Mach-Zehnder interferometer formed by bent micro-fiber embedded in polymer,” in Proceedings of the 2017 25th Optical Fiber Sensors Conference (OFS); Jeju, Korea. 24–28 April 2017; pp. 1–4.

7. R. Dekker, N. Usechak, M. Först, and A. Driessen, “Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides,” J. Phys. D Appl. Phys. 40(14), R249–R271 (2007). [CrossRef]

8. H. Xu, M. Hafezi, J. Fan, J. M. Taylor, G. F. Strouse, and Z. Ahmed, “Ultra-sensitive chip-based photonic temperature sensor using ring resonator structures,” Opt. Express 22(3), 3098–3104 (2014). [CrossRef] [PubMed]

9. G. Liu, M. Han, and W. Hou, “High-resolution and fast-response fiber-optic temperature sensor using silicon Fabry-Pérot cavity,” Opt. Express 23(6), 7237–7247 (2015). [CrossRef] [PubMed]

10. R. Boeck, M. Caverley, L. Chrostowski, and N. A. F. Jaeger, “Grating-assisted silicon-on-insulator racetrack resonator reflector,” Opt. Express 23(20), 25509–25522 (2015). [CrossRef] [PubMed]

11. H. T. Kim and M. Yu, “Cascaded ring resonator-based temperature sensor with simultaneously enhanced sensitivity and range,” Opt. Express 24(9), 9501–9510 (2016). [CrossRef] [PubMed]

12. Y. Zhang, P. Liu, S. Zhang, W. Liu, J. Chen, and Y. Shi, “High sensitivity temperature sensor based on cascaded silicon photonic crystal nanobeam cavities,” Opt. Express 24(20), 23037–23043 (2016). [CrossRef] [PubMed]

13. J.-M. Lee, “Ultrahigh temperature-sensitive silicon MZI with titania cladding,” Front. Mater. 2(36), 1–4 (2015).

14. X. Guan, X. Wang, and L. H. Frandsen, “Optical temperature sensor with enhanced sensitivity by employing hybrid waveguides in a silicon Mach-Zehnder interferometer,” Opt. Express 24(15), 16349–16356 (2016). [CrossRef] [PubMed]

15. M. Uenuma and T. Motooka, “Temperature-independent silicon waveguide optical filter,” Opt. Lett. 34(5), 599–601 (2009). [CrossRef] [PubMed]

16. H. Xu, M. Hafezi, J. Fan, J. M. Taylor, G. F. Strouse, and Z. Ahmed, “Ultra-sensitive chip-based photonic temperature sensor using ring resonator structures,” Opt. Express 22(3), 3098–3104 (2014). [CrossRef] [PubMed]

17. D. Martens and P. Bienstman, “Comparison between vernier-cascade and mzi as transducer for biosensing with on-chip spectral filter,” Nanophotonics 6(4), 703 (2017). [CrossRef]

Temperature sensor with enhanced sensitivity based on silicon Mach-Zehnder interferometer with waveguide group index engineering

Abstract

1. Introduction

2. Principle and analysis

3. Fabrication and results

Conclusion

Funding

References

Cited By

Figures (7)

Equations (5)

Optics Express