Real-time compensation of errors in refractive index shift measurements of microring sensors using thermo-optic coefficients

We report a method for compensation of errors caused by temperature fluctuations in refractive index measurements using Silicon photonic microring sensors. The method involves determination of resonance wavelength shifts caused by thermal fluctuations using real-time measurement of on-chip temperature variations and thermo-optic coefficient (TOC) of analyte liquids. Resistive metal lines patterned around Silicon microrings are used to track temperature variations and TOC of analyte is calculated by measuring wavelength shifts caused by controlled increments in device temperature. The TOC of de-ionized water is determined to be −1.12 × 10−4/ ◦C, with an accuracy of ±8.26 × 10−6/ ◦C. In our system, chip-surface temperature variations were measured with an instrument limited precision of 0.004 ◦C yielding a factor of 16 enhancement in tracking accuracy compared to conventional, bottom-of-chip temperature measurement. We show that refractive index detection limit of the microring sensor is also improved by the same factor. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement OCIS codes: (130.0130) Integrated optics; (130.6010) Sensors; (230.5750) Resonators. References and links 1. M. Estevez, M. Alvarez, and L. Lechuga, “Integrated optical devices for lab-on-a-chip biosensing applications,” Laser Photonics Rev. 6, 463–487 (2012). 2. D. X. Xu, A. Densmore, A. Delâge, P. Waldron, R. McKinnon, S. Janz, J. Lapointe, G. Lopinski, T. Mischki, E. Post, P. Cheben, and J. H. Schmid, “Folded cavity SOI microring sensors for high sensitivity and real time measurement of biomolecular binding,” Opt. Express 16, 15137–15148 (2008). 3. J. Niehusmann, A. Vörckel, P. H. Bolivar, T. Wahlbrink, W. Henschel, and H. Kurz, “Ultrahigh-quality-factor silicon-on-insulator microring resonator,” Opt. Lett. 29, 2861–2863 (2004). 4. K. De Vos, I. Bartolozzi, E. Schacht, P. 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Introduction
Silicon photonic sensors have been studied extensively for measurement of refractive index shift in liquids.Their unique advantages such as small size and the potential for large-scale manufacture using CMOS compatible technologies have made them promising candidates for applications in several areas including healthcare, biomedical research and environmental monitoring [1].Among various implementations of Silicon photonic sensors, microring resonators have been investigated widely because of their compactness [2], high quality factors [3] and scalability for multi-analyte sensing using arrays of sensor elements [4,5].An important figure-of-merit of the Silicon photonic sensor is its detection limit, or the smallest change of refractive index that can be reliably measured by the system.In the past, highly sensitive Silicon microring sensors capable of measuring index shifts with a detection limit close to 10 −7 Refractive Index Units (RIU) have been reported [6].An important factor that influences the detection limit of the Silicon microring sensor is the variation in operating temperature of the device.This has several causes such as fluctuations in the ambient temperature, differences in the temperatures of sensor chip and the external analyte reservoir and local heating caused by viscous dissipation [7].Owing to the high thermo-optic coefficient (TOC) of Silicon (1.86 × 10 −4 / • C) [8], small temperature fluctuations of the device can cause significant but undesirable shifts of resonances in a microring sensor [9].Usually, closed loop controller platforms using Peltier Thermo-Electric Coolers (TECs) are employed to compensate random temperature fluctuations.However, it is difficult to track and correct localized thermal variations on the chip surface using external temperature controllers in real-time with sufficient accuracy.This is due to the considerably large response time of closed loop controllers, which typically ranges from a few seconds to above a minute depending on the thermal mass of the sensor system.More importantly, the Silicon carrier and buried oxide layers in an SOI wafer present a barrier for real-time measurement of surface temperature variations using a bottom-of-the-chip temperature sensor.In the past, reference microring resonators have been employed to compensate for measurement errors caused by temperature fluctuations on the sensor surface [10,11].In this approach, resonance shifts caused by temperature variations are tracked using a dedicated reference microring unexposed to the analyte being probed.Subtraction of resonance shift of reference microring from that of the sensor ring gives the required signal shift caused by a change in refractive index of analyte.However, this method suffers from a few drawbacks.Firstly, imperfections in fabrication processes can result in differences between dimensions of waveguides forming reference and sensor microrings, causing an imbalance in the spectral responses to temperature shifts.Furthermore, the spatial separation between the reference and sensor microrings can result in differences of temperature variation profiles resulting in imperfect compensation of errors in wavelength shifts.To overcome these drawbacks, we propose and demonstrate the use of analyte TOCs for compensating errors in RI measurements caused by variations in ambient temperature.TOCs of analyte liquids are extracted from measurements of resonance wavelength shifts induced by controlled increments in the chip temperature.Metal rings patterned around Silicon microrings are used to monitor fluctuations of ambient temperature through measurement of variations in electrical resistance.Using this method, thermo-optic coefficients of three standard liquids; De-ionized water, Ethanol and Isopropanol were measured and are shown to be in good agreement with literature reports.Specifically, the TOC of De-ionized water was measured as −1.12 × 10 −4 / • C with estimated error limits of ±8.26 × 10 −6 / • C. Chip surface temperature tracking is demonstrated with an instrument limited accuracy of 0.004 • C. Furthermore, we recorded a 16 factor enhancement in temperature tracking accuracy in comparison to global-scale monitoring.It is shown that the refractive index measurement precision of the microring is also improved by the same factor.We also discuss sensing schemes that eliminate the requirement of TEC based temperature controllers for RI shift measurements in specific cases where TOCs of analytes are known beforehand as standard values.

Theory
Resonance shifts observed in a microring sensor can be expressed as the sum of two components; the first caused by variation in analyte index and the second by fluctuations in ambient temperature.That is, Here, ∆λ sen is the shift in resonance caused by variation in analyte index, δλ δT cl is the rate of resonance wavelength shift with cladding liquid index change and ∆T denotes fluctuations in ambient temperature.We note that Eq. ( 1) can directly be used to extract the wavelength shift component ∆λ sen .However, it is advantageous to express the second term on right hand side of Eq. ( 1) in terms of thermo-optic coefficients since this may be known beforehand for standard analytes.If the TOC an analyte is not known, it can be extracted through measurements of wavelength shift rate δλ δT cl .Any variation in the temperature of microring causes shifts in the refractive indices of the waveguide core, buried oxide and the cladding liquid.In turn, this causes a net change in the effective index of the microring waveguide.Using the theory developed for athermal operation of Silicon photonic devices [12], one can express the net effective index change per unit variation in temperature as, Here, Γ i is the confinement factor in core, buried oxide or the upper/side cladding while dn i dT are the thermo-optic coefficients.The confinement factor Γ is defined as [13], In this expression, n s is the refractive index of the waveguide constituent (core/cladding/oxide) under consideration.In the numerator, integration is performed over the cross section of the constituent 's'.Integral in the denominator covers the waveguide cross section entirely.γ s is the fraction of power propagating within the region 's' and is termed as the 'fill factor'.Presence of group index n g in Eq. ( 3) indicates that confinement factors depend on the group velocity of propagating mode.To determine the TOC of analyte cladding ∂n cl ∂T , we rewrite the Eq. ( 2) as, The rate of change of effective index δn e f f δT is obtained by measurement of resonant wavelength shifts dλ dT , and substitution of results in the following expression: where, λ r es is the resonance wavelength.Furthermore, the TOC of Silicon ∂n c o ∂T is determined by performing resonance shift measurements with air cladded microrings and compared with values reported in literature.It can be obtained using the following equation: In this case, the thermo-optic coefficient of air is neglected since the refractive index of air is relatively invariant to temperature variations [14].Furthermore, in both Eqs. ( 6) and ( 4), the TOC of buried oxide ∂n b o x ∂T is taken as 8.57 × 10 −6 / • C from literature reports [15].Confinement factors Γ i are computed by determining fill factors γ i using modal simulations since we have accurate knowledge of the dimensions and refractive indices of core and the claddings.
Once the TOC is determined accurately, we can express Eq.(1) as, We further approximate this equation in terms of wavelength shift rate δλ δT air and TOC of analyte as, This approximation is valid since we show later that the fill factors of core, oxide and the cladding regions do not change significantly for air and liquid coverings.We can thus express the sensing component of resonance shift as, The constant K 1 = ∆λ ∆T air can be measured as an initial calibration and used subsequently for correction of wavelength shifts.The second constant K 2 = λ r e s n g Γ cl can be determined through simulations (for Γ) and spectrum measurements (for λ r es and n g ).Using the corrected wavelength shift ∆λ sen and the resonance shift rate ∆λ ∆n cl , the expected refractive index shift of analyte can now be obtained using the expression,

Design of TOC measurement system
Schematic of the system used for wavelength shift measurements is shown in Fig. 1(a).The photonic chip consists of several identical Silicon microring resonators for redundancy.Metal rings are patterned concentrically around each resonator, at a distance of about 2µm, for measurement of temperature variations.Low resistance Gold contact lines are defined for electrical probing of metal rings.A PDMS (Polydimethylsiloxane) reservoir structure provides containment for liquid analyte.The chip is placed on a temperature controlled platform consisting of a peltier heater powered by a temperature controller instrument.A copper base plate is mounted on the peltier element for equalization of temperature and efficient transfer of heat to the sensor chip.A Resistance Temperature Detector (RTD) element attached to the copper base plate was interfaced to the controller for closed-loop tracking of chip temperature.Waveguides and microrings were implemented using photonic wires (400 nm × 220 nm) operating with fundamental TE-like mode at 1550 nm wavelength band.Since the core material Silicon has a linear expansion coefficient of 2.59 × 10 −6 / • C, change in waveguide dimensions over the relatively small operating temperature range (about 12 • C) is not considered in our analysis.We used finite element method modal

Device fabrication and experimental methods
An SOI wafer with 220 nm thick device layer and 2µm buried oxide was used for fabrication of the sensor chip.In the first step, Electron beam (e-beam) lithography was performed using a negative tone resist (ma-N2401) for definition of photonic wires, microrings and bases for grating couplers.The radius of microrings was designed to be 100 µm, and the width of metal ring was set to 2 µm.A dry etch step using fluorine chemistry was used to transfer resist patterns to the SOI device layer.Following this, a second E-beam lithography process was carried out using a positive tone (PMMA) resist coating for patterning gratings over previously formed bases.These patterns were transfered onto SOI layer using dry etch.A third step of e-beam exposure process (with PMMA resist) was employed for definition of metal ring patterns.This was followed by sputtering of metal bi-layer (Titanium-10 nm/ Platinum 50 nm) and lift-off processes to obtain metal structures.Subsequently, optical lithography and metal lift off (Chromium-10 nm/ Gold-90 nm) steps were used for definition of low resistance contact strips for electrical probing.A positive tone resist (S1813) was used for this process.Finally, a containment structure prepared using PDMS was bonded over the sensor chip to serve as a reservoir for analyte liquid over microrings.An optical source-detection module consisting of a tunable Laser (1505-1620 nm), and an InGaAs power meter was used for spectral measurements.Grating couplers fabricated on chip were used to couple light in and out of the photonic sensor chip through a single mode (SMF-28) optical fibre.A high precision source-measurement unit was used to monitor the electrical resistance of metal rings and thereby track the on-chip temperature variations.

Calibration of resistive metal rings
The on-chip resistive metal ring was first calibrated using a device probe station equipped with a high precision thermal chuck and a semiconductor device analyzer.This experiment was performed with air cladded microrings and hence the PDMS reservoir was not filled with any liquid.Electrical resistance of the metal ring was monitored for increasing temperatures of the chuck.From the resistance-temperature plot, we extracted the slope of resistance variation to be 2.45 Ω/ • C, as shown in Fig. 3(a) as the reference plot.Subsequently, we used the assembly described in Sec. 2 to perform resistance slope measurements.In this case, the closed-loop temperature controller was used to heat the photonic chip to the desired temperature.As mentioned earlier, a source measurement unit (SMU) was used to monitor the electrical resistance of the metal ring.In this case, the mean slope (3 trials) of resistance variation with temperature was measured to be 2.46 Ω/ • C, as shown in Fig. 3(a).This experiment was repeated after filling the PDMS reservoir with DI-water to understand the effect of thermal mass of liquids on chip surface temperature variation.We ensured that the voltage applied to metal rings for resistance measurement was kept below the electrolytic potential of water (1.23V) to avoid electrolysis.The measured slope of resistance variation (mean value) in this case was 2.48 Ω/ • C, as seen in Fig. 3(b).Evidently, the thermal mass of a small volume of water (few microliters) does not cause significant difference in the temperature variation in comparison to that with air covering the device.

Measurement of thermo-optic coefficients
The theory described in the previous section was first used to determine the TOC of Silicon.A good agreement of our measurements with literature reports would validate the described TOC measurement method.The PDMS reservoir was left unfilled so that air forms the upper and side claddings of the waveguide.Temperature of the photonic chip was varied using the closed loop controller while resonant wavelength shifts were monitored.Measured full width half maximum (FWHM) of resonances was about 0.1 nm, with an FSR of 0.79 nm.A linear fit was used to express the wavelength shift as a function of the chip temperature [Fig.4(a)].Mean slope ∆λ ∆T air of three trials was calculated to be 62.72 pm/ • C [Fig.4(b)].Upon substitution of relevant parameters in Eq. ( 6) the TOC of Silicon was calculated as 1.92 × 10 −4 / • C. While this value is about 3.2% higher than the commonly reported Silicon TOC of 1.86 × 10 −4 / • C, we note that the TOC itself is a function of temperature.Specifically, Frey.et.al. [8] have tabulated TOC values of Silicon for different temperatures and a range of wavelengths.Based on this reference, we computed the value of Silicon TOC at a mean temperature of 35 • C to be 1.93 × 10 −4 / • C, which differs by about 0.5% from our measurement.For experiments with De-ionized water, the PDMS reservoir was filled with a small quantity of the liquid using syringes.Wavelength shift measurements were performed as described before.owing to the negative thermo-optic coefficient of water.Using Eq. ( 4) and simulated parameters of Tab. 1 we calculated the TOC of DI-Water to be −1.12 × 10 −4 / • C.This value compares well with those reported previously in literature, as shown in Tab. 2. Next, we measured the TOCs of organic solvents Ethanol and Isopropanol.Optical constants of these liquids have been well documented in literature.We limited the experiments with solvents to a maximum of two trials to avoid disintegration of PDMS reservoir due to swelling [17].Between measurements involving different liquids, the chip was cleaned using DI water, dried with nitrogen flow and heated to remove trace moisture.For Ethanol [Fig.6(a)], we see that the wavelength shift slope is reduced further to 18.95 pm/ • C, owing to stronger negative TOC which is calculated to be −2.59 × 10 −4 / • C. In case of Isopropanol, the mean wavelength shift slope (of two trials) is negative at -7.99 pm/ • C. That is, the effective index shift rate ∂n e f f ∂T of Eq. ( 5) is negative indicating that the effect of TOC of cladding liquid outweighs that of core Silicon, as seen in Fig. 6(b).Upon substitution of relevant parameters in Eq. ( 4), we obtain the TOC of Isopropanol to be −4.25 × 10 −4 / • C. Thermo-optic coefficients measured using the described method are largely in good agreement with literature reports, as seen in Tab. 2, although a slight deviation is observed in case of Ethanol.As mentioned before, we could not perform multiple measurement trials with organic solvents owing to the possibility of damage to the PDMS structure.Better convergence with literature reports is expected with more measurement iterations using a compatible reservoir material.

Fluid
Our study Literature Reports References

Calculation of error limits for TOC measurements
It is important to determine the influence of uncertainties in various simulated and measured parameters on the calculations of thermo-optic coefficient.We analyzed the effect of variation of several critical parameters in Eq. ( 4) and their effect on the TOCs of fluids.Major contributions towards uncertainties in TOC calculations arise from discrepancies in the wavelength shift slope measurements and variations in the width of waveguides used for fill factor simulations.Other sources of deviations in TOC calculations include uncertainty in the absolute refractive index of liquids used in simulations, and variations in field confinement factors over the measurement temperature range.However, our calculations showed that the latter two sources are at least an order of magnitude lower than the first two in terms of contribution towards variations in measurements, and were therefore not analyzed further.Random variations in slopes of resonance wavelength shifts are a result of various noise affecting the measurement system.To obtain an estimate of this variation, we performed seven iterations of slope measurements for the DI-water analyte using the procedure described earlier.
Results of these measurements are plotted in Fig. 7.The coefficient of determination (R 2 value) for curve fits was greater than 0.99 in all trials indicating good linearity of wavelength shifts and also the quality of estimated slopes.Standard deviation (σ ∆λ/∆T ) of seven wavelength shift slopes values was calculated to be 1.044 pm/ • C .The mean value of slope measured in this set of trials (37.96 pm/ • C) differs slightly from that shown in Fig. 5(b) due to some differences in calibration of the closed loop temperature controller system.Upon substitution of Eq. ( 5) in Eq. ( 4) and subsequent differentiation of the equation with respect to the slope ∆λ ∆T we obtain the following expression.
This equation translates variations in slope measurements (σ ∆λ/∆T ) into equivalent uncertainty in TOC estimations which is calculated to be e ∆λ/∆T = 6.42 × 10 −6 / • C. Next, we determined the effect of variations in width of waveguide cores on the estimates of TOC.Through measurements on SEM images taken at different positions on the microring, we computed the mean and standard deviation (σ w ) of widths to be respectively 387 nm and 4.5 nm.Upon differentiation of Eq. ( 4) with respect to width of waveguide core, we obtain the following expression: Here, ∂γ c o ∂w and ∂γ cl ∂w are the rates of change of field fill factors in the core and analyte fluid clads with respect to change in width (w) of the core.In deriving Eq. ( 12), we have not considered the effect of variation in the buried-oxide fill factor since the contribution of the term is more than an order of magnitude lower than those due to variations in γ cl and γ co .Using modal simulations with waveguide core as the variable we found the derivatives of fill factors as ∂γ c o ∂w = 1.09/µm and ∂γ cl ∂w = −0.625/µm.Substituting these results in Eq. ( 12) we obtain the contribution towards uncertainty in TOC to be e w = 5.19 × 10 −6 / • C. The combined effect deviations introduced by slope shift uncertainty e ∆λ/∆T and core width variations e w is obtained by computing the square root of squares of individual contributions.This value is computed to be e T OC−DIW = 8.26 × 10 −6 / • C which is about 7 % of the calculated TOC of DI water.If the device is used for measurement of variations in TOC due to changes in physical/chemical properties of liquids, the detection limit of TOC is desired.This is taken as three times the standard uncertainty, which for our system computes to be 2.47 × 10 −5 / • C.

On-chip temperature tracking using metal rings
Lastly, we performed experiments to demonstrate the precision temperature tracking capability using the metal rings.Ambient thermal fluctuations cause shifts in the optical resonances of microrings as well as variations in the electrical resistance of metal rings.The extent of temporal correlation between these signals depends on their spatial separation.For these measurements, the controller was set to maintain a fixed temperature at the copper base plate.Resonant wavelength shifts and electrical resistance variations were monitored simultaneously over a few minutes, with a sampling interval of about 5 seconds [Fig.8].For resistance measurements, three consecutive values (acquired within about 0.3 seconds) were averaged to obtain a single data point for noise reduction.Curve fitting was used for tracking wavelength resonance minimum precisely.These experiments were performed with air as the upper and side claddings.However, we note that the method can be implemented for liquid analyte claddings as well.To understand the effect of spatial separation on the resonance and resistance shift signals, we first measured the wavelength shift in one microring while monitoring electrical resistance of a metal ring whose centre was about 500 µm away from that of the microring.Results of this experiment are shown in Fig. 8(a).We see different profiles of wavelength shifts and resistance variations, indicating that relatively small spacing of a few hundred micrometers results in de-correlation of local temperature fluctuations.In the second experiment, another device having the metal ring concentrically patterned around the Silicon microring as shown in Fig. 2(b) was used.As seen in the figure, spacing between the metal strip and Silicon waveguide is about 2 µm.In this case, a very good correlation between resistance variation and resonance shifts is observed in the plots shown in Fig. 8(b), proving that the temperature tracking must be performed in close proximity of the sensing microring for best results.This is also clear from the correlation plots shown in Fig. 8(c).Using the resistance variation coefficient of 2.48 Ω/ • C determined previously, we plot the fluctuation of ambient temperature in Fig. 8(d).The measurement precision of resistance depends on the noise performance of electrical equipment, which in this case is a source measurement unit (Keithley 2400).Based on the instrument specifications, the noise levels at the probing voltage (1V) and current (0.83 mA) levels were taken as 10 µV and 10 nA.From these values, we estimated the uncertainty in resistance calculations to be 0.0109 Ω, after accounting for noise reduction achieved by averaging three samples.This results in a temperature measurement accuracy of 0.004 • C using the resistance variation coefficient of 2.48 Ω/ • C.
An important comparison between the accuracies of temperature measurement at the surface and bottom of the chip be drawn by analyzing data plotted in Fig. 3.By performing residual analysis on the reference plot of Fig. 3(a), we obtained the standard deviation of differences between the chuck and on-surface temperatures as 0.072 • C. Therefore, by monitoring the temperature variation on-chip near the sensor microring, we obtain a tracking accuracy enhancement by a factor of 16.39.Equation.( 9) may be used to understand how this enhancement translates to improved detection limits of refractive index.When the refractive index of the analyte liquid is unaltered, the sensing component of wavelength shift (λ sen ) must be zero.Any resonance shift observed (λ obs ) is now due to fluctuations in ambient temperature.Owing to more accurate compensation of temperature induced shifts, the uncertainty in resonance shifts is reduced by a factor of 16.39 using on-chip temperature tracking in our system.In effect the refractive index detection limit is improved by the same factor in accordance with Eq. ( 10), assuming the optical readout equipment can measure resonance shifts with sufficient precision.More importantly, if the TOC of analyte is known beforehand, and the wavelength shift rate with air cladding ∆λ ∆T air is specified for the chip at manufacture, the necessity of a closed loop temperature control is obviated, enabling considerable reduction in system complexity and operational costs.

Conclusion
We have reported a method for compensation of errors caused by temperature variations in Silicon microring sensors.Specifically, the thermo-optic coefficient is used for in conjunction with real-time, on-chip temperature monitoring to compensate for deviations in measured wavelength shifts.Using the field confinement theory in high contrast waveguides, we have formulated an expression for describing the thermo-optic coefficient of a liquid in terms of field confinement factors.Variations in temperature near the microring is tracked by monitoring electrical resistance of a metal ring structure.Experiments for measurement of thermo-optic coefficients of Silicon and analyte liquids are described.TOC values determined through our experiments are in good agreement with literature reports.We have also discussed possible errors in TOC calculations resulting from uncertainties of various parameters.In our experiments, we could demonstrate an improvement in temperature tracking accuracy by a factor of 16, limited only by noise in electrical probing instruments.A dedicated low noise electronic circuit can potentially provide better resistance measurement precision, enabling further improvements in error compensation of refractive index shift measurements.Furthermore, we have used an external peltier heater linked to a closed loop temperature controller for heating the chip during TOC measurements.As an alternative, the metal ring used for temperature monitoring can itself possibly be used to heat the analyte while simultaneously tracking variation in resistance to deduce temperature increments.We were not successful in achieving this due to electrolysis of polar liquids, once the applied voltage to the metal ring exceeded the electrolytic potential.To circumvent this problem, a thin layer of insulating di-electric can be coated to electrically isolate the metal ring from the analyte liquid.With the improvements suggested here, one can realize a compact, high performance refractive index and thermo-optic coefficient sensor that can achieve better detection limits than device configurations reported previously in literature.

Fig. 1 .
Fig. 1.Design and simulation of Silicon microring TOC sensor (a) A schematic showing the photonic sensor chip.(b) Simulation result showing the distribution of electric field (TE-like mode) along the cross section of a photonic wire waveguide.

Figure. 2
shows images of patterns at various stages of fabrication.

Fig. 2 .
Fig. 2. Images of fabricated microrings and metal rings for thermo-optic coefficient measurement.(a) Scanning Electron Microscope (SEM) image of Silicon microring surrounded by platinum metal ring (b) Magnified view of the wire waveguide and metal ring (c) Microscope image showing gold contact lines for electrical probing of metal rings

Fig. 3 .
Fig. 3. Measurements of metal ring resistance versus temperature (a) With air covered microrings.The reference data was obtained using a calibrated thermal chuck.Three trials were performed using our characterization assembly (b) With DI-water covered microrings.The R 2 value exceeded 0.99 for all linear fits.

Fig. 4 .
Fig. 4. Measurements for determination of TOC: Silicon (a) Positions of a transmission resonance for different temperatures.(b) Shift in resonance position as a function of temperature (3 trials).R 2 value for all curve fits exceeded 0.99.
The TOC was calculated by substituting wavelength shift slopes ∆λ ∆T cl and the simulated parameters of Tab. 1 in Eq. (4).The mean slope (3 trials) of resonance wavelength shift is 42.95 pm/ • C [Fig.5].The decreased slope of wavelength shift relative to that of air clad is a result of reduction in the rate of change of effective index shift ∂n e f f ∂T

Fig. 5 .
Fig. 5. Measurements for determination of TOC: De-ionized water (a) Positions of a transmission resonance for different temperatures.FWHM of resonances is about 0.3 nm.relative to that of air cladding (b) Shift in resonance position as a function of temperature.R 2 value for all curve fits exceeded 0.99.

Fig. 6 .
Fig. 6.Measurements for determination of TOC: Organic liquids (a) Resonance wavelength shifts for ethanol cladding.(b) Shifts in resonance wavelength for IPA cladding.In this case, the slope is negative owing to very strong (negative) TOC of the analyte.

Fig. 7 .
Fig. 7. Determination of error limits of TOC of water.Seven iterations of wavelength shift slope measurements were performed.

Fig. 8 .
Fig. 8. Measurement of ambient thermal fluctuations.(a) Wavelength shift and resistance measurements on Silicon microring and a metal ring spaced apart by about 500 µm (centre to centre), showing uncorrelated variations of quantities.(b) Measurements for concentric microring and metal ring as shown in Fig. 2(b).(c) Cross-correlation plots of wavelength shift and resistance variation signals.A good correlation is observed between the signals for small separation between microring and metal ring at zero delay position.In contrast, no clear trend is visible in the correlation output for large separation between metal and silicon rings.(d) Temperature variation as calculated by resistance measurement, compared with the read-out of the temperature controller.