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Abstract
We demonstrate a thermoreflectance-based thermometry technique with an ultimate temperature resolution of 60 µK in a 2.6 mHz bandwidth. This temperature resolution was achieved using a 532 nm-wavelength probe laser and a ∼1 µm-thick silicon transducer film with a thermoreflectance coefficient of −4.7 × 10−3 K−1 at room temperature. The thermoreflectance sensitivity reported here is over an order-of-magnitude greater than that of metal transducers, and is comparable to the sensitivity of traditional resistance thermometers. Supporting calculations reveal that the enhancement in sensitivity is due to optical interference in the thin film.
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1. Introduction
Thermoreflectance-based thermometry is a well-established optical technique that is commonly employed for hot spot detection of microelectronic devices [1–5] and characterization of thermal energy transport in nanomaterials [6–8]. The basis of this scheme is the thermo-optic effect, which refers to the variation in a material’s optical properties with temperature. Leveraging this effect, temperature changes of the sample are detected in real time by monitoring the reflected intensity of a focused laser beam. Characteristic advantages of the thermoreflectance approach include the following: a non-contact modality, a diffraction-limited spatial resolution as low as ∼250 nm, and sub-picosecond temporal resolution [9]. However, a major limitation of this scheme is the relatively poor temperature sensitivity compared to that of resistance thermometers [10] and bimaterial cantilever-based sensors [11]. A thermoreflectance approach with enhanced temperature sensitivity is key to the advancement of high-resolution thermal imaging and calorimetry techniques, as well as pump-probe techniques for characterizing the thermophysical properties and Kapitza resistances of multilayered materials [9,12,13].
The sensitivity of the thermoreflectance detection scheme is characterized by the coefficient of thermoreflectance, κ ≡ R−1(∂R/∂T), where R is the reflectance and T is the temperature of the sample. Traditional thermoreflectance set-ups that leverage visible probe lasers (i.e., 400 nm – 780 nm wavelength) and transducers comprised of metal thin films (e.g., Au, Al) achieve a typical thermoreflectance coefficient on the order of ∼1 × 10−4 K−1 at room temperature [14,15]. Similar κ values were obtained with bare silicon substrates [16,17]. For reference, this sensitivity is over an order-of-magnitude worse than the analogous temperature coefficient of resistance (TCR) of commonly-employed platinum resistance thermometers [10] (e.g., TCR ≈ 2 × 10−3 K−1). To date, the best temperature resolution achieved using a thermoreflectance scheme with these materials is ∼10 mK at room temperature [18,19].
In this work, we demonstrate a κ value exceeding the TCR of platinum resistance thermometers by exploiting optical interference effects in a thin film comprised of single-crystal silicon. This work is significant because resonant enhancement of thermoreflectance sensitivity with semiconductor thin films has not been explored in detail. An early report [16] attributed the highly-variable and nonlinear thermoreflectance response of ∼2 µm-thick polysilicon layers to thin-film interference, which the authors suggested may complicate thermal imaging. The authors of a more recent study [20] reported a κ value of 10−3 K−1 for a ∼3 µm-thick silicon cantilever, which represents a ten-fold enhancement compared to the thermoreflectance response of bulk silicon. No physical explanation for this apparent enhancement was provided. Recently, Reihani et al. [21] demonstrated an extremely high sensitivity (κ > 30 K−1) due to optical interference in a 130 µm-thick transparent substrate comprised of GaAs, though temperature gradients within such a thick substrate may be significant and can obscure quantitative temperature measurements. In this work, we achieve the highest thermoreflectance coefficient and best temperature resolution ever reported for a thin film transducer, which supports thermometry with high spatiotemporal resolution and is relatively easy to fabricate compared to other silicon photonic thermometers [22,23]. Further, this work addresses the following questions: (1) What experimental factors determine the thermoreflectance coefficient and temperature resolution? (2) To what extent can these quantities be optimized?
2. Experimental methods
The instrumentation comprising our custom thermoreflectance set-up is illustrated schematically in Fig. 1(a). The beam of a solid-state laser (continuous-wave, linearly-polarized, 532-nm wavelength) is expanded and then split using a polarizing beamsplitter (PBS). One beam (i.e., the reference beam) is directed to a silicon photodiode (PD) in order to monitor fluctuations in the output power of the laser. A band-pass filter (BPF) and aspheric lens (AL) are used to block stray light and focus the collimated beam onto the detector. The other beam (i.e., the sensing beam) is circularly polarized using a quarter-wave plate (QWP) and then coupled into the entrance pupil of a microscope objective (50X, 0.55 NA) using a 50:50 beamsplitter (BS). The sensing beam is focused to a diffraction-limited spot on the sample surface, and the reflected intensity is monitored with a second PD that is identical to the reference detector. A half-wave plate (HWP) on a rotation mount is used to match the light intensity incident on each photodiode. The raw signal from each PD is collected with a commercial transimpedance amplifier (TA) and the outputs are then subtracted using a low-noise instrumentation amplifier (IA) with a differential gain gd = 100.
Fig. 1. (a) Simplified schematic illustration of the thermoreflectance set-up. Optical components include the optical isolator (ISO), beam expander (BE), half-wave plate (HWP), polarizing beamsplitter (PBS), quarter-wave plate (QWP), dichroic mirror (DM), beamsplitter (BS), band-pass filter (BPF), aspheric lens (AL), and neutral density filter (NDF). (b) Illustration of the SOI sample cross-section. The thicknesses of the layers are not drawn to scale. From top to bottom: 3 nm native oxide layer, 1080 nm silicon device layer, 1990nm buried oxide layer, and 500 µm silicon substrate.
The sample itself is mounted to a custom thermostat that can stabilize the sample temperature to within ±100 mK of the set-point using proportional-integral-derivative (PID) feedback control. The position of the sample is adjusted with a 3-axis translation stage driven by piezoelectric inertia actuators that provide linear adjustments in steps as small as 20 nm. A charge-coupled device (CCD) camera is used to image the field-of-view of the objective, which allows us to focus and laterally align the sample to the laser spot.
As shown in Fig. 1(b), the sample is comprised of a silicon-on-insulator (SOI) wafer with an undoped, single-crystal device layer. The Si device layer of this SOI sample, which was acquired commercially from WaferPro (www.waferpro.com), is highly polished but is expected to vary in thickness by approximately 30% across the sample. The thickness of the Si device layer thSi at the location of our probe laser spot was determined to be 1080 nm based on a combination of atomic force microscopy (AFM) and scanning electron microscopy (SEM) measurements (see the Supplement 1, Section S1 for details). This estimated thickness was found to be in excellent agreement with the results of spectroscopic ellipsometer measurements, which also determined the thickness of the buried oxide (BOX) layer and the native oxide layer to be 1990nm and 3 nm, respectively. The ellipsometer measurements further indicate that the thicknesses of these oxide layers are highly uniform across the sample.
3. Results and discussion
3.1 Characterization of the thermoreflectance response
Comparing the sensing PD signal for the SOI sample to that of a well-characterized reference sample (a broadband mirror with near-unity reflectance), the absolute reflectance of the SOI sample at room temperature was found to be 0.346. For comparison, we conducted finite-difference time-domain (FDTD, Lumerical) simulations of a Gaussian beam (0.55 NA) incident on a SOI stack with identical layer thicknesses and zero surface roughness. The simulated reflectance is in excellent agreement with this measured result. Further, these simulations verify that self-heating of the sample by the probe beam is negligible.
The reflectance of the SOI sample as a function of temperature is displayed in Fig. 2(a). Here, the temperature of the sample, which is thermally well-coupled to the thermostat, was adjusted in steps of 1 °C. To measure the change in reflectance at each set-point, the output power of the probe laser was sinusoidally driven at a frequency of 91 Hz and the differential PD signal at the modulation frequency was collected with the lock-in amplifier (7.8 mHz bandwidth). Based on the slope of the best-fit line to the data in Fig. 2(a), the thermoreflectance coefficient was found to be κSOI = (−4.7 ± 0.1) × 10−3 K−1. This sensitivity value is over an order-of-magnitude larger than the thermoreflectance coefficient of bare silicon and gold, and is modestly larger than the TCR of platinum resistance thermometers. As a control experiment, we repeated this test for a sample comprised of a 100 nm-thick aluminum film evaporated onto a bare silicon substrate. There was no observed change in reflectance of the Al sample with temperature, which is expected since the thermoreflectance coefficient of Al is near-zero for 532 nm-wavelength light [15,24]. For each of these measurements, potential artifacts due to thermal expansion of the thermostat were eliminated by using the piezoelectric actuators to prevent the sample from drifting out of focus as it was heated (see SI, Section S2 for thermal expansion data).
Fig. 2. (a) Measured (red circle) and simulated (black line) reflectance R of the SOI sample between 25°C and 35°C. The red dash line represents the best-fit line to the measured data. The measured reflectance at each temperature was obtained by collecting the lock-in output signal with a sampling rate of 5 samples/second and then averaging the data over 20 minutes. Vertical error bars represent the standard deviation of sampled data. (b) Simulated reflectance R (black line) and thermoreflectance coefficient κ (blue line) of the SOI sample as a function of device layer thickness thSi. In this simulation the thickness of the BOX layer and native oxide layer were fixed at 1990nm and 3 nm, respectively. The red circles mark the device in this work.
Overlayed on Fig. 2(a) is the simulated thermoreflectance response of the SOI sample, which is in excellent agreement with the measured results. Inputs to the model are the temperature-dependent optical constants of the Si device layer, which we characterized separately using a spectroscopic ellipsometer with an integrated sample heating stage (see SI, Section S3 for details of the measurement approach and fitting results). Figure 2(b) provides the simulated thermoreflectance response as a function of the thickness of the Si device layer thSi. Sharp interference peaks are periodically observed for κ and R as the thickness is swept, illustrating that the thermoreflectance response of this sample is extremely sensitive to the device layer thickness. The peaks in κ and R are laterally offset such that local maxima in κ occur where the reflectance is most sensitive to thickness. Correspondingly, the reflectance at such locations is highly sensitive to variations in the optical path length due to temperature-induced changes in the refractive index. Our simulations also reveal that the buried oxide layer and native oxide layer have only a minor effect on the magnitude of the thermoreflectance response (see SI, Section S4 for supporting calculations).
3.2 Demonstration of high-resolution thermometry
With the κ value of the sample obtained through these calibration steps, thermoreflectance-based thermometry is now possible. Temperature changes of the sample are quantified according to ΔT = ΔV/κgdVref, where Vref is the common-mode voltage signal at the input of the instrumentation amplifier, and ΔV is the amplified differential output. The noise floor of the measurement can be estimated from the power spectral density (PSD) plots in Fig. 3. The noise spectrum in Fig. 3(a) was acquired by collecting ΔV with a digital spectrum analyzer, while the SOI sample was maintained at a temperature of 25 °C and the output power of the probe laser was fixed at 8 mW. Flicker noise dominant at low frequencies (see inset) becomes negligible at frequencies above 430 Hz, where the noise floor plateaus to a value of 6.4 × 105 nV2/Hz. The blue curve in Fig. 3(b) represents the PSD with the laser off, which captures the electronic noise in the photodiodes and amplifiers. The green curve in Fig. 3(b) is the difference between the blue curve and the total PSD from Fig. 3(a). This additional “drift” noise is attributed to fluctuations of the laser output, temperature fluctuations of the sample, and mechanical vibrations of the optical components. At low frequencies the drift noise dominates, and the noise floor can potentially be lowered by improving the thermal and mechanical stability of the set-up. At high frequencies the electronic noise dominates and can only be lowered through careful circuit design.
Fig. 3. (a) Power spectral density (PSD) of the noise referred to the output of the instrumentation amplifier. Inset provides a magnified view of this data for frequencies between 0 Hz and 25 Hz. (b) Estimated PSD of the electronic noise (blue), and noise due to drift of the optomechanical components (green).
The temperature resolution of this thermoreflectance-scheme is presented in Fig. 4(a). To generate this plot, the sample was locally heated using a second pump laser with a wavelength of 488 nm (see Fig. 1). Simulation results presented in the SI (Section S4 and S5) reveal that local optical heating of the SOI sample produces the same thermoreflectance response as uniform sample heating by the thermostat. The pump laser was coupled into the objective using a longpass dichroic mirror (DM) and the focused laser spot was laterally aligned with the probe spot using a kinematic positioner. In this measurement scheme, the pump laser was driven with a waveform generator to sinusoidally modulate its output power. With the heating frequency fh of the pump laser fixed, the amplitude of its output power was systematically reduced. The resulting temperature changes were recorded using the probe laser with an unmodulated output power of 8 mW, and a lock-in amplifier with a bandwidth of 2.6 mHz. As the heating power was systematically reduced, the measured temperature rise decreased linearly until the signal fell below the noise floor. This procedure provides an accurate estimate of the temperature resolution.
Fig. 4. (a) Measured temperature rise of the SOI sample as a function of voltage amplitude driving the pump laser. Note that the voltage amplitude is proportional to the amplitude of the laser output power. Results for heating frequencies fh of 11 Hz (light blue) and 500 Hz (dark blue) are compared. For each heating power, the lock-in output signal was collected with a sampling rate of 5 samples/second and the data was averaged over 15 minutes. Vertical error bars represent the standard deviation of the sample data. The solid horizontal lines represent the estimated noise floor. The color bands represent the uncertainty of these estimates. (b) Same measurement as in (a) but with a bare gold sample. Heating frequencies fh of 11 Hz (light yellow) and 500 Hz (dark yellow) are compared.
As shown in Fig. 4(a), the temperature resolution with the SOI sample is 120 µK and 60 µK for a heating frequency fh of 11 Hz and 500 Hz, respectively. The improved temperature resolution at higher heating frequencies is consistent with the PSD plots from Fig. 3. Although the local temperature of the sample can be optically modulated at much higher frequencies (see SI, Section S6 for the measured frequency response), no additional improvement in the temperature resolution is expected for heating frequencies above 500 Hz since the noise spectrum is flat. For comparison, we repeated this test with a sample comprised of a 270 nm-thick gold film evaporated on a glass substrate, which we measured to have a thermoreflectance coefficient κAu = -2.6 × 10−4 K−1. As shown in Fig. 4(b), the temperature resolution with this Au sample is only 3.27 mK and 0.95 mK at 11 Hz and 500 Hz, respectively. The greatly improved temperature resolution with the SOI sample can be attributed to its enhanced thermoreflectance coefficient compared to that of gold.
4. Conclusion
In summary, we have demonstrated a resonantly-enhanced thermoreflectance sensitivity of −4.7 × 10−3 K−1 at room-temperature due to optical interference in a ∼1 µm-thick silicon film. Leveraging this enhanced sensitivity, we were able to achieve thermoreflectance-based thermometry with an ultimate temperature resolution of 60 µK in a 2.6 mHz bandwidth. This temperature resolution is ∼10× better than what can be achieved with transducers comprised of gold films, and is on par with the resolution of resistance thermometers [10]. In principle, the enhanced thermoreflectance response due to thin-film interference can be further improved by using shorter wavelength probe lasers or by encapsulating the transducer film with transparent dielectric layers [24,25]. Since film thickness is not perfectly controlled, the thermoreflectance response of a particular sample can be optimized by tuning the angle-of-incidence, numerical aperture, or wavelength of the probe beam. In principle, this optical sensing scheme will facilitate high-resolution studies of transient thermal transport and conversion processes in layered semiconductors and emerging nanomaterials.
Funding
Office of Naval Research (4720008832); National Science Foundation (2044788).
Acknowledgments
This work was partially supported by the Wisconsin Center for Semiconductor Thermal Photonics, with funding from the Wisconsin Alumni Research Foundation (WARF) via the Research Forward Initiative. Further, the authors gratefully acknowledge use of facilities and instrumentation supported by NSF through the University of Wisconsin Materials Research Science and Engineering Center (DMR-1720415).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
References
1. P. E. Raad, P. L. Komarov, and M. G. Burzo, “Thermal characterization of embedded electronic features by an integrated system of CCD thermography and self-adaptive numerical modeling,” Microelectron. J. 39(7), 1008–1015 (2008). [CrossRef]
2. R. Schlag, M. A. Ras, V. Arlt, et al., “Precision determination of thermoreflectance coefficients for localised thermometry,” in Proceedings of 21st International Workshop on Thermal Investigations of ICs and System (IEEE, 2015), pp. 1–5.
3. M. G. Burzo, P. L. Komarov, and P. E. Raad, “Noncontact transient temperature mapping of active electronic devices using the thermoreflectance method,” IEEE Trans. Compon. Packag. Technol. 28(4), 637–643 (2005). [CrossRef]
4. D. Kim, C. Jeong, J. Kim, et al., “Laser scanning confocal thermoreflectance microscope for the backside thermal imaging of microelectronic devices,” Sensors 17(12), 2774 (2017). [CrossRef]
5. S. Martin-Horcajo, J. W. Pomeroy, B. Lambert, et al., “Transient thermoreflectance for gate temperature assessment in pulse operated GaN-based HEMTs,” IEEE Electron Device Lett. 37(9), 1197–1200 (2016). [CrossRef]
6. S. Sandell, E. Chávez-Ángel, A. El Sachatet, et al., “Thermoreflectance techniques and Raman thermometry for thermal property characterization of nanostructures,” J. Appl. Phys. 128(13), 131101 (2020). [CrossRef]
7. J. Maire, R. Anufriev, and M. Nomura, “Ballistic thermal transport in silicon nanowires,” Sci. Rep. 7(1), 41794 (2017). [CrossRef]
8. J. Zhu, X. Wu, D. M. Lattery, et al., “The ultrafast laser pump-probe technique for thermal characterization of materials with micro/nanostructures,” Nanoscale Microscale Thermophys. Eng. 21(3), 177–198 (2017). [CrossRef]
9. J. Zhu, D. Tang, W. Wang, et al., “Ultrafast thermoreflectance techniques for measuring thermal conductivity and interface thermal conductance of thin films,” J. Appl. Phys. 108(9), 094315 (2010). [CrossRef]
10. S. Sadat, E. Meyhofer, and P. Reddy, “High resolution resistive thermometry for micro/nanoscale measurements,” Rev. Sci. Instrum. 83(8), 084902 (2012). [CrossRef]
11. C. Canetta and A. Narayanaswamy, “Sub-picowatt resolution calorimetry with a bi-material microcantilever sensor,” Appl. Phys. Lett. 102(10), 103112 (2013). [CrossRef]
12. R. Cheaito, J. T. Gaskins, M. E. Caplan, et al., “Thermal boundary conductance accumulation and interfacial phonon transmission: Measurements and theory,” Phys. Rev. B 91(3), 035432 (2015). [CrossRef]
13. J. Jeong, X. Meng, A. K. Rockwell, et al., “Picosecond transient thermoreflectance for thermal conductivity characterization,” Nanoscale Microscale Thermophys. Eng. 23(3), 211–221 (2019). [CrossRef]
14. Y. Wang, J. Y. Park, Y. K. Koh, et al., “Thermoreflectance of metal transducers for time-domain thermoreflectance,” J. Appl. Phys. 108(4), 043507 (2010). [CrossRef]
15. R. B. Wilson, B. A. Apgar, L. W. Martin, et al., “Thermoreflectance of metal transducers for optical pump-probe studies of thermal properties,” Opt. Express 20(27), 28829 (2012). [CrossRef]
16. M. Abel, T. Beecham, S. Graham, et al., Noncontact Surface Thermometry for Microsystems: LDRD Final Report. (2006), pp. SAND2006-6369, 899367.
17. J. Heller, J. W. Bartha, C. C. Poon, et al., “Temperature dependence of the reflectivity of silicon with surface oxide at wavelengths of 633 and 1047 nm,” Appl. Phys. Lett. 75(1), 43–45 (1999). [CrossRef]
18. P. M. Mayer, D. Lüerßen, R. J. Ram, et al., “Theoretical and experimental investigation of the thermal resolution and dynamic range of CCD-based thermoreflectance imaging,” J. Opt. Soc. Am. A 24(4), 1156 (2007). [CrossRef]
19. D. Luerssen, J. A. Hudgings, P. M. Mayer, et al., “Nanoscale thermoreflectance with 10mk temperature resolution using stochastic resonance,” in Proceedings of 21st IEEE Semiconductor Thermal Measurement and Management Symposium (IEEE, 2005), pp. 253–258.
20. D. Sarkar, S. W. Oxandale, T. J. Hieber, et al., “Thermal property measurements of Si µ-cantilever beams using the suspended thermoreflectance technique,” in International Mechanical Engineering Congress and Exposition, Vol. 10 (American Society of Mechanical Engineers, 2019), p. V010T12A008.
21. A. Reihani, E. Meyhofer, and P. Reddy, “Nanokelvin-resolution thermometry with a photonic microscale sensor at room temperature,” Nat. Photonics 16(6), 422–427 (2022). [CrossRef]
22. H. Xu, M. Hafezi, J. Fan, et al., “Ultra-sensitive chip-based photonic temperature sensor using ring resonator structures,” Opt. Express 22(3), 3098 (2014). [CrossRef]
23. N. N. Klimov, T. Purdy, and Z. Ahmed, “Fabry-Perrot cavity-based silicon photonic thermometers with ultra-small footprint and high sensitivity,” in Advanced Photonics (Optical Society of America, 2015), p. SeT4C.4.
24. T. Favaloro, J.-H. Bahk, and A. Shakouri, “Characterization of the temperature dependence of the thermoreflectance coefficient for conductive thin films,” Rev. Sci. Instrum. 86(2), 024903 (2015). [CrossRef]
25. G. Tessier, G. Jerosolimski, S. Holé, et al., “Measuring and predicting the thermoreflectance sensitivity as a function of wavelength on encapsulated materials,” Rev. Sci. Instrum. 74(1), 495–499 (2003). [CrossRef]
