Research Article www.afm-journal.de Thermal Properties of Nanocrystalline Silicon Nanobeams Jeremie Maire,* Emigdio Chávez-Ángel, Guillermo Arregui, Martin F. Colombano, Nestor E. Capuj, Amadeu Griol, Alejandro Martínez, Daniel Navarro-Urrios, Jouni Ahopelto, and Clivia M. Sotomayor-Torres 1. Introduction Controlling thermal energy transfer at the nanoscale and thermal proper- ties has become critically important in many applications since it often Depending on the application, materials with widely varying thermal properties limits device performance. In this study, the effects on thermal conduc- may be required. While for thermoelectric tivity arising from the nanoscale structure of free-standing nanocrys- applications ultra-low thermal conductivity talline silicon films and the increasing surface-to-volume ratio when is essential,[1,2] high thermal dissipation fabricated into suspended optomechanical nanobeams are studied. rates are mandatory for thermal manage- Thermal transport and elucidate the relative impact of different grain size ment in microelectronics.[3] Therefore, it distributions and geometrical dimensions on thermal conductivity are is crucial to understand thermal transport at the nanoscale to design structures with characterized. A micro time-domain thermoreflectance method to study optimized thermal properties for a given free-standing nanocrystalline silicon films and find a drastic reduction application. Optomechanics[4] is one such in the thermal conductivity, down to values below 10 W m–1 K–1 is used, application for which one typically wants with a stronger decrease for smaller grains. In optomechanical nanostruc- to avoid absorption and the resulting tures, this effect is smaller than in membranes due to the competition heating, either to operate the resonator in the quantum regime, which is why of surface scattering in decreasing thermal conductivity. Finally, a novel 2D structures are usually preferred over versatile contactless characterization technique that can be adapted to any nanobeams, or even to induce amplifica- structure supporting a thermally shifted optical resonance is introduced. tion by dynamical back-action.[5] However, The thermal conductivity data agrees quantitatively with the thermore- other approaches use thermal properties flectance measurements. This study opens the way to a more generalized to control the mechanical resonator, for thermal characterization of optomechanical cavities and to create hot- example, self-pulsing-induced lasing[6–8] or bolometric back-action. Therefore, the spots with engineered shapes at the desired position in the structures as a direction towards thermal management means to study thermal transport in coupled photon-phonon structures. in optomechanics depends on the targeted application, making it essential to acquire J. Maire, E. Chávez-Ángel, G. Arregui, M. F. Colombano, N. E. Capuj D. Navarro-Urrios, C. M. Sotomayor-Torres Depto. Física Catalan Institute of Nanoscience and Nanotechnology (ICN2) Universidad de La Laguna CSIC and BIST San Cristóbal de La Laguna 38200, Spain Campus UAB, Bellaterra, Barcelona 08193, Spain N. E. Capuj E-mail: jeremie.maire@u-bordeaux.fr Instituto Universitario de Materiales y Nanotecnología J. Maire Universidad de La Laguna Institut de Mécanique et d’ingénierie (I2M) UMR5295, CNRS-UB-ENSAM Santa Cruz de Tenerife 38071, Spain Talence 33405, France A. Griol, A. Martínez G. Arregui, M. F. Colombano Nanophotonics Technology Center Depto. Física Universitat Politècnica de València Universidad Autónoma de Barcelona València 46022, Spain Bellaterra, Barcelona 08193, Spain D. Navarro-Urrios MIND-IN2UB The ORCID identification number(s) for the author(s) of this article Departament d’Enginyeria Electrònica i Biomèdica, Facultat de Física can be found under https://doi.org/10.1002/adfm.202105767. Universitat de Barcelona Martí i Franquès 1, Barcelona 08028, Spain J. Ahopelto © 2021 The Authors. Advanced Functional Materials published by Microelectronics and Quantum Technology ­Wiley-VCH GmbH. This is an open access article under the terms of the VTT Technical Research Centre of Finland Ltd Creative ­Commons Attribution License, which permits use, distribution and P.O. Box 1000, Espoo FI-02044 VTT, Finland ­reproduction in any medium, provided the original work is properly cited. C. M. Sotomayor-Torres Catalan Institute for Research and Advances Studies ICREA DOI: 10.1002/adfm.202105767 Barcelona 08010, Spain Adv. Funct. Mater. 2022, 32, 2105767 2105767 (1 of 9) © 2021 The Authors. Advanced Functional Materials published by Wiley-VCH GmbH www.advancedsciencenews.com www.afm-journal.de direct information on thermal properties instead of having cavity, and compare the results to those obtained by µ-TDTR. We them as free parameters in complex models. show how optical resonances with different profiles can induce a In the context of micro- and nanoscale thermal transport, thermal dissipation rate variation of up to 20% in a single optical single crystal silicon (c-Si) has been widely used as a platform cavity. Our results provide new insights on the thermal charac- to study thermal engineering with structures like phononic teristics of nc-Si devices, which may find application in optics, crystals. Si nanostructures exhibit strongly reduced thermal optomechanics, and energy-harvesting devices. conductivity,[9–14] non-diffusive thermal transport,[15] and tuning of the thermal conductivity through the modified dispersion relation in phononic crystals.[16,17] In these structures, surface 2. Nanocrystalline Silicon Films and Structural phonon scattering is the main mechanism impacting thermal Analysis properties when the dimensions are smaller than the mean free path of phonons in the bulk material, that is, in the range The membranes and nanobeams were fabricated on wafers of 100 nm to a few micrometers.[18–22] Nanocrystalline Si (nc- with a thick silicon dioxide film and a 220 nm thick nc-Si layer Si) is a specific type of polycrystalline Si in which the grain on top of the oxide, resembling the SOI wafers typically used in size is well below 1 µm. Due to the relatively easy tuning of the fabrication of OM devices. The wafers were produced by the the mechanical, optical, electrical, and thermal properties by following process. A thick SiO2 layer is first grown by wet oxida- tailoring the stress and grain-size,[23] as well as controlled mate- tion at 1050 °C on a Si wafer, followed by a 220 nm thick layer of rial fabrication with conventional low-temperature amorphous amorphous Si (a-Si) deposited at 574 °C by low-pressure chem- Si deposition techniques, nc-Si is widely used in micro-electro- ical vapor deposition (LPCVD). Four wafers were annealed at mechanical systems offering a cost-competitive alternative to different temperatures: 650 °C (OMS1), 750 °C (OMS2), 850 °C crystalline silicon in many practical scenarios such as 3D inte- (OMS3), and 950 °C (OMS4) for 60 min. The annealing con- gration.[24] In nc-Si, the scattering of phonons at grain bounda- verts the amorphous Si to nc-Si, with the grain size distribution ries adds to other phonon scattering mechanisms. This kind of ranging from a few nm to a few hundreds of nm. The thick- scattering further reduces the thermal conductivity in nc-Si, cf. ness of the nc-Si films after annealing was 211 nm measured by c-Si, in nanostructures such as phononic crystals.[25,26] In this spectroscopic reflectometry. work, we quantify the relative effect of grain boundary scat- Bright field planar TEM images of the nanocrystalline film tering on thermal conductivity in corrugated optomechanical annealed at 950 °C (OMS4) and the corresponding selective area (OM) nanobeams. Recently, nc-Si was shown to be an excel- diffraction pattern are shown in Figure 1. The crystallites do not lent, versatile, and cost-competitive alternative to its crystalline exhibit a preferential orientation. The image is representative of counterpart to exploit OM non-linear dynamics under ambient all the samples used in this work with only the grain size distribu- conditions, with non-linear dynamic functions such as mechan- tion obtained by analyzing dark-field TEM images varying with ical lasing and chaos, over a much larger frequency bandwidth annealing temperature. In all samples, the crystallite size has a compared to Silicon-on-Insulator (SOI) devices.[27] A comple- log-normal distribution with the average crystallite size of 163 mentary study of various properties of nc-Si thin films realized (OMS1), 171 (OMS2), 187 (OMS3), and 215 nm (OMS4). The a-Si at different annealing temperatures focused on different grain layer is under compressive stress after deposition and annealing sizes and tensile stress.[23] converts it to tensile, measured to be 290 (OMS1), 250 (OMS2), Here, we investigate the thermal properties of nc-Si mem- 170 (OMS3), and 90 MPa (OMS4). More information about the branes and OM nanobeam cavities with different grain sizes, structural and mechanical properties of these nc-Si wafers and which are structurally characterized by image processing of structures made from them can be found in Ref. [23]. dark-field transmission electron microscope (TEM) images. To identify the effects arising from the nanocrystallinity of To access the thermal decay rates and conductivity, we use two the material, identical reference samples were fabricated on pump-probe techniques. For a direct assessment, we use micro commercial SOI wafers with a 220 nm thick single-crystalline time-domain thermoreflectance (µ-TDTR) as a proven technique Si layer. Since measurements are performed in air, all struc- and extract the thermal conductivity by fitting the experimental tures possess a layer of native oxide on their free surfaces. temperature rise with finite element modeling (FEM). We This layer has been shown to decrease thermal conductivity in demonstrate that the thermal conductivity of the nanocrystal- ultrathin membranes with thickness below 30 nm.[9] However, line membrane is at least four times lower than its crystalline the intensity of the effect decreases for thicker membranes and counterpart, with a further reduction by a factor of 2 when grain is thus expected to be small for the structures investigated in size decreases to an average of 163 nm. A similar phenomenon this manuscript. Furthermore, since all structures possess this occurs in the nanobeams studied here but its relative impact is native oxide layer, it does not impact the relative analysis of smaller than in membranes as it competes with enhanced sur- their thermal properties. A summary of the structural charac- face scattering stemming from the lower dimensions of these teristics of all samples is given in Table 1 and samples will be nanobeams. We further introduce a new two-laser measurement designated by their average grain size from now on. technique for direct measurements of thermal properties of in operandi OM nanobeams, similar to time-stretch spectroscopy used for microspheres.[28] This technique is based on the cooling 3. Thermal Conductivity Measurements by µ-TDTR rate of an optical resonance to measure the thermal decay rate of the cavity. We unveil the potential of this technique, which The thermal properties of a device are affected by the structure can be readily applied in current OM devices with an optical of the material itself, the processing steps, the operating condi- Adv. Funct. Mater. 2022, 32, 2105767 2105767 (2 of 9) © 2021 The Authors. Advanced Functional Materials published by Wiley-VCH GmbH www.advancedsciencenews.com www.afm-journal.de Figure 1. Structure of nanocrystalline silicon. a–c) Bright field planar TEM images of the nc-Si film with an average grain size of 215 nm and Ta = 950 °C with increasing zoom, showing the randomly oriented grains and their relatively large size distribution. d) Selective area electron dif- fraction image. tions, and the geometry of the device. It has been shown that the surface can play a major role in thermal conductivity when the surface-to-volume ratio (S/V) is large.[9] We use µ-TDTR technique to measure the thermal conductivity of the nanocrys- talline films and the nanobeams. The thermal conductivity extracted with this technique corresponds to the ability of the Figure 2. Structures for µ-TDTR measurements. a) SEM image of material to conduct heat by accounting for the effects of nano- a suspended nc-Si membrane. b) SEM image of the nanobeams. The patterning, such as phonon boundary scattering and the reduc- Bragg mirror of the bottom left beam is shown in red and half of the OM tion in the volume of material. µ-TDTR has been previously cavity in blue. The central gold pad that is the transducer for µ-TDTR used to characterize the thermal properties of numerous nano- measurements is highlighted in yellow. structures, including membranes, nanobeams,[29,30] phononic crystals,[31–35] or phonon lenses,[36] and to demonstrate effects ture gradient to vanish is measured and its inverse gives the such as heat focusing,[36] ballistic thermal transport,[29,30,37] and heat dissipation rate. The cooling curve can be described with to highlight the contribution of the wave nature of phonons a single-parameter exponential decay in time, exp(−γ t), where to thermal transport at cryogenic temperatures.[17] We use two γ is the heat dissipation rate of the system. Further details different sample designs shown in Figure 2, one to investigate about the technique and a schematic of the setup are given the role of the nanocrystalline material and the other to inves- elsewhere.[17,36] tigate the role of surfaces. The gold pad in the middle of the The nanobeams consist of an OM cavity flanked on both samples acts as a transducer and as the detector. The temper- sides by an OM Bragg mirror to prevent the leakage of the ature of this pad is directly related to its reflectivity, which is co-localized optical and mechanical modes. Each part of the OM probed by a continuous-wave laser (532 nm). A 405 nm pulsed nanobeam consists of a repetition of unit cells comprising a cen- laser periodically heats the metal and lets it cool down between tral beam with stubs on both sides and a cylindrical hole in the pulses. The heating time is chosen to allow the system to reach center. The OM nanobeam is shown in Figure 2. The OM cavity a steady state. The temperature gradient across the structures used to confine optical and GHz mechanical modes corresponds then progressively disappears as the heat flows from the central to the central region of 12 unit cells in which the pitch, hole diam- pad to the heat bath. The characteristic time for the tempera- eter, and stub width along the beam axis progressively decrease towards the center by a factor Γ, which is typically around 0.8. Table 1. Summary of structural characteristics of fabricated samples. On both sides of this region, the Bragg mirrors consist of 10 unit cells. The nominal values of the pitch, hole diameter, and stub Thickness [nm] (monitor Ta [°C] Average grain Tensile stress width are 500, 300, and 250 nm, respectively. The dimensions wafers) size [nm] [MPa] perpendicular to the beam axis, which are nominally identical in c-Si 220 −39 the Bragg mirrors and in the cavity are the width of the central OMS4 211 950 215 90 beam (500 nm) and the depth of the stub (500 nm). A detailed OMS3 850 187 170 schematic is shown in Figure S2, Supporting Information, and the fabrication process of these OM nanobeams is detailed OMS2 211 750 171 250 elsewhere,[8,38] whereas the fabrication of the structures for OMS1 650 163 290 Adv. Funct. Mater. 2022, 32, 2105767 2105767 (3 of 9) © 2021 The Authors. Advanced Functional Materials published by Wiley-VCH GmbH www.advancedsciencenews.com www.afm-journal.de µ-TDTR measurements is summarized in the Supporting Information. We first investigate the effect of nanocrystals on thermal transport by measuring nominally identical suspended mem- branes fabricated on the wafers with different annealing tem- peratures Ta. In these structures, the only phonon scattering mechanism that is not intrinsic to the material is surface scat- tering at the top and bottom surfaces of the membranes. As this scattering only depends on the spacing between the sur- faces, which is identical for all samples, and the surface quality, the differences in heat dissipation rates solely stem from the crystallinity. For each of the nanocrystalline samples, we measure three nominally identical structures. We then calculate the average value of the heat dissipation rate γ and the standard deviation of the measurements gives the error bars. The results are shown in Figure 3a. It is clear in the figure that γ increases with annealing temperature and it is not an intrinsic intrinsic feature, instead it directly depends on the geometry, as it can be seen that the shorter membranes dissipate heat faster. The intrinsic thermal property is the thermal conductivity. Due to the geometry of the structure, neither the 1D nor the 2D heat equation can be used to analytically deduce the thermal conduc- tivity. Hence, we use FEM simulations to virtually reproduce our µ-TDTR experiments, with a heating phase modeled by an inward heat flux in the metal pad, of the same duration as the experimental heating, and a cooling phase. The temperature is “probed” at the center of the metal pad. In this 3D FEM model, thermal conductivity is the only free parameter. The heat dissipation rates obtained for different values of the thermal conductivity are then compared with the experimental dissipa- tion rate to extract the experimental thermal conductivity. The uncertainty on the measurement of the structure dimensions (±3 nm) results in an error in thermal conductivity of less than 5%. Further details of the measurement system and FEM simu- Figure 3. Thermal properties of nanocrystalline Si membranes. a) Heat lations are provided in Refs. [17,36,39]. dissipation rate γ measured as a function of the annealing temperature The results of that analysis as a function of the grain size Ta and the corresponding average grain size for two membrane lengths L. are shown in Figure 3b. For comparison, the values for c-Si are b) Thermal conductivity of the same membranes as a function of Ta given, with the x-axis representing the membrane thickness, (light blue dots). The blue “c-Si membranes” line corresponds to a fit of the µ-TDTR data for crystalline silicon, adapted from Ref. [33] The red which is the limiting dimension in that particular case. For each star indicates the estimated thermal conductivity of a 220 nm thick c-Si average grain size, the thermal conductivity value is a weighted membrane. The small blue dots represent the thermal conductivity of average of the data displayed in Figure 3a. Data from c-Si mem- c-Si membranes measured by Raman thermometry[13] and the TTG tech- branes measured by µ-TDTR,[33] Raman thermometry,[13] and nique.[22] The stripes represent calculations for membranes based on the transient thermal gratings (TTG)[22] yield thermal conductivity Fuchs–Sondheimer model (blue) and for circular nanowires (220 nm between 40 and 90 W m−1 K−1 for the dimensions covered by diameter and fixed carrier-reflection parameter Rb = 0.5) using a Mayadas model. this study. Due to fabrication limitations related to buckling of single c-Si membranes, we could not measure their thermal conductivity. Nonetheless, the Fuchs–Sondheimer model Rb = 0.5. In Figure 3b, we see that the expected thermal con- has been extensively used to describe that effect and it shows ductivity is indeed lower in these nanowires than in the mem- extremely good agreement with the reported values in the lit- branes. Details of these calculations are given in Supporting erature.[29] In such membranes, thermal transport still occurs Information. In the nc-Si membranes studied in this work, in two directions. Whereas membranes are 2D structures and thermal transport is impeded in all three directions. We observe the dimension can be linked to thermal properties due to the that even when the average grain size of 215 nm (Ta = 950 °C) interfaces, we have introduced calculations about nanowires of these membranes is similar to the thickness, the thermal as an example of one-dimensional structures to cover a wider conductivity is reduced by 54% compared to the single crystal range of structures. We thus calculate the thermal conductivity case. This reduction increases to 77% in the sample with the in nanowires of diameter 220 nm using a Mayadas model, in smallest average grain size of 163 nm. To explain these results, which thermal transport is 1D. We also introduce grains in the it is important to note that although specular phonon scattering simulated nanowires, with a fixed carrier-reflection parameter events can occur at atomically flat surfaces at room tempera- Adv. Funct. Mater. 2022, 32, 2105767 2105767 (4 of 9) © 2021 The Authors. Advanced Functional Materials published by Wiley-VCH GmbH www.advancedsciencenews.com www.afm-journal.de Figure 4. Impact of nanostructuring and grain size on the heat dissipa- tion rate. Heat dissipation rate γ measured with the µ-TDTR technique as a function of nanobeam length and annealing temperature Ta. The grey dots show the rate measured from geometrically identical single- crystalline nanobeams. Inset. Average γ of 6.25 µm long nanobeams as a function of the annealing temperature. Errors bars are shown with the data from SOI samples only for clarity and correspond to the standard deviation of the measurement in structures of identical length. Figure 5. Impact of S/V ratio on heat dissipation rate. Heat dissipation rate γ as a function of the S/V ratio in nanobeams made of nc-Si with an average ture,[40] thermal transport is considered diffusive overall.[22] The grain size of 163 (Ta = 650 °C, blue), 215 nm (Ta = 950 °C, red), and of single difference in thermal conductivity between crystalline and crystalline silicon c-Si (grey). Data is shown for two nanobeam lengths: 6.25 nanocrystalline silicon membranes therefore mainly stems (squares) and 7.25 µm (circles). The colored stripes are guides to the eye. from the scattering events at grain boundaries, whose frequency of occurrence in nc-Si is directly linked to the grain size distri- towards the central island of the OM structure (see Figure S1, bution. Furthermore, a recent experimental study on 145 nm- Supporting Information). In our experiments, the measured thick crystalline Si membranes[41] shows that phonons with a values of heat dissipation rate γ are sufficiently insensitive mean free path above 215 nm contribute nearly 20% to thermal to Γ. Therefore, no distinction is made in the rest of this conductivity at room temperature. This proportion is expected work between structures with different Γ values. The inset to to be relatively higher in our membranes due to the increased Figure 4 shows that the grain size impacts heat dissipation in thickness and subsequent shift of the mean free path distri- a similar way as in membranes, with an increase of the heat bution towards higher values. Anufriev et al.[41] showed that dissipation rate by more than 30% comparing samples made phonon mean free path smaller than 400 nm contributes sig- out of nc-Si annealed at Ta = 650 °C and Ta = 950 °C. However, nificantly to thermal conductivity in a 145 nm thick membrane. the difference with c-Si is much smaller than in the suspended This suggests that the grain size distribution in our samples membranes since the heat dissipation is ≈19% slower in nc-Si covers the range of mean free paths with the strongest contri- nanobeams with Ta = 950 °C than in identical nanobeams made bution to thermal conductivity. It explains the strong suppres- of c-Si. This phenomenon is attributed to the fact that the heat sion of the thermal conductivity measured here. Furthermore, dissipation is already strongly suppressed in c-Si nanobeams we see that our experimental values of thermal conductivity lie due to surface phonon scattering. below the expected values for nanocrystalline nanowires from Due to the multiple parameters involved, evaluating the the Mayadas model with a carrier reflection parameter of 0.5. impact of geometry on the thermal properties is not straight- Although no direct quantitative comparison is possible between forward. Two main parameters have been extensively used in these two sets of values, they suggest that the transmission at the literature as a way to encompass the effect of geometry in grain boundaries in our samples might be lower than the value nanostructures and phononic crystals, namely, the neck size— input in the model. High spatial resolution measurements on the smallest width available for phonons to travel through— single grain boundaries could shed light on the transmission at and the S/V ratio to highlight the importance of surface scat- single grain interfaces. tering. We varied the geometry for each sample by increasing The role of the S/V ratio in nc-Si OM nanobeams is shown the hole diameter and reducing the width of the central beam in Figure 4 where the same trend observed in nc-Si membranes as well as the width and length of the stubs. These changes is qualitatively observed also for OM nanobeams, that is, the effectively increase the S/V ratio and are schematically shown heat dissipation rate decreases with increasing length and with in the upper part of Figure 5. The data confirms that for a decreasing grain size. In the case of periodic nanobeams, Γ given S/V ratio, that is, for a similar geometry, the heat dissi- corresponds to the decrease of the geometrical parameters pation rate increases with increasing grain size but remains Adv. Funct. Mater. 2022, 32, 2105767 2105767 (5 of 9) © 2021 The Authors. Advanced Functional Materials published by Wiley-VCH GmbH www.advancedsciencenews.com www.afm-journal.de Table 2. Summary of thermal characteristics of membranes and nanobeams. Membranes Nanobeams S/V = 116.4 ± 0.8 nm−1 S/V = 127.9 ± 1.2 nm−1 Κ [W m−1 K−1] Κ/Κc-Si Κ [W m−1 K−1] Κ/Κc-Si Κ/Κmembrane Κ [W m−1 K−1] Κ/Κc-Si Κ/Κmembrane c-Si 91.5 1 42.73 1 0.47 25.33 1 0.28 215 nm 22.8 0.249 16.06 0.38 0.70 8.71 0.34 0.38 187 nm 14.9 0.163 9.63 0.23 0.65 6.43 0.25 0.43 171 nm 10.9 0.119 5.95 0.14 0.55 2.09 0.08 0.19 163 nm 10.3 0.113 5.27 0.12 0.51 3.22 0.13 0.31 lower than that of c-Si. It is interesting to note that for the thermal conductivities. The thermal conductivity data for nano- highest S/V ratio, which corresponds to the smallest neck, heat beams with an average grain size of 187 nm will be compared is dissipated nearly as fast in c-Si as it is in the sample with to values obtained by the optical resonance cooling technique. Ta = 950 °C. This observation suggests that as surface scattering increases and the neck becomes small enough—below 75 nm in our samples—the impact of crystallinity becomes negligible 4. Thermal Dynamics by Optical for that sample. The second observation is highlighted by the Resonance Cooling colored areas in Figure 5. Note that these colored areas are visual guides and not fits the data. Given that heat is dissipated The nanobeams studied here have been extensively used as a through the nanobeams but also through air, the slope of each platform for OM experiments, including self-pulsing,[6,8] cha- area qualitatively indicates the relative impact of geometry on otic behavior,[7] injection locking,[42] and synchronization,[43] heat dissipation. We see in Figure 5 that nanocrystalline mate- among others.[23,27] In this context, non-linear dynamics rial has less dependence on the S/V ratio compared to single involving self-pulsing limit cycle have played a key role. Such c-Si and the geometry seems to have a lower impact as the non-linear dynamics involve not only free carrier dispersion grains become smaller. but also the temperature increase of the cavity, which directly We summarize the µ-TDTR data in Table 2. The data obtained depends on the thermal properties of the nanostructure. Of from membranes is compared to its crystalline counterpart esti- particular interest is the thermal decay rate Γth. This thermal mated from µ-TDTR in the literature, whereas the data from decay rate is used in modeling to explain the dynamics of the nanobeams is normalized to that of the corresponding mem- system,[6] but so far has only been estimated. Here, we dem- brane and to that of the c-Si nanobeam of a similar S/V ratio. onstrate a way to directly measure Γth using the cooling rate of An increase of the S/V ratio corresponds to an overall decrease the optical resonance of an OM cavity, since the heat dissipa- in the nanobeam neck, stub width and depth, and an increase tion rate γ obtained by µ-TDTR is not strictly equivalent to Γth in hole diameter. The data for nanobeams is obtained for a in OM devices due to the added contribution of the suspended length of 6.25 µm as shown in the inset to Figure 4. We see that central section and gold pad and their heat capacity. Details of the thermal conductivity for the high S/V ratio structure with the method are given in the Supporting Information. Briefly, an average grain size of 187 nm has the lowest reported thermal two tuneable laser beams, with wavelengths around 1.5 µm and conductivity. This specific value, lower than expected, is attrib- polarization states independently controlled, are multiplexed uted to uncertainties, which are larger for structures with lower into a tapered fiber. The thinnest part of the taper is twisted Figure 6. Principle of optical resonance cooling. a) Schematic of the experimental configuration involving the fiber loop and the nanobeam. The red to blue gradient along the beam represents the temperature distribution induced by the pump, whereas the probe laser is represented in yellow. b) Optical transmission spectra through the optical fiber in the sample with an average grain size of 187 nm. The transmission measured at low power, that is, without heating the cavity, is shown in the blue trace. Heating of the cavity at higher laser power (5 mW) is shown in the red trace, with the first optical resonance thermally shifted to a longer wavelength. The spectra are obtained by sweeping the pump laser from short to long wavelengths. Adv. Funct. Mater. 2022, 32, 2105767 2105767 (6 of 9) © 2021 The Authors. Advanced Functional Materials published by Wiley-VCH GmbH www.advancedsciencenews.com www.afm-journal.de into a loop, which is then positioned parallel to the nanobeam First, we turn on the pump laser in a blue-detuned position, as shown schematically in Figure 6a. The distance between the at a shorter wavelength compared to the empty “cold” cavity fiber and the nanobeam is approximately 0.2 µm so that the resonance, that is, the position of the resonance without pho- long tail of the evanescent field of the fiber mode locally excites tons in the cavity, which corresponds to the 1st resonance at the resonant optical modes of the cavity. The light traveling 1545.5 nm in Figure 7. The wavelength of the pump laser is through the fiber from either laser can couple to the optical then continuously increased, and as this pump laser couples to cavity modes if its wavelength corresponds to one such reso- the resonance in the cavity, the transmission through the fiber nance. When measurements are performed in transmission, exhibits a dip. At fixed laser power, we continue increasing the the light that was not coupled to the resonance continues its wavelength of the pump laser, thus continuously shifting the path through the optical fiber. The signal is then separated so resonance until it is approximately 4.5 nm away from its “cold” that each branch is dedicated to one laser. The signal in each position while verifying that the cavity remains below the self- branch goes through an in-line bandpass filter adjusted to one pulsing limit. The spectrum of a thermally shifted resonance is of the two lasers and is then detected by a fast InGaAs pho- shown in red in Figure 6b. The probe laser is then turned on todetectors (12 GHz bandwidth). The signals from both detec- at a wavelength between the initial position of the resonance tors are then transmitted to and recorded by an oscilloscope. measured at low laser power and the position thermally shifted All measurements are performed in an anti-vibration cage at by 4.5 nm by the high-power pump laser, and the wavelength- ambient temperature and atmospheric air pressure. More filter is adjusted to the probe laser. A waveform generator then details of the measurement system to characterize OM cavities gives an impulse to the pump laser, switching it off, which trig- are given in previous work[42] and a schematic of the setup is gers the acquisition of the waveform of the probe laser on the shown in Supporting Information. oscilloscope. This cycle is repeated for each new wavelength To obtain the thermal decay rate Γth we rely on a pump- of the probe laser, effectively mapping the spectrum between probe technique. The first three cold resonances of the meas- the cold and heated wavelengths of the optical resonance. The ured structure are shown in Figure 6b with the blue line. recorded curves, examples of which are displayed in Figure 7b, Figure 7. Thermal measurements using optical resonance cooling. a) Schematic of the different wavelengths of the probe laser in-between the cold and hot resonance. b) Temperature of the cavity measured at different wavelengths of the probe laser. The cooling speed, or decay rate, is extracted from the exponential decay curve (dotted line). c) Oscilloscope-recorded optical signal for different probe laser wavelengths. As the pump-probe wavelength difference increases, that is, as the resonance cools down, the dip in the signal gets broader and occurs at a later time. Adv. Funct. Mater. 2022, 32, 2105767 2105767 (7 of 9) © 2021 The Authors. Advanced Functional Materials published by Wiley-VCH GmbH www.advancedsciencenews.com www.afm-journal.de are then fitted with a Lorentzian function to identify the 5. Discussion and Conclusions transmission minimum. It is interesting to note that as the resonance cools down, the dip in the signal gets broader and In summary, we have used several different experimental tech- more asymmetric, which is a direct consequence of the slowing niques to investigate the structural and thermal properties of down of the cooling with increasing delay. The wavelength of OM crystal cavities made of nanocrystalline silicon. Dark- the probe laser is converted to a temperature rise using the field TEM analysis shows that different annealing tempera- thermo-optic coefficient. This coefficient gives the shift of the tures result in different grain size distributions, which affect optical resonance with temperature increase and was measured the thermal properties of the material. We used micro-time- to be 0.09 nm K−1 in our previous work.[27] The temperature rise domain thermoreflectance to measure heat dissipation rates in is then plotted against the time elapsed after switching off the the nanocrystalline thin films and observe a strong reduction pump laser, as shown in Figure 7, and fitted with an exponen- compared to the single-crystalline films. This is attributed to tial decay function. The extracted decay rate then corresponds to phonon scattering at the grain boundaries. A recent study on the thermal decay rate Γth. To extract the thermal conductivity, c-Si membranes[41] suggests that the grain size distribution in we use finite element method (FEM) simulations by importing our samples covers the range of mean free paths that contribute the nanobeam geometry from an SEM image and reproducing most to thermal conductivity, thus potentially explaining the the experimental situation in a 3D FEM model. We first calcu- low measured values of thermal conductivity. Measurements of late the optical resonances of the optical cavity and use it as a the mean free path distribution in our nc-Si membranes should heater. Once the temperature in the cavity has reached a steady- be the focus of a future study to quantify this aspect. We then state, we turn off the heater and monitor the cooling rate of the investigated the thermal properties of released OM nanobeams. nanobeam. The simulation is repeated for different values of In such structures, the geometrical dimensions are small with the thermal conductivity of the nanobeam and the extracted respect to phonon mean free path, which means that surface decay rates are matched to the experimental value to identify scattering has a strong effect on thermal conductivity. We the real thermal conductivity. Additional details about the setup showed that the thermal conductivity is very low in nanocrys- and the thermal conductivity extraction are given in the Sup- talline nanobeams, well below 10 W m−1 K−1, and depends on porting Information. the grain size. However, the impact of the grain boundaries in Figure 7 shows the results of the measurements of the first nanobeams is lower than in membranes as the grain boundary optical resonance of an OM nanobeam made out of the nc-Si scattering competes with the surface scattering stemming with an average grain size of 187 nm (Ta = 850 °C). The cavity from nanostructuring. Finally, we have developed a novel tech- and Bragg mirrors comprise 6 and 10 cells on each side, respec- nique to directly measure thermal decay in nanostructures tively, resulting in a nanobeam length of 16.5 µm. This meas- with an optical cavity. The method can be readily adapted to urement was repeated for the 2nd and 3rd optical resonance existing OM structures. By using a pump-probe technique to of the same cavity. The three resonances display thermal decay measure the cooling rate of a localized optical resonance, we times of 1.40, 1.67, and 1.61 µs, respectively. The different decay were able to extract thermal decay rates in nanobeams without times are attributed to differences in the spatial mode profile any modification of the structure. The values obtained are con- of each of the optical resonances, as shown in the Supporting sistent with those from the thermoreflectance technique and Information. The extracted thermal conductivity for each of show the strong potential of this novel contactless method for the optical resonance is then 7.71, 7.04, and 7.56 W m−1 K−1, all nanostructures with optical cavities. The results presented respectively, giving an average thermal conductivity of in this work clarify the impact of grain boundaries on thermal 7.44 ± 0.29 W m−1 K−1. Although no direct quantitative compar- transport in silicon micro- and nano-structures, in a context ison with µ-TDTR measurements is possible due to differences in which crystalline state is a key parameter in NEMS and/or in geometry, namely, the absence of the central island and trans- NOEMS. Moreover, the versatility of the new characterization ducer, the thermal conductivity falls within the range obtained technique paves the way to more standardized measurements by the µ-TDTR method for similar geometries (see Table 2). of thermal properties and to potentially study the impact of Note that the extracted thermal conductivity considers the strain on thermal and optomechanical properties. exact geometry, including the presence of the optical fiber next to the nanobeam. In optomechanics experiments, the optical fiber plays an important role in dissipating heat, which can be Supporting Information observed, for example, in the change of the self-pulsing fre- quency mentioned above. Indeed, the volume of the fiber being Supporting Information is available from the Wiley Online Library or much larger than that of the nanobeam compensates for the from the author. low thermal conductivity of glass, at 1.4 W m−1 K−1, especially when considering nc-Si nanobeams with low thermal conduc- tivity. The optical fiber, therefore, constitutes one of the main Acknowledgements factors limiting the sensitivity of the technique in extracting This work was supported by the European Commission FET Open project the thermal conductivity of the nanobeams. The measurements PHENOMEN (G.A. Nr. 713450). ICN2 was supported by the S. Ochoa presented here nonetheless show the validity of this method to program from the Spanish Research Agency (AEI, grant no. SEV-2017- determine thermal conductivity but more importantly to obtain 0706) and by the CERCA Programme / Generalitat de Catalunya. ICN2 the thermal decay rate associated with OM cavities in real char- authors acknowledge the support from the Spanish MICINN project SIP acterization configuration. (PGC2018-101743-B-I00). D.N.U. and M.F.C. acknowledge the support Adv. Funct. Mater. 2022, 32, 2105767 2105767 (8 of 9) © 2021 The Authors. Advanced Functional Materials published by Wiley-VCH GmbH www.advancedsciencenews.com www.afm-journal.de of a Ramón y Cajal postdoctoral fellowship (RYC-2014-15392) and a [15] J. A. Johnson, A. A. Maznev, J. Cuffe, J. K. Eliason, A. J. Minnich, Severo Ochoa studentship, respectively. E.C.A. acknowledges financial T. Kehoe, C. M. S. Torres, G. Chen, K. A. Nelson, Phys. Rev. Lett. support from the EU FET Open Project NANOPOLY. (GA 829061). 2013, 110, 025901. A.M. acknowledges support from Ministerio de Ciencia, Innovación y [16] N. Zen, T. A. Puurtinen, T. J. Isotalo, S. Chaudhuri, I. J. Maasilta, Universidades (grant PGC2018-094490-B, PRX18/00126) and Generalitat Nat. 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