Nanophotonics 2020; 9(16): 4819–4829 Research article Daniel Navarro-Urrios*, Martín F. Colombano, Jeremie Maire, Emigdio Chávez-Ángel, Guillermo Arregui, Néstor E. Capuj, Arnaud Devos, Amadeu Griol, Laurent Bellieres, Alejandro Martínez, Kestutis Grigoras, Teija Häkkinen, Jaakko Saarilahti, Tapani Makkonen, Clivia M. Sotomayor-Torres and Jouni Ahopelto Properties of nanocrystalline silicon probed by optomechanics https://doi.org/10.1515/nanoph-2020-0489 enhance and optimize their functionality for devices and Received August 26, 2020; accepted September 30, 2020; applications. Here, we report on the optical, mechanical published online October 15, 2020 and thermal properties of nanocrystalline silicon probed by means of optomechanical nanobeams to extract infor- Abstract: Nanocrystalline materials exhibit properties mation of the dynamics of optical absorption, mechanical that can differ substantially from those of their single losses, heat generation and dissipation. The opto- crystal counterparts. As such, they provide ways to mechanical nanobeams are fabricated using nanocrystal- line films prepared by annealing amorphous silicon layers *Corresponding author: Daniel Navarro-Urrios, Catalan Institute of at different temperatures. The resulting crystallite sizes Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus and the stress in the films can be controlled by the UAB, Bellaterra, 08193 Barcelona, Spain; and MIND-IN2UB, annealing temperature and time and, consequently, the Departament d’Enginyeria Electrònica i Biomèdica, Facultat de Física, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain, properties of the films can be tuned relatively freely, as E-mail: dnavarro@ub.edu. https://orcid.org/0000-0001-9055-1583 demonstrated here by means of electron microscopy and Martín F. Colombano, Catalan Institute of Nanoscience and Raman scattering. We show that the nanocrystallite size Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, and the volume fraction of the grain boundaries play a key 08193 Barcelona, Spain; and MIND-IN2UB, Departament d’Enginyeria role in the dissipation rates through nonlinear optical and Electrònica i Biomèdica, Facultat de Física, Universitat de Barcelona, thermal processes. Promising optical (13,000) and me- Martí i Franquès 1, 08028 Barcelona, Spain Jeremie Maire and Emigdio Chávez-Ángel, Catalan Institute of chanical (1700) quality factors were found in the opto- Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus mechanical cavity realized in the nanocrystalline Si UAB, Bellaterra, 08193 Barcelona, Spain resulting from annealing at 950°C. The enhanced absorp- Guillermo Arregui, Catalan Institute of Nanoscience and tion and recombination rates via the intragap states and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, the reduced thermal conductivity boost the potential to 08193 Barcelona, Spain; and Depto. Física, Universidad Autónoma de Barcelona, Bellaterra, 08193 Barcelona, Spain exploit these nonlinear effects in applications including Néstor E. Capuj, Depto. Física, Universidad de La Laguna, 38200 San Nanoelectromechanical systems (NEMS), phonon lasing Cristóbal de La Laguna, Spain; and Instituto Universitario de and chaos-based devices. Materiales y Nanotecnología, Universidad de La Laguna, 38071 Santa Cruz de Tenerife, Spain Keywords: annealing; cavity optomechanics; nano- Arnaud Devos, Institut d’Electronique, de Microélectronique et de crystalline silicon. Nanotechnologie, Unité Mixte de Recherche, CNRS 8250, Avenue Poincaré, CS 60069, F-59652 Villeneuve d’Ascq Cedex, France Amadeu Griol, Laurent Bellieres and Alejandro Martínez, Nanophotonics Technology Center, Universitat Politècnica de 1 Introduction València, 46022 València, Spain. https://orcid.org/0000-0001-5448- 0140 (A. Martínez) Nanoscale optomechanical cavities (OMCs) [1] promise a Kestutis Grigoras, Teija Häkkinen, Jaakko Saarilahti, Tapani route toward flexible, efficient and reliable interfaces to Makkonen and Jouni Ahopelto, VTT Technical Research Centre of transfer classical and or quantum information between Finland Ltd, P.O. Box 1000, FI-02044 VTT, Espoo, Finland microwave and optical frequency domains in a single chip. Clivia M. Sotomayor-Torres, Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, In the nonlinear regime, these devices are very attractive 08193 Barcelona, Spain; and Catalan Institute for Research and for room temperature applications, such as mass sensing Advances Studies ICREA, 08010 Barcelona, Spain [2], nonvolatile memories [3], chaos-based applications [4] Open Access. © 2020 Daniel Navarro-Urrios et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 International License. 4820 D. Navarro-Urrios et al.: Properties of nanocrystalline silicon probed by optomechanics and coupled oscillator networks for neuromorphic chemical vapor deposition (LPCVD). The amorphous Si computing [5, 6], among others. The strong interaction layer was converted to a nanocrystalline one by annealing between light and mechanical modes has been demon- it for 60 min at different temperatures Ta to prepare the set strated in OMCs made of silicon nitride (Si3N4) [7], gallium of nc-SOI wafers for the OMCs. The thickness of the nc-Si arsenide (GaAs) [8], aluminum nitride (AlN) [9, 10], dia- films before and after annealing was measured using mond [11, 12] and crystalline silicon (c-Si) [13, 14]. In monitor wafers processed in the same batch as the device particular, the well-established silicon-on-insulator (SOI) wafers. The thickness of the amorphous Si layer before technology has been the cornerstone in most of the leading annealing was 219 ± 4 nm, measured by spectroscopic experimental results, including ground state cooling [15] reflectometry at the center and in the middle of each and the observation of single photon/phonon quantum quadrant on monitor wafers. After annealing at 750 and correlations [16] to name but a few. An interesting alter- 950°C, the measured thickness of both monitor wafers was native to SOI is nanocrystalline silicon (nc-Si)-on-insulator 211 ± 4 nm. The change in volume, when the material is (nc-SOI). nc-Si is formed by thermal annealing of originally transformed from amorphous to nanocrystalline, converts amorphous silicon to transform it into a polycrystalline the originally compressive stress in the amorphous Si film material. The process was developed in the early 80s [17] to tensile stress in the nanocrystalline film. The amount of and is used in Microelectromechanical systems (MEMS) stress can be controlled by the annealing temperature and technology due to the relatively easy tuning of mechanical, time. The measured tensile stress of the samples after optical, electrical and thermal properties by doping, annealing ranged from 90 to 290 MPa. The residual stress tailoring the size of the crystallites and the stress in the was estimated from the change in the curvature of the films [17, 18]. Recently, it was demonstrated that nc-Si is wafers after the deposition and annealing of the nc-Si films also an excellent and cost-competitive alternative to c-Si using Stoney’s equation [21] with the biaxial modulus for for optomechanical devices taking advantage of nonlinear (100) Si wafers [22]. Table 1 summarizes the properties of effects while operating in ambient conditions [19]. the samples discussed in this work. Nonlinear dynamic functions, such as phonon lasing and The size of the nanocrystallites in the annealed films chaos, were demonstrated with broader bandwidth than ranges from a few nanometers to roughly the thickness of measured in equivalent SOI devices, as well as wafers [19]. the film, with the size distribution depending on the The dynamic behavior depends on the optical and me- annealing temperature and time. To investigate the effect chanical losses and on heat generation and extraction rates of annealing temperature on the microscopic structure of of the OMCs [4, 20]. These properties can be tuned rather the films, a detailed study of the structure and size distri- flexibly in nc-Si films by varying the processing parame- bution of the nanocrystallites was carried out using ters. In this work, we use optomechanical nanobeams to transmission electron microscopy (TEM). A bright-field probe the properties of nanocrystalline films, focusing on TEM micrograph of the sample OMS4 is shown in Figure 1A. the optical and mechanical behavior and, especially, on The structure in the image is representative of the whole set dissipation rates. A set of nominally identical nanobeam of nc-Si samples. Selective area electron diffraction (SAED) OMCs were fabricated on nc-SOI wafers annealed at confirmed that all the annealed samples are polycrystalline different temperatures. The pristine nc-Si films own with no preferential crystalline orientation (see the inset to different nanocrystallite size distribution and tensile Figure 1A) in contrast to films deposited at higher tem- stress. perature for which the initial growth mode is poly- crystalline. The size distribution of the nanocrystallites was obtained by dark-field TEM analysis method, as detailed in the supplementary material. Briefly, an aperture is placed 2 Nanocrystalline silicon-on- in the diffraction plane, effectively blocking electrons dif- insulator substrates fracted outside the range determined by the aperture. This creates images in which only nanocrystallites with a spe- The substrates for the optomechanical nanobeam cavities cific crystalline orientation appear bright on the dark consisted of an undoped, nominally 220-nm thick nc-Si background. By moving the aperture, all orientations can film on a 1000-nm thick thermal oxide layer grown on low- be inspected. The size of the nanocrystallites is estimated doped 150-mm (100) Si wafers. The thick SiO2 layer was using a threshold in the brightness of their images along grown by wet oxidation at 1050°C. The measured resulting two perpendicular directions fixed for each of the samples. thickness was 1013 nm. On the oxide, a layer of amorphous Both are taken into account as if they belong to different Si was deposited at 574°C from silane by low pressure nanocrystallites, which leads to a broadening of the size D. Navarro-Urrios et al.: Properties of nanocrystalline silicon probed by optomechanics 4821 distribution. The statistical analysis includes more than This work This work This work This work This work This work [, ], Ref. 500 nanocrystallites in each sample. The average size and Table : Summary of the main characteristics of the samples studied. The values measured on the wafers and those obtained from the OMCs are in the blue- and red-headed columns, size distribution were extracted from these data. The average size was found to increase with annealing tem- increase @  photons (K) . –  –   Temperature intracavity perature from 163 (annealing at 650°C) to 215 nm (anneal- ing at 950°C), and the size distribution became broader as the nanocrystallites grew larger, as shown in Figure 1B. Note that this average grain size is used as a simplified representation of the size distribution to highlight the trend with annealing temperature. The shift toward larger grains . GHz  Q-factor @ –     Mechanical with increasing annealing temperature is further shown in the cumulative size distribution (see supplementary ma- terial). Thus, it is deduced that the volume fraction of the grain boundaries within the layers, representing the vol- ume occupied by the nanocrystallite boundaries with decay rate @ . μm Intrinsic optical (× s−) . – . . . . respect to the total volume of the nc-Si layer (ηGB), de- creases upon annealing. We also investigated the nc-Si films by Raman spectroscopy using a 532-nm laser, keeping the laser power low enough to avoid heating effects, and sound       Longitudinal velocity (m/s) compared the results with the reference c-Si samples measured spectra. The typical optical phonon mode of crystalline Si centered at 520 cm−1 is observed in all samples, and in the nc-Si, it exhibits an asymmetric Refractive Average nc size (nm) – –     broadening in the low frequency side increasing the full width at half maximum (FWHM) of the peak. This broadening is typically associated with the presence of an initial amorphous phase [25], nanocrystallites of  nm . index @ . – . –  nm) . (. @ different sizes [26] and grain boundaries [27]. In this study, the latter two are more likely since the amorphous phase contribution usually shows spectral features at significantly lower energies, around ∼480 cm−1 [28]. This − −    (MPa)  Stress is further supported by the SAED images, which indicate that the films are polycrystalline with no halos arising from the amorphous phase. The FWHM of the peak de- Thickness (nm) – – (monitor wafers)     creases with Ta (see the inset to Figure 1C), which is interpreted as arising from the smaller grain boundary fraction volume (ηGB decreases) and the concomitant shift of the distribution toward larger nanocrystallites. The sound velocity of the nc-Si films was measured by Ta – –     (°C) OMC, nanoscale optomechanical cavity. picosecond acoustics [29]. Interestingly, the sound velocity in all annealed samples was 8510 m/s, which is slightly Amorphous Si-reference higher than that in (100) Si but lower than in (111) and (110) Si. This may be a consequence of the polycrystalline na- Annealed a-Si Annealed a-Si Annealed a-Si Annealed a-Si ture, averaging the velocities in different crystallographic Reference Si Description directions. The sound velocity of the as-deposited amor- phous Si was measured to be 7950 m/s, suggesting that the growth mode of the LPCVD Si at 574°C is close to switching respectively. from amorphous to polycrystalline. This can also be seen in Sample OMS OMS OMS OMS the SAED images of the as-deposited Si (see supplementary name a-Si c-Si material). 4822 D. Navarro-Urrios et al.: Properties of nanocrystalline silicon probed by optomechanics 5 nm-1 A B 500 nm C Figure 1: Nanocrystallite size distribution in the nc-Si films. (A) Bright-field TEM image of the sample OMS4, showing the randomly oriented nanocrystallites. The inset shows a selective area electron diffraction (SAED) image of the sample. (B) Histograms of the crystallite size distribution of samples annealed at different temperatures Ta. The analysis includes more than 500 nanocrystallites in each sample, and a log-normal distribution is used to fit the histograms. The average nanocrystallite size (xc) is shown by the vertical dashed black lines; (C) Raman scattering spectra of the reference c-Si (blue) and the nc-Si layers annealed at 650 and 950°C (green and black, respectively). The full width at half maximum of the Raman peak as a function of the annealing temperature is shown in the inset. The dashed horizontal line corresponds to the value measured from the c-Si reference sample. TEM, transmission electron microscopy; nc-Si, nanocrystalline silicon. 3 Optomechanical with respect to that of the mirror cells is 0.85. The length of the OMC beam is 15 μm. After patterning, the beam is characterization of the released by removing the oxide layer beneath the beam. nanobeams The characterization of the optical and mechanical modes supported by the OMCs was performed using the Nanobeams with optomechanical cavities were fabricated setup shown in Figure 2. The emission of two tunable lasers in nc-SOI wafers to study the coupling of light and me- covering the spectral around 1.55 μm (L1 and L2) with chanical vibrations in nc-Si. The fabrication process of the independently controlled polarization states is multi- plexed into a tapered fiber. The tapered part of the fiber has OMCs is described in detail in the study by Gomis-Bresco a loop to enhance the spatial resolution. The loop is placed et al. [30]. Briefly, the OMC geometry is based on a unit cell parallel to the OMC, in contact to an edge of the released consisting of a parallelogram with a cylindrical hole in the window with a gap between the fiber and the OMC of about center and two symmetric stubs on the sides as shown in the 200 nm. The long tail of the evanescent field of the taper Scanning electron microscope (SEM) image in Figure 2. The excites locally the resonant optical modes of the OMC. The cavity region in the center of the beam consists of 12 cells optical signal is measured either in transmission or in with the pitch (a), the radius of the holes (r) and the length reflection using fast InGaAs photoreceivers PD1 and PD2 of the stubs (d) decreasing quadratically toward the center with bandwidths of 12 GHz. As a general rule, we used the of the beam. Ten-period mirrors are placed on both sides of reflection configuration to extract the optical linewidth of a the central region. The nominal geometrical values of the resonance and the transmission configuration to assess the cells of the mirror are a = 500 nm, r = 150 nm and d = 250 nm. transmitted power and the fraction coupled to the mode. The ratio of the geometrical parameters of the central cell Once in optical resonance, the mechanical motion of the D. Navarro-Urrios et al.: Properties of nanocrystalline silicon probed by optomechanics 4823 Figure 2: Schematics of the experimental setup to measure the properties of the optomechanical nanobeams. A tapered fiber loop is placed in close proximity to the OMC nanobeam, shown in the SEM image (not in scale). L1 and L2 are tunable lasers, λ-mux is a wavelength multiplexer, λ-filter is a Fabry–Perot wavelength filter, SG denotes a signal generator, VOA is a variable optical attenuator, FPC1 and FPC2 are the fiber polarizer controllers, SA stands for a spectrum analyzer and PD1 and PD2 denote the photodetectors. The signals can be detected in transmission or reflection mode. OMC, nanoscale optomechanical cavity. cavity, activated by the thermal Langevin force, modulates diffusion, is often the dominant factor determining the the cavity mode, and the signal is recorded using a spec- mechanical energy dissipation in microsized and nano- trum analyzer with a bandwidth of 13.5 GHz. All the mea- sized beam resonators [32]. An experimentally validated surements are performed in an antivibration cage at theory to describe the TED was first established by Zener atmospheric pressure and temperature. and Siegel [33] for homogeneous materials. This theory was recently extended to polycrystalline materials, in which an enhancement of the TED is expected due to both the reduction of the overall thermal diffusivity of the material 3.1 Mechanical properties and to the intercrystalline damping as a consequence of additional dilatational strains created at the grain bound- When the excitation laser wavelength is in resonance with aries [34]. It is also well known that providing mechanical the optical cavity mode, it is possible to transduce ther- tensile prestress, or strain, is an effective way to reduce mally activated mechanical modes in the sample. Radio- mechanical losses [31, 35], a step in part associated with frequency (RF) signals of the mechanical breathing modes mitigation of the TED [36]. appearing at about 2.4 GHz are shown in Figure 3 in a The results shown in Figure 3 reflect that a balance normalized frequency scale. We studied the behavior of the between the two contributions described above determine mechanical quality factor Qm and its dependence on Ta. the overall mechanical dissipation rates in the mechanical The results are shown in the inset to Figure 3. It is clear that modes under study: (i) mechanical tensile strain and Qm increases with Ta, whereas the quality factor decreases (ii) thermoelastic damping. The results suggest that TED with increasing tensile stress in the nc-Si layer, as opposed has stronger impact than the tensile strain on the Qm of to c-Si- or Si3N4-based nanomechanical resonators [31]. For the nc-Si OMCs annealed between 650 and 850°C, while at the highest annealing temperature, Qm is about 1.7 × 103, 950°C, the Qm overcomes the value measured on the c-Si which is a factor of two to three times higher than what was OMC, as mentioned above. It is worth noting that the small found in equivalent c-Si OMCs at room temperature and compressive stress in the c-SOI sample leads to buckling of represents a major achievement of the current work. the released OMC, which may degrade the Qm. Finally, we Thermoelastic damping (TED), resulting from heat have also quantified thermomechanic dispersive effects on generation due to vibration and dissipation from thermal these modes to be about −40 kHz/K. 4824 D. Navarro-Urrios et al.: Properties of nanocrystalline silicon probed by optomechanics Figure 3: Normalized RF spectra of a mechanical breathing mode in optomechanical nanobeams. The mode appearing at about 2.4 GHz was measured in the nc-Si OMC1 and OMS2 and the refer- ence c-Si OMC. The frequency scale is normalized to allow comparison of the linewidths of different samples. The inset shows the evolution of the mechanical Q- factor as a function of annealing tempera- ture and the measured tensile stress. The dashed horizontal line corresponds to the value measured in the c-Si reference OMC. OMC, nanoscale optomechanical cavity. 3.2 Optomechanical and thermal properties mechanism [37], determine the optical and thermal prop- erties of nc-Si OMCs. The optical losses become smaller in Low excitation power optical spectra measured in the samples annealed with increasing Ta, explained above by OMCs are shown in Figure 4A. It is worth noting that the drop in grain boundary volume and, possibly, of the from now on we deal with the fundamental and the trap density at the boundaries. second-order optical modes of the OMCs (indicated in the Since at optical energies falling below the band gap, Si- notation with subindices 1 and 2, respectively). The based optical resonators have three main power- obtained spectra confirmed that the frequencies of the dependent optical loss mechanisms: (i) two-photon ab- resonant peaks are similar in all samples within a range of a sorption (TPA), (ii) trap-assisted carrier generation and (iii) few nanometers. This is not surprising since the nc-Si free carrier absorption (CA) within the conduction and layers in all samples have the same thickness and refrac- valence bands; the dependence of κi,1 on the number of tive index as measured by spectroscopic reflectometry (see intracavity photons no was studied. The first scales with no2 Table 1). However, the intrinsic optical decay rate of the while the second is linear in no and depends on the trap fundamental mode κi,1 at the resonant wavelength density. The third mechanism is linear with the excited λr,1 ≈ 1.54 μm, extracted indirectly by measuring the overall carrier density N and the number of photons in the cavity no. decay rate (κ1) and the coupled power fraction in resonance In what follows, CA, consisting of the latter two [19], decreases in samples annealed at higher tempera- mechanisms, is discussed as giving rise to the main optical tures, as shown in Figure 4B. The lowest κi,1 value is still a loss mechanism in nc-Si. The trap states inside the band factor of 1.5 higher than that of a c-Si OMC with the same gap are thermally populated up to the Fermi level lying geometry and leads to an intrinsic optical Q-factor of inside the band gap in our samples. They provide a reser- Qi,1 = 1.3 × 104 at Room temperature (RT). We deduce that voir for carrier generation to the conduction band, and the the material losses are the dominant loss mechanisms in empty trap states then generate holes. To quantify the roles nc-Si-based OMCs since the radiative losses depend on the of these optical loss mechanisms, a pump-and-probe geometrical shape and thus can be assumed to be inde- technique was used in which the second-order mode of pendent from Ta. We postulate that the main intrinsic op- the OMC is excited using the laser L2 with input power (Pin) tical loss mechanism arises from scattering at the grain of the order of hundreds of μW, while the fundamental boundaries and from the carrier involving interface states mode is probed with the laser L1 with sufficiently low within the band gap. As the wavelength is below the band power so that its effect on κi,1 can be neglected (see gap energy of silicon, the carrier generation taking place Figure 4A). Given that the number of intracavity photons no via gap states and the ensuing relaxation via phonon follows the Lorentzian shape of an optical resonance, emission, i.e., a Shockley–Read–Hall recombination i.e., no  no, max Δλ2r, 2 4(λL2 − λr, 2 )2 + Δλ2r, 2 , the followed D. Navarro-Urrios et al.: Properties of nanocrystalline silicon probed by optomechanics 4825 A B Figure 4: Optical transmission and intrinsic optical decay rate of the first-order mode. (A) Typical optical transmission spectrum of OMC (OMS4) under study displaying the first two optical modes excited with lasers C L1 and L2, respectively, in a pump-and- probe experiment to determine the intrinsic optical decay rate κi,1. (B) Intrinsic optical loss rate when the pump laser L2 is switched off, i.e., the second mode photon population is set to no = 0, as a function of the annealing temperature of the nc-Si layers. The dashed horizontal line corre- sponds to the value measured in the c-Si reference sample. (C) Intrinsic optical loss rate of the fundamental mode as a function of the intracavity photon population. nc-Si, nanocrystalline silicon; OMC, nanoscale optomechanical cavity. procedure to adjust no is to fix the input power and where according to the study by Johnson et al. [38], the decrease the relative detuning between the laser L2 following equation is derived: wavelength λL2 and the resonance wavelength of the second-order mode λr,2. When the laser is in resonance ∂κi, 1∂n no  σCA cn N, (2) o g with the second-order mode, the expression becomes no  no, max  2P in λr, 2 κe, 2 κ22 hc, κe,2 and κ2 being the extrinsic and σCA and ng are the CA cross section, including absorption overall optical decay rates of the second-order mode, to and from the traps and free CA, and the group veloc- respectively, h is the Plancks constant and c the speed of ity index, respectively. A value of ∂κi,1/∂no ≈ 2 × light. In this particular experiment, the light extracted 107 s−1 photon−1 can be extracted from the slope of the linear from the fundamental cavity mode is collected in a fit of the data. These results indicate that the carriers are reflection configuration using a circulator and a tunable generated in both samples by single-photon absorption Fabry–Perot filter in resonance with the laser L1 to filter involving midgap states occupied with similar carrier out the contribution of light from the second mode. The concentration No, which in turn is determined by the output of the laser L1 is modulated using a signal thermal statistical distribution, the average cross section generator, the output of which is used as the reference to (σo) and the interband recombination rate (ΓC). Thus, it is a lock-in amplifier receiving the signal from the photo- possible to express the optically excited carrier density in diode PD2 to improve the signal-to-noise ratio, see nc-Si N as follows: Figure 2. We verified experimentally that κ2 and κe,2 are both almost an order of magnitude larger than κ1, and, N ≈ σ o N oΓ no (3) C therefore, are not affected by photon numbers up to no ≈ 104. The c-Si reference sample does not show a significant The results in Figure 4C show that the intrinsic optical dependence of κi,1 on no. The effects of trap-assisted carrier decay rate κi,1 increases with the number of intracavity generation and TPA on κi,1 seem to be negligible and are photons no in all nc-Si samples as a consequence of losses beyond the detection limit of our experiment. We can by carriers generated by the absorption of light stored in neglect the effect of TPA in the nc-Si OMCs since the the second mode, as will be described below. The results probability of this absorption mechanism is very low and measured from OMS3 and OMS4 show single linear the impact would be comparable to c-Si. The results show behavior with a similar slope, which can be modeled by the that the concentration of gap states in the c-Si OMC is much following equation: lower than in the nc-Si OMCs, which is expected. In the κi, 1 (no )  κi, 1 (0) + ∂κi, 1∂n no (1) sample OMS1, two linear regimes appear and the transition o between them occurs at rather low number of intracavity 4826 D. Navarro-Urrios et al.: Properties of nanocrystalline silicon probed by optomechanics photons of no,t = 0.2 × 103, with the weaker dependence of which show that the dependence of the optical loss rate on ∂κi,1/∂no occurring at higher no. The slope of the linear fit in no is similar in all the nc-Si OMCs, i.e., the carrier concen- the region with high photon number is similar to the tration does not depend on Ta. An exception is the high other nc-Si samples, i.e., ∂κi,1/∂no ≈ 2 × 107 s−1 photon−1. slope region observed in OMS1 at low no, the contribution Therefore, in all the nc-Si samples, the slope suggests that of which to the carrier concentration can be neglected the gap states in the grain boundaries have similar con- given that the number of photons exceeds by an order of centration, average cross section, decay rate and occupa- magnitude of the saturation value no,t. tion probability. It is interesting to note that, while the We have previously demonstrated that the free CA and linear slope of the optical power–dependent losses seems the subsequent carrier relaxation within the conduction band to be independent of Ta, the offset value is seen to decrease is the main heat source in single crystal Si OMCs [4, 19, 20]. In with increasing annealing temperature. Thus, scattering at nc-Si, the density of the interface states can easily be above the boundaries or direct photon absorption involving the 1020 eV−1 cm−3, which has an important role in increasing intragap interface states may be the dominating factors interband carrier recombination Γc and the material heating defining the behavior of the losses at no = 0 in the nc-Si rates, and, consequently, the relative importance of free CA as OMCs, i.e., in the absence of photons in the cavity [39]. The a heating mechanism is reduced. Thus, by considering that dependence of the intrinsic losses on the photon popula- both heating processes should be considered in nc-Si, we can tion also shows that the number of thermally populated deduce that, at equilibrium the temperature increase in trap states is relatively large and that they refill thermally in nanobeam OMCs is given as follows: a short time scale because no saturation effects can be seen in the measurements. Nevertheless, the microscopic 1 αCA no ΔT ≈ (σo N o no ) + βC  (4) mechanisms involving the dependence of the trap capture Γth ΓC cross section and the trap density on the annealing tem- perature remain to be investigated. The steep slope observed in OMS1 at low no seems to be related to a different kind of defect state with much larger cross section and with depletion of the carrier population when the number of photons in the cavity approaches to a saturation value denoted by no ≈ no,t. Considering that the heat dissipation has a direct impact on the frequency bandwidth of the self-pulsing dynamics occurring in the OMCs [19], the behavior of heat dissipation rates of the OMCs was studied as a function of Ta. A single laser configuration was used to excite the fundamental optical mode λr,1 and adjusted Pin to obtain no,max ≈ 2700 in all samples. As expected, a red-shift of λr,1 associated to the thermooptical (TO) dispersion was observed in response to an effective temperature increase ΔT in the cavity region. The contribution of the TO effect is Figure 5: Temperature increase of OMC nanobeams fabricated in nc- the origin of the saw-tooth spectral shape of the trans- SOI wafers with different annealing temperature Ta for a fixed mission obtained when measuring a spectrum by sweeping photon number of 2.7 × 103. from short to long wavelengths, with the longest wave- The dashed horizontal line corresponds to the value extracted from length so that λL1 = λr,1 and no = no,max, as shown in the inset the measurements of the c-Si reference sample. The average nanocrystallite size (xc) is also shown. The inset shows the to Figure 5. For comparison, the inset also shows the op- transmission curves with respect to the resonance value, at low laser tical transmission spectrum obtained at low Pin. Under power, obtained at the same value of the maximum intracavity photon these experimental conditions, it is possible to compare the number (no,max). The transmission signals, which arise from the contribution of the TO effect in each OMC by measuring the interplay of the Free carrier absorption (FCA) and the TO effect, are maximum λr,1 shift. Since the TO coefficient was deter- normalized to the values just after the resonance is lost. The red dashed curve illustrates a transmission curve at low laser power mined to be ∂λr,1/∂ΔT = 0.09 nm/K, regardless of the crys- measured from sample OMS3 (Ta = 850 °C) so that no significant TO talline arrangement of the nc-Si films [19], the spectral effect is observed. nc-Si, nanocrystalline silicon; OMC, nanoscale shifts can be directly related to ΔT (see Table 1). At this optomechanical cavity; nc-SOI, nanocrystalline silicon (nc-Si)-on- point, it is necessary to recall the results of Figure 4C, insulator; TO, thermooptical. D. Navarro-Urrios et al.: Properties of nanocrystalline silicon probed by optomechanics 4827 where αCA is defined as the rate of temperature increase per boundaries within the layers. This appears to be the origin photon and unit of optically excited carrier density asso- of the extracted tendencies of optical, mechanical and ciated to CA, including both the trap-assisted and free CA, thermal decay rates, suggesting that the dominant factors βC is the rate of temperature increase per unit of optically are associated with physical phenomena occurring within excited carrier density associated with interband recom- and at the grain boundaries and are related to the midgap bination and Γth is the rate at which heat leaks out of the states. Regarding the optical losses of the photonic cav- cavity, either through the anchor points at the ends of the ities, it is concluded that intrinsic damping losses decrease OMC or by convection and or conduction to the surround- with annealing temperature, probably due to a reduced ing environment. In Figure 5, we plot ΔT for a fixed value of scattering at grain boundaries and to the effect of anneal- no as a function of Ta. Since, based on the results shown in ing on midgap interface states. The best optical and me- Figure 4C, it can be inferred that σoNo/ ΓC has a weak chanical quality factors at room temperature, 1.3 × 104 at dependence on Ta, and assuming that αCA and βC are also 1.5 μm wavelength (around 200 THz) and 1.7 × 103 at independent of Ta, the differences in ΔT can be associated 2.4 GHz, were found in OMCs fabricated on nc-Si wafers to variations in Γth. Therefore, there is a clear increase of Γth annealed at 950°C, i.e., with the smallest grain boundary with Ta, which is directly connected to the increase of the volume. The relatively strong CA losses are due to carriers thermal diffusivity and conductivity of the OMC. The in- generated by single-photon absorption mediated by the crease in nanocrystallite size with Ta is consistent with the midgap traps at the grain boundaries, which are indepen- measured increase in thermal conductance of the OMC dent of the annealing temperature in the studied range. The since smaller nanocrystallites lead to enhanced phonon thermal decay rate significantly increases with the scattering at the grain boundaries and hence to lower annealing temperature due to enhanced thermal conduc- thermal conductivity [40–42]. Therefore, samples with tivity and diffusivity, which can be associated to phonon smaller nanocrystallites, i.e., corresponding to lower Ta in scattering at the grain boundaries. The mechanical decay this case, have lower thermal conductivity and conduc- rates seem to be dominated by thermoelastic dissipation, tance. A direct comparison of Γth between the nc-Si and c-Si which depends directly on the thermal diffusivity and, OMCs is not possible because Eq. (4) does not hold for therefore, decreases with annealing temperature. We have single crystal silicon since it implies that carriers are verified that the dissipative part of the optical and me- generated by single-photon absorption. Nevertheless, the chanical resonances is not affected up to temperatures of change in temperature ΔT extracted for c-Si is much smaller 100°C, which may have important advantages for certain than that of nc-Si, and it is deduced that Γth is much smaller technological applications. in nc-Si as a consequence of phonon scattering at the grain In a comparison to results from cavities made on SOI boundaries [43]. A dependence of Γth on Ta consistent with wafers, i.e., of single crystal silicon, of identical geometry, it data shown in Figure 5 was detected independently by was established that the main differences were a more efficient measuring the time domain thermoreflectivity of nc-Si optical absorption by single photons at the telecom wave- membranes (see supplementary material). length of 1.5 μm, a stronger recombination via midgap states and lower thermal conductivity, all leading to an enhanced nonlinear behavior, especially at room temperature. 4 Conclusions Finally, this work lends support to technological ap- proaches using nc-Si since the layer structure and its In summary, optical, mechanical and thermal properties thickness can be tuned to optimize desired device proper- and, especially, the dissipation rates of optomechanical ties. In particular, these results indicate that engineering nanobeams fabricated in nc-Si-on-insulator wafers have the grain or crystallite size– and grain boundary–depen- been investigated. The annealing temperature of the orig- dent properties provides a powerful way to tune the inally amorphous silicon films is found to have a strong properties and therefore the performance of opto- effect on the material properties and, consequently, on the mechanical systems. behavior of the optomechanical cavities. The structural properties were characterized by TEM, picosecond acoustic methods and Raman spectroscopy. The films consisted of Associated content randomly oriented crystallites ranging from a few nm to a few hundreds of nm. The size distribution shifts toward Further details on the analysis of the dark-field TEM images larger crystalline domains with increasing annealing tem- and of the time-domain thermo-reflectance (TDTR) mea- perature, which yielded a smaller volume fraction of grain surements are provided in Supplementary Material. 4828 D. Navarro-Urrios et al.: Properties of nanocrystalline silicon probed by optomechanics Acknowledgments: The authors thank F. J. Belarre Triviño [12] M. Mitchell, B. Khanaliloo, D. P. Lake, T. Masuda, J. P. Hadden, and B. Ballesteros Pérez for the TEM sample preparation and and P. E. Barclay, “Single-crystal diamond low-dissipation cavity optomechanics,” Optica, vol. 3, p. 963, 2016. images. [13] M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and Author contribution: All the authors have accepted O. Painter, “Optomechanical crystals,” Nature, vol. 462, p. 78, responsibility for the entire content of this submitted 2009. manuscript and approved submission. [14] D. Navarro-Urrios, J. Gomis-Bresco, S. El-Jallal, et al., “Dynamical Research funding: The following support is gratefully back-action at 5.5 GHz in a corrugated optomechanical beam,” AIP Adv., vol. 4, 2014, Art no. 124601. acknowledged: the European Commission project [15] J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, et al., “Laser cooling PHENOMEN (H2020-EU-FET Open GA no. 713450), the of a nanomechanical oscillator into its quantum ground state,” Spanish Severo Ochoa Excellence program (SEV-2017- Nature, vol. 478, p. 89, 2011. 0706), CMST and ECA: the Spanish MICINN project SIP [16] R. Riedinger, S. Hong, R. A. Norte, et al., “Non-classical (PGC2018-101743-B-I00), DNU and AM: the Spanish correlations between single photons and phonons from a MICINN project PGC2018-094490-B-C22. DNU holds a mechanical oscillator,” Nature, vol. 530, p. 313, 2016. [17] G. Harbeke, “Growth and physical properties of LPCVD Ramón y Cajal postdoctoral fellowship (RYC-2014-15392); polycrystalline silicon films,” J. Electrochem. Soc., vol. 131, MFC and GA hold a S. Ochoa and a M. S. Curie COFUND p. 675, 1984. BIST postgraduate studentship, respectively. [18] M. Ylönen, A. Torkkeli, and H. Kattelus, “In situ boron-doped Conflict of interest statement: The authors declare no LPCVD polysilicon with low tensile stress for MEMS conflicts of interest regarding this article. applications,” Sens. Actuators A Phys., vol. 109, p. 79, 2003. [19] D. Navarro-Urrios, N. E. Capuj, J. Maire, et al., “Nanocrystalline silicon optomechanical cavities,” Opt. Express, vol. 26, no. 8, pp. 9829–9839, 2018. References [20] D. Navarro-Urrios, N. E. Capuj, J. Gomis-Bresco, et al., “A self- stabilized coherent phonon source driven by optical forces,” Sci. [1] M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity Rep., vol. 5, 2015, Art no. 15733. optomechanics,” Rev. Mod. Phys., vol. 86, p. 1391, 2014. [21] G. G. Stoney and C. A. Parsons, “The tension of metallic films [2] Y. T. Yang, C. Callegari, X. L. Feng, K. L. Ekinci, and M. L. Roukes, deposited by electrolysis,” Proc. R. Soc. Lond. Ser. A, Contain. “Zeptogram-scale nanomechanical mass sensing,” Nano Lett., Pap. Math. Phys. Character, vol. 82, p. 172, 1909. vol. 6, p. 583, 2006. [22] G. C. A. M. Janssen, M. M. Abdalla, F. van Keulen, B. R. Pujada, [3] M. Bagheri, M. Poot, M. Li, W. P. H. Pernice, and H. X. Tang, and B. van Venrooy, “Celebrating the 100th anniversary of the “Dynamic manipulation of nanomechanical resonators in the Stoney equation for film stress: developments from high-amplitude regime and non-volatile mechanical memory polycrystalline steel strips to single crystal silicon wafers,” Thin operation,” Nat. Nanotechnol., vol. 6, p. 726, 2011. Solid Films, vol. 517, p. 1858, 2009. [4] D. Navarro-Urrios, N. E. Capuj, M. F. Colombano, et al., [23] D. E. Aspnes and A. A. Studna, “Dielectric functions and optical “Nonlinear dynamics and chaos in an optomechanical beam,” parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from Nat. Commun., vol. 8, 2017, Art no. 14965. 1.5 to 6.0 EV,” Phys. Rev. B, vol. 27, p. 985, 1983. [5] M. F. Colombano, G. Arregui, N. E. Capuj, et al., “Synchronization [24] E. Iwase, P.-C. Hui, D. Woolf, et al., “Control of buckling in large of optomechanical nanobeams by mechanical interaction,” micromembranes using engineered support structures,” Phys. Rev. Lett., vol. 23, no. 1, p. 017402, 2019. J. Micromech. Microeng., vol. 22, p. 065028, 2012. [6] G. Heinrich, M. Ludwig, J. Qian, B. Kubala, and F. Marquardt, [25] I. Theodorakos, I. Zergioti, V. Vamvakas, D. Tsoukalas, and “Collective dynamics in optomechanical arrays,” Phys. Rev. Lett., Y. S. Raptis, “Picosecond and nanosecond laser annealing and vol. 107, p. 043603, 2011. simulation of amorphous silicon thin films for solar cell [7] M. Davanço, S. Ates, Y. Liu, and K. Srinivasan, “Si3N4 applications,” J. Appl. Phys., vol. 115, p. 43108, 2014. optomechanical crystals in the resolved-sideband regime,” [26] I. H. Campbell and P. M. Fauchet, “The effects of microcrystal Appl. Phys. Lett., vol. 104, p. 41101, 2014. size and shape on the one phonon Raman spectra of [8] K. C. Balram, M. I. Davanço, J. D. Song, and K. Srinivasan, crystalline semiconductors,” Solid State Commun., vol. 58, “Coherent coupling between radiofrequency, optical and p. 739, 1986. acoustic waves in piezo-optomechanical circuits,” Nat. [27] S. Veprek, F.-A. Sarott, and Z. Iqbal, “Effect of grain boundaries Photonics, vol. 10, p. 346, 2016. on the Raman spectra, optical absorption, and elastic light [9] J. Bochmann, A. Vainsencher, D. D. Awschalom, and scattering in nanometer-sized crystalline silicon,” Phys. Rev. B, A. N. Cleland, “Nanomechanical coupling between microwave vol. 36, p. 3344, 1987. and optical photons,” Nat. Phys., vol. 9, p. 712, 2013. [28] H. Richter, Z. P. Wang, and L. Ley, “The one phonon Raman [10] C. Xiong, W. Pernice, X. Sun, C. Schuck, K. Y. Fong, and H. Tang, spectrum in microcrystalline silicon,” Solid State Commun., vol. “Aluminum nitride as a new material for chip-scale 39, p. 625, 1981. optomechanics and nonlinear optics,” New J. Phys., vol. 14, [29] P. A. Mante, J. F. Robillard, and A. Devos, “Complete thin film p. 095014, 2012. mechanical characterization using picosecond ultrasonics and [11] M. J. Burek, J. D. Cohen, S. M. Meenehan, et al., “Diamond nanostructured transducers: experimental demonstration on optomechanical crystals,” Optica, vol. 3, p. 1404, 2016. SiO2,” Appl. Phys. Lett., vol. 93, p. 71909, 2008. D. Navarro-Urrios et al.: Properties of nanocrystalline silicon probed by optomechanics 4829 [30] J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, et al., “A one- [38] T. J. Johnson, M. Borselli, and O. Painter, “Self-induced optical dimensional optomechanical crystal with a complete phononic modulation of the transmission through a high-Q silicon band gap,” Nat. Commun., vol. 5, 2014, Art no. 4452. microdisk resonator,” Opt. Express, vol. 14, p. 817, 2006. [31] S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, and [39] H. C. Card, “The photoconductivity of polycrystalline H. G. Craighead, “High quality factor resonance at room semiconductors,” J. Appl. Phys., vol. 52, p. 3671, 1981. temperature with nanostrings under high tensile stress,” J. Appl. [40] S. Uma, A. D. McConnell, M. Asheghi, K. Kurabayashi, and Phys., vol. 99, p. 124304, 2006. K. E. Goodson, “Temperature-dependent thermal conductivity of [32] Y. Sun, D. Fang, and A. K. Soh, “Thermoelastic damping in micro- undoped polycrystalline silicon layers,” Int. J. Thermophys., vol. beam resonators,” Int. J. Solids Struct., vol. 43, p. 3213, 2006. 22, p. 605, 2001. [33] C. M. Zener and S. Siegel, “Elasticity and anelasticity of metals,” [41] H. Dong, B. Wen, and R. Melnik, “Relative importance of grain J. Phys. Colloid Chem., vol. 53, p. 1468, 1949. boundaries and size effects in thermal conductivity of [34] V. T. Srikar and S. D. Senturia, “Thermoelastic damping in fine- nanocrystalline materials,” Sci. Rep., vol. 4, p. 7037, 2014. grained polysilicon flexural beam resonators,” [42] B. Jugdersuren, B. T. Kearney, D. R. Queen, et al., “Thermal J. Microelectromech. Syst., vol. 11, p. 499, 2002. conductivity of amorphous and nanocrystalline silicon films [35] S. S. Verbridge, D. F. Shapiro, H. G. Craighead, and J. M. Parpia, prepared by hot-wire chemical-vapor deposition,” Phys. Rev. B, “Macroscopic tuning of nanomechanics: substrate bending for vol. 96, p. 1, 2017. reversible control of frequency and quality factor of nanostring [43] M. Nomura, Y. Kage, J. Nakagawa, et al., “Impeded thermal resonators,” Nano Lett., vol. 7, p. 1728, 2007. transport in Si multiscale Hierarchical architectures with [36] S. Kumar and M. Aman Haque, “Stress-dependent thermal phononic crystal nanostructures,” Phys. Rev. B, vol. 91, relaxation effects in micro-mechanical resonators,” Acta Mech., p. 205422, 2015. vol. 212, p. 83, 2010. [37] D. Macdonald and A. Cuevas, “Validity of simplified Shockley– Read–Hall statistics for modeling carrier lifetimes in crystalline Supplementary Material: The online version of this article offers sup- silicon,” Phys. Rev. B, vol. 67, p. 75203, 2003. plementary material (https://doi.org/10.1515/nanoph-2020-0489).