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 Reaching silicon-based NEMS performances with 3D printed nanomechanical resonators - Nature Communications Results .State of the art of MEMS and NEMS . Following a detailed literature analysis, we looked at the relation between the quality factor (i.e., resonator coherence) and the mass of the device, the key factors which affect resonator sensitivities, and evaluated if our 3D printed devices can reach the standard silicon-based NEMS performances. Figure? 1 presents the values of quality factors measured at room temperature as a function of device masses of a large set of resonators analyzed from the literature. In order to conduct as much as possible a comprehensive study, we analyzed more than 40 devices spanning over 16 orders of magnitude of device masses, divided into four different categories (detail of the analysis method and data references are reported in the Supplementary Information). Three categories are somehow related to standard lithographic technology: bottom-up NEMS (graphene, nanotube, and nanowires devices)32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40, top-down NEMS4 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52, and MEMS resonators53 , 54 , 55 , 56 , 57. The fourth is represented by devices fabricated with the alternative techniques described previously12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21. For this analysis, we considered resonators of different geometries including membrane, clamped–clamped beams, and clamped free-beams (i.e., bridges and cantilever, respectively). As shown in Fig.? 1 , despite the different geometries, materials, and dimensions, a clear unique growing trend of the quality factor was found for the first three categories (proportional to resonator mass as m1/3 )2. While devices fabricated with alternative technologies show quality factors around two orders of magnitude lower concerning this trend. For this analysis, we do not consider highly stressed silicon nitrate devices and soft-clamped resonators based on dissipation dilution58 , 59. These approaches allow to obtain NEMS with a much higher quality factor of the reported trend (i.e., new record of Q ?=?8?×?10 8 ) but need very complex fabrication techniques and large resonator size.Fig. 1: Quality factors of mechanical resonators from literature as a function of the fabrication method and device mass. The quality factors of mechanical resonators at room temperature are extracted from the literature (references are reported in Supplementary Figs.? S1 , S2 , and S3 , and Supplementary Note? 1 ) and divided regarding the fabrication method. Two of our devices with the best performances in terms of high Q factor value and low device mass for each printed resonator structure (cantilever, bridge, and membrane) are reported as star points. The trend of Q∝ m1/3 is reported as a dashed line. Full size image Thanks to our 3D printing approach, which is based on the conversion of soft hybrid structure into a rigid constitutive material with high-quality factor and low loss factor, we can surpass the performances of common devices which are fabricated with alternative techniques (stacked on MEMS size) and reach the trend of standard semiconductor-based NEMS, both in Q values and device dimensions.Device fabrication . Our devices are fabricated by printing a precursor solution ink with TPP technique, followed by an additional heating step at elevate temperatures to transform the structure from hybrid to rigid crystalline material (scheme in Fig.? 2a , details in the “Methods” section)31. To prepare the precursor solution, metal chloride salts are first dissolved in an aqueous solution containing propylene glycol and acrylic acid. Upon addition of propylene oxide, the pH of the solution increased and initiates condensation between the metal ions to create metal oxide oligomers60. Due to the presence of the acrylic acid, a coordinative bond is formed between the metal ion and the acrylic acid, thus enabling a photopolymerization reaction by using suitable photoinitiators. After printing and washing the structures, the printed objects are heated to 1500?°C, first to remove the organic content, then to eliminate the pores, to achieve dense polycrystalline structures. Nd:YAG material is used for its high elastic modulus compared to the standard silicon-based NEMS61, and to demonstrate the use of a material with intrinsic properties such as gain medium. To demonstrate the feasibility of rapid prototyping NEMS with performances comparable to their silicon-based counterparts, we printed NEMS resonators with the three most common designs: clamped–clamped beams (bridges), single-clamped beams (cantilevers), and circular membranes (Fig.? 2b, c and d ). We printed resonators of different dimensions, with lengths ranging from 20 to 50??m, width from 2 to 5??m, and thickness between 250 and 2000?nm. The dimensional control depends mainly on the printing parameters and the shrinkage of the printed object during the thermal process after printing. The TPP process enables printing objects having features as small as 100?nm62. In our study, we start from a solution, obtain a hybrid object, followed by conversion of the hybrid structure (organic–inorganic) into an inorganic, dense crystalline structure. These processes lead to a significant shrinkage, and therefore it is theoretically possible to go down to features in the range of tens of nanometers. After the thermal post-printing process, the printed resonators are composed of only inorganic polycrystalline Nd:YAG (as reported by EDX spectrum before and after thermal step, as shown in Supplementary Fig.? S4 ) without any organic materials. As a result of solvent evaporation, burning of the organic material, and crystallization to the dense crystal structure, the material sintering is accompanied by a dimensions reduction. To compare the actual dimensions with the computer design file, we calculated the ratio between the measured dimensions of printed structures after the thermal treatment process and the theoretical ones (used for the design). The size measurements were made by SEM imaging, and the analysis was computed over more than 200 resonators. The Gaussian fit reports a mean value of 68.7% of device isotopically shrinkage with a standard deviation of 5.3% (Supplementary Fig.? S5 ). Although the size reduction can help to achieve very small features, it could result in deformation of the final device geometries, especially for the circular membrane which is the most complicated to fabricate due to stress-induced during the thermal process (image of a device broken by thermal stress in Supplementary Fig.? S6 ). However, as it was presented in other publications, the deformation can be suppressed by printing the structures on guiding lines or domes63 , 64. Furthermore, after the thermal post-printing, the surface becomes rough due to the crystallization of the structure (as seen in Supplementary Fig.? S6 ). To achieve a smoother surface, it is theoretically possible to gain smaller size grains by changing the heating conditions65 , 66, selectively etch the YAG crystals with hot phosphoric acid67, and transforming the structure into a single crystal by abnormal grain growth68 , 69. The final yield of the 3D printed NEMS devices is above 75%.Fig. 2: Scheme of the fabrication process and images of the printed NEMS devices.a Scheme of the fabrication process starting from the precursor solution preparation, followed by TPP printing to photopolymerize locally the solution, structure washing, and final heating step to remove organic content and achieve densification and crystallization. b CAD scheme and c SEM image of a chip composed of six cantilevers of two different widths. d Images of the bridge, cantilever, and membrane devices before and after the heating step at 1500?°C. All the scale bars correspond to 10??m. Full size image Mechanical and vibrational properties . The post-printing thermal process is the fundamental step to remove all the organic compounds and obtain resonators composed only of ceramic material with high-quality factor and frequency stability. Friction losses are responsible for the low performances of reported polymeric devices, like standard 3D printed resonators, limiting the quality factor below 100 (Figs.? 1 and 3a for devices before post-printing thermal process). In ceramic devices, the friction losses are reduced by three orders of magnitude29, thus being not the limiting element on the quality factor. It was observed that the Q of the printed resonators increases by two orders of magnitudes after the heat treatment (Fig.? 3a ). Further confirmation of the conversion into rigid materials comes from the analysis of the NEMS resonance frequencies after the thermal process. Fundamental resonance frequency f0 of a mechanical resonator dominated by bending rigidity11 , 30is: $${f}_{0}=A{(E/\rho )}^{1/2}t/{L}^{2}$$ (1)where E is Young’s modulus, ρ is the mass density, t and L are the thickness and length of the resonator as measured by SEM imaging (for circular membrane the length is substituted with the radius) and A is a modal coefficient with value 1.028 for bridges, 0.162 for cantilevers and 0.469 for membrane. Figure? 3b reports all the NEMS resonance frequencies as a function of t / L2 ratio which well agree with the theoretical predictions (dash lines) obtained from Eq. ( 1 ) using the literature values for Nd:YAG of E ?=?290?GPa and ρ ?=?4550?kg/m 3 61. Data confirm the absence of significant tensile stress and the resonators can be considered in a bending rigidity regime. The printed devices are completely converted into rigid structures with Young’s modulus higher than silicon and comparable to silicon nitride one, as confirmed by independent analysis of stiffness from thermomechanical resonator motion and atomic force microscopy (AFM) nanoindentation (see Supplementary Note? 2 ). Both measurements technique confirm that the Young’s modulus of the devices corresponds to that of Nd:YAG61 , 70. Figure? 3c reports an example of nanoindentation force curve fitted to a Hertz model71with E ?=?292?GPa. The inset shows the results obtained over 30 different points on the device. Results from the sapphire substrate and those obtained on a reference sample (fused silica) are reported as well, as a comparison.Fig. 3: Resonance and quality factor analysis of 3D printed NEMS resonators.a Amplitude spectra of cantilever device (pale lines) centered around the fundamental resonance mode before and after the thermal treatment. Q values are extracted from Lorentzian fitting (thick lines). b Fundamental mode resonance frequency of the printed devices after thermal treatment as a function of the ratio thickness over square length t / L2 (for membrane device L is substitute with the radius). Dashed lines reported the plot of Eq. ( 1 ) for cantilevers, bridges, and membranes using material properties of Nd:YAG (Young’s modulus and density). c Example of an AFM nanoindentation force curve as a function of the separation δ obtained on a membrane device. The line corresponds to the least-squares fit obtained by using the Hertz model with Young’s modulus E ?=?292?GPa, calculated by assuming a Poisson ratio equal to $$\nu =0.275$$for Nd:YAG. The inset reports the result obtained by averaging over 30 different points on the device along with the Young’s modulus obtained on the nearby sapphire substrate and on a reference fused silica sample. d Measured Q factor of 3D printed nanomechanical resonators as a function of device thickness. Dashed lines represent Q contribution from surface loss (green line, Eq. ( 2 )) and thermomechanical damping (blue line, Eq. ( 3 )), the thick red line shows the resulting Q factor Q?1 ?=? Qsurf?1 ?+? QTED?1 . Full size image The quality factor of the printed NEMS has been analyzed with three different equivalent methods, driving and measuring the resonator in its linear regime, measuring the thermomechanical motion of the resonators (i.e., Brownian motion), and evaluating the ring-down time of the device. In the first two methods, Q is extracted from the Lorentzian fitting of the square of the amplitude motion signal. In the ring-down approach, Q is computed from the energy dissipation of the damped resonator by fitting the exponential decay of the amplitude signal after stopping the actuation. Thermomechanical measurement is more reliable because independent of an external driving force, but since it is based on a very small resonator vibration induced by thermal force, it represents the noisier approach. Lorentzian fitting of driven resonator linewidth is very accurate while the device is in its linear regime and the Q is not very high, up to a point where the width of the vibration peak is comparable to experimental set-up frequency resolution. The ring-down method instead is particularly used for very high Q s and long retention times. All the three methods applied to our bridges, cantilever and membrane resonators gave very consistent measurements within the experimental and fitting errors (Fig.? 4 ). In a condition of high vacuum ( p ?~?10 ?7 ?mbar), 3D printed rigid nanomechanical resonators show quality factors from 1500 up to 15,000 (data reported in Fig.? 3d ), a range consistent with the quality factor of semiconductor unstressed NEMS (Fig.? 1 ). We observe a strong dependence of Q with the thickness of the resonators. Higher Q are observed for thinner devices (around 200–400?nm) with a decrease of t up to 1000?nm. For higher thickness Q shows a monotonic increase. Resonator damping is not limited by friction losses because of the conversion from soft to rigid materials, as described before, neither by radiation loss at the clamping which gives a contribution for all thickness, Qclamp ?>?10 5 (details in Supplementary Note? 3 ). The quality factor of our devices is dominated by two factors, surface friction ( Qsurf ) and thermoelastic damping ( QTED ). Surface loss caused by surface roughness, impurity, and adsorbates is a fundamental damping source in nanometric thick resonators because of the high surface to volume ratio. For wide resonators, Qsurf has a linear dependence with resonator thickness t as: $${Q}_{{{{{{{\mathrm{surf}}}}}}}}=\frac{E}{6{h}_{s}{E}^{{\prime} }}t$$ (2)where h sis the surface layer thickness and E ′ the complex Young’s modulus30 , 72. Thermoelastic damping is generated by the temperature gradient across the resonator thickness induced by the strain due to flexural vibration. QTED dependence over the resonator thickness is more complex and can be described by the Zener model as $${Q}_{{{{{{{\mathrm{surf}}}}}}}}={\left({\Delta }_{E}\frac{\omega {\tau }_{E}}{1+{(\omega {\tau }_{E})}^{2}}\right)}^{-1}$$ (3)with ω the resonator eigenfrequency, ΔE =Eα 2 T / C pthe relaxation strength and τ E =t 2/ π 2 χ the relaxation time ( α, C p, and χ are the material thermal expansion coefficient, heat capacity, and thermal diffusivity, respectively)73. The resulting quality factor Q ( t ) ?1 ?=? Qsurf?1 ?+? QTED?1 plotted as a function of the thickness (red line in Fig.? 3d ) well describes the experimental Q of our devices. Below 600?nm, damping is governed by a combination of the two factors, while for higher thicknesses the losses are only dependent on thermoelastic damping.Fig. 4: Quality factor analysis with different experimental approaches. Experimental quality factor of bridge (upper panel), cantilever (central panel), and membrane (lower panel) devices extracted with three different approaches: driven the resonator to resonance, thermomechanical motion, and ring-down. Full size image Frequency stability and mass sensitivity . Frequency stability of a resonator, predicted for NEMS by Roukes et al.74 , 75as 〈 δf / f0 〉?~?(1/2 Q )?10 ? DR /20 , is not only dependent on Q , but also on the dynamic range DR , the power level associated with the ratio between the maximum linear driven amplitude and the noise amplitude. Amplitude vibration of printed NEMS has been tested under different piezodisk voltage actuation to evaluate the linear range up to the onset of nonlinearity. Above the maximum linear driving amplitude, the resonators show typical shark-fin resonance lineshape due to geometrical nonlinearity (i.e., Duffing nonlinearity) with amplitude-dependent resonance frequency (Fig.? 5a ) and lineshape dependence over the sweeping frequency direction (Fig.? 5b ). The ratio between the thermomechanical noise signal and the maximum linear driven signal for the cantilever device yields to a large dynamic range DR ?~?76?dB (Fig.? 5c ) in line with other reported NEMS resonator76. Theoretical frequency stability of around 10 ?8 is expected from the above formula. The experimental frequency stability has been measured for all three device families with open-loop Allan deviation for integration time between 0.5?ms and 30?s (Fig.? 6a ). Minimum of Allan deviation is registered in the range 0.1–1?s with values of 0.7?×?10 ?9 , 1.2?×?10 ?8 , and 4?×?10 ?8 for cantilever (as predicted above for single-clamped structures), bridge and membrane device, respectively. With these frequency stability values, the theoretical mass sensitivity of the 3D printed rigid NEMS is in the attogram range with a minimum of 0.45?ag for cantilever devices with 200-nm thickness. To compare the frequency stability and mass sensitivity with other devices in literature, we integrate the performances of our best resonators in a literature review plot presented by Sansa et al. (with the addition of some more recent works, Fig.? 6b )45. Our devices have very good performances in line with the top-down NEMS family and general trend over device mass ( ∝ m?1/2 ), confirming that approach is a valid alternative to silicon-based technology, but while using a much simpler and flexible fabrication technique. Demonstration of mass sensing capability of the 3D printed resonator is shown in Fig.? 6c and d . A test mass (silica sphere with 0.5-?m diameter, details in the “Methods” section) has been deposited close to the cantilever tip causing a frequency shift of resonance peak of around 2?kHz. From the resonance frequency shift, a value of 116.6?fg of adsorbed mass can be computed, which is in line with the mass of a single silica bead of 124?fg (estimated from data provided by the distributor).Fig. 5: Dynamic range of 3D printed devices.a Amplitude spectra of cantilever device for different piezodisk driving voltages. Above 750?mV, resonance curves show Duffing lineshape due to geometrical nonlinearity. b Nonlinear resonance frequency dependence over frequency sweep direction (indicated by the arrows). c Dynamic range of 3D printed cantilever between the amplitude of thermal noise spectrum and maximum linear driven signal. Full size image Fig. 6: Frequency stability of 3D printed devices and mass sensing.a Open-loop Allan deviation for the three types of resonators. Minimum detectable mass for each device is computed as δm= ?2 mδf / f0 . b Frequency stability of mechanical resonators from literature as function of device mass and fabrication approach. The graph is an integration with our devices (stars) and more recent literature works of the analysis presented by Sansa et al.45. Dashed line represents the general trend 10 ?12.2m?1/2 reported in ref.45. References of literature work are reported in Supplementary Figs.? S10 , S11 , and Supplementary Note? 3 ). c SEM image in false colors of a 3D printed cantilever after silica bead adsorption. Silica bead is evidenced by red color and red arrow. Scale bar corresponds to 2??m. d Resonance frequency peaks of a cantilever device before and after mass addition. The frequency shift corresponds to a mass addition of around 117?fg. Full size image In addition to ultralow mass detection, the high Q and lower mass make our resonators a very good candidate for highly sensitive force sensors. Force sensitivity is ultimately limited by thermal fluctuation to a value of 3.7?fN/√Hz for a cantilever device computed as: $${dF}=\sqrt{4{k}_{{{{{{{\mathrm{eff}}}}}}}}\frac{{k}_{b}T}{2\pi {fQ}}}$$ (4)where keff represents the effective spring constant or stiffness extracted from the thermal noise spectrum of Figs.? 4 and 5c , which represents a high sensitivity for room temperature nanomechanical sensors (details on the computation of effective stiffness in Supplementary Note? 2 ). Higher sensitivity could be reached with strain-engineered phononic crystal devices, which on the counterpart are much more complicated to fabricate and have larger overall dimensions due to millimetric damping dilution structures58 , 59. . From：
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