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Multimodal real-time frequency tracking of cantilever arrays in liquid environment for biodetection: Comprehensive setup and performance analysis

We present a nanomechanical platform for real-time quantitative label-free detection of target biomolecules in a liquid environment with mass sensitivity down to few pg. Newly fabricated arrays of up to 18 cantilevers are integrated in a micromachined fluidi chamber, connected to software-controlled fluidi pumps for automated sample injections. We discuss two functionalization approaches to independently sen-sitize the interface of different cantilevers. A custom piezo-stack actuator and optical readout system enable the measurement of resonance frequencies up to 2 MHz. We implement a new measurement strategy based on a phase-locked loop (PLL), built via in-house developed software. The PLL allows us to track, within the same experiment, the evolution of resonance frequency over time of up to four modes for all the cantilevers in the array. With respect to the previous measurement technique, based on standard frequency sweep, the PLL enhances the estimated detection limit of the device by a factor of 7 (down to 2 pg in 5 min integration time) and the time resolution by more than threefold (below 15 s), being on par with commercial gold-standard techniques. The detection limit and noise of the new setup are investigated via Allan deviation and standard deviation analysis, considering different resonance modes and interface chemistries. As a proof-of-concept, we show the immobilization and label-free in situ detection of live bacterial cells ( E. coli ), demonstrating qualitative and quantitative agreement in the mechanical response of three different resonance modes. N5 (a) , N6 (b) and N7 (c) , the standard deviation shows an increase of up to a factor 4 with respect to the level in buffer. In order to avoid fluidic effects, the measurements in bacteria environment are collected 20 minutes after cells injection in the microfluidic chamber. We attribute this phenomenon to the laser scattering resulting from the presence of bacterial cells moving and floating in the measurement chamber, and in the fluidic space between laser and resonators.


I. INTRODUCTION
In the past 20 years, microcantilever biosensors operated in liquid demonstrated outstanding sensing capabilities. [1][2][3][4] Several labelfree nanomechanical assays have been developed, targeting the real-time detection of specifi biomarkers in physiological environment. 5,6 The detection of molecules of clinical interest such as proteins, 7 RNA, [8][9][10] and cells [11][12][13][14][15] achieved comparable or better performances to commercial gold-standard techniques. The most widely used method in clinical environment is the enzyme-linked immunosorbent assay (ELISA), which exhibits sub-picomolar limitof-detection, but requires long analysis times, expensive reagents, and does not provide quantitative information. 16 We recently demonstrated a direct one-step label-free quantitative immunoassay investigating malaria vaccines, with cantilever arrays with a sensitivity that is on par with the gold-standard multi-step ELISA procedure in serum. 7 Other micro/nanomechanical technologies able to achieve the detection of biomolecules in liquid environment include quartz-crystal microbalance (QCM), 17 surface-plasmon resonance (SPR), 18 suspended microchannel resonators (SMR), 19 surface acoustic wave (SAW) devices, 20 and membrane-type surface stress (MSS) sensors, 21 among others. An exhaustive overview and comparison of the above-mentioned technologies, as well as other biosensing techniques, is provided in the excellent review by Arlett et al. 22 Operating the sensors in liquid is paramount in order to mimic physiological conditions and target clinical applications. However, in-flui operation adds a considerable level of complexity to the experimental procedure, requiring thorough engineering of the experimental protocol and measurement setup. 23 The transduction strategy needs to be selected and implemented while taking into account the mechanical damping caused by the liquid around the resonators, so as to maximize the signal-to-noise ratio, thus boosting sensing performance.
Analytes binding to the sensitized surface of a cantilever sensor can be detected evaluating either the stress-induced quasistatic deflectio (static mode operation) or via the mass-induced resonance frequency shift (dynamic mode operation). Cantilever mechanical behavior is strongly affected by the surrounding medium and environmental changes (e.g., temperature, viscosity, and pH), [24][25][26] which constitute competitive effects toward the biomolecular recognition. The best strategy to circumvent these effects is to use multiple microcantilevers on the same chip. Microfabricated cantilever arrays present a number of advantages: (i) internal control toward unspecifi binding can be achieved by passivating the interfaces of selected sensors; (ii) possibility to perform a differential readout among multiple sensors. This allows us to correct for thermal drifts or environmental changes, but it also makes possible to compare the binding of the same analyte to different surfaces or antigens; 7 (iii) the mechanical response from sensors sensitized with the same biochemical functionalization can be averaged, thus increasing statistical robustness of experimental results; (iv) possibility to study multiple biochemical interactions within the same experiment; (v) reduction in time and cost of a single test.
In this paper, we provide the comprehensive description of a nanomechanical platform for real-time quantitative label-free detection of target biomolecules in liquid environment with mass sensitivity down to few pg. We include a short description of the device microfabrication process and functionalization strategies. With respect to our previous publications, we introduce a larger cantilever array with up to 18 sensors that allow more versatility in functionalization and averaging of identically sensitized sensors. Moreover, we describe a newly implemented measurement strategy for dynamic mode analysis, via a phase-locked loop (PLL). This approach allows us to track the evolution of the resonance frequency over time of up to 4 resonance modes, for as many sensors as needed (18 in this work). The introduction of the PLL tracking enhances the estimated detection limit of the device by a factor of 7. A custombuilt piezoceramic stack actuator, together with an optimized optical readout system, provides access to a measurement frequency range between 1 kHz and 2 MHz. Furthermore, we perform an analysis of the frequency noise and an estimation of sensing capabilities of our measurement setup, considering different resonance modes and interface chemistries. As a proof-of-concept, we show the immobilization and label-free real-time in situ detection of live bacterial cells (E. coli) in 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (HEPES) buffer, demonstrating qualitative and quantitative agreement in the mechanical response of three different resonance modes.

A. Design and fabrication
The devices used in this study are silicon cantilever arrays containing 15 to 18 sensors. The microfabrication process (Tyndall National Institute, Cork, Ireland) is based on three photolithography steps, schematically represented in Fig. 1. The fabrication starts from a silicon-on-insulator (SOI) wafer substrate, 100 mm in diameter, with a 7 μm Si layer on 2 μm SiO 2 (WaferPro LLC). A 5 μm plasmaenhanced chemical vapor deposition (PECVD) SiO 2 hard mask is deposited on the wafer backside and patterned via photolithography and dry etching [Figs. 1(a) and 1(b)] to defin the backside opening geometry. Subsequently, a 30 nm-thick stress-release SiO 2 layer is thermally grown on the wafer front, followed by 100 nm low pressure chemical vapor deposition (LPCVD) Si 3 N 4 [ Fig. 1(c)]. A second photolithography, followed by Si 3 N 4 dry etching and SiO 2 wet etching in KOH, define the hinge region of the resonators [ Fig. 1(d)]. Careful adjustment of wet etching conditions allows us to etch down 5 μm of the 7 μm silicon device layer, to achieve 2 μm-thick cantilevers. After Si 3 N 4 and SiO 2 removal in wet solutions (hot H 3 PO 4 and 10:1 HF, respectively), shown in Fig. 1(e), the resonator geometry is patterned via a third photolithography followed by silicon dry etching [ Fig. 1(f)]. 100 nm aluminum is deposited via evaporation on the wafer front as a protective layer during the wafer-through dry silicon backside etching [ Fig. 1(g)]. In this step, PECVD SiO 2 acts as a and profil (f) are define via two photolithographic steps. A protective layer is deposited on the wafer front in order to proceed with the backside wafer-through etching (g) and fina release in wet etching solutions (h). The wafer is shown in the cross section, with dimensions not to scale. hard mask, while the buried SiO 2 is an etching stop layer. Resonators are finall released via Al and SiO 2 wet etching in BHF.
The fina devices consist of 15 cantilevers arrays (500 μm long, 95 μm wide, and 2.3 μm thick) and 18 cantilevers array (400 μm long, 70 μm wide, and 2.3 μm thick). Each wafer contains 308 chips, which can be easily detached with manual tweezers, thanks to cleavage lines define in the firs lithographic step. The hinge, patterned via the second photolithography, allows for precise definitio of the resonator length, which could otherwise vary among adjacent sensors, due to the isotropic release at the end of the fabrication process. In addition, the backside of every chip is patterned into a comb-like structure, which extrudes out of the chip body and serves to prevent cross contamination during capillary functionalization, as will be explained in Sec. II B. Figure 2 shows SEM images of a completed 18-microcantilever array chip, where the comb structure and a zoomed-in image on the hinge region are clearly visible.
The devices described in this paper are operated in dynamic mode, have a spring constant down to 0.4 N/m, and a mass down to 160 ng. However, thinner sensors have also been fabricated (1 μm thick) by increasing the KOH wet etching time in Fig. 1(e). Thinner cantilevers result in a lower spring constant (down to 0.03 N/m), more suitable for static mode operation where quasi-static deflectio is targeted.

B. Functionalization
One of the many advantages of using an array with multiple microresonators is the possibility to functionalize the surface of each cantilever with different specifi molecules. [1][2][3] This allows us to shows a side view of the hinge region, which define the mechanical clamping point and, thus, the length (and resonance frequency) of the resonators. The comblike structure close to the chip body is visible underneath the sensors. It extends between the chip body and the hinge, so as to prevent cross contamination while ensuring hinge covering during functionalization via capillaries. tackle multiple biorecognition events within the same experiment, maximizing the binding efficienc of target molecules, as well as enabling the passivation of some resonators to act as controls toward non-specifi binding. A differential readout between cantilevers in the array allows us to directly compare the binding efficienc of the same analyte to different molecules or receptors.
In order to prepare the sensors for functionalization, shortly before experiment, the chip is coated via metal evaporation (Temescal FC-2000, Scotech) with 3 nm of titanium, and 23/33 nm gold on the top and the bottom face, respectively. The different gold thickness between the cantilever top and the bottom side facilitates static mode operation. 25 Furthermore, the gold fil has the double function of (i) self-assembling and anchoring the functionalization molecules via a thiol group on the interface of the cantilevers and (ii) maximize surface reflectivit for optical detection.
We focus on two functionalization strategies, namely, glass microcapillaries and inkjet spotting, which are adapted to the newly implemented 15 and 18 sensor arrays.

Microcapillaries
Sterile and disposable glass microcapillaries (King Precision Glass, Inc.) are aligned with the cantilever array with the help of a custom-made platform that ensures fir clamping and micrometer precision movement in three directions (see Fig. S1). Resonators are then gently inserted into the microcapillaries, as shown in Fig. 3. For both designs of 15 and 18 sensors, the chip width is 3 mm, while the sensor pitch is 205 and 170 μm, respectively. Two different config urations are, therefore, adopted: 18 sensor chips are aligned with 9 capillaries with a 335 μm outer diameter (295 μm I.D.), so as to contain 2 sensors each, as shown in Fig. 3(a). 15 sensor arrays are aligned with a set of 5 capillaries with an outer diameter of 610 μm (570 μm I.D.) so that each capillary contains three cantilevers, as shown in Fig. 3(b).
In order to ensure full sensor functionalization, the hinge regions need to be fully covered by the microcapillaries. The comb structure at the backside of the wafer prevents the microcapillaries to reach the chip body, which would offer a cross contamination path between adjacent capillaries. 27 The back-end of microcapillaries is inserted in larger glass tubes (708744 Brand TM Blaubrand TM IntraMARK TM , Fig. S1), which facilitate the solution injection by means of an automatic pipette and serve as reservoirs during incubation time, which typically ranges from a few minutes to 1 h.

ARTICLE scitation.org/journal/rsi
The glass microcapillary technique minimizes cross contamination among adjacent sensors and allows us to fully immerse the resonators in solutions, so as to simultaneously and uniformly coat top and bottom surfaces. Solutions need to be injected one by one (about 10-30 μl per capillary), but this can be achieved rather quickly, minimizing the fillin delay between the firs and the last capillary to less than 2 min. Moreover, incubation time is easy to control. However, maximum attention needs to be paid during the microcapillary placement and clamping, in order to facilitate chip alignment and avoid sensor rupture. In addition, the solution must be injected in each reservoir via one continuous pumping step to promote the capillary flo toward the sensors and to avoid the formation of air bubbles.

Inkjet spotter
Inkjet spotting offers an alternative method for chip functionalization and is usually recommended for large devices or even for wafer-level functionalization. 27 We use a MD-P-705-L inkjet dispensing system (microdrop Technologies GmbH) equipped with a three-axis micropositioning system that reaches an absolute ±5 μm accuracy. A piezo-driven glass autopipet (AD-K-501) with a 30-70 μm nozzle diameter allows us to dispense single droplets, corresponding to volumes between few tens to few hundreds of pl. A stroboscopic camera system allows visual monitoring of droplet ejection to control dimensions and prevent satellite droplets, via adjustment of piezo-voltages and pulse durations. The vertical separation between the nozzle and the substrate is typically 0. A software interface allows us to control pitch and number of ejected droplets on each sensor with ±1 μm repetition precision: selecting adequate parameters, droplets merge into a continuous layer covering one side of the entire cantilever length [ Fig. 4(d)]. 18 sensors can be one-side coated in about 20 s with a single autopipet flui loading (max. 25 μl). Automated dispensing patterns can also be programmed (see Movie 1 in the supplementary material), by assigning offsets or definin matrix geometries, which is particularly useful to functionalize different sensors with different solutions. In the latter case, the autopipet must be thoroughly emptied and washed before loading a different solution, to avoid contamination. Moreover, in order to avoid cross contamination via evaporation, solutions need to be spotted in the order of decreasing volatility. 27 With respect to microcapillaries, inkjet spotting is faster, allows us to minimize the liquid volumes, does not require manual alignment, and allows us to quickly create dispensing patterns on the target surface. The latter can be a key feature for specifi experiments, as both static and dynamic mode sensing are affected by surface stress, 28,29 receptor layer, and analyte binding locations. 15,30,31 In addition, it is scalable to large arrays and can coat arbitrary structures in non-contact mode. The major limitation is the ability to coat only one side of the chip at the time. However, our custom-built chip holder allows for a quick manual fli upside down and repositioning. In addition, it is possible to wet both top and bottom surfaces of the cantilever by spotting the droplet closer to the lateral edge of the resonator (see Movie 2 of the supplementary material). Humidity inside the dispensing area and chip temperature are critical parameters on which both incubation/functionalization time and steady solution concentration depend. We read humidity levels with a commercial sensor (Inkbird IHC-200) placed in close proximity to the chip and adjust humidity (usually 70% relative humidity) via a custom-made water nebulizer vapor injection system connected to compressed air. The chip temperature is regulated through a feedback control system integrated within the spotter equipment, in order to keep sensor surfaces at the dew point temperature.

III. TRANSDUCTION
Cantilever arrays are mounted into a microfluidi measurement chamber, micromachined in polyether ether ketone (PEEK) and previously described in Ref. 23. Briefly the chamber serves to mechanically clamp the chip and to immerse it in a 6 μl microfluidi volume, for in-liquid measurements. Microfluidi inlets and outlets connect the chamber to a fluidi line, software-controlled via a system of solenoid valves (ASCO Valve, Inc.) and automated syringes (Kent Scientifi Corporation, Lee Company), which enables nl to ml injection volumes and exchange of multiple samples during experiments. 23 In order to ensure temperature stability and insulation, the whole setup (including fluidi pumps and tubings) is enclosed in a thermally insulated box. The platform box is designed as a modular aluminum frame with foil-faced, polyisocyanurate (PIR) rigid insulation boards (Ballytherm Ltd.). The internal temperature is regulated via meandering water line floo heating and a fine-tune Published under an exclusive license by AIP Publishing

ARTICLE scitation.org/journal/rsi
proportional-integral-derivative (PID) feedback thermal circulator control system (Peter Huber Kältemaschinenbau AG), resulting in stable internal temperature with 0.02 ○ C precision. 32 Dynamic mode operation is achieved via a custom-built piezoceramic stack actuator, placed in a pocket underneath the chip and isolated from the fluidi volume by using a 200 μm-thick PEEK membrane. 23 Mechanical signals are detected via an optical beam deflectio (OBD) readout, 33 able to detect cantilever oscillation with sub-nanometer resolution.

A. Piezo-stack actuator
Due to geometry and frequency range requirements, the piezostack actuator is assembled in-house from commercial piezoelectric sheets (Noliac, CTS).
Given the flui around the resonators and the presence of a PEEK membrane between the actuator and the chip, large displacement and good mechanical coupling are key requirements for efficien actuation. The selected actuator material is NCE51, a softdoped piezoelectric ceramic, characterized by high electromechanical coupling factors that result in large induced deflections 34 NCE51 piezoelectric sheets with screen printed Ag electrodes on opposite sides are diced into 2 × 2 mm 2 and 3 × 2 mm 2 chips and bonded faceto-face via conductive epoxy glue (EPO-TEK ® E4110; Epoxy Technology, Inc.). Copper bus wires (0.1 mm diameter, 0822942, BLOCK Transformatoren-Elektronik GmbH) are glued to the diced chips with viscous conductive epoxy resin (EPO-TEK EJ2189) and are used to electrically connect same-polarity faces of adjacent stacked chips ( with a fin brush around the short wires and the full body of the actuator, in order to confer robustness to the whole structure while not constraining its vibration. 35 The stack actuator is mounted into the pocket underneath the chip and glued to the PEEK membrane with a thin layer of two-component hard epoxy glue (Torr Seal ® , Kurt J. Lesker Company). At the backside of the piezo-stack actuator, a 15 × 10 × 2 mm 3 glass ceramic plate (MACOR, Radionics Ltd.) serves as a mechanical reflecto and is used to apply a gentle pressure toward the actuator, thus maximizing the mechanical coupling between the piezo-actuator and the cantilever chip. The measurement chamber is then closed with a Peltier element and a metallic plate tightly screwed to the PEEK body.
By combining multiple piezoceramic chips, the resulting stack is able to achieve a larger displacement than the one of a single chip, while maintaining a low drive voltage range and submillisecond response times. 36 Three-and five-stac actuators have been fabricated, also varying the single layer thicknesses, as shown in Fig. 5. However, when comparing different configurations threestack devices show larger induced displacements on the PEEK membrane with respect to five-laye stacks (see Fig. S2). We believe that this is due to fabrication variability, as a result of the manual process of gluing and aligning wires and piezoelectric chips. However, all fabricated actuators show successful and comparable performances: once integrated in measurement chambers, cantilever resonance modes were detected up to 2 MHz, given actuation voltages between 1 and 5 V (see Fig. S3).

B. Optical detection system
The mechanical oscillation of microcantilever sensors is detected via an OBD readout. 33 A laser diode beam (830 nm, 10 mW; Thorlabs Ltd.) is focused close to the tip of cantilevers and reflecte back to a two-cell photosensitive detector (PSD, S5870, Hamamatsu Photonics K.K.). The laser is mounted on an optical cage, previously described in Refs. 23 and 32, which contains optical elements to collimate and focus the beam with a radius of about 7 μm on the reflectiv cantilever gold surface.
Key requirement to use cantilevers as sensors is the precise positioning of the laser toward the tip of the cantilevers and on the flexura node for optimal oscillation amplitude detection. To do so, the optical cage hosting the laser is moved by a system of four microtranslation stages, two manual and two electric [M-122.2DD and M-110.1DG Physik Instrumente (PI) GmbH & Co. KG]. This micropositioning system allows us to focus the laser spot across the array with two-axis micrometer precision to sequentially scan all sensors (horizontal x range: 5 mm range with 50 nm precision; vertical y range: 25 mm with 100 nm precision). At first the laser spot is coarsely placed close to the firs cantilever of the array to perform an automated full array scan (a detail in Fig. 6). Subsequently, a fine scan allows us to identify and store the optimal nodal point coordinates per resonator, through the dedicated home-built LabView module (National Instruments): each device is actuated while the laser position is adjusted with micrometer precision close to the resonator free end, so as to fin the coordinates that maximize the vibrational amplitude. Scanning the chip area not only allows the optimal and consistent positioning of the laser on the sensors but also provides a quality control of the array itself.
The microcantilever oscillation causes a shift in the position of the reflecte beam on the 10 × 10 mm 2 two-cell PSD (S5870, Hamamatsu Photonics K.K.). PSD current signals from the two optical sensor cells are converted into voltage and combined into sum and differential signals through a custom-made electronic amplificatio circuit 35 (see Fig. S4). The sum signal corresponds to the intensity of the incident laser on the full PSD surface, while the differential voltage relates to the position of the reflecte laser spot and, thus, is modulated by cantilever oscillation. The two PSD output signals are firs amplifie and filtere through a low-noise preamplifie (SR560, Stanford Research Systems) and later acquired at 60 MSa/s by using an oscilloscope card (PCI-5105, 60 MHz bandwidth, 12-bit resolution; National Instruments).
The PSD is biased with a home-built power supply (±15, +5 V) that features built-in overload protection and minimizes the noise floo power spectrum. 37 The selected PSD has a rise time of 100 ns, which results in a maximum detectable frequency of 10 MHz. However, the actual optical readout bandwidth is limited by the custom-made I-V converter electronic circuit. Operational amplifier (LT1361, Analog Devices, Inc.) and the RC filte stage (5.6 kΩ and 2.2 pF) have been selected so as to guarantee linear and fast optical detection up to few MHz, thus enabling the tracking of higher resonance modes. 29 Indeed, the readout system, considering the PSD and electronic I-V converter circuit, has a fina cutoff frequency of 4.8 MHz and a gain of 1, calculated according to Ref. 38.
Considering the full transduction scheme, the upper limit of the current measurement bandwidth is set by the actuation stage, as the operational frequency of the piezo-stack actuator reaches a maximum of 2 MHz (Figs. S2 and S3).

IV. PHASE-LOCKED LOOP IMPLEMENTATION
The established method for mechanical response detection of cantilever arrays in liquid, with up to eight sensors, consists of carrying out a frequency sweep analysis around the resonance modes of each device. 5,23 A continuous sweep scan across the array allows us to track the real-time evolution of the amplitude and phase responses of the oscillating structures, experimentally determined as explained in Ref. 6, while samples and analytes are injected in the measurement chamber and bind to the sensitized resonators. This method has demonstrated a mass resolution down to 10 pg and a time resolution (time interval between two consecutive measurements on the same cantilever) of about 20 s, when tracking three resonance modes of eight sensors. 7 In this manuscript, we implement a new method that allows us to extend the measurement capability to as many sensors as needed (18 in the newly developed arrays), without losing temporal resolution and while improving the sensing performance by more than sevenfold. A proportional-integral-derivative (PID) controlled phase-locked loop (PLL) is built via an in-house developed LabVIEW (National Instruments) code, directly interfaced with the experimental hardware and able to track up to 4 modes of 18 sensors in parallel over several hours.
Before experiment, the cantilevers are mounted in the microflu idic chamber and immersed in a buffer solution to stabilize for up to 2 h. After this equilibration step, a frequency sweep is performed for each cantilever and resonant mode to determine the optimal phase shift (between the driving signal and the response signal) that maximizes the resonant motion amplitude. To do so, a harmonic signal is produced by a waveform generator card (PCI-5406, 40 MHz bandwidth, 16-bit resolution; National Instruments) and sent to both the piezo-stack actuator and a high-speed data acquisition card (PCI-5105, 60 MHz bandwidth, 12-bit resolution; National Instruments). A custom-written LabVIEW program (NI-TClk Synchronization VIs) enables picosecond synchronization between the drive and acquisition cards, connected via a RTSI bus cable.
Subsequently, the PID parameters are evaluated through the Ziegler-Nichols auto-tuning method: 39 each cantilever is excited to an arbitrary frequency (typically ±1 kHz of the selected resonant frequency), while the phase responses are recorded and used by the auto-tuning algorithm to determine the fine-tune PID parameters for each sensor. Note that selecting an excitation frequency shift close to the one expected for the specifi experiment yields the best PID parameters.
Finally, the piezo-stack actuator sequentially drives each cantilever around its nominal resonance frequency for a few ms, while the phase responses are separately acquired. The optimized PID parameters are used to compute the adjustment to the driving frequency that maintains the phase of each device constant (locked) at resonance. The PID computation of the frequency is performed simultaneously for all sensors, thus allowing for up-scaling to as many cantilevers and as many resonant modes as needed. In a typical experiment, four resonant modes and 18 cantilevers are measured, resulting in 72 parallel PID controllers. If the system is ideally unperturbed, the frequency that locks the phase (resonant frequency) would remain constant, but upon perturbation (e.g., mass adsorption and temperature or flui density changes), the frequency will shift accordingly. The time between the collection of two consecutive frequency measurements when the laser is kept on one sensor is 80 ms (1 ms acquisition, 10 MSa/s). However, when scanning the full array of 18 sensors, the time delay between two consecutive measurements on the same cantilever is in the order of few seconds

V. DETECTION LIMIT AND NOISE
The binding of target molecules on the sensitized surface of cantilevers induces a frequency shift that can be converted into mass uptake Δm via the following equation 24,26 (see the supplementary material for more details): where fr,n is the resonance frequency of the n-th mode of vibration, m f = ρ f πb 2 L/4 is the flui mass load on the cantilever, calculated as the mass of a flui cylinder with the radius equal to half the cantilever width b, Γ f r (Re, κn) is the real component of the hydrodynamic function and depends on flui properties through the Reynolds number Re and on the normalized mode number κn, βn = α 2 n /(2π √ 3), αn being the n-th positive root of 1 + cos αn cosh αn = 0, from the Euler Bernoulli beam theory, and k and mc are the cantilever stiffness and mass, respectively.
Equation (1) needs an accurate knowledge of flui density and viscosity over the full experiment duration, in order to precisely compute the hydrodynamic function values. We previously introduced an accurate approximation of the hydrodynamic function over large Reynolds numbers. 24 However, in a differential analysis, the average frequency shift of a set of sensors (typically functionalized with the same molecules) is evaluated with respect to another set on the same array (either control sensors or devices with a different functionalization). By doing so, accurate knowledge of fluidi properties over the whole experiment is no longer required, and the differential mass uptake between the two sets of sensors can be derived from Eq. (1) and written as follows (see the supplementary material): where f 1,n and f 2,n are the resonance frequencies of cantilevers (or average resonance frequency of cantilever sets) 1 and 2. This not only allows us to be independent of environmental variations (e.g., temperature and flui viscosity) but also allows us to directly compare the binding efficienc of the same analyte toward different chemistries in the same time frame and under identical experimental conditions. The mass resolution δmn relative to the n-th mode of resonance, under the assumption of small added mass, can be written as follows (see the supplementary material): where δfn is the frequency noise. The normalized frequency noise δfn/fr,n can be evaluated computing the Allan deviation of the frequency σA(τ), define as the statistical variance of N measured normalized frequency values y(t) over an average time τ, as as follows: 40 (4) Figure 7 shows the typical Allan deviation plot of the fift flexu ral mode of a microcantilever sensor in PBS, stabilized at 26 ○ C, and allows us to identify the noise contributions in our measurement system. Higher modes of vibration, between 300 kHz and 1.5 MHz, are normally considered due to larger responsivity to mass uptake 29 and compatibility to our measurement setup. Frequency points are collected while keeping the laser spot on one single sensor, acquiring at 10 MSa/s sample rate for intervals of 1 ms, with a time resolution of 80 ms. σA(τ) allows us to directly estimate the mass sensitivity of the system, via Eq. (3), and to recognize the most typical noise contributions. The left part of the plot, below 10 s of integration time, can be calculated as follows, assuming white noise behavior 41 (thin blue line in Fig. 7): where Qn is the quality factor of the considered resonance mode, N is the noise level measured as the square root of the power spectral density around resonance (LabVIEW, FFT Power Spectrum, and PSD VI) in V/ √ Hz, S is the amplitude of the output signal detected via a PSD in V, and BW is the measurement bandwidth, define as 1/τ. The measured data lie in the same range of the theoretical estimated limit; however, they exhibit different scaling laws with respect The left asymptote of the AD plot is in good agreement with the theoretical limit, calculated from power spectral density measurement, as shown in Eq. (5). It scales as τ −0.3 , indicating that low integration times are not dominated by white noise (which typically scales as τ −0.5 ). The system noise is dominated by a thermal drift after an integration time of about 10 s. The main source of frequency noise in our biological experiments (i.e., binding molecules to receptors placed on a sensor surface) is, therefore, the thermal drift, considering that biological processes occur in a time range in the order of tens of seconds to minutes.  Fig. 7), indicating that low integration times are not dominated by white noise (e.g., thermomechanical noise), which typically scales as τ −0.5 . Flat 1/f noise contribution (∼τ 0 ) is visible around 10 s, while larger integration times are dominated by the system thermal drift (∼τ α , with 0.5 < α < 1), as shown in black dashes in Fig. 7.
Measuring at 10 s integration time ensures the lowest noise level and, thus, the best mass resolution, down to 0.3 pg according to Eq. (3). However, the relevant time range for biological molecular detection normally corresponds to several minutes, due to analyte diffusion kinetics and transient binding to the resonators, which depend both on the sample concentration and target molecule size. The thermal drift, thus, represents the main source of noise in our experimental conditions.
In order to compare the sensing performance of the PLL method to the previous frequency sweep strategy (sweep method), a 15-cantilever array is loaded in the measurement chamber fille with PBS. After a stabilization of 2 h at 26 ○ C, frequency data are acquired for 30 min via the sweep method and immediately after for 30 min via the PLL. The 10 min standard deviation of resonance frequency for ten cantilevers is measured three times over the data collection. The average frequency standard deviation of the array over a time window of 10 min is 39 ± 5 and 6 ± 1.5 Hz for sweep and PLL, respectively, considering mode 5. 30 ± 4 and 4 ± 2 Hz for sweep and PLL, respectively, were obtained for mode 6 (see Fig. S5 and Table S1). The PLL improves the frequency noise by up to a factor of 7 with respect to the sweep method. We, thus, estimate the same improvement in terms of mass resolution, thus pushing down to about 2 pg the detection limit of 10 pg, previously reported for sweep analysis. 7 In addition, the PLL method is faster than the sweep, allowing to improve the time resolution by more than a factor of 3: consecutive frequency measurements were collected every 20 s via sweep and every 6 s with PLL, when considering the same number of sensors and resonance modes (Table S1).
We also investigate the effect of different surface chemistry on the resonators, via the capillary functionalization with hydrophilic (aliphatic thiol molecules terminated with COOH, PEG, or NH 2 groups) and hydrophobic (aliphatic thiol molecules terminated with the CH 3 group) self-assembled monolayers (Fig. S6). No substantial effect on the frequency noise was observed, independent of the chemical functionalization. The Allan deviation ranges in the same order of magnitude with less than a factor of 3 difference (Fig. S6). This is a positive finding as microcantilevers are regularly functionalized with different chemicals in order to immobilize proteins with high binding efficiency In addition, the resonance modes considered (fift to eighth, corresponding to frequencies between 450 and 1200 kHz) show Allan deviation differences by less than a factor of 4. Mode 6 exhibits the best performance, achieving frequency stability down to 10 5 considering an integration time of 5 min, which is equivalent to an estimated mass resolution of 3 pg, when considering Eq. (2) [Figs. S6(a) and S6(c)].

A. Bacteria detection
To demonstrate multimodal quantitative biological measurements with the new developed devices and system, we detect living bacteria binding on the surface of functionalized gold-coated cantilevers.
An array of 18 sensors (400 × 2.3 × 70 μm 3 ) is functionalized via the glass microcapillary method. Cantilevers are split into four groups, evenly distributed across the array and incubated for 10 min in 2 mM ethanol-based solutions of self-assembling thiol molecules terminated with CH 3 , NH 2 , PEG, and COOH groups (see the supplementary material for detailed description). The chip is subsequently rinsed in pure ethanol for 10 min, nanopure water for 5 min, and stored overnight in HEPES buffer (pH = 7; Sigma-Aldrich) at 26 ○ C. The following day, the measurement box enclosing the full setup and fluidi samples is thermally stabilized at 26 ○ C. Finally, the chip is mounted in the HEPES-fille measurement chamber and left for stabilization for 2 additional hours.
E. coli bacterial cells (XL10-Gold ® Ultracompetent Cells, Agilent) are revived from frozen stock via overnight incubation at 37 ○ C and 180 rpm in a Luria-Bertani (LB) broth (Sigma-Aldrich). During machine priming and thermalization, 1 ml of overnight bacteria solution is inoculated in 10 ml fresh LB. The bacterial growth protocol is timed to have fresh cells in the exponential growth phase to be injected into the microfluidi chamber. While the PLL tracks resonance frequencies in HEPES buffer, the cells are resuspended in HEPES buffer at 26 ○ C and diluted to 10 6 cells/μl. The bacteria solution is loaded in the automated syringe pump and pushed up to the valve-controlled fluidi inlet of the measurement chamber. By doing so, the bacteria solution has about 40 min to equilibrate at 26 ○ C before direct injection onto the resonators (100 μl @ 50 μl/min).
PLL tracking is set up for 15 cantilevers (three sensors broke during manual handling of the chip) and four modes of resonance. Frequency values are acquired at 10 MSa/s for 1 ms every PLL cycle, with a resulting time resolution of 11 s. Frequency data are collected for 1 h in HEPES buffer and for 40 min after injection of bacterial cells into the microfluidi chamber. Figures 8(a)-8(c) show the time evolution of the average resonance frequencies of cantilevers with analogous functionalization, for three modes of resonance, as bacteria are injected into the chamber, at t = 0. As can be seen, resonance frequencies start decreasing immediately after bacteria injection and reach a plateau after about 10 min. Sensors functionalized with COOH and NH 2 exhibit the largest frequency shift, thus mass uptake, while PEG-functionalized cantilevers undergo the lowest frequency variation. This can be explained with the presence of charges on COOH and NH 2 functional groups, which interact with the charged bacteria membranes, resulting in a weak but effective ionic immobilization.
Conversely, PEG does not exhibit free charges and is normally used as a passivation layer, to act as control toward non-specifi binding. 42 Differential mass uptakes are calculated according to Eq. (2) with respect to PEG sensors, which are used as reference devices, as shown in Figs. 8(d)-8(f). The three modes confir the same qualitative and quantitative behavior: in all cases, a differential mass uptake between 1.5 and 1.9 ng is observed for NH 2 sensors, between 1 and 1.3 ng for COOH sensors, 30 min after bacteria injection. Differential analysis allows removing the effect of non-specifi binding, visible in the PEG-functionalized control cantilevers, as well as any global drift in the system (e.g., temperature variations). Interestingly, we observe that in bacteria solution, the frequency noise increases up to a factor of 4 with respect to levels in buffer, when considering the average of the frequency standard deviation over a time window of 10 min (Fig. S7). We attribute this phenomenon to the increase in optical noise due to laser scattering caused by bacterial cells moving and floatin in the measurement chamber. Under such conditions, the equivalent mass noise increases from few pg up to 60 pg. Given that the bacterial mass uptake is in the order of few nanograms, as seen in Figs. 8(d)-8(f), this noise increase does not limit our experiment. In addition, when considering the detection of smaller analytes such as proteins 7 or DNA fragments, 10 a noise increase after sample injection has never been observed, probably due to the fact that such analytes belong to a much lower size range and, thus, do not affect the optical laser path to and from the resonators.

VI. CONCLUSIONS
We report on the development of a nanomechanical measurement system, which allows the real-time detection of living cells via the tracking of up to 18 cantilevers and up to four resonance modes, simultaneously. With respect to previous publications, this work demonstrates more than three times faster and up to seven times more sensitive detection of larger arrays of microcantilevers in liquid. Such an achievement is the result of upscaling of the chip fabrication, from eight to 18 sensors per chip, along with the optimization of an optical detection readout and the implementation of the PLL method as the measurement strategy.
Sensor arrays are fabricated via standard cleanroom technology. A custom-built piezo-stack actuator is fabricated and allows us to drive resonators in liquid up to 2 MHz, while a commercial PSD is integrated in an in-house developed electronic readout system.
We implement the PLL measurement method, which allows us to track up to 18 × 4 mechanical signals over several hours, with a time resolution below 15 s. For each sensor, the PLL generates a closed feedback loop that allows us to drive the cantilevers close to resonance, while tracking the real-time evolution of the resonance frequency. Frequency noise analysis of the new devices and setup shows that, in the relevant time range for biological events (few minutes), the main noise contribution is the system thermal drift. When compared to the previous sweep method, routinely implemented for eight cantilever arrays, the PLL exhibits better sensing performance and faster operation. For the four modes considered (fift to eighth, corresponding to frequencies between 450 and 1200 kHz), Allan deviation analysis allows us to estimate a mass resolution down to 2 pg at 5 min integration times.
In addition, we show that measurement performance is not heavily affected by sensor surface chemistry. We report less than a factor of 3 difference in frequency noise of sensors with four 92, 065001 -S1

III. SELF ASSEMBLED MONOLAYERS
In order to functionalize the gold surface of the cantilevers with self-assembled monolayers (SAM), the gold-coated chip is removed from the storage box (Argon, 0.07 MPa) and immersed in ethanol (C2H6O, HPLC Grade) for 30 minutes. Subsequently, possible organic residues are cleaned via 10 minutes of UV exposure (Boekel UV-Ozone cleaner, 135500), which also serves to activate the gold surface and clean it from environmental organics prior to functionalization 1, 2 . The chip is immersed and kept in fresh ethanol until the mounting in the capillary functionalization platforms.
Microglass capillaries and tube reservoirs are cleaned and kept in ethanol solution. Before functionalization, they are dried on filter paper and placed under heat lamp (Osram SICCATHERM infrared heat lamp 375 W) for 10', to ensure total removal of ethanol. The chip is incubated in the glass microcapillaries filled with SAM solutions for 10 minutes, and stored in fresh ethanol at 4°C overnight, one day before experiment.
In case of planned bacterial detection, after functionalization the chip would be rinsed in ethanol, nanopure water, and incubated in the same buffer used in the experiment (e.g. HEPES buffer) at 26°C overnight, as explained in the main text.

IV.
PIEZOSTACK ACTUATORS Figure S2: Displacement in air of the 200 μm-thick PEEK membrane, designed to host the cantilever array chip on one side, and the piezostack actuator on the other side. The piezostack is actuated with 1Vpp voltage signal generated via a function generator (DS345, Stanford Research) over a frequency range between 50 kHz to 2 MHz. The membrane deflection is detected via a fiber-optic vibrometer (OFV-552, Polytech), by focusing the laser spot at the center of the PEEK membrane. Three piezostack actuators configurations are compared, with different number of layers and thickness: a stack of 5 piezoceramic layers, each 1 mm thick (black line); two stacks of 3 piezoceramic layers, with thickness of 0.5/1/0.5 mm (red line) and 0.5/2/0.5 mm, respectively (purple line). For the three devices, the best actuation efficiency is measured between 350 kHz and 1 MHz. A higher number of layers is expected to result into a larger displacement, however the 0.5/1/0.5 mm 3-stack actuator exhibits the largest actuation efficiency. We attribute this outcome to the manual fabrication process, which includes several stages of gluing and alignment, thus affecting the consistency of the final device. However, all devices were integrated into microfluidic measurement chambers, and provided successful actuation of microcantilevers up to 2 MHz, given an actuation voltage between 1 and 5 V. : Performance comparison between the former SWEEP method (red data points) and the newly implemented PLL (blue data points). The resonance frequencies (mode 5 (a) and mode 6 (b)) of a cantilever array (500 μm long, 2.3 μm thick and 95 μm wide) in PBS buffer were acquired for 30 minutes with each method, sequentially. As also shown in Table S1, the PLL is more than 3 times faster than the SWEEP, when considering identical number of sensors and modes. This is due to the fact that the PLL excites a single frequency value per cycle, while the SWEEP provides actuation over a frequency range that has to be wide enough to enable signal fit to a damped resonator model, in order to later extract the resonance frequency value 4 . In addition, when considering the resonance frequency standard deviation over a time window of 10 min (in the order of the time range of interest for our measurements), we observe an improvement in frequency stability of up to 7-fold with the PLL. We expect an improvement of the same magnitude in terms of mass resolution, thus pushing down to about 2 pg the previous SWEEP detection limit of 10 pg 5 .  Figure S6: Allan Deviation plots in the time range of interest for devices (400 μm long, 2.3 μm thick and 70 μm wide) in PBS at 26 °C. Each line is the average of 3 sensors functionalized as in section V and with the same molecules, namely hydrophilic (aliphatic thiol molecules terminated with PEG, NH2 and COOH groups) or hydrophobic (aliphatic thiol molecules terminated with CH3 group) self-assembled monolayers. All plots show the same linear thermal drift behavior, with Allan deviation slope independent of mode number and functionalization. PEG (a), CH3 (b), NH2 (c) and COOH (d) functionalization do not drastically affect the frequency stability, which lies in the same range, with less than a factor 3 variation, when considering same mode and different interface chemistry. Considering different mode numbers [N5 (≈450 kHz), red triangles; N6 (≈680 kHz), grey squares; N7 (≈920 kHz), black pointing down triangles; N8 (≈1200 kHz), blue diamonds], it is visible how mode 8 is generally noisier by up to a factor 4, when compared to the better performing modes 6 and 7. At 5 minutes integration time, considering Eq. 3 in the main text, we can estimate a mass resolution between a minimum of 3 pg (mode 6, a) and c)) and and a maximum of 12 pg (mode 8, b)).
92, 065001 -S1  N7 (c), the standard deviation shows an increase of up to a factor 4 with respect to the level in buffer. In order to avoid fluidic effects, the measurements in bacteria environment are collected 20 minutes after cells injection in the microfluidic chamber. We attribute this phenomenon to the laser scattering resulting from the presence of bacterial cells moving and floating in the measurement chamber, and in the fluidic space between laser and resonators.