arXiv subjects

Silvan Schmid

Publications and source records attributed to Silvan Schmid.

At least 19 recordsLinked to original sources

arXiv2026

Reduction of intrinsic losses in nanomechanical silicon nitride resonators through thermal treatment in ultrahigh vacuum

Since the discovery of dissipation dilution, silicon nitride (SiN) nanomechanical resonators have set the benchmark for ultracoherent mechanical systems, with geometry and strain engineering driving remarkable gains in the $f \cdot Q$ product. Surface loss, however, has remained the dominant and largely unaddressed dissipation channel. Here, we demonstrate a geometry-independent approach that directly targets surface loss: thermal treatment in ultrahigh vacuum. Treatment at 1000$^{\circ}$C enhances the intrinsic quality factor of dissipation-diluted SiN membrane resonators by up to a factor of 20, reduces the surface loss eightfold, and simultaneously increases the tensile stress. Photothermal infrared spectroscopy and $\textit{in situ}$ X-ray photoelectron spectroscopy trace the enhancement to thermally activated silanol condensation - the conversion of surface hydroxyl terminations into siloxane bridges - and the reversibility of both quality factor and stress under controlled humidity confirms the surface-chemical origin. These results establish surface chemistry as a tunable parameter for next-generation ultracoherent nanomechanical resonators.

physics.app-ph↗

arXiv2026

Mode-dependent photothermal responsivity mapping of tensile-stressed nanomechanical resonators

The photothermal responsivity of a tensioned nanomechanical resonator, the fractional frequency shift per absorbed optical power, depends on which vibrational mode is tracked and where the heat is deposited. We derive a closed-form model of this dependence for square membranes by treating the membrane as a grid of independent tensile fibers, each responding to its mean temperature. The responsivity map splits into a mode-independent conduction envelope and a mode term that peaks on the antinodal rows and columns of the mode, not at the antinodes, because fibers rather than points carry the modal strain energy. Scanning photothermal measurements of the $(1,1)$, $(1,2)$, $(2,1)$, and $(2,2)$ modes of a square silicon nitride membrane confirm the predicted maps with a correlation $r \geq 0.998$, with the envelope amplitude as the only fitted parameter. On trampoline resonators, the tether-limited thermal conductance flattens the envelope, making the mode term directly visible in raw scans. The measured mode-resolved maps provide the design input for dual-mode photothermal sensing with common-mode drift suppression, identifying pairs, such as a membrane's $(1,1)$/$(2,2)$ or a trampoline's torsional modes, as candidates that combine large differential responsivity with a shared thermal and mechanical environment.

physics.app-ph↗

arXiv2026

HF Etching and Silanization: Evidence for the Role of Surface Hydroxyl Groups in Silicon Nitride Resonator Loss

Silicon nitride $SiN_x$ nanomechanical resonators are central to sensing, quantum technologies, and fundamental physics experiments due to their exceptional mechanical quality factors (Q). However, as resonator thickness approaches the nano-scale, surface-related dissipation limits performance. Here, we investigate the role of surface chemistry in low-stress Si-rich SiNx membranes through a combination of hydrofluoric acid (HF) etching and trimethylchlorosilane (TMCS) silanization, correlated with surface characterization and mechanical measurements. Preliminary analysis by TEM-EELS, XPS, RBS/ERDA, and XRR reveals a native oxide surface layer (1-2 nm). Surface modification by HF and TMCS was subsequently evaluated using XPS, photothermal FTIR, contact-angle measurements, and intrinsic quality factor ($Q_{int}$) characterization. While HF etching effectively removes the native oxide and TMCS introduces hydrophobic $Si-(CH_3)_3$ termination, neither oxide thickness nor surface energy correlates with mechanical dissipation. TMCS treatments produce the largest enhancements, increasing $Q_{int}$ by up to 50%, whereas HF etching alone yields lower gains of 20-25%. These findings suggest surface hydroxyl groups as a key contributor to energy loss in $SiN_x$ resonators and demonstrate that chemical functionalization can substantially suppress surface dissipation.

cond-mat.mtrl-sci↗

arXiv2026

Determination of the intrinsic mechanical quality factor in high-stress silicon nitride resonators

Recent advances in silicon nitride nanomechanical resonators have pushed mechanical quality factors to ultra-high values by combining stress-induced dissipation dilution with mode-shape engineering. Neither mechanism alters the intrinsic quality factor $Q_{\mathrm{intr}}$. Targeting the intrinsic loss itself therefore remains an untapped route to even higher $Q$. Doing so first requires reliable quantification of $Q_{\mathrm{intr}}$, which has proven challenging. Here we present a robust methodology that quantifies $Q_{\mathrm{intr}}$ by combining automated mode identification with systematic ringdown measurements over a large number of mechanical modes. Applied to high-stress silicon nitride membranes, it reveals a systematic dependence of $Q_{\mathrm{intr}}$ on thickness that cannot be described using established models, particularly in the ultra-thin limit. We account for this trend with a phenomenological model that incorporates a thickness-dependent loss channel. Together, our method and model open a route toward a microscopic understanding of intrinsic dissipation and toward directly mitigating its loss channels.

physics.app-ph↗

arXiv2026

Position-Dependent Calibration and Frequency Stability in On-Axis Optical Transduction of Vertical InP Nanowire Resonators

We present a quantitative framework for on-axis optical transduction of vertical InP nanowire resonators, correlating laser position to signal amplitude, calibration, and frequency stability. Photothermal resonance detuning is used to reconstruct the local beam intensity profile and to calibrate the photodetector signal using the thermomechanical noise. A noise model incorporating shot noise and spatial variation in substrate reflectance predicts the position-dependent Allan deviation. We find that the optimal detection position lies near the steepest intensity gradient, and that increasing laser power does not significantly improve frequency stability, because the accompanying temperature rise enhances thermomechanical noise and offsets the signal gain. These results establish design guidelines for optimizing nanowire-based sensors in on-axis optical detection schemes.

physics.app-ph↗

arXiv2025

Design optimization of silicon nitride nanomechanical resonators for thermal infrared detectors: a guide through key figures of merit

Thermomechanical infrared (IR) detectors have emerged as promising alternatives to traditional photon and thermoelectric sensors, offering broadband sensitivity and low noise without the need for cryogenic cooling. Despite recent advances, the field still lacks a unified framework to guide the design of these nanomechanical systems. This work addresses that gap by providing a comprehensive design guide for IR thermal detectors based on silicon nitride drumhead and trampolines. Leveraging a validated analytical model, we systematically explore how geometry, tensile stress, and optical properties influence key performance metrics such as thermal time constant, noise-equivalent power, and specific detectivity. The analysis encompasses both bare silicon nitride and structures with broadband absorber layers, revealing how different parameter regimes affect the trade-off between sensitivity and response speed. Rather than focusing on a single device architecture, this study maps out a broad design space, enabling performance prediction and optimisation for a variety of application requirements. As such, it serves not only as a reference for benchmarking existing devices but also as a practical tool for engineering next-generation IR sensors that can operate close to the fundamental detection limit. This work is intended as a foundational resource for researchers and designers aiming to tailor IR detectors to specific use cases.

physics.ins-det↗

arXiv2025

Picogram-Level Nanoplastic Analysis with Nanoelectromechanical System Fourier Transform Infrared Spectroscopy: NEMS-FTIR

We present a photothermal infrared spectroscopy-based approach for the chemical characterization and quantification of nanoplastics. By combining the high sensitivity of nanoelectromechanical systems (NEMS) with the wide spectral range and ubiquity of commercially available Fourier transform infrared (FTIR) spectrometers, NEMS-FTIR offers a time-efficient and cryogen-free option for the rapid, routine analysis of nanoplastics in aqueous samples. Polypropylene, polystyrene, and polyvinyl chloride nanoplastics with nominal diameters ranging from 54 to 262 nm were analyzed by NEMS-FTIR with limits of detection ranging from 101 pg to 353 pg, one order of magnitude lower than values reported for pyrolysis-gas chromatography-mass spectrometry of nanoplastics. The absorptance measured by NEMS-FTIR could be further converted to absolute sample mass using the attenuation coefficient, as demonstrated for polystyrene. Thanks to the wide spectral range of NEMS-FTIR, nanoplastic particles from different polymers could be readily identified, even when present in a mixture. The potential of NEMS-FTIR for the analysis of real samples was demonstrated by identifying the presence of nanoplastics released in water during tea brewing. Polyamide leachates in the form of fragments and smaller oligomers could be identified in the brewing water without sample pre-concentration, even in the presence of an organic matrix. Accelerated aging of the nylon teabags under elevated temperature and UV radiation showed further release of polyamide over time.

physics.ins-det↗

arXiv2025

Uncooled Thermal Infrared Detection Near the Fundamental Limit Using a Nanomechanical Resonator with a Broadband Absorber

This paper introduces a thermal infrared detector utilizing a nano-optomechanical silicon nitride (SiN) resonator, equipped with a free-space impedance-matched (FSIM) absorber composed of a platinum (Pt) thin film, offering a broadband spectral absorptance on average of 47%. To reduce photothermal back-action caused by intensity fluctuations of the readout laser, the FSIM absorber incorporates a circular clearance for the laser. The study provides a comprehensive characterization of the thermal time constant, power responsivity, and frequency stability of the resonators, with experimental results compared to analytical models and finite element method (FEM) simulations. The fastest thermal response is observed for the smallest 1 mm resonators, with a thermal time constant tau_th = 14 ms. The noise equivalent power (NEP) of the resonators is assessed, showing that the smallest 1 mm resonators exhibit the best sensitivity, with NEP = 27 pW/sqrt(Hz) and a respective specific detectivity of D* = 3.8e9 cm sqrt(Hz)/W. This is less than three times below the theoretical maximum for an ideal IR detector with 50% absorptance. This places our resonators among the most sensitive room-temperature IR detectors reported to date offering an extended spectral range from the near-IR to far-IR. This work underscores the potential of nano-optomechanical resonators for high-performance IR sensing applications.

physics.ins-det↗

arXiv2024

Optimal Sensing of Momentum Kicks with a Feedback-Controlled Nanomechanical Resonator

External disturbances exciting a mechanical resonator can be exploited to gain information on the environment. Many of these interactions manifest as momentum kicks, such as the recoil of residual gas, radioactive decay, or even hypothetical interactions with dark matter. These disturbances are often rare enough that they can be resolved as singular events rather than cumulated as force noise. While high-Q resonators with low masses are particularly sensitive to such momentum kicks, they will strongly excite the resonator, leading to nonlinear effects that deteriorate the sensing performance. Hence, this paper utilizes optimal estimation methods to extract individual momentum kicks from measured stochastic trajectories of a mechanical resonator kept in the linear regime through feedback control. The developed scheme is illustrated and tested experimentally using a pre-stressed SiN trampoline resonator. Apart from enhancing a wide range of sensing scenarios mentioned above, our results indicate the feasibility of novel single-molecule mass spectrometry approaches.

eess.SY↗

arXiv2024

Room temperature, cavity-free capacitive strong coupling to mechanical motion

The back-action damping of mechanical motion by electromagnetic radiation is typically overwhelmed by internal loss channels unless demanding experimental ingredients such as superconducting resonators, high-quality optical cavities, or large magnetic fields are employed. Here we demonstrate the first room temperature, cavity-free, all-electric device where back-action damping exceeds internal loss, enabled by a mechanically compliant parallel-plate capacitor with a nanoscale plate separation and an aspect ratio exceeding 1,000. The device has four orders of magnitude lower insertion loss than a comparable commercial quartz crystal and achieves a position imprecision rivaling optical interferometers. With the help of a back-action isolation scheme, we observe radiative cooling of mechanical motion by a remote cryogenic load. This work provides a technologically accessible route to high-precision sensing, transduction, and signal processing.

cond-mat.mes-hall↗

arXiv2024

Stress-Dependent Optical Extinction in LPCVD Silicon Nitride Measured by Nanomechanical Photothermal Sensing

Understanding optical absorption in silicon nitride is crucial for cutting-edge technologies like photonic integrated circuits, nanomechanical photothermal infrared sensing and spectroscopy, and cavity optomechanics. Yet, the origin of its strong dependence on film deposition and fabrication process is not fully understood. This Letter leverages nanomechanical photothermal sensing to investigate optical extinction $\kappa_{\mathrm{ext}}$ at 632.8 nm wavelength in LPCVD SiN strings across a wide range of deposition-related tensile stresses ($200-850$ MPa). Measurements reveal a reduction in $\kappa_{\mathrm{ext}}$ from 10$^3$ to 10$^1$ ppm with increasing stress, correlated to variations in Si/N content ratio. Within the band-fluctuations framework, this trend indicates an increase of the energy bandgap with the stress, ultimately reducing absorption. Overall, this study showcases the power and simplicity of nanomechanical photothermal sensing for low absorption measurements, offering a sensitive, scattering-free platform for material analysis in nanophotonics and nanomechanics.

physics.optics↗

arXiv2024

Comparative Analysis of Nanomechanical Resonators: Sensitivity, Response Time, and Practical Considerations in Photothermal Sensing

Nanomechanical photothermal sensing has significantly advanced single-molecule/particle microscopy and spectroscopy, and infrared detection through the use of nanomechanical resonators that detect shifts in resonant frequency due to photothermal heating. However, the relationship between resonator design, photothermal sensitivity, and response time remains unclear. This paper compares three resonator types - strings, drumheads, and trampolines - to explore this relationship. Through theoretical modeling, experimental validation, and finite element method simulations, we find that strings offer the highest sensitivity (with a noise equivalent power of 280 fW/Hz$^{1/2}$ for strings made of silicon nitride), while drumheads exhibit the fastest thermal response. The study reveals that photothermal sensitivity correlates with the average temperature rise and not the peak temperature. Finally, the impact of photothermal back-action is discussed, which can be a major source of frequency instability. This work clarifies the performance differences and limits among resonator designs and guides the development of advanced nanomechanical photothermal sensors, benefiting a wide range of applications.

physics.app-ph↗

arXiv2024

Optimized Signal Estimation in Nanomechanical Photothermal Sensing via Thermal Response Modelling and Kalman Filtering

We present an advanced thermal response model for micro- and nanomechanical systems in photothermal sensing, designed to balance speed and precision. Our model considers the two time constants of the nanomechanical element and the supporting chip, triggered by photothermal heating, enabling precise photothermal input signal estimation through Kalman filtering. By integrating heat transfer and noise models, we apply an adaptive Kalman filter optimized for FPGA systems in real-time or offline. This method, used for photothermal infrared (IR) spectroscopy with nanomechanical resonators and a quantum cascade laser (QCL) in step-scan mode, enhances response speed beyond standard low-pass filters, reducing the effects of drift and random walk. Analytical calculations show the significant impact of the thermal expansion coefficients' ratio on the frequency response. The adaptive Kalman filter, informed by the QCL's input characteristics, accelerates the system's response, allowing rapid and precise IR spectrum generation. The use of the Levenberg-Marquardt algorithm and PSD analysis for system identification further refines our approach, promising fast and accurate nanomechanical photothermal sensing.

physics.app-ph↗

arXiv2023

Resonance frequency tracking schemes for micro- and nanomechanical resonators

Nanomechanical resonators can serve as high performance detectors and have potential to be widely used in the industry for a variety of applications. Most nanomechanical sensing applications rely on detecting changes of resonance frequency. In commonly used frequency tracking schemes, the resonator is driven at or close to its resonance frequency. Closed-loop systems can continually check whether the resonator is at resonance and accordingly adjust the frequency of the driving signal. In this work, we study three resonance frequency tracking schemes, a feedback-free (FF), a self-sustaining oscillator (SSO), and a phase-locked loop oscillator (PLLO) scheme. We improve and extend the theoretical models for the FF and the SSO tracking schemes, and test the models experimentally with a nanoelectromechanical system (NEMS) resonator. We employ a SSO architecture with a pulsed positive feedback topology and compare it to the commonly used PLLO and FF schemes. We show that all tracking schemes are theoretically equivalent and that they all are subject to the same speed versus accuracy trade-off characteristics. In order to verify the theoretical models, we present experimental steady-state measurements for all tracking schemes. Frequency stability is characterized by computing the Allan deviation. We obtain almost perfect correspondence between the theoretical models and the experimental measurements. These results show that the choice of the tracking scheme is dictated by cost, robustness and usability in practice as opposed to fundamental theoretical differences in performance.

physics.ins-det↗

arXiv2023

Self-Sustaining Oscillator with Frequency Counter for Resonance Frequency Tracking in Micro- and Nanomechanical Sensing

Nanomechanical sensors based on detecting and tracking resonance frequency shifts are to be used in many applications. Various open- and closed-loop tracking schemes, all offering a trade-off between speed and precision, have been studied both theoretically and experimentally. In this work, we advocate the use of a frequency counter as a frequency shift monitor in conjunction with a self-sustaining oscillator (SSO) nanoelectromechanical system (NEMS) configuration. We derive a theoretical model for characterizing the speed and precision of frequency measurements with state-of-the-art frequency counters. Based on the understanding provided by this model, we introduce novel enhancements to frequency counters that result in a trade-off characteristics which is on a par with the other tracking schemes. We describe a low-cost field-programmable-gate array (FPGA) based implementation for the proposed frequency counter and use it with the SSO-NEMS device in order to study its frequency tracking performance. We compare the proposed approach with the phase-locked-loop based scheme both in theory and experimentally. Our results show that similar or better performance can be achieved at a substantially lower cost and improved ease-of-use. We obtain almost perfect correspondence between the theoretical model predictions and the experimental measurements.

eess.SP↗

arXiv2023

Photothermal Microscopy & Spectroscopy with Nanomechanical Resonators

In nanomechanical photothermal absorption spectroscopy and microscopy, the measured substance becomes a part of the detection system itself, inducing a nanomechanical resonance frequency shift upon thermal relaxation. Suspended, nanometer-thin ceramic or 2D material resonators are innately highly-sensitive thermal detectors of localized heat exchanges from substances on their surface or integrated into the resonator itself. Consequently, the combined nanoresonator-analyte system is a self-measuring spectrometer and microscope: responding to a substances transfer of heat over the entire spectrum for which it absorbs, according to the intensity it experiences. Limited by their own thermostatistical fluctuation phenomena, nanoresonators have demonstrated sufficient sensitivity for measuring trace analyte as well as single particles and molecules with incoherent light or focused and unfocused coherent light. They are versatile in their design, support various sampling methods and hyphenation with other spectroscopic methods, and are capable in a wide range of applications including fingerprinting, separation science, and surface sciences.

physics.ins-det↗

arXiv2023

Nanomechanical Photothermal Near Infrared Spectromicroscopy of Individual Nanorods

Understanding light-matter interaction at the nanoscale requires probing the optical properties of matter at the individual nano-absorber level. To this end, we have developed a nanomechanical photothermal sensing platform that can be used as a full spectromicroscopy tool for single molecule and single particle analysis. As a demonstration, the absorption cross-section of individual gold nanorods is resolved from the spectroscopic and polarization standpoint. By exploiting the capabilities of nanomechanical photothermal spectromicroscopy, the longitudinal localized surface plasmon resonance (LSPR) in the NIR range is unravelled and quantitatively characterized. The polarization features of the transversal surface plasmon resonance (TSPR) in the VIS range are also analyzed. The measurements are compared with the finite element method (FEM), elucidating the role played by electron-surface and bulk scattering in these plasmonic nanostructures, as well as the interaction between the nano-absorber and the nanoresonator, ultimately resulting in absorption strength modulation. Finally, a comprehensive comparison is conducted, evaluating the signal-to-noise ratio of nanomechanical photothermal spectromicroscopy against other cutting-edge single molecule and particle spectroscopy techniques. This analysis highlights the remarkable potential of nanomechanical photothermal spectromicroscopy due to its exceptional sensitivity.

physics.optics↗

arXiv2023

Towards practical mass spectrometry with nanomechanical pillar resonators by surface acoustic wave transduction

Nanoelectromechanical systems (NEMS) have proven outstanding performance in the detection of small masses down to single proton sensitivity. To obtain a high enough throughput for the application in practical mass spectrometry, NEMS resonators have to be arranged in two-dimensional (2D) arrays. However, all state-of-the-art electromechanical transduction methods rely on electrical lines placed close to the mechanical resonators, which drastically restricts the density of 2D resonator arrays. An exception is the transduction by surface acoustic waves (SAWs), which has so far only been shown for the transduction of single nanomechanical pillar resonators. Here, we demonstrate the transduction of pillar pairs by surface acoustic waves. The pillars have a diameter of 700 nm and show a mass responsivity of -588$\pm$98 ng$^{-1}$. The distances between the pillar pairs are 70 nm and 14.3 $μ$m. SAW transduction enabled us to measure both pillars of each pair with electrical lines no closer than 300 $μ$m, illustrating the potential of SAWs to transduce dense arrays of pillar resonators, a crucial step towards practical mass spectrometry with NEMS.

physics.app-ph↗