Mass Sensing – An Overview

November 8, 2022 by Romain Stomp

Introduction

Among sensing applications, mass measurements have received a lot of attention with the shrinking of devices and the ability to detect individual particles. We have witnessed the shift from macroscopic devices such as the micro-balance to micrometer-size resonator devices and, now, to 2D or 1D materials with exquisite resolution down to a single proton's mass [1].

Such applications benefit from resonance enhancement effects: for example, they take advantage of a vibrating beam, a graphene drum or a clamped nanowire. These micro- and nanomechanical resonators need to be controlled via different feedback loops, sometimes coupled with electrostatic, magnetic, or optical actuation and detection schemes.

In this blog post, we’ll walk you through an overview of the mass sensing applications that have been addressed with Zurich Instruments' products, in recognition of the great work achieved by our customers in the lab.

Optomechanical Systems Towards Microwave Frequencies

Microelectromechanical systems (MEMS) benefit from inexpensive piezoelectric materials that can be batched, produced and used in a variety of sensing applications, from gyroscopes or accelerometers to mass sensing. If the detection is performed optically, due to various constraints or to improve the detection sensitivity, one refers to optomechanical sensors. Vibrating beams and micro-cantilevers represent the most common geometries, offering a large surface area for absorbates while exhibiting good dynamical response.

Thanks to their small size and low-loss crystallographic structure, such sensors benefit from a high resonance frequency, above the MHz, and high quality factors Q, usually above 1000. By controlling the sensor with a phase-locked loop (PLL), any change of mass of the vibrating beam, for example, is detected through a shift in frequency as illustrated in Figure 1. This technique can be applied to the first, the second or a higher eigenmode of the resonator to measure not only a change in mass but also a landing position of the particle or a change in the stiffness of the vibrating beam [2, 9].

Mass sensing

Figure 1: Use of resonance tracking techniques to measure changes in absorbed mass.

Such resonance enhancement techniques can be extended to RF-MEMS setups, or to surface acoustic waves (SAWs) up to several GHz. Thanks to our new generation of microwave lock-in amplifiers, the GHFLI and SHFLI Lock-in Amplifiers, the previous achievement demonstrated in the MHz range can now be extended to even higher frequency, lower feedback latency and faster data transfer rate.

From Bulk to 2D to 1D

The mass of bulk materials has been measured with micro-balances as well as with miniaturized mass sensors. Among these conventional techniques, mass spectrometry is the most common one, sorting particles by their mass-to-charge ratio. However, for non-destructive measurements, with no sample preparation or for better sensitivity, reduced dimensionality greatly improves the ultimate mass resolution down to the femto- or zeptogram. This is usually achieved by using the resonance effect of nanomechanical sensors, as explained in the previous section.

It is thus very important to optimize the geometry and dimensionality of the sensor for friction and to ensure a high quality factor while leaving enough space for the particle to absorbate on the membrane or nanowire. Suspended graphene drums and clamped carbon nanotubes (CNT) are ideal candidates for such systems and are depicted in Figure 2. In this transistor-like configuration, a source and drain can detect any change in the current while the back gate is used as a capacitive actuator to bring the suspended structure into resonance. Given the open geometry, optical lenses can be added for visual inspection or other detection schemes.

Mass sensing

Figure 2: Highly sensitive mass detector based on 2D and 1D materials such as graphene or carbon nanotubes (CNT).

Antoine Lavoisier's principle of mass conservation shifted the analysis of chemical reactions from qualitative to quantitative by measuring mass before and after each experiment. This led to the promotion of the metric system and, later on, to the International System of Units (SI). By now, mass sensitivity allows for the measurement of individual atoms or molecules absorbed on a variety of chemically selective substrates. Some of the main applications for mass sensing are:

  • Mass metrology: Mass is among the 7 SI base units. Accurate mass measurements are key for quantitative analysis and for defining the physical constants of nature.

  • Chemically sensitive layer monitoring: During chemical synthesis, the mass of molecules changes and can be monitored during a chemical reaction.

  • Gas absorption studies: Gas sensors measure a change in the absorbed mass from the environment to a substrate that is usually vibrating to detect a change in its resonance frequency.

  • Thin-layer thickness measurements: As the thickness changes, so does the stiffness of the absorbed layer that can be measured from the resonator characteristics.

Online Resources from Zurich Instruments

From long-standing collaborations and knowledge exchange with the community, Zurich Instruments has produced or helped produce a number of resources found on this website and collected here for convenience:

  • Application note on optomechanical mass sensing: This is probably the best starting point as it covers several applications related to mass sensing and explains the experimental details of optical balances, nanomechanical and microcapillary resonators for mass spectrometry.

  • Application page on MEMS-based sensors: If you need to understand your resonator response prior to any measurement, this application page covers the three main measurements strategies to do so. And in case you never considered dissipation as a relevant information channel, check the page on non-contact AFM featuring both PLLs and automatic gain controllers.

  • PLL white paper: Since shifts in resonance frequency provide the most accurate physical measurements, understanding and optimizing PLLs is crucial for understanding mass sensing applications. This white paper covers all main PLL use cases.

  • Interviews with scientists: Get insights from Tomás Manzaneque García, Behraad Bahreini or Dal Wilson on how they use Zurich Instruments' products in their lab for their research.

  • Scientific publications making use of Zurich Instruments' lock-in amplifiers for mass sensing: You’ll be surprised to see how many seemingly different setups benefit from our instruments and keep their complexity low. See also the papers highlighted below.

Conclusion

This blog post provides an overview of various techniques and applications available for mass sensing, most of which are used routinely in the lab by our customers. Reduced dimensionality and higher resonance frequencies are the two main drivers for ultimate mass sensitivity. With its wide range of lock-in amplifiers, each of them available with multi-frequency demodulations and multiple feedback loops, Zurich Instruments has been serving this community since its early days and will continue to support its growth towards an ever broader range of mass sensing applications.

Zurich Instruments Lock-in Amplifiers

Acknowledgments

Thank you to Jelena Trbovic for valuable feedback, as well as to Adrien Noury and Adrian Bachtold for input related to graphene drums and carbone nanotubes.

References

# Title Authors Highlight
1 A nanomechanical mass sensor with yoctogram resolution. Chaste J. et al. NEMS intertial sensor based on a 2 GHz carbon nanotube resonator.
2 Mass and stiffness spectrometry of nanoparticles by multimode nanomechanical resonators Malvar O. et al. Procedure for obtaining the mass, position and stiffness of the analytes arriving at the resonator from the adsorption-induced eigenfrequency jumps.
3 Piezoelectric MEMS Resonators for Cigarette Particle Detection Toledo J. et al. Common use cases for particle detection via mass sensing using change in resonator frequency.
4 A Study on Parametric Amplification in a Piezoelectric MEMS Device Gonzalez Y. et al. Overcoming the effects of damping in liquid environnement by parametric amplification methods.
5 Layering Transition in Superfluid Helium Adsorbed on a Carbon
Nanotube Mechanical Resonator
Noury A. et al. Superfluid helium film absorbed on nanotube, with layer by layer growth monitoring.
6 A Fully Differential SOI-MEMS Thermal Piezoresistive Ring Oscillator in Liquid Environment Intended for Mass Sensing Bhattacharya S. et al. Ring-shaped resonator to improve mass sensing for biomedical applications by minimizing the effect of viscous damping in liquid environments.
7 High-speed multiple-mode mass-sensing resolves dynamic nanoscale mass distributions Olcum S. et al. Multi-frequency technique to enhance measurement bandwidth for mass tomography of nanoscale analytes.
8 Improving mechanical sensor performance through larger damping Roy S. et al. A high Q does not always improve stability as it can vary inversely to SNR when operated near intrinsic limit.
9 Nanomechanical mass sensing and stiffness spectrometry based on two-dimensional vibrations of resonant nanowires Gil-Santos, E. et al Multifrequency technique applied to a 1D nanomechanical resonator.
10 Mass Sensing for the Advanced Fabrication of Nanomechanical
Resonators
Gruber et al. Focused electron beam-induced deposition (FEBID) to grow platinum particles at the free end of singly
clamped nanotube cantilevers.
11 Diamagnetically levitating resonant weighing scale Chen et al. Passive levitation provides low-power consumption while driving the resonance electromagnetically.
12 Atmospheric Pressure Mass Spectrometry of Nanoparticles by Nanoelectromechanical Systems Erdogan et al. New method to overcome the limitations of NEMS small-area sensing and in-vacuum operation by integrating on-chip focusing lens.

If you see that an important publication on mass sensing that features Zurich Instruments' products is missing, please let us know! We'll add it to this blog post and to our publications page.