Single-particle mass spectrometry with arrays of frequency-addressed nanomechanical resonators

One of the main challenges to overcome to perform nanomechanical mass spectrometry analysis in a practical time frame stems from the size mismatch between the analyte beam and the small nanomechanical detector area. We report here the demonstration of mass spectrometry with arrays of 20 multiplexed nanomechanical resonators; each resonator is designed with a distinct resonance frequency which becomes its individual address. Mass spectra of metallic aggregates in the MDa range are acquired with more than one order of magnitude improvement in analysis time compared to individual resonators. A 20 NEMS array is probed in 150 ms with the same mass limit of detection as a single resonator. Spectra acquired with a conventional time-of-flight mass spectrometer in the same system show excellent agreement. We also demonstrate how mass spectrometry imaging at the single-particle level becomes possible by mapping a 4-cm-particle beam in the MDa range and above.

NEMS with respect to the deposition rate on their surface measured with a QCM. Red curve corresponds to NEMS#1 and the color progressively turn to blue for smaller devices until dark blue for NEMS#19. We deposited a maximum mass of ~ 4 fg << ~ 1 pg (total resonator mass) to remain in the linear regime. This comparison yields the product . with t the thickness of the resonator and its density. Mass sensitivity and effective mass for each mode is finally calculated from this product, width and length of each resonator. Figure 6: TOF spectra obtained with tantalum clusters of increasing size and mass. The plot shows that both intensity and width of peaks degrade very quickly beyond 2MDa. There are two reasons for this degradation: first heavy ions are less accelerated and the ion detector of the TOF Mass Spectrometer becomes less efficient 2 . Secondly, the cluster source might produce a lower number of aggregates. Because of this degradation, we limited our mass range of operation below 3MDa.

Supplementary Figure 7: Mass resolution for increasing masses.
These numerical calculations present the mass uncertainty obtained for particles of different masses, obtained from the measured frequency stability of a given NEMS in the array. This mass uncertainty depends on the landing position on the beam (normalized, with 0 and 1 being the clamped ends and 0.5 the center). Only a fixed (shown here) portion of the beam is considered in all the analysis in order to obtain a chosen mass resolution. This mass uncertainty increases when the particle lands close to the anchors, where the motion becomes small. How close and how much the resolution increases depends on the particle mass. But for high enough masses (>2.5MDa), the mass resolution does not depend on measured mass anymore. This shows that the resolving power of NEMS-MS increases for heavier particles, with proportionally narrower peaks.

Supplementary Figure 8: Mass spectrum of each individual NEMS for the 7.4 nm tantalum clusters.
Each spectrum obtained with every individual NEMS is represented here with a different color. Their intensities are normalized by the total number of events in the overall spectrum. This plot clearly shows the variability across the array and how this variability contributes to the broadness of the overall peak. Figure 9: Mass uncertainty of every detected particle for the 7.4 nm tantalum clusters. Each dot is the mass uncertainty of a detected particle obtained from the measured frequency stability of the resonator (both modes) on which the particle landed. The x axis is the position of the particle along the beam normalized by the length of the beam (0 is an anchored end, 0.5 is the middle of the beam). Each NEMS in the array is associated to a different color in the plot. The solid lines show the theoretical mass uncertainties calculated for particles of a fixed 2.15MDa mass. This plot shows that while the average mass resolution is about 250kDa across all events and all NEMS, ie very similar to an individual NEMS, there is a large spread in mass uncertainties. This mass uncertainty is proportional to both effective mass of the resonator and its frequency stability. While the relation between the former to resonator length is well established, the latter is less known. This explains why mass uncertainty in the plot is not a monotonic function of resonator length. In any case, this spread contributes to the broadness of the overall spectrum.

Electrical signal with arrays
In a frequency addressed architecture, all N resonators are connected in parallel and the array can be modeled as shown in Supplementary Figure 2. At a given time, only one of the resonators is in motion, so the resistance of the nanogauges in all the others is balanced, resulting in a virtual ground between them. In this case, the equivalent circuit is as shown Supplementary Figure 3, very similar to that of a single resonator.
The load impedance at the output of the resonator is = // 0 −1 ≈ 0 −1 , as ≈ 10 Ω and 0 ≈ 1 Ω We can then use Millman's theorem to find the voltage 1 : The approximation is valid when N is large, and 0 −1 ≪ 0 . The measurement voltage is then