Table 1.
Imaging resolution capabilities of current micro- and nanomechanical resonators.
| Device type | Dimensions (L × w × t) | Frequency resolution | Resolvable feature size |
|---|---|---|---|
| Closed-loop frequency measurements: predicted resolution | |||
| Silicon microbeam11 | 200 × 33 × 7 (μm) | AD = 1 × 10−8 | 370 nm |
| Silicon nanobeam7 | 10 × 0.3 × 0.1 (μm) | AD = 8 × 10−8 | 15 nm |
| Graphene nanoribbon6 | 1760 × 200 × 0.14 (nm) | AD = 1.3 × 10−6 | 4.2 nm |
| Single-walled carbon nanotube15 | 150 × 1.7 × 1.7 (nm) | AD = 2 × 10−6 | 0.3 nm |
| Passive thermal-noise frequency measurements in current study | |||
| Silicon microcantilever | 397 × 29 × 2 (μm) | SD = 10−4 | 9 μm |
For closed-loop frequency measurements the diameters of the smallest measureable analytes are tabulated for the cases of a hollow silicon microbeam11, silicon nanobeam7, graphene nanoribbon6 and a single-walled carbon nanotube15. Doubly-clamped beam geometries are employed. The actual device dimensions and deduced experimental values for resonator frequency instability are listed. Frequency fluctuations are characterized by the Allan deviation (AD), which was either reported in the reference indicated, or deduced from the reported mass sensitivity. The resolvable feature size is defined as the approximate size (standard deviation) of an analyte for which the measurement signal-to-noise ratio is unity. The resolvable feature size is calculated assuming a hemispherical particle with a mass density of 2 g cm−3 that strongly adsorbs onto these resonators. We use the analyte-induced frequency shifts in the four lowest-frequency mechanical modes, which are assumed to have identical frequency stabilities (consistent with our experimental findings). For passive thermal-noise frequency measurements we use the observed resolvable feature size in current proof-of-concept measurements. The measured standard deviation (SD) in frequency is given. The differences in resolvable feature size for passive measurement of the microcantilever and the closed-loop measurements of the microbeams are due to their disparity in frequency noise.