Mass spectrometry is a powerful analytical technique which is widely adopted to determine the molecular mass of samples, elemental composition and structural information, making it an indispensable tool in qualitative and quantitative applications including biological research, chemical measurements, astrophysical analysis and environmental monitoring^1-4. Specifically, mechanical oscillator-based mass sensors are widely utilized for high-sensitivity on-chip mass spectrometry by monitoring the intrinsic mechanical frequency shift $\Delta {\omega }_{\text{mi}}$ when an additional mass is adsorbed onto the oscillator, as shown Fig. 1a^5-13. Based on the relationship $\Delta m=-2(m_{\text{eff}}/{\omega }_{\text{mi}})\Delta {\omega }_{\text{mi}}$, a higher intrinsic vibrational frequency ${\omega }_{\text{mi}}$, smaller effective mass $m_{\text{eff}}$, and smaller intrinsic mechanical frequency shift $\Delta {\omega }_{\text{mi}}$ could lead to a higher mass resolution $\Delta m_{\text{res}}$, as shown in Fig. 1b. Therefore, cantilever^14-1616, nanobeam^6,12, nanotube^17-19, and nanowire²⁰ oscillators are commonly used, owing to their advantages of relatively small effective mass and high mechanical frequency (in the range of kHz to GHz). Over the past decade, mass resolutions from zeptograms^12,16,21 to yoctograms^9,22 have been achieved employing mechanical oscillator-based structures in a vacuum or cryogenic environment. However, due to the large mechanical dissipation caused by the hydrodynamic force in the ambient environment in which the typical mechanical Q factor is only in the order of tens or hundreds^20,23-25, ultrasensitive mass sensing under ambient conditions has not yet been reported. (When the resonance drift of the mechanical frequency caused by the disturbance of noise is much smaller than the mechanical linewidth, the minimum measurable frequency shift $\Delta {\omega }_{\text{res}}$ is mainly determined by the linewidth of the resonance). Allan deviation is an important parameter for characterizing the frequency stability and analyzing the sensing resolution, which is commonly the main parameter that limits the mass resolution. In the current experiment, phonon lasing narrowed the linewidth of the mechanical mode, causing mechanical frequency shift to the same order of the Allan deviation. Therefore, the mass shift can be conveniently retrieved by the frequency shift and the minimum measured frequency shift can be used, i.e. the mechanical linewidth, to calculate the minimum measured mass shift, which is the mass resolution in the experiment. It is of great significance to conduct mass sensing studies in ambient conditions since the ambient environment is employed in various applications such as biosensing, gas sensing, environmental monitoring and on-chip fabrication^26-30. Specifically, the ambient conditions is extremely important in biosensing, since various biological particles can be inactivated in vacuum and low-temperature environment. These biological particles were identified and analyzed using mass detection, as shown in Fig. 1c. Among them, the detection of oligonucleotides and proteins require a mass resolution that is as small as zeptograms. For practical applications, detection of serum immunoglobulin (IgM), a type of protein, in the blood and the proportion of its isoforms is very important for analyzing the biological immune system, which requires a mass resolution of 190 kDa at least ($\Delta m_{\text{res}}\sim 3.2\times 10^{-19}\mathrm{g}=320\text{zg}$, the quality of the lightest isoform). However, the best mass resolution reported under ambient conditions³⁰ is at the magnitude of attogram (10⁻¹⁸ g), which still cannot meet all the requirements of biological tests. Therefore, the development of ultrahigh-sensitivity sensing techniques remains challenging but is very significant in various fields. It has been predicted that the detection sensitivity of protein mass is around 10⁻¹⁹ g using optomechanical crystal (OMC) cavity³¹, which indicates OMC cavity is possibly applicable for sensitive mass detection. Sub-pg mass sensing has been achieved in microtoroid optomechanical oscillator by the narrow linewidth of phonon lasing combined with harmonic optical modulation³².

In the current work, a new approach that utilizes phonon lasing to achieve an ultra-narrow mechanical linewidth was proposed, it allows a predicted maximum mass resolution up to zeptograms (10^-20 g) at room temperature in an ambient environment. The designed sensor structure is a larger-center-hole optomechanical crystal cavity, as shown in Fig. 1d, which is referred to as the hole in the center defect region and exhibit a larger radius than that on both sides33., 34., 35., 36.. Its sensing ability was demonstrated by experimentally depositing silica masses of different weights on the OMC cavity, as shown Fig. 1e. The results predict that the proposed method allows a maximum resolution of 65 ± 19 zg ($\Delta m_{\text{res}}\sim 6.5\times 10^{-20}\mathrm{g}$), which approaches the mass of a protein, even an oligonucleotide³⁷. This is of great value for possible future applications in biological researches such as oligonucleotide drug delivery³⁸ or the Human Proteome Project³⁹.

Narrower mechanical linewidth could lead to higher mass resolution, as shown in Fig. 1a. In this study, a mass sensing that was phonon lasing enhanced was proposed, which dramatically causes the narrowing of the mechanical linewidth⁴⁰. Here, the optical gradient force generated by the radiation pressure was utilized to measure and amplify the mechanical mode. In this process, the blue detuned pump light is scattered to lower frequency due to the mechanical motion, providing energy to the mechanical system. It is an effective gain to the mechanical system and will compensate for the energy loss from the other damping channels. In addition, since the compensation for the mechanical dissipation provided by the optical gradient force is proportional to the photon number in the OMC cavity, a high optical Q factor is required to be taken into consideration when designing the OMC cavity to achieve a higher optical gradient force and favor the phonon lasing. Moreover, OMC cavities with lower intrinsic mechanical dissipation are beneficial for phonon lasing. Therefore, in the current work, the larger-center-hole OMC cavity shown in Figs. 1d and 2a, which was proposed in our previous study33., 34., 35., 36., was selected due to its high optical Q factor and low intrinsic mechanical dissipation for the phonon lasing enhanced mass sensor.

The OMC cavity was designed and optimized using the finite element method (FEM). Here, a localized optical fundamental mode (i.e., y-component of the normalized electric field E_y) with a wavelength of 1546.8 nm, as shown in Fig. 2b, and a localized mechanical fundamental mode with a mechanical frequency of 4.43 GHz, as shown in Fig. 2c, were formed in the cavity through the optical and mechanical bandgaps, respectively. In addition, by using the definition of effective mass in reference⁴¹, the calculated effective mass for the designed structure was 133 fg. Fig. 2d shows the measurements adopting the experimental setup (details for the structural design, fabrication, and measurements in could be seen in Supplementary Notes 1-2). The fundamental optical mode (λ = 1557.6 nm) is observed in the transmission spectrum, as shown in Fig. 2e. As shown in the inset of Fig. 2e, the intrinsic optical Q factor was estimated to be 160,000 based on the Lorentzian fitting of the fundamental optical mode. Moreover, results show that the localized mechanical fundamental mode exhibited a relatively narrow linewidth of approximately 3 MHz (Q∼1,500) under ambient conditions with a high frequency of 4.526 GHz, as shown in Fig. 3b (gray data points). Therefore, the designed structure is of high optical intrinsic Q factors and low intrinsic mechanical property to favor phonon lasing under ambient conditions.

Phonon lasing was experimentally achieved in the OMC cavity by increasing the optical input power to amplify the Stokes scattering process, as shown in Fig. 3. The wavelength of the input laser (TLD) shown in Fig. 2d was adjusted in the blue-detuned regime. The detuning Δ is defined as $\Delta ={\omega }_{\text{in}}-{\omega }_{\text{o}}$, where, ${\omega }_{\text{in}}$ and ${\omega }_{\text{o}}$ depict the frequencies of the input laser and the cavity resonance, respectively. An apparent threshold shown in Fig. 3a was found to be the optical input power increased along a narrowed mechanical linewidth after reaching the threshold, indicating that phonon lasing was achieved in the fabricated OMC cavity. Subsequently, the mechanical linewidth can be narrowed up to three orders of magnitude, ranging from 2.6 MHz to 5.4 kHz, to realize ultrasensitive mass sensing under ambient conditions, as shown in Fig. 3b.

In this section, the experiment to verify a phonon lasing enhanced mass sensing was discussed. The experimental scheme based on the sensing principle $\Delta m=-2(m_{\text{eff}}/{\omega }_{\text{mi}})\Delta {\omega }_{\text{mi}}$ is as follows: Firstly, a focused ion beam (FIB) was used to deposit a small amount of material (silica) on the side wall of the OMC cavity via ion beam induced deposition, as shown in Fig. 1e (details can be seen in Supplementary Notes 3), resulting in the mechanical frequency shift $\Delta {\omega }_{\mathrm{m}}$. The deposition parameters were adjusted to control the weights of the added masses. Finally, masses of different weights were obtained for mass sensing in the experiments. The limitation and repeatability of the mass deposition process using FIB were further discussed in Supplementary Note 3.

The intrinsic mechanical frequency shift $\Delta {\omega }_{\text{mi}}$ caused by mass deposition was measured firstly, and then the corresponding $\Delta {\omega }_{\mathrm{m}}$ was measured under phonon lasing to illustrate the experimental results of the enhancement of the sensing resolution. Fig. 4a shows the intrinsic mechanical variation modes for three different deposition parameters. The gray data points represent the measured ${\omega }_{\text{mi}}$ prior to mass deposition, which are used as references when exhibiting the mechanical frequency shift corresponding to the added masses. Meanwhile, the red, green, and blue data points represent the measured mechanical vibration modes after depositing different weights of SiO₂ masses, whicl leads to frequency shifts of 29.2, 41.97 and 54.44 MHz, respectively. The homologous masses evaluated by the sensing principle (see details regarding the calculation method of the deposited mass in Supplementary Note 4) are 0.181, 0.264 and 0.345 fg, respectively, corresponding to the insets in Fig. 4c with the same color. Based on the figure, it is apparent that a greater weight could cause a larger mechanical frequency shift, which agrees well with the theoretical analysis in the current work.

Then, the phonon lasing amplification mechanical vibration was measured accordingly, as shown in Fig. 4b with the same color. The mechanical linewidth was narrowed from MHz to kHz, which is favourable to the proposed ultra-sensitive mass sensing method. The measured mechanical frequency ${\omega }_{\mathrm{m}}$ consists of the intrinsic mechanical frequency ${\omega }_{\text{mi}}$ and the mechanical frequency deviation ${\omega }_{\text{md}}$ induced by the optical spring effect ${\omega }_{\mathrm{m}}={\omega }_{\text{mi}}+{\omega }_{\text{md}}$. The responsivities $\Re =\Delta \omega /\Delta m$ were measured under the intrinsic and phonon lasing conditions of the designed OMC cavity so as to experimentally evaluate the influence of the optical spring effect, as shown in Fig. 4c. The black and red circles represent the measured mechanical frequency shift $\Delta {\omega }_{\mathrm{m}}$ under the condition that the input laser is far away from the cavity resonance (intrinsic mechanical vibration) and after phonon lasing for different deposited masses, respectively. The black and red dashed lines correspond to the linear fittings with responsivities of −154.0 and −154.1 MHz fg⁻¹, wherein the negative sign indicates a decreasing mechanical frequency when the mass is deposited on the cavity. These two sets of data are consistent with each other and demonstrate that the optical spring effect-induced mechanical frequency deviation ${\omega }_{\text{md}}$ can be neglected in the proposed phonon lasing enhanced mass sensing approach in the OMC cavity. Therefore, the deposition-induced mechanical frequency shift under phonon lasing is approximately equal to the intrinsic mechanical frequency shift (i.e. $\Delta {\omega }_{\mathrm{m}}\approx \Delta {\omega }_{\text{mi}}$) and can be used to directly determine the mass of the added mass Δm. It is found that the optical spring effect-induced mechanical frequency deviation ${\omega }_{\text{md}}$ can be neglected in the proposed sensing approach (see the detailed theoretical analysis in Supplementary Notes 5), in which the calculated optical spring-induced frequency deviation was no more than 3% relative to the deposited mass-induced frequency shift.

Finally, the sensing resolution was analyzed. The mechanical linewidth is narrowed from 4.2 MHz to its phonon lasing value of approximately 5 kHz by applying Lorentzian fitting to the spectra, as shown in Fig. 4a and Fig. 4b, respectively. It is evident that the experimentally resolvable frequency shift can be significantly improved after phonon lasing, and the mechanical linewidth can be narrowed to approximately 10 kHz even after deposition. The minimum detectable mass is predicted to be $\Delta m_{\text{res}}=\Delta {\omega }_{\text{res}}/\Re \sim 65\text{zg}=6.5\times 10^{-20}\mathrm{g}$ based on the responsivity $\Re$ and 3 dB resolvable linewidth $\Delta {\omega }_{\text{res}}$. This high-resolution is an order of magnitude higher than those estimated using the reported routine approaches with Allan deviation³⁰.

Furthermore, the Allan deviation⁴² is also used for the characterization of the frequency stability and analysis of the sensing resolution uncertainty (see details in Supplementary Note 6) in the current work. The Allan deviation of the fundamental mechanical mode after phonon lasing is shown in Fig. 5 with a minimum deviation of 5.8 kHz, which allows for a resolution uncertainty of 38 zg. With this, the resolution of the proposed phonon lasing enhanced ultra-high-sensitive mass sensing in the order of tens of zeptograms is possible for practical applications, which sheds light on on-chip mass sensing components.

In this study, a phonon lasing enhanced ultra-high-sensitivity mass sensing system was put forward, which describes the direct relationship between the measured mechanical frequency shift $\Delta {\omega }_{\mathrm{m}}$ and the added mass Δm under ambient conditions. The validity of the method adopted in the current work was experimentally verified by depositing masses with different weights on the cavity and measuring the corresponding sensing responsivity of the cavity in the range of intrinsic mechanical vibration and phonon lasing. Moreover, the mechanical frequency deviation caused by the optical spring effect can be neglected due to the fact that the measured mechanical frequency shifts $\Delta {\omega }_{\text{mi}}$ and $\Delta {\omega }_{\mathrm{m}}$ coincides well with each other (i.e. $\Delta {\omega }_{\mathrm{m}}\approx \Delta {\omega }_{\text{mi}}$). In addition, the mechanical linewidth was narrowed to 10 kHz even after the deposition, and the measured Allan deviation showed a frequency stability of 5.8 kHz, thereby indicating a predicted minimum detected mass of $\Delta m_{\text{res}}\sim 65\pm 19\text{zg}$ in the experiment. This high resolution shows the potential application of the ultra-sensitive mass sensing in various fields such as biological research, gas sensing and environmental monitoring under ambient conditions.

However, one of the key limits of the proposed mass sensing method with utilizing OMC cavities is that the mechanical mode is extremely localized and the sensitivity is exquisitely dependent on the landing locations of the nanoparticles. This limit may be solved by detecting the mechanical frequency change of multi-modes^31,43,44 in the OMC cavities, which also show different mode distributions with various responses for the landing locations, thus making it possible for position detection⁴⁵. Another limit of this study is that the deposited mass is not calibrated experimentally in the current work, and a parallel time-of-flight mass spectrometer may be employed in the further experiments for this purpose⁷. Another sensing limit of the method with using phonon lasing of the OMC cavities is that it is difficult to be used in the liquid sensing where the phonon lasing is difficult to be achieved. What's more, the Allan deviation can be further improved to decrease the uncertainty of the sensing in the work by introducing multimode phonon lasing⁴⁶.

The optomechanical cavity in the current work is a larger-center-hole OMC cavity. The periodic unit cell of OMC exhibits the width of 550 nm, lattice constant of 365 nm, the height of 220 nm and diameter of center hole of d0=204nm. In the defect unit cells, the diameters of center holes vary with $d_i=d_0+i(d_7-d_0)/7,i=0,1,\cdots ,7$ and $d_7=256.5\text{nm}$. The designed structure was fabricated on a 220 nm thick silicon-on-insulator (SOI) wafer with a 3 µm buried oxide layer. The pattern was defined using the electron beam lithography (EBL) and transferred to the 220 nm silicon layer by inductively coupled plasma (ICP) etching. A buffered hydrofluoric acid (HF) solution was adopted for wet etching to remove the buried oxide layer beneath the nanobeam and release it for further measurements. In the experiment of mass sensing, the silica for mass sensing was deposited by focused ion beam (FIB).

Supplementary materials Supplementary material associated with this arti- cle can be found, in the online version, at doi: 10.1016/j.chip.2023.100050.

Funding The National Natural Science Foundation of China (Grant No. U22A6004); The National Key Research and Development Program of China (2022YFF1501600, 2018YFB2200402).

Acknowledgments K.C. and F.P. contributed equally to this work. K.C. and F.P. conceived the study. K.C., F.P., and Z.C. performed the theoretical analysis, K.C. and Y.H. supervised the project and advised the device optimization, F.P. and G.B. conducted the sensing experiments, F.P., K.C., and N.W conducted the precision analysis and experiments, F.P. and Z.H conducted the experimental setup. K.C. and F.P. composed the paper, X.F., F.L., W.Z. and Y.H. discussed the results and reviewed the manuscript. The authors would also like to express their sincere gratitudes to the Innovation Center of Advanced Optoelectronic Chip, Institute for Electronics and Information Technology in Tianjin, Tsinghua University for their help with the fabrication of the device.

Data availability Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Declaration of Competing Interest The authors declare no competing interests.