Mass sensing for the advanced fabrication of nanomechanical resonators
G. Gruber, C. Urgell, A. Tavernarakis, A. Stavrinadis, S. Tepsic, C. Magen, S. Sangiao, J. M. de Teresa, P. Verlot, A. Bachtold
MMass sensing for the advanced fabrication ofnanomechanical resonators
G. Gruber, † C. Urgell, † A. Tavernarakis, † A. Stavrinadis, † S. Tepsic, † C.Magén, ‡ , ¶ S. Sangiao, ‡ , ¶ J. M. de Teresa, ‡ , ¶ P. Verlot, § and A. Bachtold ∗ , † † ICFO – The Institute of Photonic Sciences, Av. Carl Friedrich Gauss 3, 08860 Castelldefels(Barcelona), Spain ‡ Instituto de Ciencia de Materiales de Aragón (ICMA), Universidad de Zaragoza-CSIC, 50009Zaragoza, Spain ¶ Laboratorio de Microscopías Avanzadas (LMA), Instituto de Nanociencia de Aragón (INA),Universidad de Zaragoza, 50018 Zaragoza, Spain § School of Physics and Astronomy - The University of Nottingham, University Park, NottinghamNG7 2RD, United Kingdom
E-mail: [email protected]
Abstract
We report on a nanomechanical engineering method to monitor matter growth in real timevia e-beam electromechanical coupling. This method relies on the exceptional mass sens-ing capabilities of nanomechanical resonators. Focused electron beam induced deposition(FEBID) is employed to selectively grow platinum particles at the free end of singly clampednanotube cantilevers. The electron beam has two functions: it allows both to grow materialon the nanotube and to track in real time the deposited mass by probing the noise-driven me-chanical resonance of the nanotube. On the one hand, this detection method is highly effectiveas it can resolve mass deposition with a resolution in the zeptogram range; on the other hand, a r X i v : . [ phy s i c s . a pp - ph ] J a n his method is simple to use and readily available to a wide range of potential users, since itcan be operated in existing commercial FEBID systems without making any modification. Thepresented method allows to engineer hybrid nanomechanical resonators with precisely tailoredfunctionality. It also appears as a new tool for studying growth dynamics of ultra-thin nanos-tructures, opening new opportunities for investigating so far out-of-reach physics of FEBIDand related methods. Keywords: Mechanical resonators, NEMS, nanofabrication, mass sensing, carbon nanotube, elec-tron microscopyNanomechanical devices are exquisite sensors of mass deposition and external forces.
Thesesensing capabilities enabled advances in mass spectrometry, surface science, scanningprobe microscopy, and magnetic resonance imaging.
The highest sensitivity is achievedwith carbon nanotube resonators because of their tiny mass compared to the other operationalmechanical resonators. However, a general challenge with such small transducers is to providethem with a physical function, which can be e.g. magnetic, chemical, or optical. Conventionalnanofabrication processes, such as electron-beam lithography and reactive-ion etching, are diffi-cult to employ with such small suspended structures without altering their sensing capabilities.Developing new methods to engineer nanoscale resonators with high precision and providing themwith a specific functionality is in high demand as it would enable a whole range of new technolog-ical and scientific applications.In this work we report a nanofabrication method enabling ultra-sensitive, versatile functional-ization of carbon nanotube resonators inside a scanning electron microscope (SEM). Usingfocused electron beam induced deposition (FEBID), we report the mass-controlled growthof Pt particles on carbon nanotube nanomechanical sensors, enabling their optomechanical fun-cionalization. The deposited mass is tracked in real time by monitoring frequency changes of thenoise-driven oscillations of the nanotube resonator. Measuring the nanomechanical vibrations re-lies on e-beam electromechanical coupling and is accomplished using the same electron-beam2 a) Electron gunGas injectionsystemNanotubeSE detectorSpectrum analyzerSi chip Particle growthSE µm =44(2) nm th σ beforeafter − −
100 0 100 2000246 x (nm) I SE ( a . u . ) beforeafter (c)(b)(d) (e) R = 1.98 fg/s dep (f) t (s) f r e s ( k H z ) t (s) ∆ m ( f g ) G I S s t a r t B e a m s t o p G I S s t a r t B e a m s t o p 𝜏 =0.22 s int BW =3 kHz
240 250 26000.511.52 f (kHz) S xx ( a . u . ) Figure 1: (a) Schematic of the setup: The electron beam is set on the apex of the suspendednanotube cantilever, creating a secondary electron (SE) current, which is detected and fed into aspectrum analyzer. Using the gas injection system (GIS) a nanoparticle is grown on the nanotube,resulting in a shift of the observed resonance frequency. (b) SEM images of a nanotube before andafter the deposition of a particle, with 3x magnified view of the apex (right side). (c) Profiles ofthe SE current I SE along the dashed lines marked in (b) with Gaussian fits (solid lines). (d) Typicalresonance signal used to count the resonance frequency. (e) Monitoring of the resonance frequencyduring the deposition; at t ≈ t ≈
11 s it was closed and thebeam exposure stopped. (f) Deposited mass determined from (e) using Eq. 3.as that used for FEBID. We demonstrate the high sensitivity and versatility of this method, whichenables us to address mass changes over more than six orders of magnitude, with a resolution downto the zg range.The samples consist of carbon nanotubes grown via chemical vapor deposition on silicon sub-strates. The nanotubes stick to the surface due to Van der Waals forces. Some nanotubes extendover the substrate edge, forming cantilevers. We used cantilevers with lengths between 1 µm and15 µm and spring constants between 10 − N/m and 2 . × − N/m in order to investigate the ro-bustness of our method.All SEM and FEBID experiments were conducted in a Zeiss Auriga field emission electronmicroscope equipped with a gas injection system (GIS). The acceleration voltage of the electronbeam was 5 kV and the typical beam current was 200 pA. The precursor gas was methylcyclopen-tadienyl(trimethyl)platinum(IV) in order to grow a Pt deposit onto the sample surface when illu-minated by the electron beam. All the experiments reported below have been completed with theGIS nozzle being placed ≈
500 µm above the substrate.3 schematic of the experimental setup used for the deposition experiments is depicted in Fig.1(a). The electron beam is set onto the apex of the nanotube in spot mode while monitoringthe secondary electron (SE) current I SE . The signal is displayed in the frequency domain viafast Fourier transform (FFT). The data are real-time processed using a fast peak-search customcomputer program, enabling us to extract the mechanical resonance frequency at a rate betweentypically 0.5 Hz and 5 Hz.Figure 1(b) shows a nanotube before and after the deposition process with the deposited par-ticle clearly visible. Furthermore, the free end of the nanotube appears blurred due to the motionfluctuations. The spring constant k can be extracted from the variance of the displacement σ using the equipartition theorem k = k B T σ (1)where k B is the Boltzmann constant and T is the temperature. Figure 1(c) shows the SE cur-rent profiles taken along the dashed lines marked in Fig. 1(b) before and after the deposition withGaussian fits to determine σ . The resulting spring constant k = . ( ) × − N/m is the same inboth cases. This shows that k is not affected by the deposition process and any permanent changesin the mechanical resonance frequency are consequently associated with mass deposition (see fur-ther discussion below). Specific care was dedicated to avoid broadening of the observed peak byback-action phenomena during imaging. This was achieved by averaging multiple frames usingthe fastest scanning speed (122 ms/frame).The mass of the Pt particle is monitored in real time during its formation. This is done bycontinuously acquiring the resonance spectrum of the noise-driven vibrations of the nanotube withthe electron beam. We typically use high resolution bandwidth settings in order to enable a highsampling rate. Figure 1(d) shows a typically obtained signal used to count the frequency for themass detection. The resolution bandwidth of the measurement in this case was BW = f res relates to the effective mass m ∗ of the mechanical eigenmode via theequation: f res = π (cid:114) km ∗ . (2)4igure 1(e) shows the evolution of f res over time. Here, the GIS nozzle was opened at t ≈ f res decreases over time, which is the expected evolution in presence of mass adsorption.The deposition was limited to the apex of the nanotube, such that the spring strength can be rea-sonably assumed to remain unchanged. Therefore, the deposited mass ∆ m ( t ) yields to a frequencyshift, independent from the shape of the eigenmode: ∆ m ( t ) = k π (cid:32) f , t − f , (cid:33) (3)where f res , t and f res , are the resonance frequencies measured during the deposition at time t andprior to the deposition, respectively. In the limit of high signal-to-noise ratio, themass determination does weakly depend on the SE emission rate. Additionally, we performedoptomechanical measurements in order to gain independent confirmation of the post-depositionmechanical properties (Section 2 of Supporting Information). These measurements ensure that theelectromechanical coupling has negligible impact on the mechanical resonance frequency and thatthe observed changes are due to mass deposition.Figure 1(f) displays the corresponding evolution of the deposited mass over time. After sometransient regime, the deposition becomes linear in time, allowing us to extract the deposition rate R dep = .
98 fg/s from a linear fit. At t ≈
11 s the GIS valve was closed and the beam exposure wasstopped to avoid spurious growth. The resonance frequency at the end was f res = . ( ) kHz andthe total mass of the particle seen in Fig. 1(b) is ( . ± . ) fg. Optomechanical measurementsof this resonator yield to a post-deposition mechanical resonance frequency f = .
04 kHz with5 − D epo s i t ed m a ss ( ag ) Deposition rate (zg/s) R = 0.34 fg/s dep R = 0.93 ag/s dep R = 5.8 zg/s dep
1 µm500 nm500 nm (a) t = s d e p t = m i n d e p (b)(c)(d) t (s) ∆ m ( f g ) t (s) ∆ m ( ag ) t (s) ∆ m ( z g ) Figure 2: (a) Deposition rate and deposited mass for all the fabricated devices, with depositiontimes t dep in the range between 1 s and 10 min. The different operation modes are marked bydifferent colors, and exemplary measurements are shown in (b)-(d). (b) Mass deposition in defaultGIS operation mode (GIS nozzle open, precursor in the chamber at a pressure in the range of p =( − ) × − mbar). (c) Mass deposition in low-pressure mode (GIS nozzle closed, precursorresiduals in the chamber with p = ( − . ) × − mbar). (d) Mass deposition in the backgroundvacuum regime (after more than 24 h of pumping, p = ( . − ) × − mbar). The SEM imageson the right show each nanotube before and after the deposition. The spring constants determinedbefore and after the deposition are k = . ( ) × − N/m for (b), k = . ( ) × − N/m for (c),and k = . ( ) × − N/m for (d).a quality factor Q ≈ These include the focus of the electron beam, the temperature of the substrate,the temperature and flux of the precursor molecules, and the pressure of residual gas in the cham-6er. The deposition rate is also affected by the amplitude of the nanotube vibrations, since theamplitude can be larger than the electron-beam diameter, resulting in a net decrease of the effec-tive deposition cross-section. The different GIS operation modes as well as illustrative results arediscussed in the following.We start with the default operation mode of the GIS, which was also used for the measurementsin Fig. 1. When the nozzle is opened the precursor gas is released into the chamber resultingin a strong increase of the chamber pressure. The pressure typically saturates in the range p =( − ) × − mbar, while the background vacuum pressure is typically ≈ × − mbar. Itresults in measured deposition rates between 0 .
28 fg/s and 11 fg/s. Figure 2(b) shows a typicalmeasurement in this operation mode, demonstrating a constant deposition rate R dep = .
34 fg/sover a time as long as 50 s. The deposited mass is more than 30 times larger than the initiallymeasured mass of the nanotube cantilever.We explored lower Pt deposition rates by reducing the pressure. This is achieved by firstpurging the GIS nozzle with precursor molecules and then pumping the chamber for severalminutes. As such, we investigated deposition of precursor molecules in a pressure range p =( − . ) × − mbar resulting in observed deposition rates ranging between 0 .
93 ag/s and 8 . R dep = .
93 ag/s isequivalent to roughly 2900 Pt atoms or 1800 precursor molecules per second.The lowest deposition rates were attained by pumping the chamber for more than 24 h with theGIS nozzle closed and heated so residual precursor molecules could desorb from the nozzle andbe pumped away. It is assumed that in this regime the chamber gas is predominantly composed oforganic molecules resulting in e-beam deposition of amorphous carbon. The base pressure in thisbackground vacuum regime was in the range p = ( . − ) × − mbar and the observed deposi-tion rates were between 5 . R dep = . c) (d) T h i c k n e ss ( n m )
50 nm x (nm) y ( n m ) Shell 200 nm 200 nm (a) (b)
Figure 3: (a) and (b) SEM images of a nanotube before and after the deposition of a particle with amass m dep = .
33 fg determined by the resonance frequency measurement. (c) High-angle annulardark-field (HAADF) STEM image of the particle. The visible darker shell is likely the result ofthe subsequent manipulation of the nanotube with the electron beam (see text). (d) Thickness mapof the particle determined by low-loss EELS using the elemental composition of Table 1 and thelog-ratio method. results in an effective mass resolution of 13 zg. This estimation includes the spurious contributionof the deposition of C atoms, so that it represents an upper bound of the mass resolution of thenanotube resonator. The deposited mass of 330 zg does not result in a distinctive feature on thenanotube in the SEM images. In this case, the electromechanical measurement enables us to re-veal the evolution of the structure that is totally invisible in the SEM image. Besides controllingthe growth process, this demonstrates the relevance of e-beam electromechanical coupling as apowerful complementary embedded tool to scanning electron microscopy.We assessed the material density of a Pt particle and its chemical composition by carryingout scanning transmission electron microscopy (STEM) measurements. The experiments wereperformed using a C s -corrected FEI Titan transmission electron microscope equipped with a FEI X-FEG high brightness Schottky emitter. The acceleration voltage was 80 kV. Chemical analysis wasconducted via energy-dispersive x-ray spectroscopy (EDXS) using an EDAX detector. Thicknessmeasurements were performed by electron energy loss spectroscopy (EELS) employing a GatanTridiem 866 ERS energy filter.A nanotube grown on a STEM copper grid is shown in Figs. 3(a) and (b) before and afterdepositing a mass of 1 .
33 fg. In a subsequent deposition step the nanotube was coated with materialdown to the clamping point to minimize the effects of motion fluctuations. During this step weavoided exposing the particle directly to the electron beam. Figure 3(c) displays a high-angle8nnular dark-field (HAADF) image recorded in the STEM and reveals a core-shell structure. Theshell appears darker than the core, suggesting that it has a lower density or a lower relative Ptcontent than the core particle. It is likely that the shell was formed during the second depositionstep and the growth induced by secondary electrons. Previous FEBID works showed that Pt atomsassemble together to form nanometer-scale clusters inside an amorphous C matrix. Table 1: Atomic fraction and mass fraction of C, Pt, and O determined by EDXS measurements ofthe particle in Fig. 3(c).Element Atomic fraction ( % ) Mass fraction ( % ) Carbon 84.6 41.5Oxygen 8.8 5.8Platinum 6.6 52.7The particle composition was determined by EDXS measurements (Table 1). The observedoxygen content is attributed to the air molecules that diffuse into the particle during the transfer ofthe device from the SEM to the STEM. The atomic C:Pt ratio determined by EDXS is 12.8:1. Thisratio is somewhat larger than the value 8:1 reported previously, suggesting additional amorphouscarbon deposition in our experiment, especially during the second deposition step.Next, we conducted spatially-resolved low-loss EELS measurements to map the particle thick-ness (Fig. 3(d)). The thickness at each point of the map was determined via the log-ratio methodusing the electron inelastic mean free path determined by the elemental composition in Table 1. We obtain the volume V = . × − cm for the particle core by integrating the thickness overthe map surface, and by subtracting the volume of the 6 nm thick shell. This results in the den-sity ρ (cid:39) .
44 g/cm for the particle core using the mass 1 .
33 fg. With this result we are able toestimate the density of the amorphous C-matrix ρ C = ( ρ − ξ ρ Pt ) / ( − ξ ) where ξ is the normal-ized atomic Pt concentration in the pseudo-binary composite Pt ξ C − ξ and ρ Pt = .
45 g/cm is thebulk density of Pt. Our estimation ρ C (cid:39) .
95 g/cm compares well with low-quality amorphous(hydro-)carbon deposits, which are typically in the range ( . − . ) g/cm . The mass monitoring method opens new possibilities to study the growth of ultra-thin nanos-tructures using FEBID.
It may be applied to study how the mass deposition and the9aterial composition depend on experimental growth parameters, such as the electron beam cur-rent, the gas-injection rate, and the precursor and substrate temperature. Our technique is partic-ularly attractive to investigate transients at the beginning of the growth. The good time resolutionin the monitoring of the growth rate could be used to test different growth models, e.g. involvingvarious precursor dissociation mechanisms (triggered by primary and secondary electrons), pre-cursor coverage, or thermal effects. It may also be employed to test new precursors and to monitorpurification steps aiming to improve the material quality. Furthermore, mass monitoring using ourmethod could be applied to study the growth and the milling with a focused ion beam.In summary, we have reported a method allowing high-resolution mass monitoring of thegrowth of a Pt nanoparticle on a nanotube resonator via in situ electromechanical readout ina FEBID system. The method can be readily employed in any existing SEM or STEM setupwithout requiring any further modification. The demonstrated mass and time resolution offers aprecise control on the deposited mass to engineer nanomechanical sensors, especially since var-ious materials can be grown with FEBID.
This may lead to new advances in one- and two-dimensional magnetic force microscopy and magnetic resonance force microscopy. Our technique may also be employed with semiconducting nanowire resonators made from e.g.GaN, SiC, and InAs as well as microfabricated top-down resonators.
This work is supported by the ERC advanced Grant 692876, the Foundation Cellex, the CERCAProgramme, AGAUR, Severo Ochoa (SEV-2015-0522), the Grants FIS2015-69831-P, MAT2017-82970-C2-1-R, and MAT2017-82970-C2-2-R of MINECO, the Fondo Europeo de Desarrollo Re-gional (FEDER), and the project E13_17R from Aragon Regional Government (ConstruyendoEuropa desde Aragón). This project has received funding from the European Union’s Horizon2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No665884. P. Verlot acknowledges support from the ERC starting grant 758794 ’Q-ROOT’.Experimental help by L. Casado from the Laboratory of Advanced Microscopies (LMA) isacknowledged. 10 upporting Information AvailableNon-linearities observed via e-beam electromecnanical coupling
Figure 4 shows how the spectrum determined by e-beam electromechanical coupling evolves dur-ing the deposition of Pt on a carbon nanotube. For this measurement, spectra were recorded every ≈ .
32 s with a resolution bandwidth BW ≈ ≈
400 kHz. At eachtime step, multiple equidistantly-spaced peaks can be observed (labeled n = , , , ... Furthermore, the graph shows an increase inthe signal-to-noise ratio and peak intensities as the particle grows. This indicates an increase ofthe coupling strength of the e-beam electromechanical coupling due to a larger volume interactingwith the e-beam and a higher secondary electron (SE) yield. Furthermore, it hints towards thepresence of self-oscillations. f ( k H z ) t (s) 1010101010 -3-4-5-6-7 S ( a . u . ) II n = 1 n = 2 n = 3 n = 10 Figure 4: Evolution of the spectra recorded via e-beam electromechanical coupling during thedeposition of Pt on a carbon nanotube. 11 ptomechanical measurement of f res In order to confirm the resonance frequency f res determined by e-beam electromechanical cou-pling, we conducted optomechanical measurements. The measurement in Fig. 5 shows thethermally-driven peak with the resonance frequency f res = .
04 kHz at room temperature. Thisvalue is reasonably close to the one observed using the e-beam electromechanical coupling f res = . −14 −13 −12 f (kHz) S xx ( a . u . ) DataFit
Figure 5: Optomechanical measurement of the thermally-driven resonance peak (red) of the nan-otube shown in Fig. 1 of the main text at room temperature and Lorentzian fit (black).
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