Atomic monolayer deposition on the surface of nanotube mechanical resonators
Alexandros Tavernarakis, Julien Chaste, Alexander Eichler, Gustavo Ceballos, Maria Carmen Gordillo, Jordi Boronat, Adrian Bachtold
aa r X i v : . [ c ond - m a t . m e s - h a ll ] A p r Atomic monolayer deposition on the surface of nanotubemechanical resonators
A. Tavernarakis, J. Chaste, ∗ A. Eichler,
1, 2, † G.Ceballos, M. C. Gordillo, J. Boronat, and A. Bachtold
1, 2 ICFO - Institut de Ciencies Fotoniques,Mediterranean Technology Park, 08860 Castelldefels, Barcelona, Spain Institut Catal`a de Nanotecnologia, Campus de la UAB, E-08193 Bellaterra, Spain Departamento de Sistemas F´ısicos,Qu´ımicos y Naturales, Universidad Pablo de Olavide,Carretera de Utrera, km 1, E-41013 Sevilla, Spain Departament de F´ısica i Enginyeria Nuclear,Universitat Polit`ecnica de Catalunya,B4-B5 Campus Nord, 08034 Barcelona, Spain
Abstract
We studied monolayers of noble gas atoms (Xe, Kr, Ar, and Ne) deposited on individual ultra-clean suspended nanotubes. For this, we recorded the resonance frequency of the mechanical motionof the nanotube, since it provides a direct measure of the coverage. The latter is the number ofadsorbed atoms divided by the number of the carbon atoms of the suspended nanotube. Monolayersformed when the temperature was lowered in a constant pressure of noble gas atoms. The coverageof Xe monolayers remained constant at 1/6 over a large temperature range. This finding revealsthat Xe monolayers are solid phases with a triangular atomic arrangement, and are commensuratewith the underlying carbon nanotube. By comparing our measurements to theoretical calculations,we identify the phases of Ar and Ne monolayers as fluids, and we tentatively describe Kr monolayersas solid phases. These results underscore that mechanical resonators made from single nanotubesare excellent probes for surface science.
PACS numbers: 68.43.-h, 62.25.Jk, 81.07.DeKeywords: √ × √ n, m ), namely when ( n − m ) / − mbar range. We prepared the nanotube by thoroughly current annealing it inorder to remove contamination from the surface. The monolayer of Xe was found to be themost robust phase. Its coverage remained constant at 1/6 over a large temperature range,indicating the formation of a √ × √ ∼ · − mbar. Thenanotube was cleaned by current annealing. Noble gas atoms were dosed from a room-temperature supply with a pinhole microdoser. We studied 3 nanotubes yielding similarresults. We discuss in the following the data for one device. Data for a second device areshown in Supplementary Material, Sec. VIII.Monolayers of noble gas atoms formed on the nanotube when the temperature ( T ) waslowered while keeping a constant pressure of noble gas in the cryostat chamber. The for-3ation was monitored by measuring the resonance frequency f (that is, by continuouslyrecording the response of the nanotube resonator to the driving frequency). Figure 1(d)shows prominent jumps of f to lower frequencies upon lowering T (see arrows), indicat-ing the sudden adsorption of a large quantity of atoms onto the nanotube. For comparison,when we did not dose atoms, the temperature dependence of f is weak and monotonic (greycurve labeled “pristine” in Fig. 1(d)). This weak dependence is attributed to the thermalexpansion of the electrodes which modifies the spring constant of the nanotube resonator[17]. The coverage at T is extracted using ϕ ( T ) = N ads ( T ) N C = m C m ads " A · f ( T ) f ( T ) ! − , (1)where N C is the number of C atoms of the suspended nanotube, N ads is the number ofadsorbed atoms on the nanotube, and m C and m ads are the atomic masses of carbon andadsorbed atoms, respectively. Here, f is the resonance frequency when dosing atoms foradsorption, and f is the resonance frequency when not dosing atoms and keeping the nan-otube pristine. The constant A is introduced to account for variations in the spring constantbetween the measurement of f ( T ) and that of f ( T ); indeed, the spring constant can bedifferent, if for instance the gate voltage applied in the measurement of f ( T ) differs fromthat of f ( T ) (Supplemental Material, Sec. IV). The constant A is fixed so that ϕ = 0 athigh T . In Eq. 1, we assume that the spring tension is insensitive to the tension inducedby the interaction between noble gas atoms, which is two orders of magnitude weaker thanthat of covalent C-C bonds [7].Figure 2(a) shows the temperature dependence of the coverage while dosing Kr atoms.Above a characteristic temperature T c ≃
48 K, the coverage remains at zero. On loweringtemperature, the coverage jumps to ϕ ≃ / T ≃
26 K.This behavior can be accounted for by the balance of atoms impinging on and departingfrom the nanotube. For
T > T c , an impinging atom departs very rapidly from the nanotube,so that the number of adsorbed atoms remains close to zero (Fig. 1(e)). For T < T c , itis energetically favourable for the atoms to stay on the nanotube (Fig. 1(f)) – the atomsforming a layer with ϕ ≃ /
6. This layer is likely a monolayer, because the coverage ϕ ≃ / T << T c , the coverage gets larger than ϕ = 1 /
6, indicatingthat Kr atoms start to form the second layer. The coverage grows in a monotonic way4ithout any additional plateaus even when the coverage gets larger than one (SupplementaryMaterial, Sec. VII). The absence of additional plateaus above ϕ = 1 / ϕ ≃ / ◦ C under vacuum for two days to reach a basepressure of ∼ · − mbar. We again measured the coverage upon lowering T while dosingKr atoms. Fig. 2(b) shows that T c is much lower than before, and the coverage at T . T c issignificantly lower than 1/6. We had to anneal the nanotube with a current of ∼ µ A inorder to recover the same measurement as in Fig. 2(a). These measurements suggest thatthe growth of monolayers is extremely sensitive to contamination, since a simple exposureto air prevents the formation of homogeneous monolayers. Another advantage of currentannealing is that it brings the nanotube back to its pristine state after the adsorption ofnoble gas atoms on its surface.We grew different monolayers on the nanotube by dosing Xe, Kr, Ar, and Ne (Fig. 3).The nanotube surface was cleaned by current annealing before each growth. Upon decreasingtemperature, the coverage increases rapidly from 0 to a plateau with ϕ ≃ /
6, indicating thegrowth of the monolayer. The characteristic temperature of the monolayer growth dependson the atomic species; T c is higher when the atomic mass is larger (Fig. 3). We attribute theorigin of the variation of T c to the polarizability of the atomic species and the van der Waalsinteraction between the atom and the nanotube; the polarizability and the interaction bothincreasing with the atomic radius. We also carried out experiments where we evaporated themonolayers from the nanotube by continuously increasing the temperature of the cryostatfrom 4 to ∼
100 K. The coverage jumped from ≃ / ∼
10 K higher than T c (Supplemental Material, Sec. V).We measured the time of the growth of monolayers from ϕ = 0 to ϕ = 1 / T c varies from one measurement to the next. However, the plateau incoverage at 1 / T (Fig. 4(b)).We now discuss the nature of the monolayers of Xe, Kr, Ar, and Ne. For this, wecarried out theoretical calculations to predict whether the solid phases are commensurateor incommensurate in the limit of zero temperature. In addition, we estimated the meltingtemperature of the different solid phases. To this end, we performed a series of Monte Carlosimulations relying on standard interatomic potentials between noble gas atoms and thecarbon atoms of the nanotube (Supplementary material, Sec. IX). This microscopic studywas carried out for nanotubes with diameters in the range 21–38 ˚A, which covers the typicaldiameters obtained with our chemical vapor deposition recipe.Our experimental findings indicate that Xe monolayers are commensurate solids. Firstly,the coverage of the monolayer is 1 /
6. Secondly, the coverage remains at this value over alarge temperature range. This robustness suggests that Xe atoms are strongly bound tothe underlying carbon surface, as it is the case for commensurate solids. Our experimentalresults are accounted for by our theoretical calculations, which predict that the solid is aregistered √ × √ ∼
80 K, which is consistent with the melting temperature measured inFig. S4.Monolayers of Ar and Ne are less stable, since the measured coverage depends significantlyon temperature for T . T c . Our calculations reveal that in the limit of zero temperature Arand Ne monolayers are incommensurate solids with coverages 0.265 and 0.403, respectively.The measured coverages at T . T c are much lower than these predicted values, suggestingthat the monolayers observed experimentally are not in the solid phase. Moreover, ourcalculations show that incommensurate solids melt at temperatures as low as 5 K when thecoverage is set to the values we typically measure at T . T c . This further indicates that themonolayers of Ar and Ne observed experimentally at 25 −
35 K are in the liquid phase.As for Kr, the measured temperature dependence of the coverage is similar to that ofXe, supporting the scenario that Kr monolayers are commensurate solid phases. This resultwould be in agreement with experimental signatures of stability of a commensurate Krlayer on graphite up to quite high temperatures, T ∼
130 K [18]. However, the coverageof Kr slightly depends on temperature in the plateau region (Fig. 3), showing that Kr6onolayers are less pinned to the carbon surface than Xe monolayers. Previous theoreticalcalculations of the Kr monolayer on graphite show that corrugation effects are extremelyimportant to get the √ × √ ∼ atoms, which is atiny amount of material difficult to detect with most experimental techniques used in surfacescience. The study of these monolayers was here possible, because nanotube mechanical res-onators are extremely sensitive probes. The second important aspect of our experiments isthat the nanotube surface was ultra-clean; this was achieved by thoroughly current anneal-ing the nanotube in ultra-high vacuum. These resonators made from ultra-clean nanotubesare promising for various future adsorption experiments, such as the measurement of newphase transitions emerging in the one-dimensional limit with narrower nanotubes, the inves-tigation of quantum effects of He monolayers adsorbed on nanotubes [21], the study of thediffusion of adsorbed atoms over the resonator surface which is a topic of increasing interest[22], and the interplay between the strong mechanical nonlinearities of nanotubes [14, 23–25]and the diffusion of atoms [26–28].We thank A. Isacsson and J. Moser for discussions. We acknowledge support from theEuropean Union through the Graphene Flagship (604391), the ERC-carbonNEMS project,and a Marie Curie grant (271938), the Spanish state (MAT2012-31338), and the Catalangovernment (AGAUR, SGR). C. G. and J. B. acknowledge partial financial support from theJunta de de Andaluc´ıa Group PAI-205, Grant No. FQM-5987, MICINN (Spain) Grants No.FIS2010-18356 and FIS2011-25275, and Generalitat de Catalunya Grant 2009SGR-1003. ∗ Present address: CNRS, Laboratoire de Photonique et de Nanostructures, UPR20, route deNozay, 91460 Marcoussis, France † Present address: Department of Physics, ETH Zurich, Schafmattstrasse 16, 8093 Zurich, witzerland.[1] A. Dillon, K. Jones, T. Bekkedahl, C. Kiang, D. Bethune, and M. Heben, Nature , 377(1997).[2] W. Teizer, R. Hallock, E. Dujardin, and T. Ebbesen, Physical Review Letters , 5305 (1999).[3] H. Ulbricht, J. Kriebel, G. Moos, and T. Hertel, Chemical Physics Letters , 252 (2002).[4] W. Shi and J. K. Johnson, Physical Review Letters , 015504 (2003).[5] J.-C. Lasjaunias, K. Biljakovi´c, J.-L. Sauvajol, and P. Monceau, Physical Review Letters ,025901 (2003).[6] H. Ulbricht, R. Zacharia, N. Cindir, and T. Hertel, Carbon , 2931 (2006).[7] Z. Wang, J. Wei, P. Morse, J. G. Dash, O. E. Vilches, and D. H. Cobden, Science , 552(2010).[8] H.-C. Lee, O. E. Vilches, Z. Wang, E. Fredrickson, P. Morse, R. Roy, B. Dzyubenko, andD. H. Cobden, Journal of Low Temperature Physics , 338 (2012).[9] J. Chaste, A. Eichler, J. Moser, G. Ceballos, R. Rurali, and A. Bachtold, Nature Nanotech-nology , 301 (2012).[10] H.-Y. Chiu, P. Hung, H. W. C. Postma, and M. Bockrath, Nano Letters , 4342 (2008).[11] B. Lassagne, D. Garcia-Sanchez, A. Aguasca, and A. Bachtold, Nano Letters , 3735 (2008).[12] K. Jensen, K. Kim, and A. Zettl, Nature Nanotechnology , 533 (2008).[13] L. W. Bruch, M. W. Cole, and E. Zaremba, Physical adsorption: forces and phenomena(Clarendon Press Oxford, 1997).[14] A. Eichler, J. Moser, J. Chaste, M. Zdrojek, I. Wilson-Rae, and A. Bachtold, Nature Nan-otechnology , 339 (2011).[15] A. K. Huttel, G. A. Steele, B. Witkamp, M. Poot, L. P. Kouwenhoven, and H. S. van derZant, Nano Letters , 2547 (2009).[16] V. Gouttenoire, T. Barois, S. Perisanu, J.-L. Leclercq, S. T. Purcell, P. Vincent, and A. Ayari,Small , 1060 (2010).[17] J. Chaste, M. Sledzinska, M. Zdrojek, J. Moser, and A. Bachtold, Applied Physics Letters ,213502 (2011).[18] E. D. Specht, A. Mak, C. Peters, M. Sutton, R. J. Birgeneau, D. L. D’Amico, D. E. Moncton,S. E. Nagler, and P. M. Horn, Z. Phys. B , 347 (1987).[19] G. Vidali and M. W. Cole, Phys. Rev. B , 6736 (1984).
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20 40 60 80050100150 pristineNeXeTemperature (K)(d) (b) f ( M H z ) drain(a)(c) T
FIG. 1: (a) Growth of an atomic monolayer on a nanotube. (b) Schematics of monolayers in thesolid phase that are commensurate (top) and incommensurate (bottom) with the carbon substrate.The adsorbed atoms are represented by red spheres, whereas the carbon surface is depicted bythe honeycomb lattice. (c) Layout of the nanotube resonator. (d) Resonance frequency uponlowering temperature while dosing Xe and Ne using a pinhole micromanipulator. The curve labeled“pristine” corresponds to the T dependance of f when we do not dose atoms. The pressure is3 · − mbar for the Xe and the Ne measurements and 3 · − mbar for the pristine measurement.(e,f) Schematics showing the balance of atoms impinging on and departing from the nanotube aboveand below the characteristic temperature T c .
10 20 30 40 50 6000.10.20.30.40.5 Temperature (K) C o v e r a g e C o v e r a g e (b)(a) Kr, before annealingKr, after annealing
FIG. 2: (a) Coverage upon dosing Kr atoms while lowering the temperature T with a rampingrate 0 .
016 K / s. (b) Same measurement recorded before having current annealed the nanotube witha T ramping rate 0 .
033 K / s. The pressure is 3 · − mbar for both measurements. C o v e r a g e C o v e r a g e C o v e r a g e C o v e r a g e Temperature (K)0 20 40 60
ArKrXeNe
FIG. 3: Coverage upon lowering temperature while dosing Xe, Kr, Ar, and Ne atoms. The pressureis 3 · − mbar for all measurements. The T ramping rate is 0 .
008 K / s for the Xe measurementand 0 .
016 K / s for the other measurements. The black line corresponds to ϕ = 1 /
20 40 60 800 C o v e r a g e Temperature (K) C o v e r a g e (b)(a) Temperature (K)
Xe Ne
FIG. 4: (a) Coverage upon lowering temperature while dosing Xe atoms. The pressure is 7 · − ,3 · − , and 3 · − mbar, and the T ramping rate is 0 . . .
008 K / s for the blue,green, and red lines, respectively. (b) Coverage upon lowering temperature while dosing Ne atoms.The pressure is 3 · − mbar for all three measurements, and the T ramping rate is 0 .
016 K / s forthe blue and the green lines and 0 .
008 K / s for the red line.s for the red line.