Understanding the Effects of Surface Chemistry on Q: Mechanical

The rate of mechanical energy dissipation in 300-nm-thick, megahertz-range micromechanical silicon resonators is sensitive to single monolayer changes...
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J. Phys. Chem. B 2007, 111, 88-94

Understanding the Effects of Surface Chemistry on Q: Mechanical Energy Dissipation in Alkyl-Terminated (C1-C18) Micromechanical Silicon Resonators Joshua A. Henry, Yu Wang, Debodhonyaa Sengupta, and Melissa A. Hines* Department of Chemistry, Baker Laboratory, Cornell UniVersity, Ithaca, New York 14853-1301 ReceiVed: August 21, 2006; In Final Form: October 31, 2006

The rate of mechanical energy dissipation in 300-nm-thick, megahertz-range micromechanical silicon resonators is sensitive to single monolayer changes in surface chemistry. Resonators terminated with a single monolayer of methyl groups have significantly higher quality factors (Q’s), and thus lower mechanical energy dissipation, than comparable resonators terminated with either long-chain alkyl monolayers (C2H2n+1, n ) 2-18) or monolayers of hydrogen atoms. This effect cannot be attributed to mechanical energy dissipation within the alkyl monolayer, as a 9-fold increase in alkyl chain length does not lead to an observable increase in dissipation. Similarly, this effect is not correlated with the chemical structure of the silicon-monolayer interface (e.g., the density of Si-H vs Si-C bonds.) Instead, the chemical trends in resonator quality and stability are consistent with a dissipation mechanism involving the coupling of long-range strain fields to localized, electronically active defects in the monolayer coatings.

1. Introduction

Q)

Micromechanical resonators are excellent transducers for force or mass detection. In these applications, an applied force or adsorbed mass is detected by a small shift in the resonator’s frequency. For example, Rugar and co-workers1 recently detected the position of a single electron spin embedded in a glass surface using a tiny magnet attached to the end of an ultrasensitive silicon cantilever. The signal averaging required for this achievement is noteworthy though. Because each data point required 13 h of averaging, the published 180 nm (linear) scan must have required more than 18 days of data collection (at 1.6 K!). Clearly, for techniques such as this to achieve widespread use, micromechanical resonators with increased sensitivity are necessary. The factors governing the ultimate sensitivity of micromechanical resonant detectors have been extensively analyzed.2,3 If all things are equal (which they rarely are), nanoscale resonators are expected to be much more sensitive than larger resonators. From the standpoint of nanofabrication technology, the development of nanoscale adsorbed mass sensors with single proton sensitivity appears feasible; the nanoscale features necessary for the realization of these high-frequency devices are within the capabilities of electron-beam lithography. Indeed, resonators capable of detecting subattogram adsorbed masses have already been reported at both cryogenic4 and room temperatures.5 Nevertheless, the ultimate sensitivity of nanoscale devices also depends on a poorly controlled (and poorly understood) parameter: the quality factor (Q) of the resonator. Q is often qualitatively described as being the number of free oscillations a resonator will undergo after an impulsive excitation; it is inversely proportional to the resonator’s rate of mechanical energy loss. More rigorously, this parameter is defined to be * Corresponding author. E-mail: [email protected]. Phone: 607-255-3040. Fax: 607-255-3040.

2π∆E f ) x1 + x2 ∆E ∆f

(1)

where E is the energy stored in the resonator, ∆E is the energy dissipated per cycle, f is the resonant frequency, and ∆f is the full width at half-maximum of the (Lorentzian) resonant response. For the case of resonant mass sensors, the smallest detectable mass is proportional to Q-1/2. In general, high sensitiVity detectors require high Q resonators. As researchers have continued to push the limits of detection sensitivity, the size of micromechanical resonators has continually decreased. During this time, a number of researchers have noted a puzzling anticorrelation between resonator size and quality factorssmaller resonators almost invariably have lower Q’s, a trend that offsets the expected gains in sensitivity from decreased size. (Decreased Q cannot be attributed to viscous drag forces, as nanoscale resonators are operated in vacuum.) This trend led a number of researchers to hypothesize a connection between Q and the state of the resonator’s surface.6-9 Following up on these suggestions, we have previously shown that energy dissipation in micromechanical resonators is often dominated by the chemical state of the surface, a surprising and unexpected conclusion. By changing a single monolayer of molecules on the surface of a 5-µm-wide, 250-nm-thick silicon resonatorsless than 0.07% of the total masssthe resonator’s quality factor can be improved by at least 70%.10,11 Interestingly, resonators terminated with a thin oxide layer, which is standard for commercial silicon devices, have particularly low Qswe have shown that at least 75% of the energy in the oxide-terminated resonators is dissipated at the surface.12 In contrast, devices terminated with a single monolayer of methyl (CH3-) groups have quality factors approximately 6 times higher than our best oxide-terminated devices. Importantly, these surface-chemistry-induced mechanical energy losses scale with the device’s surface-to-volume ratio,12 implying that surface chemistry will become increasingly important as nanoscale sensor technology advances.

10.1021/jp0654011 CCC: $37.00 © 2007 American Chemical Society Published on Web 12/13/2006

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In the following, we explore the chemical origins of surfaceinduced mechanical energy dissipation by studying the quality factors of MHz-range silicon resonators terminated with alkyl monolayers of varying chain length (i.e., varying thickness). We show that mechanical energy dissipation is not due to energy losses within the monolayer. Instead, the mechanical properties of coated resonators are correlated with the chemical passivation properties of the monolayer. High-density monolayers that resist the formation of electronic defects have the best performance. Importantly, resonators terminated with these passivating monolayers are also very stable in both vacuum and air. 2. Experimental Energy in a micromechanical resonator can be dissipated through a variety of mechanisms, including direct coupling to the supporting structure (so-called clamping losses), viscous drag losses (if the resonator is operated in a fluid medium), bulk excitations, and surface losses. In general, these losses are additive, and the total rate of mechanical energy dissipation, ktot, can be written as the sum of the component rates

ktot ) kclamping + kdrag + kbulk + ksurf + ...

Figure 1. Scanning electron micrograph of 5-µm-wide suspended silicon paddle resonator.

(2)

Since Q is inversely proportional to the rate of mechanical energy dissipation, one can equivalently write

1/Q ) 1/Qclamping + 1/Qdrag + 1/Qbulk + 1/Qsurf + ... (3) As these equations make clear, the observed quality factor may be affected by many experimental parameters. To isolate the effects of surface chemistry, (nearly) identical resonators with different surface functionalizations and low intrinsic losses were compared. The 3-D structure of micromechanical resonators introduces a second complication. Because of its ease of functionalization and well studied surface chemistry, Si(111) surfaces are ideal for comparative studies of chemical effects. Unfortunately, the fabrication of a resonator terminated entirely by {111} planes is not feasible. In the following experiments, the resonator design was chosen to minimize contributions from non-{111} facets. Si{111} planes comprised 80-90% of each resonator (depending on resonator size); the remaining surfaces are nominally {110} surfaces. 2.1 Resonator Design and Mechanical Testing. Three different sizes of MHz-range micromechanical silicon resonators were fabricated from 500-µm-thick, double-side-polished, >1000 ohm cm, float-zone Si(111) wafers (miscut 3) on the same chip. 2.2 Surface Functionalization. Resonators terminated by a single monolayer of H atoms or straight-chain alkyl groups (C1C18) were studied. Two different strategies for preparing the alkyl monolayers were used. The first strategy involved the direct reaction of terminal alkenes (1-alkenes) with H-terminated silicon surfaces at elevated temperatures.13 The second involved a two-step procedure in which a H-terminated surface was first chlorinated and then the chlorinated surface was allowed to react with a Grignard reagent at elevated temperatures.14 (We have previously shown that the more common chlorosilane-based strategy for alkyl functionalization,15 which involves the production of a thin surface oxide, produces resonators with very low Q.10) Since steric effects prevent long-chain alkyl units (CnH2n+1, n g 2) from terminating every site on a Si(111) surface,16 one might expect that the two chemistries would lead to different monolayers: the alkene preparation leading to a mixture of alkyl- and H-terminated sites, and the Grignard preparation leading to a mixture of alkyl- and Cl-terminated sites. Photo-

90 J. Phys. Chem. B, Vol. 111, No. 1, 2007 emission studies show this is not the case, as no residual Cl is detected on Grignard-prepared surfaces.16 The residual Cl atoms are presumably replaced by H atoms from either the Grignard reagent or the solvent.17 The resonator fabrication process leaves the top and side surfaces of the resonator terminated with a thin thermal oxide. Prior to functionalization, the oxide-terminated samples were rigorously cleaned using a modified RCA clean as described in ref 18. The samples were then immersed in an anisotropic etchant (50% w/v KOH, Transene) at 72.2 °C for 5 min to release the suspended structures. After rinsing in ultrapure water (Millipore Milli-Q), the samples were etched in buffered oxide etch (BOE, a 5:1 mixture of NH4F:HF, Transene) at room temperature to remove the protective thermal oxide and rinsed in ultrapure water. After this procedure, all exposed silicon atoms were H-terminated. To prepare alkyl monolayers from terminal alkenes, 1-dodecene or 1-octadecene (Aldrich, 96% and 98%, respectively) was dried under vacuum over sodium for at least 48 h and distilled at reduced pressure. Freshly prepared H-terminated silicon samples were immersed in a vial of terminal alkene under inert atmosphere and heated to 200 °C for 90 min. Once cooled, the silicon samples were vigorously rinsed in CH2Cl2 (Mallinckrodt). To prepare monolayers from Grignard reagents (CnH2n+1MgX, X ) Br or Cl), H-terminated samples were evacuated in a quartz round-bottom flask and then exposed to ∼3 Torr of Cl2(g). The quartz flask was illuminated with a 254 nm pen lamp for 3 min to produce Cl radicals. (Although PCl5 is sometimes used for this reaction, we have previously shown that PCl5 leads to extensive etching of the resonators.11) After reaction, the sample was refluxed in a solution of alkylmagnesiumhalide for 2.5 h [CH3MgBr (3 M in THF, Aldrich), C2H5MgCl (3 M in THF, Aldrich)] or 40 h [C12H37MgCl (1 M in diethyl ether, Aldrich)] under a constant flow of argon and then rinsed twice in anhydrous methanol and once in ultrapure water. After functionalization, the samples were immediately loaded into the vacuum chamber for testing or into the IR spectrometer for monolayer characterization. 2.3 Surface Characterization. The chemical composition and density of the surface monolayers were probed using IR absorption spectroscopy in the multiple internal reflection (MIR) geometry. Since the functionalized resonators were too small for direct spectroscopic analysis, a larger 0.6′′ × 1.5′′ sample cut from the same batch of Si(111) wafers was co-processed with the resonator chip and then analyzed. Before functionalization, the short ends of this sample were polished to create 45° bevels. After functionalization, IR radiation from a Fourier transform IR (FTIR) spectrometer was focused onto one bevel. The radiation then underwent ∼75 surface reflections before exiting the opposite bevel. After passing through a ZnSe polarizer, the radiation was focused onto a mercury-cadmiumtelluride (MCT) detector. H-Terminated samples displayed a single sharp vibrational resonance at 2083.6 cm-1, which is characteristic of the Si-H stretch vibration on flat Si(111) terraces.19 No oxidation or hydrocarbon contamination was observed. In contrast, alkyl-terminated samples displayed characteristic absorption bands in the C-H stretch region (∼2820-2980 cm-1). The energy of the asymmetric methylene stretch vibration (∼2920 cm-1) is particularly sensitive to monolayer density and thus a useful indicator of monolayer quality. For example, the energy of this vibration typically decreases by 6-8 cm-1 as liquid alkanes crystallize. Importantly, alkyl-terminated surfaces

Henry et al.

Figure 3. MIR-FTIR spectra of two octadecyl-terminated Si(111) surfaces illustrating the sensitivity of the monolayers to contamination. The monolayer represented by the black line was formed from pure 1-octadecene, whereas the monolayer represented by the red line was formed with 1-octadecene contaminated with a common dryness indicator, benzophenone. The decreased intensity and 6 cm-1 blue shift of the asymmetric methylene stretch in the latter (denoted by dashed lines) indicate the formation of a sparse monolayer.

prepared by the alkene- and Grignard-based syntheses had nearly identical spectra; no systematic difference between the two was found. For reference, the monolayers used in the following experiments displayed asymmetric methylene stretch vibrations at 2921.2 cm-1 (dodecyl monolayers) and 2919.0 cm-1 (octadecyl monolayers), which is comparable to the best literature values. The surface monolayers were, however, exceptionally sensitiVe to chemical purity and dryness. For example, Figure 3 shows the C-H stretching region of two C18H37-terminated surfaces. One monolayer was formed from pure 1-octadecene and the other from 1-octadecene that was distilled from a solution of 1-octadecene with benzophenone added as a dryness indicators a common practice. NMR analysis of the second solution showed 8 mol % benzophenone. The decreased absorbance and pronounced (6 cm-1) blue shift of the asymmetric methylene stretch vibration in monolayers synthesized from the benzophenone-contaminated solution shows that the contaminant interferes with complete monolayer formation. 3. Results To provide a context for the following analysis, it is useful to consider what effect macroscopic mechanics might predict for alkyl-functionalized resonators. When a thin film is applied to a macroscopic resonator, mechanical losses within the film lead to a net decrease in the resonator’s Q, as suggested by eq 3. According to the spectroscopic data presented in Section 2, the surface-tethered alkyl chains have a local chemical environment similar to that of bulk alkanes. To zeroth order, the mechanical properties of the alkyl monolayers are expected to resemble those of bulk alkanes, such as paraffin. Intuitively, wax tuning forks are expected to have very low Q; it follows that paraffin thin films are expected to have high mechanical losses. The naive expectation from macroscopic mechanics is thus that alkyl monolayers will be dissipative and that increasing the thickness of the monolayers (i.e., the length of the alkyl chains) will increase dissipation (i.e., decrease Q.) What is unclear from this simple argument is the magnitude of the effect. Will the dissipation induced by mechanical losses within a single monolayer have a measurable effect on a ∼300-nm-thick, microns-wide resonator?

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Figure 4. The initial quality factors of CH3-terminated (triangles) and C12H25-terminated (squares) resonators. Two different synthetic strategies were used to prepare the alkyl monolayers: an alkene-based (open squares) and a Grignard-based (solid squares). The synthetic strategy had no systematic effect on quality factor.

In the following, we present a number of experiments that test this zeroth-order prediction and provide insight into the mechanism of chemically induced mechanical energy dissipation. 3.1. Effect of Synthetic Strategy on Mechanical Quality. In a previous study,11 we showed that silicon resonators terminated with methyl monolayers had significantly higher Q’s than comparable resonators terminated with long-chain alkyl (-C12H25 and -C18H37) monolayers. In those experiments, the methyl monolayers were synthesized using a methyl Grignard reagent, whereas the long-chain alkyl monolayers were prepared from the corresponding 1-alkenes. In the previous study, the increased Q of methyl-terminated resonators were attributed to inherent differences between methyl and long-chain alkyl monolayers; however, those experiments could not rule out the possibility that the observed differences in Q were related to the different synthetic strategies used in preparing the monolayers. To measure the effects of synthetic strategy on Q, three different sizes of silicon resonators were terminated with dodecyl monolayers using both the Grignard-based and terminal-alkenebased syntheses. As shown in Figure 4, these two synthetic strategies produced resonators with very similar quality factors. For comparison, the quality factors of comparable methylterminated devices are also shown. (Methyl monolayers can only be produced using the Grignard-based synthesis.) Although resonators functionalized with the Grignard-reagent-based chemistry gave slightly better results in this particular run, the opposite ordering was sometimes observed in replicate experiments. From this, we conclude that the two synthetic strategies produce resonators with nearly identical properties. This conclusion is consistent with the spectroscopic data, which showed no significant difference in monolayer packing or density. 3.2. Effect of Chain Length. Alkyl chain length has a dramatic effect on initial resonator quality. Figure 5a compares the quality factors of 5.2-µm-wide resonators (f ∼ 8 MHz) that were functionalized with four different lengths of alkyl monolayers (over the range C1-C18) or a monolayer of hydrogen atoms. Methyl-terminated resonators have the highest quality factors, whereas long-chain alkyl-terminated resonators have the lowest quality factors. Interestingly, over the range C2-C18, chain length has little effect on Q. In fact, a small, but reproducible, increase in Q is seen with increasing chain length, a trend that is opposite to that predicted above. This trend is seen across all resonator sizes. Figure 6 compares the relative quality of three different sizes of functionalized

Figure 5. (a) The effect of monolayer H- and alkyl-coatings on the initial quality factor of 5.2-µm-wide silicon resonators. (b) The minimum estimated fractional amount of energy dissipated at the silicon/ monolayer interface in 5.2-µm-wide resonators. This calculation would be precise if the methyl-terminated surface dissipated no energy. Otherwise, this calculation represents a lower bound.

Figure 6. The dependence of relative quality factor, Q/Qmethyl (i.e., normalized to methyl-terminated surfaces), on chain length for three different sizes of silicon resonators. Long-chain alkyl monolayers are limited to an approximately half-monolayer coverage by steric effects, as indicated by the shaded area. The average quality of all long-chain alkyl-terminated resonators is indicated by the dashed line.

resonators to comparable methyl- and H-terminated resonators. On average, the quality of long-chain-terminated resonators is less than 60% of that of comparable methyl-terminated resonators; this average value is indicated by the dashed line in Figure 6. These data conclusively show that mechanical energy dissipation within the alkyl monolayer has a negligible effect at this length scale. As shown by Figure 6, increasing the monolayer film thickness by a factor of 9 (i.e., from C2 to C18) slightly increases resonator quality. If dissipation within the film were the dominant loss mechanism, a 90% drop in quality factor would be expected, as suggested by eq 3.20 These data strongly suggest that the observed surfacechemical dependence of Q is due to energy dissipation at the silicon-monolayer interface. The five monolayer coatings studied in this experiment fall neatly into two categories based on their size. Methyl and hydrogen are both relatively small functional groups that have van der Waals radii significantly

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Henry et al.

less than the 3.8 Å distance between binding sites on the Si(111) surface. As expected, STM investigations show that both hydrogen21 and methyl22 form complete monolayers on Si(111) surfaces. In contrast, long-chain alkyl groups (CnH2n+1, n g 2) have a van der Waals radius of 4.2 Å, which prevents them from forming a complete monolayer on Si(111) surfaces. Both simulation17,23 and experiment16,24 show that these monolayers are limited to a roughly 50% packing density; the remaining sites are H-terminated. (Recent experiments suggest that surface roughness may allow ethyl monolayers to pack at a somewhat higher density.24) As can be seen in Figure 6, functionalities that result in 100% surface coverage lead to significantly higher quality factors than those with partial surface coverage. Importantly, this chemical dependence cannot be explained simply by changes in bonding at the silicon-monolayer interface. For example, if the interfacial C-Si bonds were more dissipative than interfacial H-Si bonds, the quality factors of long-chain alkyl-terminated resonators would be halfway between those of CH3- and H-terminated resonators. This is not observed. These data can be used to set a lower bound on the relative contribution of interfacial mechanical energy dissipation. If no energy is dissipated at the CH3-Si interface (the most optimistic scenario), the quality factor of methyl-terminated resonators, Qmethyl will be given by

1/Qmethyl ∝ kclamping + kbulk

Figure 7. The quality factors of methyl-terminated (triangles), Hterminated (circles), and octadecyl-terminated (squares) 5.2-µm-wide resonators as a function of time in vacuum (white region) and later air at 100% humidity (shaded region). The alkyl-terminated resonators display a slow, roughly linear decay, whereas the H-terminated resonators decay much more rapidly.

(4)

whereas the quality factor of a comparable resonator terminated by functional group X, QX, would be given by

1/QX ∝ kclamping + kbulk + kinterface,X

(5)

(6)

Figure 8. The normalized frequency shift of 5.2-µm-wide resonators as a function of time in 10-8 Torr vacuum. The steadily decreasing frequencies seen in all cases are evidence of slow adsorption from the gas phase. The total mass adsorbed is converted to effective monolayers of H2O and displayed on the right axis. The alkyl-terminated resonators display a near-linear increase in mass as indicated by the dotted line. In contrast, adsorption on the H-terminated resonators follow Langmuir kinetics, as indicated by the exponential fit (solid line).

This calculated contribution is displayed in Figure 5b. 3.3 Long-Term Stability in Vacuum and Air. The longterm stability of the functionalized resonators in vacuum and air provides an important clue to the origins of chemically induced mechanical energy dissipation. To test the effects of surface termination on stability, micromechanical resonators terminated with -CH3 and -C18H38 were prepared and immediately loaded into the high vacuum chamber for mechanical testing. Over the course of the next 70 h, the mechanical properties of the devices were periodically measured. After 70 h, the devices were removed from vacuum, placed in a sealed chamber of air at 1 atm and 100% humidity for an additional 96 h, and then retested. The results of these experiments for 5.2 µm paddles are shown in Figure 7. Similar data for H-terminated resonators, which were not taken concurrently, are included for reference. The alkyl-terminated resonators showed a small decay in quality factor during this treatment. Over the course of 1 week, both the methyl- and the octadecyl-terminated resonators decayed to 85-90% of their initial Q. These experiments were repeated on a variety of long-chain alkyl-terminated resonators (not shown) with very similar results. The magnitude of the decay was not correlated with chain length. When the resonators were stored in a sealed container (e.g., bell jar, vacuum

chamber), the rate of decay was relatively insensitive to environment. A more rapid decay was seen when the resonators were left in an open chemistry laboratory, where they were presumably subject to a steady flux of radicals. In contrast to alkyl-terminated resonators, the quality factors of H-terminated resonators decayed rapidly, even at 10-8 Torr. After only 3 days in vacuum, H-terminated resonators lost their initial quality advantage over long-chain alkyl-terminated resonators. Further exposure of the H-terminated resonators to vacuum (or H2O-saturated air) led to steadily worsening performance. Concurrent with their decay in Q, all of the functionalized resonators displayed a monotonic decrease in resonant frequency with exposure to vacuum (or H2O-saturated air), as shown by Figure 8, suggesting that background gases were slowly adsorbing on the resonator surfaces. The magnitude of this effect was strongly dependent on the exposed surface functionality. The alkyl-terminated resonators, irrespective of chain length, were highly adsorption resistant. After 62 h in vacuum, alkylterminated resonators, on average, adsorbed only 15% of the mass of comparable H-terminated resonators. The total adsorbed mass could be calculated from the frequency shift. Assuming that adsorption had no effect on resonator stiffness, the normalized frequency shift is given by

where kinterface,X is the rate of mechanical energy dissipation by interface X. In this case, the relative contribution of interface X to the total mechanical energy dissipation of the resonator would be given by

kinterface,X QX )1kclamping + kbulk + kinterface,X Qmethyl

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δf 1 δI )f 2 I

(7)

where I is the moment of inertia of the paddle and δI is the change in the moment of inertia induced by adsorption. Since the adsorbed masses are very small, they are conveniently expressed in terms of effective monolayers of a small molecule, such as H2O. For example, if H2O were adsorbing in a (1 × 1) overlayer on all exposed surfaces of the resonator, the normalized frequency shift of a hexagonal paddle12 would be

( )(

)( )

mH2O 0.314 nm 4 1 δf ) -θ + f mSi 2 D T

(8)

where θ is the fractional H2O surface coverage, mH2O and mSi are the molecular masses of H2O and Si, respectively, 0.314 nm is the spacing between Si(111) bilayers, and D and T are the width and thickness of the paddle, respectively. As shown by the right-hand axis of Figure 8, the alkyl-terminated resonators adsorb a small fraction of a monolayer, perhaps 1020% of a monolayer, during their time in vacuum, whereas the H-terminated resonators adsorb much more. These data strongly suggest that the superior quality factors of methyl-terminated resonators over long-chain alkyl-terminated resonators cannot be attributed solely to differences in the chemical resistance or passivation of the alkyl monolayers. Once formed, the monolayers show little difference in chemical reactivity, as judged by changes in resonant frequency. Also, all alkyl-terminated resonators display similar changes in Q with time; methyl-terminated resonators are not notably more stable than resonators terminated with long-chain alkyl monolayers. 4. Discussion Chemically induced mechanical energy dissipation is not a new phenomenon. Indeed, the fundamental origins of this effect have been understood in a general sense for over half a century. The surprise in these studies is the magnitude of the effectsa single monolayer on the surface of a 300-nm-thick silicon resonator can change the rate of mechanical energy dissipation in that resonator by almost a factor of 2. In some cases, almost half of the mechanical energy in the system is being dissipated at the surface! Chemically induced mechanical energy dissipation occurs when periodic strain fields perturb localized vibrational or electronic energy levels and allow coupling and energy redistribution between the strain field and the localized states.25 For example, Mihailovitch and Parpia26 showed that mechanical energy dissipation in macroscopic silicon resonators at cryogenic temperature increased dramatically with increasing boron doping density (over the range 6 × 1013 to 6 × 1016 dopants/cm3). This dissipation was attributed to stress-induced shifts of electronic holes occupying energy split ground states. Later experiments showed that this effect was too small to be observed in micromechanical resonators at room temperature.27 Nevertheless, a number of groups27-29 have shown that thermal annealing suppresses dissipation, at least transiently, in micromechanical resonators. On this basis, they have suggested that ion-beaminduced damage of micromechanical resonators, which occurs during processing, leads to the creation of similarly dissipative defect states. Although not as well characterized as the defects in boron-doped silicon, this type of dissipation presumably has similar origins. These chemical trends in mechanical energy dissipation and long-term stability bear a striking resemblance to previous

measurements by Lewis et al. on the electronic passivation capabilities of alkyl monolayers.31,32 In high purity float zone silicon, the density of electronically active bulk defects is extremely lowsso low that the recombination of excited carriers occurs almost exclusively at surface electronic defects. As a result, the density of electronically active defects can be estimated from measurements of charge carrier lifetimes: long carrier lifetimes are indicative of low defect densities and vice versa. As first shown by Yablonovitch et al.,30 hydrogenterminated Si(111) surfaces have exceptionally low electronic defect densities; however, this termination is unstable, particularly in air, and electronic defects rapidly form in all but the highest vacuums. In contrast, methyl-terminated surfaces have an exceptionally low electronic defect density which increases very slowly with air exposure.31 In comparison, long-chain alkylterminated Si(111) surfaces have an initial defect density that is approximately double that of methyl-terminated Si(111) surfaces and similar long-term stabilities.32 In comparison, both the rate of mechanical energy dissipation and the density of electronically active defects on freshly prepared resonators and surfaces, respectively, follow the general trend

chemical oxide . long-chain alkyl > H > CH3 (The rate of mechanical energy dissipation on oxidized surfaces is from ref 12.) After an extended period of air exposure, H-terminated surfaces degrade significantly, leading to

chemical oxide > H > long-chain alkyl > CH3 A similar correlation between mechanical energy dissipation and electronic defect density was seen in studies of oxidized micromechanical resonators.33 In that case, resonators terminated by a high quality, 100-nm-thick thermal oxide had quality factors approximately double those of comparable resonators terminated with an electronically defective, 1.3-nm-thick chemical oxide. In other words, increasing the thickness of the surface oxide 100-fold and decreasing the number of electronic defects decreased the rate of mechanical energy dissipation by a factor of 2! Taken as a whole, these observations strongly suggest a correlation between the rate of mechanical energy dissipation and the density of electronically active surface defects. We therefore suggest that the dramatic dependence of resonator quality factor on surface termination is driven by interfacial defects (of uncertain structure and chemistry) that occur at the silicon surface/alkyl monolayer (or silicon surface/ hydrogen monolayer) interface. This conclusion is based on four points. First, dissipation within the monolayer can be discounted, as a 9-fold increase in chain length (from -C2H5 to -C18H37) did not lead to a corresponding increase in dissipation. Second, dissipation is not correlated with the nature of the (majority species’) interfacial bonds; interfaces with 50% Si-C and 50% Si-H bonds (e.g., -CnH2n+1, n > 2 monolayers) do not dissipate energy at a rate intermediate to those with 100% Si-C (i.e., -CH3 monolayers) and 100% Si-H terminations. This observation rules out intrinsic differences between the interfacial chemistries. Third, the observed trends in the rate of mechanical energy dissipation and its stability are highly correlated with well-known trends in surface electronic defect density. Fourth, the alkyl-functionalization synthesis strategy (i.e., Grignard- vs olefin-based) had no effect on either the quality of functionalized resonators or the measured charge carrier lifetimes.32 Importantly, mechanical energy dissipation in micromechanical resonators is not a simple function of the amount of surface

94 J. Phys. Chem. B, Vol. 111, No. 1, 2007 oxide or the oxidation resistance of the terminating monolayers the electronic quality of the oxide is important. This conclusion is supported by two observations. First, as discussed above, resonators terminated with well annealed thermal oxides are much less dissipative than those terminated with a chemical oxide.33 Second, very high-Q mechanical resonators have been fabricated from amorphous silica;34 SiO2 is not an intrinsically lossy material. The chemical structure of the dissipative electronic defects remains uncertain; however, very recent results by Webb et al.35 suggest that alkyl-termination controls the oxidation of silicon surfaces and suppresses the formation of electronically active defects. After very long exposures to air, methyl- and ethylterminated Si(111) surfaces become significantly oxidized; however, a concomitant increase in electronic defect density is not observed.24 This behavior stands in stark contrast to that of H-terminated surfaces, where oxidation leads to a rapid increase in electronic defect density. X-ray photoemission spectroscopy (XPS) studies show that alkyl- and H-terminated surfaces develop qualitatively different oxide coatings, with alkylterminated surfaces forming a preponderance of suboxide species.35 These results suggest that mechanical energy dissipation in alkyl-terminated resonators is driven by a surprisingly low number of electronically active defects. Using a simple geometric model to calculate the recombination cross-section of individual defects, the density of electronic defects on methylterminated Si(111) surfaces31 was estimated to be ∼3 × 109 cm-2. [For comparison, the Si(111) surface has ∼1.5 × 1015 atoms cm-2.] In contrast, our micromechanical resonators had a total surface area of ∼3 × 10-7 cm2. If all exposed surfaces have comparable defect densities (an assumption of unknown validity), each methyl-terminated resonator would have had ∼1000 electronically active defects. Interestingly, Webb et al.35 found that long-chain alkyl-terminated surfaces have approximately twice as many electronically active defects as methyl-terminated surfaces, whereas the measurements in Figure 6 show that long-chain alkyl-terminated resonators dissipate energy approximately 1.7 times faster than methyl-terminated resonators. Although circumstantial, this correlation suggests that surface-induced mechanical energy dissipation strongly limits the quality of even our best methyl-terminated resonators. 5. Conclusions Mechanical energy dissipation in a micromechanical silicon resonator is sensitive to submonolayer changes in surface chemistry. Resonators terminated by a single monolayer of methyl groups have significantly higher quality factors, and thus lower rates of mechanical energy dissipation, than comparable resonators terminated with either long-chain alkyl monolayers (-CnH2n+1, n ) 2-18) or hydrogen monolayers. In contrast to H-terminated resonators, alkyl-terminated resonators resist adsorption from the gas phase and have correspondingly more stable mechanical properties (i.e., f and Q). The superior performance and stability of alkyl-terminated resonators is attributed to the relatively low densities of electronic defects in the freshly prepared monolayer coatings as well as the resistance of the monolayers to chemical attack. Acknowledgment. This work was supported by the Cornell Center for Materials Research, a Materials Research Science and Engineering Center of the National Science Foundation

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