High-Performance Polycrystalline Diamond Micro - IEEE Xplore

JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 17, NO. 2, APRIL 2008

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High-Performance Polycrystalline Diamond Micro- and Nanoresonators Nelson Sepúlveda, Jing Lu, Dean M. Aslam, Senior Member, IEEE, and John P. Sullivan

Abstract—Cantilever type MEMS resonators were fabricated using boron-doped (∼5 × 1019 cm−3 ) and undoped polycrystalline diamond (poly-C) films that were grown at 600 ◦ C or 780 ◦ C. The resonator dimensions ranged from 500 µm long, 10 µm wide, and 0.7 µm thick to 40 µm long, 100 nm wide, and 0.6 µm thick. Resonance frequencies and quality factors Qs were measured in vacuum, 10−5 torr, over the temperature range of 23 ◦ C–400 ◦ C. The measured values of the temperature coefficient of the resonance frequency were in the range of −17.2– −25.6 ppm · ◦C−1 and seemed to be related to changes in the Young’s modulus with temperature. Undoped poly-C cantilevers exhibit Qs as high as 116 000, the highest value reported for a cantilever resonator fabricated from a polycrystalline film. A thermally activated relaxation process seems to limit the measured Q-values for the highly doped poly-C samples. [2007-0172] Index Terms—Energy dissipation, MEMS cantilever beams, polycrystalline diamond MEMS resonator, quality factor, RFMEMS.

I. I NTRODUCTION

B

ECAUSE the performance of a microresonator is characterized by its resonant frequency and quality factor (Q), or the product of the two, a number of recent studies have focused on increasing the resonance frequencies and Qs of poly-Si microresonators. While for some applications a Q of 1000 may be acceptable, for future applications such as those for channel select receiver architectures, a gigahertz frequency range and a Q of at least 10 000 is required. Although the miniaturization of poly-Si resonators has been used to achieve a resonance frequency of 1.169 GHz, the measured Q of 5846 reported for this frequency [1] is substantially lower than the desired value for high-end RFMEMS applications. In other studies, the elimination of anchor losses by placing the anchors at the nodes [2], the removal of surface contamination or defects [3], [4]

Manuscript received July 11, 2007; revised January 15, 2008. The work of N. Sepúlveda was supported by Bill and Melinda Gates Foundation. This work was supported by the Engineering Research Centers Program of the National Science Foundation under Award EEC-9986866. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Corporation, for the U.S. DOE’s NNSA under Contract DE-AC04-94AL85000. An earlier version of this paper, “Polycrystalline diamond RF MEMS resonators with the highest quality factors,” was presented at IEEE MEMS’06, Istanbul, Turkey, January 2006. Subject Editor G. Fedder. N. Sepúlveda is with the Department of Electrical and Computer Engineering, University of Puerto Rico at Mayagüez, Mayagüez, PR 00681 USA. J. Lu and D. M. Aslam are with the Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824 USA (e-mail: [email protected]). J. P. Sullivan is with the Sandia National Laboratories, Albuquerque, NM 87185 USA. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JMEMS.2008.918409

and the elimination of thermoelastic dissipation (TED) by using torsional microresonators [5] have been investigated to increase the Q-values. The dissipation in micromechanical resonators can be attributed to aerodynamic losses, clamping losses, surface losses and internal friction, the latter typically incorporates thermoelastic damping, phonon–phonon interactions and losses due to defects [6], [7], [10]. If Qi is the quality factor related to a particular loss mechanism, the effective quality factor Qeﬀ is given by 1 1 = . Qeﬀ Qi i

(1)

However, for most polycrystalline materials, if the clamping losses are minimized, the Q is limited by intrinsic mechanisms that involve thermally activated relaxation processes [8]–[10]. These mechanisms are usually related to grain boundary sliding or internal friction, phonon-phonon interaction or defects within the resonator material [9]. Polycrystalline diamond (poly-C) has been recently investigated for its possible use in MEMS packaging [11], [12], BioMEMS [13], and RFMEMS [13]–[16]. It has been reported that temperature fluctuations can adversely affect the frequency and Q of microresonators made of nickel [3], [4], poly-Si [17], [18], nanocrystalline diamond [19], [20], and polycrystalline silicon carbide (poly-SiC) [21]. Although a Q of 55 000 and a resonance frequency of 1.5 GHz have been reported for disk resonators made from nanocrystalline diamond [22], the thermal stability of poly-C resonators and the factors that cause Q degradation in such devices are not well understood. To study the temperature dependence of frequency and Q in poly-C cantilever beam resonators, the main focus of this paper is to measure their frequency shifts when tested at elevated temperatures and to understand their intrinsic dissipation mechanisms responsible for limiting the highest achievable Q. The highest Q-value of 116 000 measured on any poly-C structure or cantilever beam made of any polycrystalline material is reported for the first time in this paper. The smallest poly-C resonator structure, reported for the first time in the current study, is 100 nm wide, 0.7 µm thick and 40 µm long; due to its larger length, the anchor losses are virtually absent. II. E XPERIMENTAL P ROCEDURE The poly-C microresonators used in this paper have widths, thicknesses and lengths in the ranges of 10 µm, 0.6–0.7 µm, and 100–500 µm, respectively, and were fabricated using

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TABLE I PARAMETERS USED FOR POLY-C GROWTH AND PATTERNING. THE SUPERSCRIPT REPRESENTS THE SAMPLE ON WHICH THE VALUE WAS USED

Fig. 1. Process flow for the fabrication of poly-C micro- and nanoresonators. (a) Starting substrate. (b) Pattern SiO2 and deposit poly-C. (c) Pattern poly-C. (d) Release.

undoped and p-type poly-C films. The poly-C nanoresonators have widths, thicknesses and lengths in the ranges of 100–500 nm, 0.7 µm, and 40–200 µm; the lengths are kept larger to minimize the anchor losses and, therefore, to study the effects of defect-related loss mechanisms. All the resonators reported in this paper were cantilever beams. A. Fabrication of Poly-C Micro- and Nanoresonators As shown in Fig. 1, the fabrication process starts with an ntype (100) Si wafer coated with a 2-µm SiO2 layer; the details of the quality of fabricated structures and related smallest feature sizes are reported in [13]. The SiO2 layer, used as the sacrificial layer, is patterned to create the anchor holes for the poly-C cantilevers. For poly-C growth in the anchor area and on SiO2 , the seeding technique consists of the use of a diamond powder loaded water suspension, called DW [23], which is prepared by mixing 25 carats of diamond powder, with an average particle size of 25 nm, in 1000 ml of deionized water and a suspension reagent. The DW suspension is placed in an ultrasonic bath for 30 min before it is applied to the Si surface, which was etched in a diluted HF solution (1% HF in H2 O) for 10–20 s to remove the thin SiO2 layer in the anchor area. The rapid HF etch improved the DW suspension surface coverage over the sample because the freshly etched SiO2 layer becomes more hydrophilic. The DW seeding is accomplished in a conventional spinner for 30 s at 1000 r/min. To improve the seeding density, the spinning process was repeated twice to achieve a nucleation density of 1 × 1011 cm−2 [13]. After the seeding step, the samples were loaded into a microwave plasma CVD reactor for poly-C growth. To have a broad characterization of poly-C microresonators, three samples were fabricated. Sample 1 is an undoped 0.6 µm thick poly-C film grown at 780 ◦ C and sample 2 is a highly boron-doped (∼5 × 1019 cm−3 ) [23] 0.7 µm thick poly-C film grown at 780 ◦ C. Sample 3 is an undoped 0.7 µm thick poly-C film grown at 600 ◦ C. Each sample represents one specific type of polycrystalline diamond film from which different cantilever structures were fabricated and tested. The poly-C film growth parameters for all the samples are shown in Table I. The doping was done in situ using tri-methyl-boron

Fig. 2. Raman spectra for the three studied poly-C samples. Inset TEM image show cross section of polycrystalline diamond.

diluted in hydrogen (0.098%). The growth temperatures were monitored by a pyrometer and temperature fluctuation was kept below ±5 ◦ C. Fig. 2 shows the Raman spectra for the three different poly-C films. To decrease the background effect, the original intensity values of different samples should be normalized before comparison. First, a cubic polynomial fit was applied to the intensity values within a small range of wavenumbers around the peak, but excluding the diamond peak area (1250– 1300 cm−1 , 1360–1410 cm−1 ). Then, the original intensity values in the range of 1000–1600 cm−1 were normalized by the fitted value of intensity at the diamond peak (1332 cm−1 ), and this is shown in Fig. 2 as normalized intensity. The sharpest diamond (sp3 carbon–carbon bonding) peak at 1332 cm−1 can be observed for sample 2. Sample 3, which was grown at

SEPÚLVEDA et al.: HIGH-PERFORMANCE POLYCRYSTALLINE DIAMOND MICRO- AND NANORESONATORS

Fig. 3. SEM pictures of poly-C cantilever structures produced using the described fabrication process flow and dry etching technique.

600 ◦ C, exhibited smaller peaks than samples 1 and 2 which were grown at 780 ◦ C. Fig. 2 also shows TEM images of the three samples. Sample 2 seems to have a small-grain region near the Si/Poly-C interface. The patterning of the poly-C microresonators was done by photolithographically patterning an aluminum layer on top of the poly-C films to act as an etch mask. The etching of the poly-C film was performed using oxygen-based plasma in an RF reactive ion etch etching system, using the parameters shown in Table I. The etch rate for samples 2 and 3 were about 0.04 µm/min, with 0.02 µm/min observed for sample 1. After dry etching, the cantilevers were released by wet etching the samples in HF for 50 min (the wet etching also removes the aluminum etch mask layer). The fabrication technology developed in this paper is capable of producing clean and smooth poly-C structures as shown in Fig. 3. Right after the cantilevers were released, they were loaded into an ultraviolet ozone system for cleaning, and then heated to 800 ◦ C for 1 min in an argon atmosphere using rapid thermal annealing to remove any moisture. Before every measurement, the samples were cleaned using this procedure. After release and drying, the cantilevers were flat with less than approximately 1 µm out-of-plane curvature over the length of the beam even for the longest beams (400–500 µm). This indicates that there is little strain gradient in the films. In the past, this fabrication process has been used to produce beams that were fixed on both ends (a bridge structure) and they did not show buckling, which is an indication that the films were not under a state of high net compressive stress prior to release [13]. The microresonator fabrication technology developed in this paper is a continuation of diamond MEMS technologies developed earlier [11]–[14] capable of producing clean and smooth poly-C structures with a minimum feature size of 2 µm and a surface roughness of 62 nm as measured by atomic force microscopy (AFM). The fabrication of the poly-C nanoresonators was similar, except that electron beam (e-beam) lithography was used. E-beam

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Fig. 4. Testing setup for measurements using piezoelectric actuation and laser detection.

lithography enables the creation of features with dimensions as small as approximately 25 nm, and it has been used in the past to fabricate single crystal silicon nanoresonators [5], [24], [25]. In this paper, the e-beam lithography was used to define an aluminum etch mask layer on top of the poly-C film. Then the nanocantilevers were defined using the same dry etching procedure described in Table I, followed by an HF wet etch to remove the SiO2 and aluminum layers. The nanoresonators consisted of cantilever beams with lengths and widths in the range of 40–150 µm and 100–500 nm, respectively. The lengths of beams were kept in the micrometer range to minimize the anchor losses and, therefore, to study the effect of other loss mechanisms on the nanoresonators. Minimum feature sizes of 100 nm were defined in poly-C films that were 0.6 µm thick, even though the poly-C films had an RMS roughness of about 62 nm as measured by AFM. This fabrication of poly-C nanoresonators indicates that free-standing structures down to the nanoscale can be defined in polycrystalline diamond films even with notable film roughness. All the nanoresonators that were measured in this paper were fabricated from sample 1. B. Measurement System Using the laser interferometer setup shown in Fig. 4, all measurements were made at a chamber pressure below 1 × 10−5 torr to eliminate air damping losses. The actuation of the beams was done by using a spectrum analyzer to drive a piezotransducer element that was physically attached to the bottom of a ceramic cylinder. A current-controlled heater element was mounted between the ceramic cylinder and the sample holder. The temperature of the sample was kept within 1% of the set value. The detection was done by focusing a laser beam, minimum spot size of about 2 µm, onto the end of the vibrating cantilever. The laser light reflected off of the cantilever interferes with the incident laser light, producing a modulation in light intensity

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that is in phase with the cantilever motion and that is detected by the photodiode. A spectrum analyzer was used to record and analyze the time-varying signal detected by the photodiode. The effect of laser heating on the resonators was tested by looking at the frequency shift of the resonance peak with time under illumination. Even after illumination for greater than 15 min, the frequency shift of the peak was typically less than 5 Hz at 100 kHz frequency. Based on our measured temperature coefficient of frequency shift, this would correspond to less than 2◦ –3◦ temperature rise in the beams. This error in temperature is small compared to the large temperature increments (100 ◦ C) that we used in our paper of temperature-dependent properties. The use of piezoexcitation and optical detection brings two distinct advantages to the study of defect-related energy loss mechanisms: Because the excitation is external, 1) undoped and doped samples can be used and 2) the measurement technique does not have a noticeable effect on the frequency and Q (unlike the electrostatic actuation). Fig. 5. Frequency shift with temperature for sample 1 and linear fit to the measured data. The second mode data point at 200 ◦ C is missing because it was not recorded.

III. R ESULTS AND D ISCUSSIONS The resonant frequency of a cantilever beam depends on the Young’s modulus [9], [27] E c2 t (2) fo = 2πl2 12ρ where E is Young’s modulus, ρ is the density of the cantilever material; t and l are the cantilever beam thickness and length, respectively, and c is a constant that depends on the cantilever vibration mode, which for the first vibration mode of the cantilever equals 1.875 [27]. The frequency and Q-values of the poly-C cantilever beam microresonators were obtained from Lorentzian fits [26] to the measured data. If the values of fp and Q (frequency and quality factor) are obtained from the measured data, the first natural frequency (fo ) of each beam can be extracted from fp fo = Q

−1/2 2 1+ 2 −1 . Q

(3)

Fig. 6. Frequency shift with temperature for sample 2 and linear fit to the measured data.

It may be pointed out that (3) reduces to fo = fp for samples with very high values of Q. Only for low values of Q will fo and fp be measurably different. A. Poly-C Microresonators The elastic properties of poly-C vary with temperature [28] and consequently so does the poly-C Young’s modulus. The Young’s modulus of poly-Si has been reported to decrease about 8% of its room temperature value in the temperature range of 23 ◦ C–250 ◦ C [29], while the Young’s modulus for poly-C has been reported to decrease about 3% of its room temperature value in the temperature range of 23 ◦ C–400 ◦ C [28], [30]. According to (2), a shift in the Young’s modulus and density will result in a shift of the resonant frequency. For further discussion, we assume that the changes in volume density may be negligible. The shifts in the resonant frequency

Fig. 7. Frequency shift with temperature for sample 3 and linear fit to the measured data.


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TABLE II TEMPERATURE-DEPENDENT FREQUENCY PERFORMANCE FOR POLY-Si AND THE POLY-C MICRORESONATORS REPORTED IN THIS PAPER

of a microresonator due to changes in temperatures are quantified by the temperature coefficient of resonant frequency (TCf ) [2] TCf =

∆f fo × (T − To )

(4)

where fo and fT are resonant frequencies at temperatures of 300 K and T , respectively, and ∆f = fT − fo and To is the room temperature. Figs. 5–7 show the frequency shift ∆f /fo as a function of measurement temperature. In Fig. 5, the data point for the second resonance mode of the 400-µm beam at 200 ◦ C was not available. This second resonance mode was not detected during this one temperature, possibly due to the unfortunate placement of the laser spot at the node of the beam’s resonance. This was not an issue at the other temperatures. The TCf values were obtained by calculating the slopes of linear fits to the data. Table II shows a comparison of the results from other researchers for poly-Si with those for poly-C reported in this paper. While the TCf values for poly-Si structures have not been reported at temperatures above 247 ◦ C, the TCf values for samples 1–3 reported in this paper are in the range of −17.2–−25.6 ppm · ◦ C−1 in the temperature range of 23 ◦ C–400 ◦ C. For comparison purposes, the TCf values for poly-C resonators reported in this paper ranged from −13.7 to −27.4 ppm · ◦ C−1 in the temperature range of 23 ◦ C–100 ◦ C and from −11.5 to −23.1 ppm · ◦ C−1 in the temperature range of 23 ◦ C–250 ◦ C. These values show that poly-C microresonators have TCf values similar to those obtained for poly-Si bridges and free-free beams [2], as well as those obtained from geometrically compensated poly-Si structures [17], [18]. If the poly-C density is assumed to be (3520 kg · m−3 ), the temperature dependence of the poly-C Young’s modulus can be calculated from the measured frequency shifts and using (2). To improve the accuracy, the Young’s modulus was

Fig. 8. Poly-C Young’s modulus temperature dependence for the three studied samples.

determined from a fit of resonance frequency versus l−2 , where l is the lithographically defined beam length, using 5 to 10 cantilever beams per sample. Fig. 8 shows the resulting Young’s modulus values. In the temperature range of 23 ◦ C–400 ◦ C, the samples showed a Young’s modulus decrease of 2.5% for sample 1, 3.8% for sample 2 and 2.6% for sample 3. The room temperature Young’s modulus varies from sample to sample, showing the highest value of 990 GPa for sample 1. Inaccuracies in the beam dimensions affect the accuracy of the absolute magnitude of the Young’s modulus but have only a small effect on the temperature-dependence of the modulus. As can be seen from Fig. 2, the greatest source of uncertainty is the film thickness. Based on (2), errors in thickness of 10% will result in approximately 20% errors in Young’s modulus. Therefore, the spread in the absolute magnitude of the Young’s modulus among the three samples may not be statistically significant (whereas differences in the temperaturedependence of the modulus can be accurate as these measurements do not depend on the precise knowledge of cantilever dimensions). Fig. 9 shows a plot of the measured Q-values as a function of frequency and insets showing the resonance spectrum for cantilever resonators exhibiting the highest Q-value for each

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Fig. 9. Measured Q-values as a function of frequency. Inset resonant peaks show the measurement with the highest Q-value for each sample.

sample. All the resonators for the three samples were cantilever beams with lengths in the range of 100–500 µm. The measured Q-values for the cantilevers made from sample 1 are about two times larger than those for the other two poly-C films. The Q-value of 116 000 is the highest that has been measured so far for any polycrystalline diamond structure or a cantilever made of any polycrystalline material. This value is also much larger than those of nanocrystalline diamond resonators reported in the past [19], [20], [22] and is about half the value of 250 000 found for single crystal silicon resonators [25]. However, the frequency-Q product of 3.69 × 1010 is much lower than the value of 1.75 × 1013 achieved by a polysilicon resonator [1]. These results seem to indicate that high densities of impurities (sample 2) and intrinsic defects (sample 3) in poly-C may be affecting the Q-values. The reported relatively low Q-values (2500–3000) of nanocrystalline diamond (NCD) resonators may also be related to intrinsic defects, especially in the grain boundary regions where there is a high density of sp2 -bonded carbon. It is also possible that because of the short length of the NCD resonators (2 µm), the Qs may have been limited by clamping losses. NCD resonators with longer lengths and nanometer-size thicknesses may be needed to clarify this point. Fig. 10(a) shows the distribution of measured Q-values for the three poly-C samples. The majority of the measured Q-values from sample 2 are between 8000 and 40 000 and the majority of the measured Q-values on sample 3 are between 4000 and 25 000. However, sample 1 shows a much higher maximum Q and a larger variation in measured Q-values, with the majority of the measured Q-values between 4000 and 100 000.

Fig. 10. (a) Distribution of grain surface area for the three poly-C films. (b) Distribution of measured Q-values for the three poly-C films.

The Q of a resonator may be affected by intrinsic mechanisms, mechanical design of the resonator (e.g., clamping losses for short cantilevers), and extrinsic mechanisms, such as surface contamination. Resonators with high Q are especially sensitive to surface cleanliness, as dust or other particles that might be attached to the resonator surface during processing may lower the Q from its intrinsic value. We believe that the large variation in Q for sample 1 and presence of low Q-values for all of the samples might reflect the effect of processing-induced defects or residual random contamination on some cantilevers. In that case, the highest Qs for the samples should be the most indicative of the intrinsic Q of the material, i.e., we should compare the highest Qs for each sample to determine the effect of doping and microstructure on Q. To deduce what dissipation mechanisms might be operative in poly-C resonators, it is useful to compare the Qs of these resonators with the predicted Qs assuming intrinsic and design-related dissipation mechanisms. The measured Q-values from samples 1–3 are plotted as a function of resonance frequency in Fig. 11 along with calculated Q-values. The calculated Q-values assume a Q limited by each of the three most common intrinsic and design-related energy dissipation mechanisms. The curves marked QTED and Qph are the expected maximum Qs if the energy dissipation is


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grains (sample 1) shows the highest Qs, suggesting that grain boundaries could play a role in limiting Q. Most defect relaxation processes in polycrystalline materials have characteristic activation energies for defect motion [8]. If a single defect relaxation process dominates, it is often possible to determine the activation energy for defect motion by looking at the temperature dependence of Q. Most defects give a Debyelike relaxation, which limits the Q-value [10] −1 2πf τ ∗ (5) Qdefect = A 1 + (2πf τ ∗ )2

Fig. 11. Computed Q limiting curves and measured Q-values for poly-C cantilever beams fabricated form the three studied samples. A thickness of 0.6 µm was used to plot the curves. TABLE III POLY-C PROPERTIES USED TO PLOT Q LIMITING CURVES

controlled by TED and phonon–phonon scattering, respectively [10]. The curve marked Qclamp is the expected maximum Q if the energy dissipation is limited by clamping losses (mechanical damping by the beam support) [31]. The poly-C properties used for plotting the dissipation curves are shown in Table III. All the Q-values measured in this paper are below any of the computed dissipation curves shown in Fig. 11, suggesting that the Q-values are not limited by any of these dissipation mechanisms. In the absence of external defects (e.g., particles, processing film residue, etc.) the most likely mechanisms that limit Q-values in polycrystalline materials are mechanical relaxation processes associated with defect motion, including vacancy motion, interstitial motion, dislocation motion, and grain boundary sliding [9], [10]. Because the density of grains affects the amount of grain boundary defects that could be present in poly-C films, the distribution of grain sizes was investigated. If the dominant defects that cause internal dissipation were associated with grain boundaries, then one might expect that the films with the largest grain boundary area would show the lowest Qs. Fig. 10(b) shows the distribution of the grain cross-sectional area as measured at the sample surface for the three poly-C films, obtained using a procedure found in [32]. Samples 2 and 3 have, on the average, smaller grain sizes than sample 1. Although the grain sizes are larger for sample 1, the grain size distribution is large. As a result, it is difficult to estimate the absolute total grain boundary area of the three samples, but, qualitatively, the sample with the largest

where A is known as the “intensity” of the relaxation process, f is the frequency, and τ ∗ is the defect relaxation time. The defect relaxation time represents the average time needed for the defect to transition between two defect configurations. It is typically thermally activated with an Arrhenius relationship [10] A 1 −E 1 kB T (6) = e τ∗ τo where 1/τo is the characteristic atomic vibration frequency (about 1013 Hz), EA is the activation energy for the relaxation process, T is temperature and kB is the Boltzmann’s constant. According to (5) Q will be minimum at the temperature at which τ ∗ = 1/2πf , where, in this case, f represents the frequency of the resonator. Once τ ∗ is known, and assuming τo = 10−13 s, the activation energy for defect motion may be estimated using (6). Fig. 12 shows the measured Q-values for samples 1–3 as a function of temperature, using different shapes to represent data points from devices of different lengths. It can be noticed that the largest measured Q-values for sample 2 show a minimum value at a temperature around 673 K, while the other two samples do not show a clear minimum for the highest measured Q-values. This suggests that there is a dominant defect relaxation process in sample 2 which is peaked at a temperature of around 673 K. The absence of a minimum in Q for samples 1 and 3 suggests that there is likely a distribution of defect relaxation processes that are present, and no single defect process dominates. Assuming τo = 10−13 s, the minimum at 673 K for sample 2 would correspond to a defect activation energy of 1.7 eV. The most obvious source of possible defects that would be present in sample 2 and absent in samples 1 and 3 are defects associated with boron doping. Sample 2 is heavily doped (resistivity = 0.15 Ω · cm) whereas samples 1 and 3 are undoped. Whether the defect relaxation process is specifically associated with motion of the boron dopants or the motion of other defects that result from dopant incorporation in poly-C is not known. However, it is noted that the activation energy for self-interstitial diffusion in crystalline diamond is 1.3 eV [33], and the activation energy for vacancy diffusion in crystalline diamond is 2.3 eV [34]. The value of 1.7 eV is in between these values but in a range where diffusion-related defect relaxation processes may be active. B. Poly-C Nanoresonators As some physical properties of materials may change if the dimensions are reduced to below 100 nm, any structure having

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Fig. 13. SEM image and performance of a 100-nm wide polycrystalline diamond nanocantilever.

Fig. 12. Measured Q-values as a function of temperature for the three studied poly-C samples.

at least one of the dimensions 100 nm and below is called “nanoscale” if its property in question is related to this small dimension [35]. In this paper, one of the goals was to investigate the resonance properties and Q of nanoresonators fabricated out of poly-C. Because the beam widths of the nanoresonators are in the range of 100–500 nm, the resonator beams have their lowest frequency vibrational mode parallel to the sample surface. Thus, the spring constant of beams was dictated by the lithographically defined nanoscale dimensions. Measurement of the nanoresonators was difficult for the smallest cantilever beams, and we were unable to obtain frequency and Q-values for some of the structures. The measurement setup described in Section II-B is optimized for out-of-plane vibrational modes, whereas the lowest frequency and highest amplitude modes of the nanoresonators are inplane. After some experimentation and remounting of samples, detectable signals were obtained. We verified that the signals originated from the nanoresonators by observing the disappearance of the resonance signal when the laser spot was moved off of the nanoresonator and its reappearance when it was returned. There are at least three possibilities of how we were able to detect a signal from the nanoresonators: 1) The

method of mounting the sample to the ceramic heater does not ensure that the sample surface is exactly perpendicular to the axis of the laser. A tilt of the sample permits some reflections to be observed from the sidewalls of the cantilevers (which are ∼ 0.6 µm wide) and, hence, there is a component of the cantilever motion that is parallel to the laser beam axis. 2) It is possible that some contaminant particle may have adhered to the beam, providing more cross-sectional area for light scattering (although we did not observe obvious contaminants optically through our measurement setup). 3) The nanoresonator beams were spaced four µm apart, and it is possible that the laser spot included more than one beam. This would increase the total reflected light, but the width of the resonance peak may be broadened due to coupling. Fig. 13 shows SEM images of a poly-C nanocantilever along with a measured resonant peak for the smallest nanoresonator that we were able to measure. This nanocantilever had a length of 40 µm and a width of approximately 100 nm. Assuming a thickness of 100 nm, a length of 40 µm, Young’s modulus of 990 GPa, a density of 3520 kg · m−3 and using (2), the expected resonance frequency of this nanocantilever is 169 300 Hz. Our measured resonance frequency was 183 214 Hz. The resulting difference between the expected resonance frequency and the measured resonance frequency (183 214 Hz − 169 300 Hz = 13 914 Hz) could be due to errors in the beam dimensions, e.g., a trapezoidal beam cross section as opposed to a rectangular cross section. Note that the out-of plane fundamental mode resonance frequency for this structure would be over 1 MHz. Also, the second in-plane vibrational mode and the first inplane torsional mode would be over 1 MHz and over 3 MHz, respectively. Therefore, we feel confident in assigning this resonance peak to be the fundamental frequency of the lateral (in-plane) mode.


The Q for this nanocantilever is not high compared to the Q-values of the microresonators. This low Q could be due to a contaminant or coupling between nanoresonators, or it could be due to surface-related defects induced during the dry etching of the poly-C film. In contrast to the microresonator structures, the area of the cantilever surface that was etched by the RF plasma is much higher for the nanocantilever beams than the microcantilever beams. Despite the lower Q and the measurement difficulties, this paper does demonstrate the ability to achieve and measure nanoresonators in poly-C films with surface topology exceeding 100 nm, indicating that extremely small structures and devices can be successfully fabricated using polycrystalline diamond films.

[12] [13] [14] [15] [16]

[17]

IV. C ONCLUSION For cantilever beam resonators fabricated from undoped poly-C films grown at 780 ◦ C, the highest Q-value of 116 000 has been measured. For boron doped poly-C films or undoped poly-C films grown at 600 ◦ C, significantly lower Q-values were observed. The temperature dependence of the poly-C resonators was examined, and a temperature coefficient of resonance frequency in the range of −17.2–−25.6 ppm · ◦ C−1 was observed. We also report a poly-C nanoresonator structure that is 100 nm wide, 0.6 µm thick and 40 µm long.

[18]

ACKNOWLEDGMENT

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Nelson Sepúlveda was born in Puerto Rico in 1979. He received the M.S.E.E. and Ph.D. degrees from Michigan State University, East Lansing, in 2002 and 2005, respectively. During 2005, he was a Microsystems and Engineering Sciences Application Fellow with Sandia National Laboratories, Albuquerque, NM. In January 2006, he joined the faculty of the Department of Electrical and Computer Engineering, University of Puerto Rico at Mayagüez, Mayagüez, Puerto Rico. His current research work involves the characterization of different vanadium oxide thin films (i.e., VO2 and V6O13) as well as the use of these thin films for the development of MEMS devices and optically activated microwave switches. He also does research on the development of RF MEMS-based reconfigurable antennas, an area in which he currently has collaborations with the Air Force Research Laboratories, Wright–Patterson Air Force Base, Dayton, OH.

Jing Lu was born in Guizhou, China, in 1981. She received the B.S. degree in electronics from Peking University, Beijing, China, in 2003. She is currently working toward the Ph.D. degree in electrical engineering with a major in electronic materials and devices in the Department of Electrical and Computer Engineering, Michigan State University, East Lansing. Since 2006, she has been working on research projects supported by the National Science Foundation Engineering Research Center for Wireless Integrated Microsystems. Her work focused on the design, fabrication, and test of polycrystalline diamond micro- and nanoresonators for sensors and wireless interface. Her research interests include MEMS designs and simulations, CVD diamond technology, and microfabrication technology.

Dean M. Aslam (M’87–SM’93) received the M.S. degree in physics and Ph.D. degree in electrical engineering from RWTH Aachen University, Aachen, Germany, in 1979 and 1983, respectively. He is currently Associate Director of the National Science Foundation Engineering Research Center for Wireless Integrated Microsystems, Ann Arbor, MI, and an Associate Professor of electrical and computer engineering with the Department of Electrical and Computer Engineering, Michigan State University (MSU), East Lansing. Before joining MSU in 1988, he was a Research Associate with RWTH Aachen University from 1983 to 1984 and held faculty positions with the Pakistan Air Force College of Aeronautical Engineering, Risalpur, Pakistan, from 1984 to 1986 and with Wayne State University, Detroit, MI, from 1986 to 1988. His group became the first to report an all-diamond neural/cochlear probe in 2007, the incorporation of poly-C piezoresistive sensors in Si cochlear probes in 2006, the highest quality factor for poly-C cantilever beam resonators in 2005, all-diamond MEMS packaging in 2004, field emission electroluminescence in 2003, an intragrain piezoresistive gauge factor of 4000 in poly-C in 1997, and piezoresistivity in diamond and poly-C in 1991. He has published more than 124 papers. He is the holder of ten U.S. patents in the field. He is the founding Editorin-Chief of the International Journal of Nanosystems and Technology. His current research concentrates on poly-C piezoresistive sensors, biochemical nanosensors, poly-C RF MEMS micro- and nanoresonators, CNT growth in PCF channels of a micro-GC, poly-C BioMEMS (cochlear and neural probes), poly-C smart MEMS packaging, and hands-on robotics learning modules for K-12, undergraduate, and graduate teaching. Dr. Aslam was a recipient of a German DAAD Fellowship from 1975 to 1983.

John P. Sullivan received the B.S. degree in materials science from the University of Minnesota, Minneapolis, in 1989, and the Ph.D. degree in materials science and engineering from the University of Pennsylvania, Philadelphia, in 1993. In 1994, he joined Sandia National Laboratories, Albuquerque, NM, as a Research Staff Member and is currently a Principal Member of the Technical Staff with the joint Sandia–Los Alamos Center for Integrated Nanotechnologies. He is the author or a coauthor of more than 50 scientific publications and patents in the areas of electronic properties of metal/semiconductor interfaces, insulator/semiconductor interfaces, amorphous aluminum oxide and carbon thin films, and carbon- and diamond-based materials for MEMS. His current research interests include the study of electronic defects in thin films and nanoscale materials, nanomechanics and NEMS, sensors using resonant mechanical structures, and heat transport at the nanoscale.