Ultrathin Single Crystal Diamond Nanomechanical Dome Resonators

LETTER pubs.acs.org/NanoLett

Ultrathin Single Crystal Diamond Nanomechanical Dome Resonators Maxim K. Zalalutdinov,*,† Matthew P. Ray,‡ Douglas M. Photiadis,† Jeremy T. Robinson,† Jeffrey W. Baldwin,† James E. Butler,§ Tatyana I. Feygelson,§ Bradford B. Pate,† and Brian H. Houston† †

U.S. Naval Research Laboratory and ‡NRC/NRL, U.S. Naval Research Laboratory, 4555 Overlook Avenue SW, Washington, D.C. 20375 United States § SAIC, Inc., 1710 SAIC Drive, McLean, Virginia 22102, United States

bS Supporting Information ABSTRACT: We present the first nanomechanical resonators microfabricated in single-crystal diamond. Shell-type resonators only 70 nm thick, the thinnest single crystal diamond structures produced to date, demonstrate a high-quality factor (Q ≈ 1000 at room temperature, Q ≈ 20 000 at 10 K) at radio frequencies (50
600 MHz). Quality factor dependence on temperature and frequency suggests an extrinsic origin to the dominant dissipation mechanism and methods to further enhance resonator performance. KEYWORDS: Diamond, single-crystal, nanomechanical, resonator, dissipation

S

ingle-crystal diamond (SCD) is well-suited for nanomechanical devices due to its unsurpassed combination of desirable features: high rigidity and strength, high thermal conductivity, and outstanding optical properties (low absorption and high refraction index in UV-NIR range).1 For long, ultrathin, ultraflexible (Kspring , 10
3 N/m) cantilevers used for mechanical detection of spin resonance,2 these properties of SCD will translate into enhanced resolution of the optical readout. For mass sensing in subfemtogram range,3,4 the ultrathin diamond resonators offer enhanced mass sensitivity, δM ∼ Mresonator/Q, while the chemistry of the diamond surface allows advanced methods of selective functionalization that can provide specificity toward an analyte of interest.5
8 To date, nanocrystalline diamond (NCD) and ultrananocrystalline diamond (UNCD)9
14 are the primary forms in which diamond-based devices are studied. However, scaling the dimensions of NCD devices below 100 nm is impeded by the surface roughness (5
20 nm)15 and the presence of the buried seed layer at the base of the film. Even more importantly, phonon scattering at the grain boundaries reduces the thermal conductivity of NCD at low temperatures by orders of magnitude.1,15,16 In contrast, we demonstrate that our diamond devices can be as thin as 70 nm, while preserving the single crystal nature of the suspended structure. Based on the fact that the thickness of SCD nanoresonators is approaching that of multilayer graphene-based devices,17 we suggest that hybrid nanomechanical devices are feasible. We envision nanoelectromechanical devices with graphene-based radio frequency (RF) electrical components (dedicated for transduction, sensing, signal conditioning, etc.) placed on the surface of SCD structural elements. We consider the high thermal conductivity and low substrate-induced scattering associated with the diamond substrates18 as potential enabling factors r 2011 American Chemical Society

for graphene
diamond hybrids, alongside low total mass and excellent optical and mechanical properties. In this manuscript, we present both fabrication and RF operation of ultrathin (70 nm) single crystal diamond nanomechanical resonators created using a top-down lithographical approach (in contrast to unintentionally formed19,20 diamond shells). Various fabrication routes producing suspended SCD structures in the thickness range h ≈ 0.2
1 μm can be found in the literature.21
27 However, our domes are the first to demonstrate mechanical resonance. Single-crystal diamond stones (Sumitomo Electric, 3.5  3.5  1.5 mm3 type-Ib, high pressure, high temperature, HPHT)28 were polished initially in the “soft” direction and then in the “hard” direction (“superpolish”)29 in order to provide a surface roughness below 0.1 nm. A sacrificial layer was formed by implanting C+ ions with energy 180 keV and then 150 keV with a total dose 1016 cm
2. From stopping range of ions in matter (SRIM) simulations, the maximum density of implantationinduced defects is expected to be located ≈200 nm below the surface. This highly damaged region comprises the sacrificial layer. Above it, remains a top layer of diamond that accumulates a relatively low-defect density during implantation and is dubbed the device layer (Figure 1D). A sharply focused ion beam (FIB, Ga+ 30 keV, normal incidence) was used to create circular submicrometer openings (irrigation holes) in the device layer. A dry etch in H2 plasma selectively removed the sacrificial layer through the irrigation hole without damaging the device layer (Figure 1B). This selectivity was provided by tuning parameters for the H2 plasma (RF power 400 W, frequency 2.45 GHz, H2 pressure 15 Torr, Received: July 8, 2011 Published: September 13, 2011 4304

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Figure 1. AFM images of a FIB-defined dome (scan size 5  5 μm , OD 2.9 μm, part A) and a “natural” dome (scan size 8  8 μm2, OD 5 μm, part C). Optical microscopy image of five FIB patterned domes is shown in B (center to center distance between the domes on the bottom is 16.5 μm). The inset in part A shows an EBSD pattern confirming the single crystal nature of the device layer. The device layer and sacrificial implanted layer of the single crystal diamond substrate are shown in schematic cross-section in part D.

Figure 2. Resonant frequency of the fundamental mode of vibration for SCD domes as a function of the domes’ diameter. The upper data set (shown as red circles for natural domes and red triangles for FIB-made devices) was acquired after H2 plasma release but no Cl2 plasma treatment. Data shown in blue were acquired after exposure to a Cl2 ICP for 6 min 40 s (blue circles for natural and triangles for FIB-made domes). The fundamental frequencies calculated based on Young’s modulus E = 900 GPa for circular plate resonators34 (Supporting Information) shown as red solid line (plate thickness 110 nm) and dotted blue line (plate thickness 70 nm).

temperature 500
C) close to the conditions for epitaxial growth of diamond.29 However, by preventing methane (or any other source of carbon) from entering the chamber, weakly bound nondiamond carbon is removed, while carbon in the diamond phase is etched minimally. Figure 1A shows an atomic force microscope (AFM) image of a FIB-made dome (suspended shell comprised of the device layer, clamped on the periphery, orifice diameter 1 μm) released by a 2 min exposure to H2 plasma (the undercut rate can be estimated as 500 nm/min). The single-crystal nature of the suspended film was confirmed by electron backscatter diffraction (EBSD), showing characteristic patterns of Kikuchi lines (Figure 1A, inset) corresponding to the diamond lattice.30 Structures referred to as “natural” domes, with a wide size distribution, appear as an unexpected (unwanted) outcome of the plasma treatment procedure. Figure 1C shows an AFM image of such a “natural” dome, one of many, formed during a 15 min H2 plasma exposure, without any FIB assistance and scattered over the implanted surface. We argue that at least one mechanism involved in the formation of these “natural” domes is related to local mechanical damage introduced during mechanical polishing (Supporting Information), while bulk defects could be a conceivable alternative route. We note that the locally damaged regions and bulk defects occur at random locations and therefore have low probability of coinciding with the FIB-made domes. As a result, the FIB-defined domes show a consistently smaller outer diameter, since there are no mechanically introduced defects to enhance the etch rate for the sacrificial layer. While studying the mechanical response of the “natural” domes allows us to evaluate the properties of the suspended SCD film, the emphasis on FIB-defined resonators is motivated by the fact that it is straightforward to extend the fabrication technique reported in this manuscript toward a conventional lithography-based process. The thickness of the device layer h ≈ 110 nm was extracted from the SEM image of a crushed dome (see Supporting Information), while the out-of plane curvature of the large (assumed fully buckled)

Figure 3. Frequency dependence of the dissipation 1/Q for as fabricated resonators (red circles for “natural” and red triangles for FIBdefined domes) and Cl2 plasma-thinned devices (blue circles and triangles for “natural” and FIB-made domes, respectively). The straight line serves as a guide for the eye.

2

“natural” domes provides an estimate for the compressive stress σ ≈ 650 MPa created within the device layer. We demonstrate that further reduction in the thickness of the suspended single crystal diamond layer is possible via reactive ion etch in a Cl-based inductively coupled plasma (ICP). After a total etch time of 6 min 40 sec (ICP power 1500 kW, RF power 50 W, and pressure 20 mTorr), the remaining thickness of the suspended diamond film (estimated from the shift of the resonant frequency of the domes) was reduced to tdome < 70 nm, consistent with the etch rate 5.4 nm/min calibrated for bulk SCD. The resonance frequency (measured using a double-beam laser interferometric setup)31 of the fundamental mode of vibration as a function of dome diameter is shown in Figure 2 for both “natural” and FIB-fabricated domes. The diameter of the domes was extracted using an AFM. 4305

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Figure 4. Temperature dependence for the dissipation 1/Q of the plasma-thinned (70 nm) SCD natural dome (27 MHz, red circles) and FIB-made dome (51 MHz, blue circles). Dissipation for NCD bridge resonators9,12 is shown for comparison. The inset shows the temperature dependence of the internal friction in amorphous carbon films.38,39

Young’s modulus was used as a fitting parameter to best match the experimentally measured fundamental frequency of the largest (fully relaxed) domes to theoretical results that take into account the out-of-plane curvature and the opening at the apex of the dome (see Supporting Information). This fit provided a Young’s modulus of E = 900 GPa, very close to the accepted value for bulk SCD (Ebulk = 1143 GPa).32 Following exposure to a Cl2 ICP for 6 min 40 s, a notable decrease of the fundamental frequencies of the diamond domes is observed as shown in Figure 2. We estimate the final thickness of our dome resonators to be 70 nm (assuming E = 900 GPa). The Q factors for the SCD dome resonators (calculated from the half-width of the resonant √ peak) for a wide range of the dome sizes exhibit a 1/Q = η  f frequency dependence, as shown in Figure 3. Data points for both as-released and plasma-thinned domes (including naturally formed and FIB-fabricated domes) √ tend to fall along the same line in the 1/Q( f) plot. Our experimentally observed frequency dependence for dissipation is inconsistent with the predictions of a Zener-type theory for a standard anelastic solid33 (1/Q = η  f). This discrepancy suggests that geometrical factors arising from the design of the resonators (as opposed to just internal friction of the suspended film) may affect the quality factor of our SCD domes. In an effort to gain insights into the microscopic mechanism of the energy loss, we measured the dissipation as a function of temperature. Figure 4 demonstrates that even though the 27 MHz natural dome and the 51 MHz FIB-made dome have substantially different dissipation at room temperature, at 10 K the dissipation of both resonators is suppressed to similar level, yielding the highest quality factor (Q ≈ 20 000). This strong temperature dependence shows that clamping loss associated with acoustic radiation through the supporting structure35
37 cannot be a dominating loss mechanism, at least not at room temperature. This conclusion is consistent with first-principlesbased calculations (Supporting Information). We would like to note that dissipation in NCD diamond resonators9,12 has a different temperature dependence with significantly higher energy loss (Figure 4), suggesting a different loss mechanism. However, we find a striking resemblance between Q
1(T) curves for our SCD dome resonators and the temperature-dependent dissipation observed for amorphous carbon (inset in Figure 4) with the steep rise of the internal friction above 100 K (attributed to a

LETTER

Figure 5. Dissipation 1/Q for different modes of vibration for three plasma-thinned (70 nm) FIB-fabricated SCD domes at room temperature is shown by green triangles, purple squares, and red circles. For one of the domes (red circles), the dissipation was also measured at 10 K, shown by blue circles.

thermally activated Zener-type dissipation process) and a plateau below 1 K associated with tunneling states.38,39 This similarity brings attention to the remaining highly disordered sacrificial layer that surrounds our SCD dome resonators. The undercut procedure with the etch rate driven by the defect concentration can leave a residue on the bottom of the domes along the periphery (“lossy lip”, Figure 1d). Besides that, the radial component of the in-plane stress associated with the plate bending is applied directly to the wall of the sacrificial layer at the clamping line on the bottom of the domes, providing an additional mechanism for energy loss governed by the internal friction of the amorphized layer. Both these mechanisms can be classified as “arising from the design of the resonator”33 and are highly inhomogeneous (i.e., different areas of the resonators contribute differently to the total energy loss). To verify the spatially inhomogeneous nature of the energy loss, we have studied dissipation for higher overtones. Dissipation for different modes of vibration for three different FIB-fabricated domes (thickness ≈70 nm) with fundamental frequencies in the 50 MHz range is shown in Figure 5. The most prominent feature is a spike in dissipation for the fourth mode observed both at room temperature and at 10 K. Both analytic34 and finite element (Supporting Information) modeling indicate that the fourth mode is the first overtone associated with an additional circular node. We argue that when the nodal diameters associated with mode 3 are replaced by a circular node (mode 4), the high stress area is shifted toward the clamping circle (i.e., the “lossy ring”), giving rise to additional dissipation. To evaluate whether dissipation in the lossy lip can account for the observed frequency dependence of Q
1 (Figure 3), we consider a model in which the energy loss occurs within a surface ring along the circumference of the dome, while the total energy stored in the resonator is dominated by the elastic energy of the dome itself. We may write (see also Supporting Information): D t E Er ð ∇2 wÞ2r η W η 2πal t r r r 2   r 2 ð1Þ Q
1  r Wd πa D ð∇2 wÞ2d where ηr(ω) is the loss factor of the ring, Wr and Wd are the energies stored in the lossy ring and the disk, respectively, lr and tr are the width and the thickness of the lossy ring, and a and t are 4306

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the radius and thickness of the disk. Er is the Young’s modulus associated with the surface layer, and D = Edt3/12 is the bending stiffness of the disk. The energy density associated with the tension in the surface lossy layer arising from the disk bending, (Ert2/8)(32w)2, and the total elastic energy in the disk are both proportional to (32w)2, where w is the vertical displacement of the dome. However, the averages are carried out over different regions and will in general not cancel out. Assuming that the ratio Æ(32w)2ær/Æ(32w)2æd for the fundamental mode does not vary with the size of the dome (a reasonable assumption if the width of the ring is small, see Supporting Information), we find that (eq 1) predicts the scaling behavior: 1=2 Q
1  ηr =a  ηr fres

ð2Þ

This qualitative prediction is in agreement with our measurements (Figure 3) if the loss factor of the heavily damaged carbon ring, ηr, is independent of frequency in this range, a notion supported by recent measurements on the internal friction of amorphous carbon in the MHz region.40 Our model suggests that a significant improvement in Q could be achieved through patterned implantation that would create spatially localized sacrificial areas (heavily damaged buried disks in the case of domes, rectangles for cantilevers and bridges, as opposed to a continuous layer). With a prolonged release procedure, one can ensure that all the damaged material is removed, leaving a pristine SCD as a supporting structure with better control over the dimensions of the SCD devices. The most important outcome of our analysis is the fact that the implantation-induced defects, accumulated within the device layer during the formation of the sacrificial layer, are not limiting the performance of our nanomechanical resonators. This result opens the way for developing very high-performance SCD nanomechanical devices based on our fabrication approach. We anticipate that the improvement in quality factor provided by the patterned sacrificial layer will enable us to detect and to develop control over the surface-related dissipation and/or implantation-induced damage.41 To conclude, we have demonstrated the fabrication and operation of ultrathin single-crystal diamond nanomechanical resonators implemented as ultrathin (tfilm ≈ 70
110 nm) partial spherical shells (domes) of SCD clamped along the periphery. These dome resonators cover a wide frequency range 10
600 MHz and exhibit quality factors up to 4000 at room temperature (27 MHz fundamental frequency). The release procedure for these SCD domes is based on dry etch (H2 plasma) of the sacrificial layer formed by C+ ion implantation. The Young’s modulus for the suspended ultrathin diamond film, E = 900 GPa, closely matches the bulk value for SCD, Ebulk = 1143 GPa. The high quality factor, Q∼20 000, demonstrated by SCD nanomechanical resonators at low temperature (10 K), is superior to that of NCD-fabricated resonators and in combination with high thermal conductivity can be enabling for cryogenic ultrasensitive force measurements. The temperature and frequency dependence of the quality factor suggests that dissipation in the residual sacrificial layer dominates the total energy loss in our current devices. Further enhancements in the quality factor should be possible based on a modified fabrication procedure.

’ ASSOCIATED CONTENT

bS

Supporting Information. Details regarding the fabrication process, experimental technique, and theoretical analysis. This

material is available free of charge via the Internet at http://pubs. acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]

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