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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 16 — Jul. 30, 2012
  • pp: 18268–18280
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Wide cantilever stiffness range cavity optomechanical sensors for atomic force microscopy

Yuxiang Liu, Houxun Miao, Vladimir Aksyuk, and Kartik Srinivasan  »View Author Affiliations


Optics Express, Vol. 20, Issue 16, pp. 18268-18280 (2012)
http://dx.doi.org/10.1364/OE.20.018268


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Abstract

We report on progress in developing compact sensors for atomic force microscopy (AFM), in which the mechanical transducer is integrated with near-field optical readout on a single chip. The motion of a nanoscale, doubly clamped cantilever was transduced by an adjacent high quality factor silicon microdisk cavity. In particular, we show that displacement sensitivity on the order of 1 fm/(Hz)1/2 can be achieved while the cantilever stiffness is varied over four orders of magnitude (≈0.01 N/m to ≈290 N/m). The ability to transduce both very soft and very stiff cantilevers extends the domain of applicability of this technique, potentially ranging from interrogation of microbiological samples (soft cantilevers) to imaging with high resolution (stiff cantilevers). Along with mechanical frequencies (> 250 kHz) that are much higher than those used in conventional AFM probes of similar stiffness, these results suggest that our cavity optomechanical sensors may have application in a wide variety of high-bandwidth AFM measurements.

© 2012 OSA

1. Introduction

Scanning force microscopy, especially atomic force microscopy (AFM), has been an essential tool for micro-/nanoscale studies in physics, chemistry, and biology, thanks to its ability to characterize the topography of a surface down to the level of individual atoms [1

1. B. Bhushan and O. Marti, “Scanning probe microsopy—principle of operation, instrumentation, and probes,” Chap. 21, in Springer Handbook of Nanotechnology, 3rd edition, B. Bhushan, ed. (Springer, Heidelberg, Germany, 2010).

,2

2. F. J. Giessibl, “Advances in atomic force microscopy,” Rev. Sci. Instrum. 75, 949–983 (2003).

] and to locally measure very small surface forces. Although conventional AFM is well-developed, progress in MEMS and nanophotonics may provide performance improvements. For example, monolithic integration of the mechanical transducer (the AFM cantilever) and the optical readout scheme within a single silicon chip can make the system compact, stable, and compatible with low-cost, batch fabrication. Developments in cavity optomechanics [3

3. T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express 15(25), 17172–17205 (2007). [CrossRef] [PubMed]

5

5. D. Van Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force,” Nat. Photonics 4(4), 211–217 (2010). [CrossRef]

] suggest that optical readout can be done with high sensitivity through near-field coupling to optical microresonators. Within such a scheme, the cantilever size can be shrunk to nanoscale dimensions, a size regime that is difficult to effectively transduce through free-space optical techniques due to strong diffraction effects, which occur when the cantilever width is smaller than the detection beam waist, and which compete with the reflection of the detection laser at the cantilever tip and hence limit the AFM sensitivity [1

1. B. Bhushan and O. Marti, “Scanning probe microsopy—principle of operation, instrumentation, and probes,” Chap. 21, in Springer Handbook of Nanotechnology, 3rd edition, B. Bhushan, ed. (Springer, Heidelberg, Germany, 2010).

,6

6. T. Kouh, D. Karabacak, D. Kim, and K. Ekinci, “Diffraction effects in optical interferometric displacement detection in nanoelectromechanical systems,” Appl. Phys. Lett. 86(1), 013106 (2005). [CrossRef]

]. Since nanoscale cantilevers can combine high (MHz) resonance frequencies with moderate stiffness (k ≈1 N/m), their effective utilization may help increase the image acquisition speed and/or time-resolution of AFM. We recently demonstrated a silicon cavity optomechanical system designed with AFM applications in mind [7

7. K. Srinivasan, H. Miao, M. T. Rakher, M. Davanço, and V. Aksyuk, “Optomechanical transduction of an integrated silicon cantilever probe using a microdisk resonator,” Nano Lett. 11(2), 791–797 (2011). [CrossRef] [PubMed]

], in which a semicircular, doubly clamped nanoscale cantilever is held within the near-field of a high quality factor (Q) microdisk cavity (Fig. 1a
Fig. 1 (a) Working principle of the disk-cantilever device. The grey parts are the device at equilibrium. The colored cantilever shows the FEM-calculated deformed shape (with an exaggerated amplitude) of the first order, in-plane, even-symmetry mechanical mode, for a system with disk diameter of 2.5 μm, cantilever width of 125 nm, and cantilever thickness of 260 nm. The color map in the microdisk resonator represents the absolute value of the FEM-calculated electric field amplitude of the TE1,10 optical mode. The mechanical motion of the cantilever is transduced by its influence on the microdisk optical mode, which is in- and out-coupled via the optical fiber taper waveguide probe. The left scale bar is for the cantilever displacement, the right one for the electric field amplitude in the microdisk, and the electric field in the fiber probe is not in scale. (b) Scanning electron micrograph of the fabricated device with nominal parameters the same as those in (a). (c) Schematic of the device characterization system.
). Thermally driven motion of the 2.35 MHz fundamental mode of the cantilever was transduced with a displacement sensitivity of ≈(4.4 ± 0.3) × 10−16 m/(Hz)1/2.

The central element of an AFM is the cantilever spring that transduces the sample-tip interaction force [2

2. F. J. Giessibl, “Advances in atomic force microscopy,” Rev. Sci. Instrum. 75, 949–983 (2003).

]. One of the most important parameters of the cantilever is its normal spring constant k. Typically, there is a trade-off between the force sensitivity and the system stability, both of which depend on the value of k. On the one hand, to ensure high force sensitivity, k should be small, so that the ratio of the mechanical displacement signal to displacement readout noise is maximized, ideally with the cantilever thermal noise dominating the readout noise over the full bandwidth of the measurement. On the other hand, for static or small amplitude dynamic operation, the tip loses stability and jumps into contact with the sample when the positive gradient of the interaction force is larger than k, so the system becomes less stable with a smaller k and at a smaller separation distance. The gradient of the interaction force varies strongly depending on the sample and distance, ranging from ≈0.1 N/m for biological samples to ≈100 N/m for solids [8

8. A. Yacoot and L. Koenders, “Aspects of scanning force microscope probes and their effects on dimensional measurement,” J. Phys. D. Appl. Phys. 41(10), 103001 (2008). [CrossRef]

]. Therefore, the cantilever stiffness has to be carefully chosen for different samples and applications. The general stiffness range of conventional AFM cantilevers is from ≈0.01 N/m to ≈100 N/m [1

1. B. Bhushan and O. Marti, “Scanning probe microsopy—principle of operation, instrumentation, and probes,” Chap. 21, in Springer Handbook of Nanotechnology, 3rd edition, B. Bhushan, ed. (Springer, Heidelberg, Germany, 2010).

], although much softer and stiffer custom cantilevers have been reported in literature for special applications [2

2. F. J. Giessibl, “Advances in atomic force microscopy,” Rev. Sci. Instrum. 75, 949–983 (2003).

,9

9. D. Rugar, R. Budakian, H. J. Mamin, and B. W. Chui, “Single spin detection by magnetic resonance force microscopy,” Nature 430(6997), 329–332 (2004). [CrossRef] [PubMed]

].

2. Working principle

The device consists of a semicircular cantilever curved around the edge of a waveguide-coupled microdisk optical resonator with a separation of ≈100 nm, as shown in Fig. 1(a). The cantilever deformation and the resonant optical mode shown in Fig. 1(a) were calculated with a commercial finite element method (FEM) software (See Section 4.2 for more details). The cantilever is clamped at its two ends, which are far away from the disk to minimize their influence on it. When the cantilever moves with respect to the disk (due to thermal noise, for example), an optical wave circulating around the disk edge feels the resulting change in peripheral refractive index, producing an effective path length change for the microdisk’s resonant optical modes which modulates their spectral position. This is converted to an intensity modulation by coupling a light field from an input optical waveguide into the device, with the input field’s wavelength tuned to the shoulder of one the microdisk cavity modes (see Fig. 1(c)) [3

3. T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express 15(25), 17172–17205 (2007). [CrossRef] [PubMed]

,4

4. T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008). [CrossRef] [PubMed]

]. The intensity modulated output field from the disk is out-coupled through the same waveguide and detected, and the electric signal from the detector is spectrally analyzed, with the cantilever’s mechanical modes showing up as strong peaks in this RF spectrum. The displacement sensitivity of the sensor is then estimated based on the amplitudes and widths of these peaks above the photodetector-limited background and the expected thermal noise amplitude for motion based on the cantilever stiffness and mass [11

11. K. Ekinci and M. L. Roukes, “Nanoelectromechanical systems,” Rev. Sci. Instrum. 76(6), 061101 (2005). [CrossRef]

,12

12. P. R. Saulson, “Thermal noise in mechanical experiments,” Phys. Rev. D Part. Fields 42(8), 2437–2445 (1990). [CrossRef] [PubMed]

].

Although there are many mechanical modes of the suspended cantilever, we focus on the first-order, in-plane, even-symmetry mode (see Fig. 1(a)), which is most strongly coupled to the microdisk optical modes and is of most relevance to our intended AFM application [3

3. T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express 15(25), 17172–17205 (2007). [CrossRef] [PubMed]

]. The ability of our system to optically transduce a given motional amplitude for this mechanical mode is a function of several parameters. The first is the optomechanical coupling parameter gOM=dωc/dx, given by the change in the microdisk mode’s optical frequency ωc per unit change in the disk-cantilever separation x. The optomechanical coupling determines how large a frequency shift is induced in the cavity’s optical mode when the cantilever vibrates. The second parameter of importance is the microdisk’s optical quality factor Q. The optical Q determines the conversion between the frequency modulation of the microdisk optical mode created by the cantilever motion and the intensity modulation produced when the input laser is tuned to the shoulder of the microdisk optical mode. The final important parameters are the out-coupled power from the sensor and the noise equivalent power of the photodetector used to convert the optical signal to an electrical signal. The out-coupled power depends on the level of waveguide-microdisk coupling, all coupling losses within the system, and the input power, the last of which is limited in order to prevent processes like two-photon absorption and free carrier absorption (which are enhanced in microcavity geometries). The instrumental noise in the system is limited by the detector dark current, while the fundamental noise is imposed by the optical shot noise. Ideally, the out-coupled power is high enough that detection is shot-noise-limited.

Our sensor geometry has been chosen to optimize parameters such as gOM and Q. The semicircular cantilever shape increases the interaction length between the microdisk optical field and the cantilever’s mechanical mode with respect to what can be achieved with a straight cantilever [10

10. O. Basarir, S. Bramhavar, and K. L. Ekinci, “Monolithic integration of a nanomechanical resonator to an optical microdisk cavity,” Opt. Express 20(4), 4272–4279 (2012). [CrossRef] [PubMed]

,13

13. G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009). [CrossRef]

,14

14. M. Li, W. H. P. Pernice, and H. X. Tang, “Reactive cavity optical force on microdisk-coupled nanomechanical beam waveguides,” Phys. Rev. Lett. 103(22), 223901 (2009). [CrossRef] [PubMed]

] (see Section 4.2 for more details). The semicircular cantilever shape largely preserves the low optical loss possible in Si microdisks [15

15. M. Borselli, T. J. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment,” Opt. Express 13(5), 1515–1530 (2005). [CrossRef] [PubMed]

], so that Q ≥ 104 can be readily achieved. Finally, we note that while other cavity optomechanical systems [16

16. Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103(10), 103601 (2009). [CrossRef] [PubMed]

,17

17. J. Chan, T. P. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011). [CrossRef] [PubMed]

] support both higher gOM and Q values, in most cases the mechanical structure involved has not been tailored to be a force/displacement transducer as needed in AFM applications. We have also observed both damping and regenerative mechanical oscillation in vacuum actuated by the gradient force, similar with that in Ref. [16

16. Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103(10), 103601 (2009). [CrossRef] [PubMed]

]. Furthermore, we anticipate that our design can be compatible with future integration with electrostatic actuation [18

18. M. C. Wu, O. Solgaard, and J. E. Ford, “Optical MEMS for lightwave communication,” J. Lightwave Technol. 24(12), 4433–4454 (2006). [CrossRef]

,19

19. S. Sridaran and S. A. Bhave, “Electrostatic actuation of silicon optomechanical resonators,” Opt. Express 19(10), 9020–9026 (2011). [CrossRef] [PubMed]

] to drive the cantilever motion.

The goal in this work is to establish the cantilever stiffness range that can be effectively transduced using our device architecture, which, as described previously, has a large bearing on the range of AFM applications appropriate for this approach. Large changes in cantilever stiffness are achieved by adjusting the cantilever length, which in turn requires a change in the microdisk diameter in order to maintain strong optomechanical coupling. For a given cantilever length and disk diameter, further stiffness tuning is obtained by adjusting the cantilever width.

3. Device fabrication and characterization setup

The devices were fabricated on silicon-on-insulator (SOI) wafers with a 260 nm top silicon device layer, 1 μm buried SiO2 layer, and 625 μm thick Si handle wafer. A 360 nm thick positive electron beam (E-beam) resist was coated on the SOI wafer, followed by electron beam lithography. After development in hexyl acetate, the silicon device layer was etched through by an SF6/C4F8 inductively coupled plasma reactive ion etch with the patterned resist serving as the mask. After removing the resist in O2 plasma, the SiO2 layer was undercut by either 49% HF or 6:1 buffered oxide etch depending on the disk diameter, followed by a liquid CO2 critical point drying process, to release the silicon cantilever and the periphery of the disk without having the cantilever stick. Optical and scanning electron microscope (SEM) images of typical devices are shown in Fig. 2
Fig. 2 Optical microscope images (a)-(c) and SEM images (e)-(g) of three fabricated devices. The disk diameter, D, and cantilever width, w, in the devices are: (a), (e) D = 2.5 μm, w = 132 nm ± 6 nm; (b), (f) D = 10 μm, w = 172 nm ± 5 nm; and (c), (g) D = 50 μm, w = 155 nm ± 7 nm. Typical zoomed-in optical spectra of high-Q optical modes obtained from devices with (d) a 10 μm disk and (h) a 50 μm disk. The spectral widths and corresponding optical Qs are (d) ≈2.5 pm and ≈6.3 × 105, and (h) ≈0.9 pm and ≈1.8 × 106, respectively. All errors are one standard deviation unless stated otherwise.
.

4. Results and discussion

Devices with three different disk diameters (2.5 μm, 10 μm, and 50 μm; corresponding cantilever total lengths of ≈6 μm, ≈25 μm, and ≈105 μm; corresponding separation between the two cantilever clamps of 5 μm, 20 μm, and 80 μm, respectively) and several nominal cantilever widths (varying from 100 nm to 250 nm) per disk diameter were fabricated in order to achieve a cantilever stiffness range encompassing the ≈0.01 N/m to ≈100 N/m range used in most conventional AFM applications. The highest optical Qs are generally on the order of 105 for devices with 10 μm disks and 106 for those with 50 μm disks, as shown in Figs. 2(d) and 2(h). However, in many cases the highest Q optical modes were not used for optomechanical transduction, for example, if the depth of coupling was too small (<10%). Broader wavelength range optical spectra, the optical modes used in optomechanical transduction, and corresponding mechanical spectra from three typical devices are shown in Fig. 3
Fig. 3 Optical spectra (a), (c), and (e) and corresponding mechanical spectra (b), (d), and (f) of three typical disk-cantilever devices. The left figures in (a), (c), and (e) show the full-range optical spectra, with the optical modes used in transducing the corresponding mechanical spectra shown in the zoomed-in right figures (orange traces). The black arrows in the zoomed-in figures show the wavelengths used for mechanical spectrum measurements. The geometrical parameters of these devices are: (a), (b) D = 2.5 μm, w = 132 nm ± 6 nm; (c), (d) D = 10 μm, w = 172 nm ± 5 nm; and (e), (f) D = 50 μm, w = 155 nm ± 7 nm.
.

The uncertainty in the width is the one standard deviation value from the SEM width measurements, and is listed in Table 1. The uncertainty in meff due to that of the width is 10%. The uncertainty in the calculated fmech is 10% and arises from the uncertainty in the moment of inertia due to the statistical error in width and the systematic error of the cross-section shape (see Section 4.5 for more detail), and the uncertainty in meff. The uncertainty in experimentally measured fmech, Qmech, and optical Q, given by the 95% confidence intervals of the curve fitting are less than 1%, 5%, and 5%, respectively. The uncertainties in keff and xrms propagated from those in measured fmech and calculated meff are 10% and 5%. The uncertainty of the displacement sensitivity arises from the combination of the systematic variation and the measurement uncertainty of the detector voltage noise power density and the uncertainty of the voltage to mechanical displacement calibration.

4.1 Parameter range and comparison with conventional AFM

According to the data shown in Fig. 4
Fig. 4 (a) Spring constants and (b) experimentally measured fundamental mechanical frequencies of the fabricated devices. A spring constant range of over 4 orders of magnitude was achieved. The uncertainties in the fundamental mechanical frequency are not shown in (b) because they are much smaller than the data points.
and Table 1, we demonstrated that the motion of cantilevers with a stiffness ranging from ≈0.01 N/m to ≈292 N/m was effectively transduced through the optomechanical interaction with the adjacent microdisk optical cavity. A photodetector-limited displacement sensitivity as low as 0.2 fm/(Hz)1/2 was achieved for a D = 10 μm, w = 172 nm device, which is slightly improved from the best results presented in Ref. [7

7. K. Srinivasan, H. Miao, M. T. Rakher, M. Davanço, and V. Aksyuk, “Optomechanical transduction of an integrated silicon cantilever probe using a microdisk resonator,” Nano Lett. 11(2), 791–797 (2011). [CrossRef] [PubMed]

]. More importantly, the displacement sensitivity remains in the fm/(Hz)1/2 range across the full range of cantilever stiffness.

Part of the motivation in using nanoscale cantilevers for AFM is that, along with a wide accessible range of stiffness and fm/(Hz)1/2 displacement sensitivity, mechanical resonance frequencies can be higher than in conventional AFM cantilevers. We observe that this is indeed the case in our devices - the fundamental mechanical frequencies (265 kHz to 111.4 MHz) are significantly higher than those of the conventional AFM probes (10 kHz to 1.1 MHz [8

8. A. Yacoot and L. Koenders, “Aspects of scanning force microscope probes and their effects on dimensional measurement,” J. Phys. D. Appl. Phys. 41(10), 103001 (2008). [CrossRef]

]). This high frequency range, enabled by the small mass of the nanoscale cantilevers, may increase the imaging acquisition rate, decrease thermal drifts [1

1. B. Bhushan and O. Marti, “Scanning probe microsopy—principle of operation, instrumentation, and probes,” Chap. 21, in Springer Handbook of Nanotechnology, 3rd edition, B. Bhushan, ed. (Springer, Heidelberg, Germany, 2010).

], reduce ambient vibration and acoustic noise [8

8. A. Yacoot and L. Koenders, “Aspects of scanning force microscope probes and their effects on dimensional measurement,” J. Phys. D. Appl. Phys. 41(10), 103001 (2008). [CrossRef]

], and increase force sensitivity [23

23. J. L. Yang, M. Despont, U. Drechsler, B. W. Hoogenboom, P. L. T. M. Frederix, S. Martin, A. Engel, P. Vettiger, and H. J. Hug, “Miniaturized single-crystal silicon cantilevers for scanning force microscopy,” Appl. Phys. Lett. 86(13), 134101 (2005). [CrossRef]

].

The mechanical Q (Qmech) of the devices mainly depends on the cantilever size and is limited by the viscous drag damping in the environment (which is at ambient pressure). The larger the disk size, the longer the cantilever and the larger viscous drag, resulting in lower Qmech. The best Qmech achieved is around 80, less than the typical Q (a few hundred [2

2. F. J. Giessibl, “Advances in atomic force microscopy,” Rev. Sci. Instrum. 75, 949–983 (2003).

]) of a conventional AFM. We believe that there are two main reasons behind these small mechanical Qs: 1) fluid dissipation scales with the surface-to-volume ratio of the moving object at a given pressure and frequency [24

24. S. S. Verbridge, R. Ilic, H. G. Craighead, and J. M. Parpia, “Size and frequency dependent gas damping of nanomechanical resonators,” Appl. Phys. Lett. 93(1), 013101 (2008). [CrossRef]

], and 2) the squeeze-film damping effect in confined nanoflows, which arises from the ballistic impact of tightly confined fluid molecules on the moving object close to a sidewall, and is especially important for gaps comparable to the mean free path of the gas [24

24. S. S. Verbridge, R. Ilic, H. G. Craighead, and J. M. Parpia, “Size and frequency dependent gas damping of nanomechanical resonators,” Appl. Phys. Lett. 93(1), 013101 (2008). [CrossRef]

,25

25. C. Lissandrello, V. Yakhot, and K. L. Ekinci, “Crossover from hydrodynamics to the kinetic regime in confined nanoflows,” Phys. Rev. Lett. 108(8), 084501 (2012). [CrossRef] [PubMed]

]. In our case, the small cantilever width results in a large surface-to-volume ratio, while the small gap (≈100 nm) is comparable to the mean free path of air at atmosphere (≈65 nm [24

24. S. S. Verbridge, R. Ilic, H. G. Craighead, and J. M. Parpia, “Size and frequency dependent gas damping of nanomechanical resonators,” Appl. Phys. Lett. 93(1), 013101 (2008). [CrossRef]

]). Thus, both factors contribute to the low mechanical Qs. By approximating the cantilever by a set of connected spheres with a diameter of 260 nm near a fixed plane, we roughly estimate Qmech due to the confined nanoflow [25

25. C. Lissandrello, V. Yakhot, and K. L. Ekinci, “Crossover from hydrodynamics to the kinetic regime in confined nanoflows,” Phys. Rev. Lett. 108(8), 084501 (2012). [CrossRef] [PubMed]

] to be 79, 5.5, and 0.265 for devices with nominal cantilever widths of 100 nm and D = 2.5 μm, 10 μm and 50 μm, respectively. These show the same trend and are of the same order of magnitude as the experimental Qmech values of 28, 10, and 1.1, respectively. Qmech may be increased if the system is placed in vacuum. Preliminary measurements of 10 μm diameter disks with 100 nm width cantilevers show an improvement in Qmech by a factor of a few hundred, up to values as high as 2x103.

Finally, we note that our semicircular cantilevers have been fabricated to include a sharp tip at their center point, with the idea being that this will eventually be used to image surface topography in AFM measurements. For this to be feasible, the tip radius should be smaller than the lateral size of the sample surface features that are to be resolved. The typical tip radius of our disk-cantilever devices is ≈10 nm (based on SEM, not shown); in comparison, micromachined silicon and silicon nitride tips of the conventional AFM have radii from <10 nm to 50 nm [1

1. B. Bhushan and O. Marti, “Scanning probe microsopy—principle of operation, instrumentation, and probes,” Chap. 21, in Springer Handbook of Nanotechnology, 3rd edition, B. Bhushan, ed. (Springer, Heidelberg, Germany, 2010).

]. Our tip radius thus lies within the size range of the conventional AFM tips, while additional processing methods (focused ion beam milling or masked chemical etching) may be considered in the future to produce sharper tips.

4.2 Optomechanical coupling parameter gOM

The simulation results of devices with different disk diameters and curved cantilevers are shown in Fig. 5
Fig. 5 (a) Sketches of 10 μm disks with (top) a curved cantilever and (bottom) a straight cantilever. (b) Simulated optomechanical coupling parameter gOM of TE/TM optical modes in the disk for devices with different disk sizes. Results for devices with curved cantilevers are shown as solid curves, while those for devices with straight cantilevers and 10 μm disks are presented as dashed curves for comparison. The cantilever width for all devices is set to 100 nm in the simulations. (c) Simulated optical Q of the TE1,10 mode for devices with 2.5 μm disk diameter, 100 nm cantilever width, and different cantilever-disk gaps.
. Simulation results of a device with a 10 μm disk and a straight cantilever are also included to illustrate the influence of the curved cantilever design. The straight cantilever (see Fig. 5(a)) has the same total length and width as the curved cantilever, and the disk-cantilever separation is taken to be the value at the point of the closest approach, which is the center point of the cantilever. We only show a TE mode for the 2.5 μm device in Fig. 5(b), because modes of TM polarization were not observed in the experiment. All the optical modes we studied in the simulation have wavelengths close to the ones used in the experiment. According to Fig. 5(b), at a gap of 100 nm, gOM/2π ≈260 MHz/nm for 50 μm devices, 550 MHz/nm for 10 μm devices, and 4.7 GHz/nm for 2.5-μm devices (TE modes). Further improvements can be made by reducing the gap to 50 nm, in which case the values increase to 750 MHz/nm, 2.14 GHz/nm, and 15.7 GHz/nm, respectively. In comparison, gOM/2π ≈50 MHz/nm at 100 nm gap for the same TE mode of 10 μm devices with straight cantilevers (dashed curves in Fig. 5(b)), ≈11 times less than that with curved cantilevers. The gOM values with curved cantilevers are also consistently larger than those predicted in literature with geometries using straight cantilevers [10

10. O. Basarir, S. Bramhavar, and K. L. Ekinci, “Monolithic integration of a nanomechanical resonator to an optical microdisk cavity,” Opt. Express 20(4), 4272–4279 (2012). [CrossRef] [PubMed]

,13

13. G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009). [CrossRef]

], by one to two orders of magnitude. This improvement indicates one benefit of the curved cantilever design in terms of stronger optomechanical coupling, and the resulting potential for higher sensitivity in detection of the cantilever motion. The value of gOM decreases quickly when the gap increases from 30 nm to 200 nm, suggesting that a small gap is always beneficial for a large gOM, if fabrication difficulties are not considered.

4.3 Fabrication considerations

There are still some remaining difficulties in the fabrication process. For example, the gap between the cantilever and disk was not always uniformly etched through. Another difficulty is that the cantilever is relatively frequently stuck in the devices with 50-μm disks, due to its low stiffness and long length, though we have found that a post-fabrication bake at 140 °C can help prevent eventual sticking problems. Overall, the average success rate in the fabricated devices was about 50%, with a somewhat higher rate for the 2.5 μm diameter devices and a lower rate (≈20%) for the 50 μm devices.

4.4 Factors limiting the stiffness range

We believe we are approaching both the upper and the lower limits of the stiffness range that can be effectively transduced with the current disk-cantilever architecture and setup. On the soft side, the sticking issues discussed above make it increasingly difficult to obtain a freely suspended cantilever in air. We also fabricated 10 μm disks whose cantilevers had an extended length between the semicircular and clamped regions to decrease the stiffness, but the sticking issue remained. If the device is put into vacuum right after fabrication, smaller stiffness values might be possible to achieve. On the stiff side, the aforementioned limited optical Qs for 2.5 μm diameter devices, and the additional decrease in Q with increasing cantilever width, suggest that further increase of the cantilever stiffness might require redesign of the device geometry.

4.5 Influence of slanted sidewalls of the cantilever

In fabricated devices, the cantilever sidewalls are sloped, resulting in a trapezoidal cross-section. The w values listed in Table 1 were taken as the average of the top and the bottom widths as measured in the SEM. FEM simulations, on the other hand, were performed assuming that the cross-section of the cantilever is rectangular. To justify this simplification, we consider how the response of simple beams with rectangular and trapezoidal cross-sections varies. Since the deformation of the cantilever is mainly in-plane bending (See Fig. 1(a)), and the two cantilevers with different cross-sections have the same length, height, and mass, their behavior under the same excitation forces can be determined by the area moments of inertia, I. For a trapezoidal cross-section subjected to in-plane bending,
Itrap=h36(w1+w2)[w14+w24+2w1w2(w12+w22)+w2w12(w13+3w12w23w1w22w23)+(w2w12)2(w12+4w1w2+w22)],
(2)
where w1 is the top width, w2 the bottom width, h the height of the cross-section [26

26. W. C. Young and R. G. Budynas, Roark’s Formulas for Stress and Strain, 7th ed. (McGraw-Hill, 2002), App. A.

]. In the case of a rectangular cross-section with a width of w = (w1 + w2)/2 and a height of h,

Irect=w3h12.
(3)

Because the difference between w1 and w2 is determined by the etch process, and does not depend on the average w, the difference between these two area moments of inertia is larger for smaller w. Two typical sets of data are: w1 = 70 nm and w2 = 130 nm with a smallest average w of 100 nm, and w1 = 240 nm and w2 = 297 nm with a largest average w of 269 nm. According to Eqs. (2) and (3), the difference between Itrap and Irect are 8.3% and 1.1%, respectively, with Itrap always larger than Irect. This relatively small difference implies that the simulation results are reasonably reliable under the assumption of rectangular cross-sections.

4.6 Outlook

One might generically expect improved device performance (at least in terms of displacement sensitivity) if gOM and the optical Q are increased. The most straightforward route to increased gOM without influencing the cantilever stiffness is through a reduction in the disk-cantilever gap (See Fig. 5(b)). While we have had some success in fabricating smaller gaps (Ref. [7

7. K. Srinivasan, H. Miao, M. T. Rakher, M. Davanço, and V. Aksyuk, “Optomechanical transduction of an integrated silicon cantilever probe using a microdisk resonator,” Nano Lett. 11(2), 791–797 (2011). [CrossRef] [PubMed]

]), this is not yet a repeatable process, and is made challenging due to the relatively large aspect ratio needed with the current electron beam resist process (>7:1 for a 50 nm gap). In addition, smaller gaps lead to lower optical Q values at wider cantilever widths. Increasing the optical Q is beneficial, provided that the frequency shift induced by the cantilever motion, x, is within the cavity mode line shape (i.e., the linear range of the optical readout, approximately given by gOMx<ωc/Q).

Achieving shot-noise-limited detection of the optically transduced signal can be challenging within these silicon-based devices, as the amount of input power that can be injected into the microdisk cavity is limited by processes such as two-photon absorption and free-carrier absorption, which are enhanced in small mode volume, high quality factor cavities [27

27. P. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express 13(3), 801–820 (2005). [CrossRef] [PubMed]

,28

28. Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15(25), 16604–16644 (2007). [CrossRef] [PubMed]

]. As a result, one might consider optically amplifying the output signal from the system, or rather than direct photodetection, beating the output signal against a strong local oscillator in a homodyne measurement. In addition to allowing shot-noise-limited detection, such an approach can track the output amplitude and phase, the latter of which can be used as the dispersive signal needed to lock the input laser to the cavity.

For conventional AFM working in the dynamic mode, the tip oscillation amplitudes used range from a couple of nanometers to tens of nanometers. Although small amplitudes in the range of sub-nanometer help increase the sensitivity to short-range forces, the instability of the system discussed in Section 1 gets severe [2

2. F. J. Giessibl, “Advances in atomic force microscopy,” Rev. Sci. Instrum. 75, 949–983 (2003).

]. The thermally driven displacement in our devices is not sufficiently large to be used in functional AFM applications. Sufficiently large coherent cantilever oscillation can be induced in vacuum through radiation pressure forces, or alternatively using electrostatic or external piezoelectric actuation.

5. Conclusion

We experimentally demonstrated a cavity optomechanical sensor optimized for AFM applications, in which the motion of an integrated cantilever probe is optically transduced through near-field coupling to a microdisk optical cavity. Our main focus here was to demonstrate that this platform is compatible with a broad range of cantilever stiffness, and we demonstrate a stiffness range from ≈0.01 N/m to ≈290 N/m while maintaining fm/(Hz)1/2 displacement sensitivity (or better). The resonance frequencies (≈200 kHz to ≈110 MHz) of the cantilevers in our devices are much higher than those of conventional AFM, which may increase the imaging acquisition rate, reduce noise, and improve force sensitivity. This compact, monolithic sensor geometry and the large stiffness range that it can access suggest that these devices may have potential in a variety of AFM applications. With a low stiffness (≈0.01 N/m), the device may be used as an on-chip version of AFM for label-free detection and in situ characterization of microbiological samples [29

29. Y. F. Dufrêne, “Towards nanomicrobiology using atomic force microscopy,” Nat. Rev. Microbiol. 6(9), 674–680 (2008). [CrossRef] [PubMed]

]. With a high stiffness (≈290 N/m), the small amplitude and increased sensitivity to short-ranged interaction forces may be suitable for high-resolution AFM imaging. Future work will focus on integration of electrostatic actuation of nanocantilever motion, incorporation of these cavity optomechanical sensors in an AFM imaging setup, and in better understanding how techniques like radiation pressure cooling and excitation may be exploited in AFM measurements.

Acknowledgments

The authors thank Richard Kasica of the CNST NanoFab for assistance with the development of electron beam lithography process, and Marcelo Davanço for help with FEM simulations. Yuxiang Liu acknowledges support under the National Institute for Standards and Technology American Recovery and Reinvestment Act Measurement Science and Engineering Fellowship Program Award 70NANB10H026 through the University of Maryland. Houxun Miao acknowledges support under the Cooperative Research Agreement between the University of Maryland and the National Institute of Standards and Technology Center for Nanoscale Science and Technology, Award 70NANB10H193, through the University of Maryland.

References and links

1.

B. Bhushan and O. Marti, “Scanning probe microsopy—principle of operation, instrumentation, and probes,” Chap. 21, in Springer Handbook of Nanotechnology, 3rd edition, B. Bhushan, ed. (Springer, Heidelberg, Germany, 2010).

2.

F. J. Giessibl, “Advances in atomic force microscopy,” Rev. Sci. Instrum. 75, 949–983 (2003).

3.

T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express 15(25), 17172–17205 (2007). [CrossRef] [PubMed]

4.

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008). [CrossRef] [PubMed]

5.

D. Van Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force,” Nat. Photonics 4(4), 211–217 (2010). [CrossRef]

6.

T. Kouh, D. Karabacak, D. Kim, and K. Ekinci, “Diffraction effects in optical interferometric displacement detection in nanoelectromechanical systems,” Appl. Phys. Lett. 86(1), 013106 (2005). [CrossRef]

7.

K. Srinivasan, H. Miao, M. T. Rakher, M. Davanço, and V. Aksyuk, “Optomechanical transduction of an integrated silicon cantilever probe using a microdisk resonator,” Nano Lett. 11(2), 791–797 (2011). [CrossRef] [PubMed]

8.

A. Yacoot and L. Koenders, “Aspects of scanning force microscope probes and their effects on dimensional measurement,” J. Phys. D. Appl. Phys. 41(10), 103001 (2008). [CrossRef]

9.

D. Rugar, R. Budakian, H. J. Mamin, and B. W. Chui, “Single spin detection by magnetic resonance force microscopy,” Nature 430(6997), 329–332 (2004). [CrossRef] [PubMed]

10.

O. Basarir, S. Bramhavar, and K. L. Ekinci, “Monolithic integration of a nanomechanical resonator to an optical microdisk cavity,” Opt. Express 20(4), 4272–4279 (2012). [CrossRef] [PubMed]

11.

K. Ekinci and M. L. Roukes, “Nanoelectromechanical systems,” Rev. Sci. Instrum. 76(6), 061101 (2005). [CrossRef]

12.

P. R. Saulson, “Thermal noise in mechanical experiments,” Phys. Rev. D Part. Fields 42(8), 2437–2445 (1990). [CrossRef] [PubMed]

13.

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009). [CrossRef]

14.

M. Li, W. H. P. Pernice, and H. X. Tang, “Reactive cavity optical force on microdisk-coupled nanomechanical beam waveguides,” Phys. Rev. Lett. 103(22), 223901 (2009). [CrossRef] [PubMed]

15.

M. Borselli, T. J. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment,” Opt. Express 13(5), 1515–1530 (2005). [CrossRef] [PubMed]

16.

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103(10), 103601 (2009). [CrossRef] [PubMed]

17.

J. Chan, T. P. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011). [CrossRef] [PubMed]

18.

M. C. Wu, O. Solgaard, and J. E. Ford, “Optical MEMS for lightwave communication,” J. Lightwave Technol. 24(12), 4433–4454 (2006). [CrossRef]

19.

S. Sridaran and S. A. Bhave, “Electrostatic actuation of silicon optomechanical resonators,” Opt. Express 19(10), 9020–9026 (2011). [CrossRef] [PubMed]

20.

K. Srinivasan, P. Barclay, M. Borselli, and O. Painter, “Optical-fiber-based measurement of an ultrasmall volume high-Q photonic crystal microcavity,” Phys. Rev. B 70(8), 081306(R) (2004). [CrossRef]

21.

C. P. Michael, M. Borselli, T. J. Johnson, C. Chrystal, and O. Painter, “An optical fiber-taper probe for wafer-scale microphotonic device characterization,” Opt. Express 15(8), 4745–4752 (2007). [CrossRef] [PubMed]

22.

H. Miao, K. Srinivasan, M. T. Rakher, M. Davanco, and V. Aksyuk, “Cavity optomechanical sensors,” in 2011 16th International Solid-State Sensors, Actuators and Microsystems Conference (TRANSDUCERS), , (IEEE, 2011), pp. 1535–1538.

23.

J. L. Yang, M. Despont, U. Drechsler, B. W. Hoogenboom, P. L. T. M. Frederix, S. Martin, A. Engel, P. Vettiger, and H. J. Hug, “Miniaturized single-crystal silicon cantilevers for scanning force microscopy,” Appl. Phys. Lett. 86(13), 134101 (2005). [CrossRef]

24.

S. S. Verbridge, R. Ilic, H. G. Craighead, and J. M. Parpia, “Size and frequency dependent gas damping of nanomechanical resonators,” Appl. Phys. Lett. 93(1), 013101 (2008). [CrossRef]

25.

C. Lissandrello, V. Yakhot, and K. L. Ekinci, “Crossover from hydrodynamics to the kinetic regime in confined nanoflows,” Phys. Rev. Lett. 108(8), 084501 (2012). [CrossRef] [PubMed]

26.

W. C. Young and R. G. Budynas, Roark’s Formulas for Stress and Strain, 7th ed. (McGraw-Hill, 2002), App. A.

27.

P. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express 13(3), 801–820 (2005). [CrossRef] [PubMed]

28.

Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15(25), 16604–16644 (2007). [CrossRef] [PubMed]

29.

Y. F. Dufrêne, “Towards nanomicrobiology using atomic force microscopy,” Nat. Rev. Microbiol. 6(9), 674–680 (2008). [CrossRef] [PubMed]

OCIS Codes
(180.5810) Microscopy : Scanning microscopy
(140.3948) Lasers and laser optics : Microcavity devices
(230.4685) Optical devices : Optical microelectromechanical devices

ToC Category:
Microscopy

History
Original Manuscript: May 11, 2012
Revised Manuscript: July 6, 2012
Manuscript Accepted: July 16, 2012
Published: July 25, 2012

Citation
Yuxiang Liu, Houxun Miao, Vladimir Aksyuk, and Kartik Srinivasan, "Wide cantilever stiffness range cavity optomechanical sensors for atomic force microscopy," Opt. Express 20, 18268-18280 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-16-18268


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References

  1. B. Bhushan and O. Marti, “Scanning probe microsopy—principle of operation, instrumentation, and probes,” Chap. 21, in Springer Handbook of Nanotechnology, 3rd edition, B. Bhushan, ed. (Springer, Heidelberg, Germany, 2010).
  2. F. J. Giessibl, “Advances in atomic force microscopy,” Rev. Sci. Instrum.75, 949–983 (2003).
  3. T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express15(25), 17172–17205 (2007). [CrossRef] [PubMed]
  4. T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science321(5893), 1172–1176 (2008). [CrossRef] [PubMed]
  5. D. Van Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force,” Nat. Photonics4(4), 211–217 (2010). [CrossRef]
  6. T. Kouh, D. Karabacak, D. Kim, and K. Ekinci, “Diffraction effects in optical interferometric displacement detection in nanoelectromechanical systems,” Appl. Phys. Lett.86(1), 013106 (2005). [CrossRef]
  7. K. Srinivasan, H. Miao, M. T. Rakher, M. Davanço, and V. Aksyuk, “Optomechanical transduction of an integrated silicon cantilever probe using a microdisk resonator,” Nano Lett.11(2), 791–797 (2011). [CrossRef] [PubMed]
  8. A. Yacoot and L. Koenders, “Aspects of scanning force microscope probes and their effects on dimensional measurement,” J. Phys. D. Appl. Phys.41(10), 103001 (2008). [CrossRef]
  9. D. Rugar, R. Budakian, H. J. Mamin, and B. W. Chui, “Single spin detection by magnetic resonance force microscopy,” Nature430(6997), 329–332 (2004). [CrossRef] [PubMed]
  10. O. Basarir, S. Bramhavar, and K. L. Ekinci, “Monolithic integration of a nanomechanical resonator to an optical microdisk cavity,” Opt. Express20(4), 4272–4279 (2012). [CrossRef] [PubMed]
  11. K. Ekinci and M. L. Roukes, “Nanoelectromechanical systems,” Rev. Sci. Instrum.76(6), 061101 (2005). [CrossRef]
  12. P. R. Saulson, “Thermal noise in mechanical experiments,” Phys. Rev. D Part. Fields42(8), 2437–2445 (1990). [CrossRef] [PubMed]
  13. G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys.5(12), 909–914 (2009). [CrossRef]
  14. M. Li, W. H. P. Pernice, and H. X. Tang, “Reactive cavity optical force on microdisk-coupled nanomechanical beam waveguides,” Phys. Rev. Lett.103(22), 223901 (2009). [CrossRef] [PubMed]
  15. M. Borselli, T. J. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment,” Opt. Express13(5), 1515–1530 (2005). [CrossRef] [PubMed]
  16. Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett.103(10), 103601 (2009). [CrossRef] [PubMed]
  17. J. Chan, T. P. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature478(7367), 89–92 (2011). [CrossRef] [PubMed]
  18. M. C. Wu, O. Solgaard, and J. E. Ford, “Optical MEMS for lightwave communication,” J. Lightwave Technol.24(12), 4433–4454 (2006). [CrossRef]
  19. S. Sridaran and S. A. Bhave, “Electrostatic actuation of silicon optomechanical resonators,” Opt. Express19(10), 9020–9026 (2011). [CrossRef] [PubMed]
  20. K. Srinivasan, P. Barclay, M. Borselli, and O. Painter, “Optical-fiber-based measurement of an ultrasmall volume high-Q photonic crystal microcavity,” Phys. Rev. B70(8), 081306(R) (2004). [CrossRef]
  21. C. P. Michael, M. Borselli, T. J. Johnson, C. Chrystal, and O. Painter, “An optical fiber-taper probe for wafer-scale microphotonic device characterization,” Opt. Express15(8), 4745–4752 (2007). [CrossRef] [PubMed]
  22. H. Miao, K. Srinivasan, M. T. Rakher, M. Davanco, and V. Aksyuk, “Cavity optomechanical sensors,” in 2011 16th International Solid-State Sensors, Actuators and Microsystems Conference (TRANSDUCERS), , (IEEE, 2011), pp. 1535–1538.
  23. J. L. Yang, M. Despont, U. Drechsler, B. W. Hoogenboom, P. L. T. M. Frederix, S. Martin, A. Engel, P. Vettiger, and H. J. Hug, “Miniaturized single-crystal silicon cantilevers for scanning force microscopy,” Appl. Phys. Lett.86(13), 134101 (2005). [CrossRef]
  24. S. S. Verbridge, R. Ilic, H. G. Craighead, and J. M. Parpia, “Size and frequency dependent gas damping of nanomechanical resonators,” Appl. Phys. Lett.93(1), 013101 (2008). [CrossRef]
  25. C. Lissandrello, V. Yakhot, and K. L. Ekinci, “Crossover from hydrodynamics to the kinetic regime in confined nanoflows,” Phys. Rev. Lett.108(8), 084501 (2012). [CrossRef] [PubMed]
  26. W. C. Young and R. G. Budynas, Roark’s Formulas for Stress and Strain, 7th ed. (McGraw-Hill, 2002), App. A.
  27. P. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express13(3), 801–820 (2005). [CrossRef] [PubMed]
  28. Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express15(25), 16604–16644 (2007). [CrossRef] [PubMed]
  29. Y. F. Dufrêne, “Towards nanomicrobiology using atomic force microscopy,” Nat. Rev. Microbiol.6(9), 674–680 (2008). [CrossRef] [PubMed]

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