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Characterization of Semiconductor Nanowires Using Optical Tweezers Peter J. Reece,*,† Wen Jun Toe,† Fan Wang,† Suriati Paiman,‡,§ Qiang Gao,‡ H. Hoe Tan,‡ and C. Jagadish‡ †
School of Physics, The University of New South Wales, Sydney, NSW 2052, Australia Department of Electronic Materials Engineering, Research School of Physics and Engineering, The Australian National University, Canberra, ACT 0200, Australia § Department of Physics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia ‡
ABSTRACT: We report on the optical trapping characteristics of InP nanowires with dimensions of 30 ((6) nm in diameter and 215 μm in length. We describe a method for calibrating the absolute position of individual nanowires relative to the trapping center using synchronous high-speed position sensing and acousto-optic beam switching. Through Brownian dynamics we investigate effects of the laser power and polarization on trap stability, as well as length dependence and the effect of simultaneous trapping multiple nanowires. KEYWORDS: Semiconductor nanowires, optical tweezers, Brownian motion, nanoparticle metrology
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emiconductor nanowires, defined by cross-sectional dimensions of tens to hundreds nanometers and lengths of several micrometers, are currently under investigation for a range of physical and chemical properties that are derived in part by their unique nanoscale geometry. Strong light scattering by semiconductor nanowires may be utilized for enhanced light trapping in photovoltaic applications,1 nanowires combined with organic semiconductors are appropriate for bulk heterojunctions devices, and large surface to volume ratios exhibited by nanowires provide a platform for nanoscale-chemical sensing elements.2 In terms of potential device applications, both composition and geometric factors are combined to deliver new functional devices from single nanowire elements including nanolasers,3 photodetectors,4 single nanowire transistors5 and field emission sources. These elements may also be combined to create a new architecture for an integrated microprocessor.6 Semiconductor nanowire devices may include axial or radial quantum heterostructures,7 electrical doping and heterojunctions, as well as metallic or dielectric coating for supporting optical or plasmonic waveguiding. As the dimensions of the nanoscale objects are critical in determining functionality in associated devices, it is essential to develop effective tools with the ability to characterize individual objects, rather than rely on bulk or ensemble average measurements. For nanowires with well-defined geometric forms, optical tweezers offers a potentially powerful tool for investigating physical and optical properties of individual objects. With optical tweezers, nanowires may be isolated and controllably manipulated in three-dimensions,8 interrogated using spectroscopic techniques such as microphotoluminescence,9 and assembled into predetermined arrangements over fiduciary registration points for further microprocessing.10 Importantly, the natural Brownian dynamics of the nanowires trapped in an optical tweezers may also provide insights into nanowire properties. Physical properties r 2011 American Chemical Society
such as length, width, refractive index, and extinction coefficient all influence the optical gradient and scattering forces generated by laser, which in turn affects the motion of the trapped objects driven by thermal motion. Such physical parameters may be elucidated by monitoring the thermal motion of the nanowires with respect to the center of the optical trap using interferometry techniques. Part of the difficulty associated with conducting such quantitative trapping measurements on irregularly shaped objects or polydispersed suspensions, such as nanowires, is that the position calibration is unique for the particular object under investigation. This is in contrast to monodispersed spherical suspensions where all particles may be assumed to have a common optical response for the position sensitive detector (PSD)—for a given optical arrangement.11 Even for methods such as the power spectrum analysis,12 where absolute position calibration is unnecessary, the need to determine physical dimensions to account for hydrodynamic drag can often lead to uncertainty in absolute values of trap stiffness and associated optical force measurements. Methods have been proposed to circumvent this problem for microparticles; Greenleaf et al.13 used a weak secondary laser source with different wavelength as a detection beam, which allows independent control of position of the trapped object with respect to the detection beam. In this scheme, optically trapped objects are scanned across a static detection beam using precise positioning of the tweezers beam (e.g., using galvanostatic mirrors) and the response of the PSD is recorded. Here we present a new method for calibration of trapped objects based on fast acousto-optic switching and position sensitive detection using a back focal plane interferometry. This Received: March 3, 2011 Revised: April 24, 2011 Published: May 02, 2011 2375
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Figure 1. (a) Graphical representation of the experimental setup used for nanowire trapping experiments (not to scale). A 1064 nm diode pumped solid-state laser is used as the tweezers sources and a fastswitching two-axis acousto-optic deflector (AOD) is used to control the position of the trap in the focal plane. Detection of the motion of the nanowires in the trap is achieved by back-focal plane interferometry using a position sensitive detector (PSD). (b) PSD calibration method: the nanowire is first captured in the optical tweezers at the origin (xo); the tweezers and nanowire are displaced by a small amount; the beam is transiently switched back to the xo and the signal on the PSD is recorded; finally, the tweezers is switched back to capture the nanowire before it diffuses away.
technique allows for the calibration of the position sensitive detector for target objects with arbitrary dimensions, while removing the need for a secondary laser source. Making use of the concepts of trap multiplexing based on time-sharing approach,14 our technique uses a field programmable gate array (FPGA) data acquisition card to synchronize the readings from the PSD with the addressing of a two-axis acousto-opitc deflector. The calibration procedure involves moving the trapped objects to different positions around fixed trapping center and measuring the response of the PSD when the beam is briefly switched back to the origin. We apply the above method to investigate the Brownian dynamics of optically trapped semiconductor nanowires with very large aspect ratios. Specifically we investigate effects of the laser power, laser polarization, nanowire length dependence, and the effect of trapping multiple nanowires on trap stiffness. Experimental Methods. Figure 1a depicts the basic setup of the optical tweezers arrangement. A linearly polarized 1064 nm
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YAG laser (5 W Laser Quantum, 1064 Ventus) is used for the laser-trapping source; a half-waveplate and polarizing beam splitter are used to control the power at the focus. The beam is directed through a two-axis acousto-optic deflector (AOD) (NEOS Technologies, model 45035-3-6.5DEG-1.060XY) driven by two digital frequency synthesizers (DFS) operating in the range of 2545 MHz. The radio frequency sources are addressed using a FPGA data-acquisition card (National Instruments PCIe7852R) with a 30-bit digital control word and the DFS has a latching time of 20 ns. The AOD switching rate is 4.5 μs, which sets the system response. The deflected beam is directed toward the back aperture of the objective through a beam-expanding telescope to match the beam waist to the back-aperture of a 1.25 numerical aperture (NA) oil immersion objective (Nikon E-plan 100). A second half waveplate is used to control the orientation of the polarization incident on the objective. An additional relay telescope is used to ensure the AOD and back-aperture is positioned in conjugate image planes. Scattered light from optically trapped objects is collected using a long working distance objective (S Plan Fluor ELWD 40, 0.65 NA), which also acts as a condenser for bright field illumination. The interference pattern generated at the scattered light is relayed to a dual axis position sensitive detector (Pacific Silicon Sensors DL16-7PCBA3) with a bandwidth of 300 kHz. The signal from the detector is collected on the analog inputs of the FPGA data acquisition card. Direct bright-field imaging of the nanowires was done using a high-frame-rate CCD camera (Basler a602f) in combination with Kohler illumination. InP nanowires used for this study were epitaxially grown on an InP (111)B substrate by metal organic chemical vapor deposition (MOCVD).15 The semiconductor substrates were initially immersed in poly-L-lysine solution and treated with gold colloid solution containing gold nanoparticles of 30 nm in diameter. The nanowires were then grown in the MOCVD reactor using trimethylindium (TMIn) and phosphine (PH3) precursors, with the gold nanoparticles acting as seeds for the growth via the vaporliquidsolid (VLS) mechanism.16 During growth, pressure was kept at 100 mbar while the temperature was set at 490 C, the V/III ratio was set at 44, and the growth time is approximately 20 min. These growth conditions produced nanowires of very uniform cylindrical geometry of dimensions 30 ( 6 nm in diameter and up to 15 μm in length. The nanowires had a predominantly wurtzite crystal structure, which was confirmed by high-resolution transmission electron and scanning electron microscopy measurements.17 For optical tweezers experiments nanowires, were suspended in an aqueous solution by sonication of the as-grown nanowires from their native substrate; the sonication process produced a range of nanowire lengths between 2 and 15 μm. A 5 μL volume of nanowire suspension was pipetted into a sealed microfluidic chamber with a height of approximately 100 μm. To trap a nanowire in the tweezers, a freely suspended nanowire was moved in the proximity of the laser focus—for high refractive index semiconductor nanowires with lengths extending beyond the depth of focused of the optical tweezers beam, the nanowires naturally aligned with its long axis along the direction of propagation. We note that because the nanowires were regularly shaped, we see no rotation or preferential orientation within the trap. We also note that at trapping powers in the range of milliwatts to tens of milliwatts the Brownian motion is observed to be preferentially translational in nature. Time-series data of positional fluctuations within the trap were collected for periods 2376
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of 2 s at a rate of 10 kHz; low pass filtering was used to remove any nonthermal contributions to the nanowire motion before the data were analyzed. After each trapping measurement the nanowire is displaced from the trap and immobilized against the microchamber where the length of nanowire was measured. With the aid of the illustration given in Figure 1b, the position sensitive detector calibration procedure is outlined as follows: (i) a nanowire is trapped with its long axis aligned to the propagation direction of the laser and the initial trapping position is set as the trapping origin (x0, y0); (ii) the trap position is then displaced by a small distance (x0 þ Δx, y0) by modifying the AOD deflection angle; (iii) the laser is briefly (25 μs) switched to the origin and the resulting scattered field recorded (via the PSD) before the beam is switched back to the displaced position; (iv) this process is repeated 2000 times to build up a statistical average of the detector signal at this position. Steps ii to iv are then repeated for a number at difference displacements around the origin in the x and y direction. The detector provides voltage, Vx(diff), analogues for relative position of the interference pattern within the active area of the detector for the x and y axis and also a sum voltage, Vx(sum), that may be used to normalize the signal, e.g., Rx = Vx(diff)/Vx(sum). This calibration procedure then provides a relationship between the raw detector signal from the PSD and the position of the object relative to the trapping origin. Theoretical Consideration. For small displacements, the restoring force acting on an optically trapped object is proportional to its displacement from the trapping center. The strength of the optical restoring force is largely dependent on the beam geometry and the shape and dielectric properties of the trapped object. For a trapped particle within an aqueous medium, the system can be described as a highly overdamped harmonic oscillator for the three translation coordinates.18 Using the EinsteinOrnsteinUhlenbeck theory of Brownian motion, the motion of the trapped particle can be described by a Langevin equation in the form19 D2 x Dx m 2 þ γ0 þ kx ¼ ð2kB Tγ0 Þ1=2 ηðtÞ Dt Dt
ð1Þ
where m is the mass of the particle, x(t) is the trajectory of the particle, κ is the trap stiffness, γ 0 is the drag coefficient of the particle, kB is Boltzmann’s constant, T is the temperature, and η(t) denotes the stochastic process of the Brownian motion of the trapped particle. Here the first term on the left is the inertial term, the second is the viscous damping or Stokes drag, and the third term is the optical restoring force. The term on right-hand side denotes the Brownian forces at absolute temperature T. As the characteristic time for momentum relaxation through viscous damping, tp m/γ0 is very small (i.e., low Reynolds number environment) the inertial term may be neglected. Similar equations can be used to describe motion in y and z directions, but with differing trap stiffness and drag coefficients. We note that rotational and rocking motions have been neglected in this case; however under certain conditions elongated objects such as nanowires will exhibit such dynamics.20 To analyze the behavior of the Brownian motion, we use two standard methods: the power spectrum and Equipartion methods. Following from Berg-Sorensen and Flyvbjerg,12 the above equation may be approximated by Dx þ 2πfc x ¼ ð2DÞ1=2 ηðtÞ Dt
ð2Þ
where we have defined the corner frequency, fc κ/2πγ0, and D = kBT/γ0 is the Einstein equation for diffusion of particles through a fluid medium. By taking the Fourier transformation of (2) we may find the power spectrum, S, is given by the Lorentzian equation 2 j~xj D=2π2 ð3Þ ¼ 2 S T fc þ f 2 where ~x is the Fourier transform of x(t). Hence, we can obtain the value of fc by fitting a Lorentzian to our experimental data and then calculate the trap stiffness κ. Note that in order to accurately predict the trap stiffness parameter, we need to know the form of drag coefficient for the objects of interest. For spherical particles such as colloidal microspheres this is a well-known analytical expression; however for more complex shapes, such as elongated cylinders, no analytical expression is available. Here we model the nanowires as cylinders and compute the Stokes’ drag for cylindrical objects based on computational models developed by Tirado and Torre.21 The drag coefficient of a cylinder with radius r, length l, in a fluid of viscosity η0 can be written empirically as γc ¼
4πη0 l lnð1=2rÞ þ γ^
ð4Þ
where γ^ is a correction factor accounting for the ends of the nanowire, which is calculated to be 0.84.21 The nanowires used in this study have very high aspect ratios, in the range of 70300, and as such the log term in the denominator is only weakly dependent on the length of the wire and the drag coefficient is predicted to be approximately linearly dependent with respect to the length of the nanowire. The Equipartition theorem, which relates the available thermal energy of a system to the number of degrees of freedom, may be used as an alternative approach to measure the trap stiffness for an optically trapped object.11 For a particle trapped within a harmonic potential well, the probability for the displacement of a trapped particle within a potential well is given by UðxÞ PðxÞ exp ð5Þ kB T where U(x) = (1/2)κx2 and x is the displacement from the trap center. Tracking the trapped nanowires thermal motion over a period of time provides a statistical histogram of particle position, which may be then used to determine the trap stiffness. This method requires the absolute position of object displacement with respect to the trap center but has an important advantage for nanowire studies in that it is independent of the drag properties of trapped objects, so the length of the nanowire does not need to be known a priori in order to calculate trap stiffness values. This is important as the absolute lengths of specific trapped nanowires are only resolved to the resolution of the bright field imaging. Results and Discussion. Figure 2a contains the normalized detector response of an optically trapped nanowire of length 12 μm, for displacements of up to 0.6 μm from the trap center. The detector response curve exhibits a form characteristic of trapped spherical objects22 and includes a linear region near the trapping origin and a strongly nonlinear region at larger displacement; these features are consistent for all nanowire lengths tested. The graphs indicate that if the position fluctuations of the nanowire are restricted to less than approximately (200 nm then the linearity of the detector response may be preserved. Note that 2377
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Figure 2. (a) Position sensitive detector (PSD) response for the lateral displacement of a 12 μm nanowire within an optical trap. The curve has a linear response for small perturbations and a strongly nonlinear response for larger displacements. (b) The detector response in the linear regions for nanowires of different lengths. The appearance of two bands is related to the presence of clusters of multiple nanowires in solution. (c) Histogram of the position fluctuations of a single nanowire due to stochastic motion for different trapping powers. As the power of the tweezers is increased, the Brownian motion is suppressed. (d) The trap stiffness (as determined by the Equipartition method) as a function of trapping power for an optically trapped nanowire.
the calibration is only valid for conditions where the nanowire maintains its orientation with the long axis directed along the propagation direction, which is the case for high refractive index nanowires of length greatly exceeding the focal depth of the tweezers. In cases where the nanowire rotate significantly into the xy plane the asymmetry in the scattering cross-section will strongly modify the interference pattern at the back focal plane. Figure 2b displays the linear part of the calibration curve for nanowire of various lengths between 3 and 15 μm. An important observation from this graph is that the calibration curves may be resolved into discrete groups of similar values; these groupings appear to be independent of the lengths of the nanowires. One possible explanation of this is that different numbers of nanowires are simultaneously trapped in the optical tweezers. During the sonication process nanowires frequently coalesce to form bound bundles of two or more nanowires. Larger bundles of nanowires cannot be trapped as strong scattering forces from the large refractive index mismatch between the InP nanowire and the surrounding fluid exceed the gradient forces for larger diameters. From trapping experiments on single InP nanowires where lateral growth has been used to increase the diameter, we find that above 150 nm the nanowires become very difficult to
trap and estimate this to be the upper limit for trapping InP nanowires in a gradient force tweezers. However, smaller groupings of nanowires with equivalent cross sections below this critical dimension may be readily trapped and behave in a manner similar to single nanowires. We deduce that these distinct groups of calibration curves correspond to having different numbers of nanowires trapped within the tweezers and that larger numbers of nanowires within the trap will result in a steeper slope of the calibration curve. Figure 2c contains a histogram of the position fluctuation for a 10 μm nanowire at different trapping powers from 26 to 90 mW at the trapping focus; the associated trap stiffness is plotted as a function of trapping power in Figure 2d. The general trend observed is that increased trapping powers are associated with a reduction of mean variance of the fluctuations and an increase in the trap stiffness. At moderate trapping powers (26 mW) the position fluctuations of 40 nm (full width half-maximum) are observed. Increasing the power leads to an increase the localization of the nanowires up to 20 nm and trap stiffness of 50 pN/μm at higher powers (65 mW). We note that this increase is linear for lower powers, as expected from basic trapping theory but tends to flatten out at high powers. Possible explanations that could 2378
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Figure 3. (a) Trap stiffness as function of the nanowire length, as determined using the equipartion method. The appearance of two bands is related to the presence of multiple nanowires in the trap. The independence of the trapping force with respect to the length may be rationalized in terms of the depth of focus of the beam. (b) Corner frequency of trapped nanowires as a function of the nanowire length, as determined by a power spectrum analysis. The corner frequency exhibits a one on length dependence that may be linked to the Stokes’ drag perpendicular to the length of the nanowire.
account for the observed nonlinear behavior include trace absorption of the laser light in the nanowires and surrounding medium may lead to local increase in temperature which becomes measurable at higher trapping powers. If the deviation is assumed to be exclusively due to heating, we may estimate an upper bound for the local temperature increase from the equipartition theorem by considering the difference between the measured trap stiffness (assuming a temperature of 300 K) and the projected trap stiffness based on the low power trapping gradient. This calculation suggests that at trapping powers of 78 mW the local temperature is increased to 343 K. Alternatively the shape of the optical potential may change due to variations in the gradient and scattering optical forces and the emergence of nonconservative forces in the strong trapping limit.23 One practical consequence of this is that the natural positioning accuracy for nanowires for assembly or scanning probe applications may be limited to a resolution of 1020 nm without the application of active position clamping.
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Figure 4. (a) Scatter plot showing the position fluctuation of the nanowire in the trap. A clear asymmetry in the distribution is observed when comparing the x and y axis. This asymmetry translates to a difference in the trap stiffness for the two orientations. (b) Ratio of the trap stiffness in the x and y directions as a function of polarization orientation. The asymmetry in the trapping ratio changes with the orientation such that the largest trap stiffness is always in line with the direction of polarization.
In Figure 3a we consider the dependence of the trap stiffness versus nanowire length, as determined by the equipartition method. From the plots we can see that the results can again be divided into distinct bands of different values. The average value for the points in the lower band is 0.71 ( 0.24 pN μm1 mW1, and the average of the points in the upper band is 2.02 ( 0.20 pN μm1 mW1. Within one band we see that the trap stiffness of the nanowires is again independent of the length of the nanowires. Importantly, the wires with trap stiffness that fall into the upper band of stiffness values corresponds to the same wires with the larger slope in the calibration curves. This strongly suggests that the nanowires with larger slopes in the calibration curve and larger trap stiffness values are actually two nanowires. Intuitively, one would expect that for a given trapping laser power, the trap stiffness of the optical trap would depend on the length of the trapped nanowires. However, the observed length independence may be rationalized by considering the depth of focus of the optical tweezers. As the length of the nanowires extends far beyond the depth of focus of the microscope objective (∼1.0 μm), but with the gradient forces only dominate within the depth of focus, any 2379
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Nano Letters extension on the nanowire length which protrudes several wavelengths from the focus in the z direction will have a minimal contribution to increases in trapping forces. Another experimentally accessible parameter, the corner frequency, provides further insight into the physical properties of the optically trapped nanowire. As the trap stiffness, κ, is effectively a constant, we expect fc to be inversely proportional to the drag coefficient, γc. From our discussion in the previous section, to a first-order approximation, γc is proportional to the length of the nanowires, l, and hence, we expect the corner frequency to be inversely proportional to the length of the nanowires. Figure 3b (insert) shows a typical power spectrum for optically trapped nanowires indicating the power spectral density for the frequency range of 1001000 Hz. The graph exhibits a characteristic roll-off at higher frequencies, typical of optical trapping in a low Reynolds number environment. The solid line is a Lorentzian fit to the data and is used to determine the corner frequency. Figure 3b shows the results of the corner frequency as measured by the power spectrum method for trapped nanowires as a function of length. The line is a fit of the data with an inverse length dependent function—as can be seen there is good agreement between the experimental and the predicted trend. An interesting point to note here is that if the trap stiffness values are measured from the equipartition measurement, the length may be inferred from the drag coefficient without the need for direct measurement using the optical micrograph images. We note that the assumed condition for which the above trends should hold is that length of the nanowire exceeds the depth of focus of the trap and that the orientation of the nanowire is maintained. As the PSD records data in both in-plane x and y orientations, we may also investigate the trapping properties of the nanowires with respect to the polarization of the laser. Figure 4a shows a scatter plot of a nanowire in the optical tweezers where absolute position information is determined from the fastswitching calibration method; the data density has been reduced to aid the visualization of the plot. Previously we have noted a distinct asymmetry in the trap stiffness for the two orientations and suggested it was due to the intrinsic depolarization effects caused by the dielectric mismatch between nanowires and the surrounding media, where the electric fields perpendicular to the length of the nanowires are reduced by a factor of 2ε0/(ε0 þ ε).24 Figure 4b shows the ratio of the trap stiffness for the x and y directions as the orientation of the polarization of the trapping laser is rotated through 180. We find that the trap stiffness values for the two directions differ by a factor of 2 and that the ratio tracks the orientation of the linearly polarized light, such that the strongest trap stiffness is always oriented along the polarization direction. Such polarization-dependent effects are also prominent in other optical properties of nanowires, such as in photoluminescence.25 Qualitatively we might expect an increase in trapping force along the polarization direction because of an increase in the parallel component of the electric field (Ez) along the nanowire length under high NA focusing. As the depolarization effect is independent of dimensions for high aspect ratio nanowire, if the optical field at the focus of the trapping laser is known, trapping asymmetry may elucidate information about the dielectric properties of the nanowire. It is worth mentioning the applicability of the calibration method employed here to other nanoscale objects. The ability to achieve accurate absolute position information is dependent on
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(i) the object maintaining its orientation within the trap for the duration of the measurements and (ii) the diffusion rate of the object during the time in which the beam is switched back to the origin to measure the PSD signal must be significantly slower than the rate of switching that can be achieved. For nanowire the first condition may be violated for very weak traps where the additional motion of rotation and rocking may become significant, although, as such motion must be restricted to small angles for stable trapping, it is likely this would only be a perturbative effect. For more spherical nanoscale objects, such as metallic nanoparticles, the orientation-related changes in the trap will be more susceptible to thermal fluctuations, but changes to the calibration curve due to these will be less pronounced compared to the very high aspect ratio nanowires. For diffusion rate nanowires with a typical length dimension of 10 μm, the mean displacement of the nanowire away from the target position in the 25 μs measurement, given by19 (2DΔt)1/2, is approximately 3.2 nm. For stochastic motion the positioning accuracy can be improved by averaging over many measurements; however in the case of motion in a biased field, this will lead to a systematic offset in the target position. For metallic nanoparticles and quantum dots the diffusion rate is considerably greater and the anticipated offset may be greater. Improvements in the positioning accuracy may be achieved by reducing the measurement time and performing the calibration in the weak-trapping limit where the motion is predominantly stochastic. Conclusion. In conclusion we have demonstrated a robust method for calibrating the spatial response of a position sensitive detection system for individual optically trapped nanowires with arbitrary lengths in the range of 215 μm. Using this method we are able to determine physical characteristics of individual nanowires by studying their stochastic motion within the trap. Specifically we have shown that optical forces applied to nanowires are independent of length and that viscous drag is linearly proportional to the nanowire length. We have been able to discriminate between single nanowires and clusters of nanowires without the need for direct imaging. We have also shown that an asymmetry in the optical forces for the two in-plane directions is polarization dependent.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT The authors thank the Australian Research Council for the financial support of this research. Australian National Fabrication Facility is acknowledged for the access to the facilities used in this work. ’ REFERENCES (1) Garnett, E.; Yang, P. D. Light Trapping in Silicon Nanowire Solar Cells. Nano Lett. 2010, 10 (3), 1082–1087. (2) Wan, Q.; Li, Q. H.; Chen, Y. J.; Wang, T. H.; He, X. L.; Li, J. P.; Lin, C. L. Fabrication and ethanol sensing characteristics of ZnO nanowire gas sensors. Appl. Phys. Lett. 2004, 84 (18), 3654–3656. (3) Duan, X. F.; Huang, Y.; Agarwal, R.; Lieber, C. M. Singlenanowire electrically driven lasers. Nature 2003, 421 (6920), 241–245. (4) Wang, J. F.; Gudiksen, M. S.; Duan, X. F.; Cui, Y.; Lieber, C. M. Highly polarized photoluminescence and photodetection from single indium phosphide nanowires. Science 2001, 293 (5534), 1455–1457. 2380
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(5) Huang, Y.; Duan, X. F.; Cui, Y.; Lauhon, L. J.; Kim, K. H.; Lieber, C. M. Logic gates and computation from assembled nanowire building blocks. Science 2001, 294 (5545), 1313–1317. (6) Yan, H.; Choe, H. S.; Nam, S. W.; Hu, Y. J.; Das, S.; Klemic, J. F.; Ellenbogen, J. C.; Lieber, C. M. Programmable nanowire circuits for nanoprocessors. Nature 2011, 470 (7333), 240–244. (7) Lauhon, L. J.; Gudiksen, M. S.; Wang, C. L.; Lieber, C. M. Epitaxial core-shell and core-multishell nanowire heterostructures. Nature 2002, 420 (6911), 57–61. (8) Pauzauskie, P. J.; Radenovic, A.; Trepagnier, E.; Shroff, H.; Yang, P. D.; Liphardt, J. Optical trapping and integration of semiconductor nanowire assemblies in water. Nat. Mater. 2006, 5 (2), 97–101. (9) Reece, P. J.; Paiman, S.; Abdul-Nabi, O.; Gao, Q.; Gal, M.; Tan, H. H.; Jagadish, C. Combined optical trapping and microphotoluminescence of single InP nanowires. Appl. Phys. Lett. 2009, 95 (10), 101109. (10) Agarwal, R.; Ladavac, K.; Roichman, Y.; Yu, G. H.; Lieber, C. M.; Grier, D. G. Manipulation and assembly of nanowires with holographic optical traps. Opt. Express 2005, 13 (22), 8906–8912. (11) Neuman, K. C.; Block, S. M. Optical trapping. Rev. Sci. Instrum. 2004, 75 (9), 2787–2809. (12) Berg-Sorensen, K.; Flyvbjerg, H. Power spectrum analysis for optical tweezers. Rev. Sci. Instrum. 2004, 75 (3), 594–612. (13) Greenleaf, W. J.; Woodside, M. T.; Abbondanzieri, E. A.; Block, S. M. Passive all-optical force clamp for high-resolution laser trapping. Phys. Rev. Lett. 2005, 95 (20), 208102. (14) Visscher, K.; Gross, S. P.; Block, S. M. Construction of multiplebeam optical traps with nanometer-resolution position sensing. IEEE J. Sel. Top. Quantum Electron. 1996, 2 (4), 1066–1076. (15) Joyce, H. J.; Paiman, S.; Gao, Q.; Tan, H. H.; Kim, Y.; Smith, L. M.; Jackson, H. E.; Yarrison-Rice, J. M.; Zhang, X.; Zou, J.; Jagadish, C. III-V Compound Semiconductor Nanowires. Nanotechnology Materials and Devices Conference, 2009. NMDC '09; IEEE: New York, 2009; pp 5960 (16) Wagner, R. S.; Ellis, W. C. Vapor-Liquid-Solid Mechanism of Single Crystal Growth (New Method Growth Catalysis from Impurity Whisker Epitaxial þ Large Crystals Si E). Appl. Phys. Lett. 1964, 4 (5), 89. (17) Paiman, S.;Growth temperature and V/III ratio effects on the morphology and crystal structure of InP nanowires. J. Phys. D: Appl.Phys. 2010, 43 (44), 445402. (18) Dholakia, K.; Reece, P.; Gu, M. Optical micromanipulation. Chem. Soc. Rev. 2008, 37 (1), 42–55. (19) Risken, H. The Fokker-Planck equation: methods of solution and applications. 2nd ed.; Springer-Verlag: Berlin and New York, 1989. (20) Marago, O. M.; Jones, P. H.; Bonaccorso, F.; Scardaci, V.; Gucciardi, P. G.; Rozhin, A. G.; Ferrari, A. C. Femtonewton Force Sensing with Optically Trapped Nanotubes. Nano Lett. 2008, 8 (10), 3211–3216. (21) Tirado, M. M.; Garciadelatorre, J. Translational Friction Coefficients of Rigid, Symmetric Top Macromolecules - Application to Circular-Cylinders. J. Chem. Phys. 1979, 71 (6), 2581–2587. (22) Rohrbach, A.; Kress, H.; Stelzer, E. H. K. Three-dimensional tracking of small spheres in focused laser beams: influence of the detection angular aperture. Opt. Lett. 2003, 28 (6), 411–413. (23) Roichman, Y.; Sun, B.; Stolarski, A.; Grier, D. G. Influence of nonconservative optical forces on the dynamics of optically trapped colloidal spheres: The fountain of probability. Phys. Rev. Lett. 2008, 101 (12), 128301. (24) Ruda, H. E.; Shik, A. Polarization-sensitive optical phenomena in semiconducting and metallic nanowires. Phys. Rev. B 2005, 72 (11), 115308. (25) Mishra, A.; Titova, L. V.; Hoang, T. B.; Jackson, H. E.; Smith, L. M.; Yarrison-Rice, J. M.; Kim, Y.; Joyce, H. J.; Gao, Q.; Tan, H. H.; Jagadish, C. Polarization and temperature dependence of photoluminescence from zincblende and wurtzite InP nanowires. Appl. Phys. Lett. 2007, 91 (26), 263104.
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