Letter pubs.acs.org/NanoLett
Observation of Surface Plasmon Polariton Pumping of Optical Eigenmodes of Gold-Decorated Gallium Nitride Nanowires Jency Pricilla Sundararajan,* Pavel Bakharev, Ishwar Niraula, Blaise Alexis Fouetio Kengne, Quinn MacPherson, Meredith Sargent, Brian Hare, and David N. McIlroy* Department of Physics, University of Idaho, Moscow, Idaho 83844-0903, United States ABSTRACT: The photocurrent of individual gallium nitride (GaN) nanowires decorated with Au nanoparticles as function of the wavelength of light (405 nm (blue), 532 nm (green), and 632.8 nm (red)) and nanowire diameter (80 to 400 nm) is reported. The photocurrent scales with photon energy but oscillates with nanowire diameter. The oscillations are described in terms of the scattering of surface plasmon polaritons into allowed transverse magnetic electromagnetic modes of the nanowire that have maximum intensities in the undepleted region of the nanowire. These oscillations do not occur below a nanowire diameter of ∼200 nm due to the depletion layer formed at the Au−GaN interface, which completely depletes the nanowire, that is, there is an insufficient density of carriers that can be excited into the conduction band. On the basis of estimations of the depletion depth and solutions of the Helmholtz equation, the maxima in the photocurrent for d > 200 nm are assigned to the two lowest azimuthally symmetric transverse magnetic eigenmodes: (m = 0, n = 1) and (m = 0, n = 2), which have maximum electric field intensities within the undepleted region of the GaN nanowire. The outcome of this work could have far reaching implications on the development of nanophotonics. KEYWORDS: GaN nanowire, Au nanoparticles, surface plasmon polaritons, photoexcitation
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constructed nanowires with rectangular cross sections. Said devices could revolutionize opto-electric discrimination and communications. The n-type GaN NWs were grown by a vapor−liquid−solid (VLS) process at atmospheric pressure, as reported in ref 16, where the nanowires are typically hundreds of micrometers in length and have diameters ranging from 80 to 400 nm. Two terminal single GaN NW devices (schematically illustrated in the inset in Figure 1a) were constructed by suspending the nanowires in isopropyl alcohol (IPA) and transferring the nanowire/alcohol solution onto the 25 mm × 25 mm glass substrates at which time the IPA evaporates. Using standard photolithography and liftoff techniques, electrical contacts (50 nm Cr/150 nm Au) with 5 μm spacing were applied to the substrate by thermal evaporation. Nanowires with ohmic electrical contacts were identified under a scanning electron microscope (SEM), where their position, length, and diameter were logged (Figure 1a). Any additional nanowires lying between the contacts were carefully cut using an atomic force microscope (AFM) probe, thereby ensuring that they did not contribute to the conductivity measurements. The ohmic nature of the contacts to the nanowires was verified by the linear behavior of the nanowire I−V curves. The photo-
ight harvesting in semiconducting nanowires is a very active area of research with applications in nanophotonics, nanoelectronics, and photovoltaics.1−4 Photoconductivity has been reported for a wide variety of semiconducting nanowires such as SnO2,5 WO3,6 GaN,7 InP,8 CdS,9 and ZnO,10 to name a few, and can be orders of magnitude higher than the dark current.11 A number of recent studies have investigated plasmon enhancement of the photoconductivity of semiconducting nanowires.12−15 While it is now well accepted that the excitation of surface plasmon polaritons (SPP) enhances the photoconductivity of semiconducting nanowires, a detailed study of the mechanism is still lacking. Here we present the results of a study of the effect of nanowire diameter on the SPP enhanced photoconductivity of GaN nanowires (NWs) decorated with Au nanoparticles (NPs). The experimental results show that the enhancement of the photoconductivity is more complex than the simple propagation of SPP along the surface of the nanowires. Computationally it is shown that SPP enhanced photoconductivity in semiconducting nanowires arises from scattering of transverse magnetic (TM) modes of SPP originating from the Au NPs into coinciding TM optical waveguide eigenmodes of the GaN NW and that the maximum field intensity of the radiation must occur in the undepleted region of the nanowire. While this work focuses on devices constructed with as-grown GaN NWs, it demonstrates new phenomena that can be exploited in nanofabricated nanowire devices, that is, lithographically © XXXX American Chemical Society
Received: June 12, 2012 Revised: August 15, 2012
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Figure 1. (a) SEM image of a single GaN nanowire device. Inset: Schematic of Au nanoparticle decorate single GaN nanowire device. (b) Transmission electron microscope (TEM) image of GaN nanowire decorated with Au nanoparticles.
conductivity of bare GaN nanowires was measured. Their surfaces were subsequently decorated with Au NPs (6−10 nm in diameter (Figure 1b)17) by plasma-enhanced chemical vapor deposition (PECVD), which has been described in detail elsewhere.18 To ensure that Au NPs on the glass substrate were not creating electrical paths between the electrodes, the electrical conductivity and photoconductivity between the electrodes devoid of GaN NWs were measured and found to be open. The photoconductivity measurements were conducted using three diode lasers with wavelengths 405 nm (blue), 532 nm (green) and 632.8 nm (red). The laser light was transmitted via fiber optics to a microscope that focused the beam down to a spot size of ∼10 μm, where the power density at the plane of the sample was maintained at 10mW/cm2. The I−V curves of bare GaN NWs, dark or illuminated, are linear, as expected,16.19 In contrast, the I−V curves of GaN NWs decorated with Au NPs, dark or illuminated, and regardless of diameter, exhibit nonlinear behavior. This is indicative of the formation of a depletion layer of width w, originating at the surface of the nanowire,1620−22 and also affects their conductivity. The impact of the formation of the depletion layer on the dark current of Au/GaN NWs is more pronounced for smaller diameters (d). For d ≥ 200 nm, the dark current of Au/GaN NWs is a fraction of its value prior to metallization. For 200 nm > d > 100 nm, the dark current of Au/GaN NWs is an order of magnitude less than its value prior to metallization, where the depth of the depleted region within the nanowire is comparable to the radius of the undepleted region of the nanowire. For d < 100 nm, the depletion of the Au/GaN NW is complete and the dark current drops by as much as 2 orders of magnitude relative to the premetallization value. The above effect of the depletion layer on the conductivity of Au/GaN NWs is consistent with previously published results.7 The normalized photocurrent (Ip) of bare GaN NWs, where normalization is to their dark current, obey the simple power law, Ip α Px,23 where P is the illumination power of the laser at the sample, with x = 0.94, 0.27, and 0.07 for blue, green, and red lasers, respectively, independent of the nanowire diameter. The photocurrent of bare GaN NWs as a function of nanowire diameter and fixed power increases smoothly with increasing diameter and from longer to shorter wavelengths of light (inset in Figure 2). The increasing photocurrent with increasing diameter is due the larger cross section of the nanowires, that is,
Figure 2. The photocurrent of Au-decorated GaN nanowires, normalized to the dark current, as a function of nanowire diameter and excitation with 405, 532, and 632.8 nm light. Inset: the photocurrent of the GaN nanowires normalized to the dark current and prior to metallization, as a function of nanowire diameter and excitation with 405, 532, and 632.8 nm light. The lines are intended to serve as a guide.
a higher flux of light passing through the nanowire and therefore a higher probability of exciton formation. The wavelength dependence is due to the increase in the density of gap states near the conduction band minimum, which become accessible with increasing photon energy. Below a diameter of 200 nm, the photocurrent is only a few percent greater than the dark current, where it has been proposed that surface defects produce a depletion layer that almost completely penetrates the GaN NW.7 The normalized photocurrent of Au/GaN NWs as a function of diameter and excitation wavelength is summarized in Figure 2. The photocurrent of Au/GaN NWs with d < 200 nm is effectively equivalent to the values obtained prior to metallization, where the increase in photocurrent is fractionally higher than the dark current and comparable to the photocurrent of bare GaN NWs. However, above a diameter of ∼200 nm the effect of metallization is quite pronounced. Namely, the photocurrent of Au/GaN NWs (Figure 2) exhibit diameter dependent maxima that are 100−500% larger than their dark current and minima comparable to their dark current, B
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where εd = ε(ρ < a), εm = ε(ρ > a), the index i refers to the media m (metal) and d (dielectric). From the Drude model for a semi-infinite metal
315 nm, for example. Overall, the photocurrents of Au/GaN NWs relative to their dark currents are an order of magnitude higher than the corresponding photocurrents of bare GaN relative to their dark currents (inset, Figure 2). The photocurrent of Au/GaN NWs using 405 and 532 nm light track one another with a greater enhancement with 405 nm, which is to be expected, and attributed to a higher probability of populating gap states near the conduction band minimum. To a lesser degree, excitation with 632.8 nm light results in enhanced photocurrent relative to bare GaN NWs, but the maxima and minima for nanowire diameters between 200 and 315 nm are out of phase, so to speak, with the photocurrents obtained with 405 and 532 nm light, but is in phase for d > 315 nm. Recently, Lopez et al.24 reported diameter dependent oscillations of the Raman scattering intensities of Si nanowires, where the oscillations are attributed to allowed electromagnetic modes of the nanowire. To the best of our knowledge, this is the first observation of diameter dependent oscillatory behavior of the photocurrent of nanowires of any type. The absence of oscillatory behavior of the photocurrent of bare GaN NWs, concomitant with the significantly higher relative enhancement of the photocurrent observed for Au/ GaN NWs, indicates that the phenomena arises from excitation of Au surface plasmon polaritons (SPP). We propose that the enhancement and oscillatory behavior of the photoconductivity of Au/GaN NWs arises from SPP scattering associated with the discontinuous nature of the Au coating. SPP scattering transfers energy into electromagnetic (EM) waves25−28 within the nanowire. Maxima (minima) in the photoconductivity are stipulated by the excitation of the EM modes in the Au/GaN NW. The ability to populate optical eigenmodes of nanowires has been demonstrated.24 According to Snell’s law, a source placed outside of the nanowire cannot couple to its eigenmodes, as this would require an imaginary angle of incidence in order to achieve total internal reflection.29 Here, the Au NPs serve as radiative source at the nanowire surface that can pump electromagnetic energy into the eigenmodes in the circular waveguide, in this case, the nanowire. Lastly, the majority of the EM energy must reside in the undepleted region of the nanowire. This explains the absence of significant enhancement, or oscillatory behavior, for nanowires with diameters less than 200 nm, that is, the majority of EM energy density resides in the depletion layer. Therefore, the photocurrent of Au/GaN NWs is described using the standard SPP scattering model at a metal/dielectric interface, the transverse electric (TE) and transverse magnetic (TM) modes of a cylindrical waveguide, in this case, the GaN NW, and the formation of excitons. A cylindrical coordinate system (ρ, ϕ, z) is used in the model that will be developed to describe the observed phenomena, where z is parallel to the axis of the nanowire of radius a. The regions ρ > a and ρ < a correspond to the metal (Au NP) and to the dielectric (GaN NW), respectively. Starting from the source-free Maxwell’s equations for a wave and the requirement that only transverse-magnetic (TM) modes exist, one arrives at the dispersion relations for the longitudinal wavenumber k∥ and the transverse wavenumber k⊥ for the TM modes k = k0
εmεd εi 2 , ki , ⊥ = k 0 εm + εd εm + εd
εm = 1 −
ωp2 ω(ω + iγ )
(2)
where γ is the electron damping coefficient and ωp is the plasma frequency of the metal. Upon substitution into the longitudinal wavenumber, k∥, eq 1 yields k (ω) =
ω c
(ω 2 − ωp2)εd (1 + εd)ω 2 − ωp2
(3)
From eq 1, the attenuation depths of the SPP in the metal (hm) and the dielectric (hd) are defined as hi = 1/ki,⊥. At large k∥, when the nonretarded surface-plasmon conditions are fulfilled, the skin depth is defined by hi ∼ 1/k∥, indicative of strong localization of the electromagnetic surface-plasmon field at the metal/dielectric interface. For all computations presented herein, ωp = 13.8 × 1015 rad/sec30 for Au and εd = 7.3 for GaN.31 The GaN electric permittivity corresponds to the incident wavelength λ = 405 nm. The Drude model for the electromagnetic surface-plasmon skin depth in GaN gives hd = 35 nm. Hence, the attenuation length is less than the radii (a) of GaN NWs used in this study. To adequately model the photoconductivity of the Au/GaN NWs it is necessary to account for the formation of a depletion layer in the GaN NW due to the Schottky interface at the boundary between the Au NPs and the GaN NW. This depletion width (w) can be expressed as w=
2εdϕd e−Nd
= 110 nm (4)
for an applied voltage through the Schottky barrier Va= 0 V, where ϕd is a built in potential for the GaN NW; e− is the elementary charge; and Nd is the electron donor number density. For ϕd = 0.75 V and Nd = 6.6 × 1022 m−3, w = 110 nm. A significant increase of the photocurrent is expected when the EM energy density in the nanowire is spatially localized in the undepleted region of the nanowire, that is, antinodes of the EM waves coincide with the undepleted region (ρ < a − w) of the nanowire.The optical eigenmodes of the cylindrical waveguide (nanowire) have the form ⎡ E ⃗ (r ) ⎤ ⎡ E ⃗ (ρ ) ⎤ ⎢ m , n ⎥ = ⎢ m , n ⎥exp(ih z) m,n ⎢ ⃗ ⎥ ⎢ ⎥ ⎣ Hm , n(r )⎦ ⎣ H⃗ m , n(ρ)⎦
(5)
where hm,n is the axial wavenumber of the mode with an azimuthal index m and a radial index n. The vector functions Em,n(ρ) and Hm,n(ρ) are solutions of the Helmholtz equation and describe the field distribution of an eigenmode (m,n). The source-excited field corresponding to the eigenmodes in the nanowire is given by the following expansion ⎡ E ⃗ (r ) ⎤ ⎢ ⎥= ⎢⎣ H⃗ (r )⎥⎦
⎡ ⎤ (±) (r ) ⎥ E⃗ (±)⎢ m , n am , n ⎢ ⎥ (±) m,n ⎢⎣ H⃗ m , n (r )⎥⎦
∑
(6)
where am,n(±) are the excitation coefficients of the respective modes
(1) C
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∫v J ⃗(r)·E−⃗ m,n(∓)(r)dv
am , n(±) = Nm , n−1
(7)
where Nm,n is the normalization quantity, J(⃗ r) is the longitudinal SPP current density and the superscripts (+) and (−) correspond to z > 0 and z < 0, respectively. According to eq 7, and because the SPP current is longitudinal, only TM modes (Em,n;z ≠ 0) in the nanowire can be excited by the SPP. Omitting the arbitrary integration constants, the components of the TM modes can be expressed in terms of Bessel functions of the first kind Jm ⎡ cos(mϕ)⎤ ⎥ Ez ; m , n = Jm (κm , nρ /a)exp( −ihm , nz)⎢ ⎢⎣ sin(mϕ) ⎥⎦ Eρ; m , n = −i
Eϕ; m , n = −i
hm , na κm , n
⎡ cos(mϕ)⎤ ⎥ J ′m (κm , nρ /a)exp( −ihm , nz)⎢ ⎢⎣ sin(mϕ) ⎥⎦
mhm , na 2 ρκ
2 m,n
⎡ cos(mϕ) ⎤ ⎥ Jm (κm , nρ /a)exp( −ihm , nz)⎢ ⎢⎣−sin(mϕ)⎥⎦ (8)
Hz ; m , n = 0, Hρ; m , n = − Hϕ; m , n = Zm , n =
Eϕ; m , n Zm , n
Eρ; m , n Zm , n hm , n k0
,
,
Z0
where κm,n is the transverse wavenumber of the mode and Z0 is the electromagnetic wave impedance in freespace. The results of numerical computations of the radial intensities of the selected TM modes in the dimensionless transverse coordinate x = ρ/a are presented in Figure 3. The calculations were performed for the incident wavelength λ = 405 nm and a nanowire radius a = 200 nm. The modes (m,n) = (0,1) and (0,2) are the lowest modes with intensity centered on the axis of the nanowire (Figure 3), where the (0,2) has a significant larger intensity. Both of these modes will contribute to the photocurrent since they reside within the undepleted region of the nanowire. The maximum intensities of modes (1,1) and (2,1) (not shown) occur at ρ ≅ a − w, just outside the undepleted region, and therefore contribute minimally to the photocurrent. For a 200 nm radius nanowire, all allowed modes with m ≠ 0 fall completely in the depleted region of the nanowire; for example (3,1) in Figure 3. For a 200 nm radius nanowire the (0, 2) mode is the primary mode. The cutoff of any noteworthy photoconductivity at a nanowire diameter of ∼208 nm in Figure 2 indicates, for all intents and purposes, that nanowires with diameters ≤200 nm are completely depleted, and therefore, unresponsive to light. This is consistent with the single digit μA dark currents of Au/GaN NWs with diameters less than 200 nm. With increasing diameter, the fraction of the depleted region of nanowire volume decreases. However, assuming the density of nanoparticles on the surface remains relatively constant and provided each nanoparticle can deplete a fixed volume of the nanowire, the depletion width will be constant and independent
Figure 3. The intensity distribution of the EM modes of a 400 nm diameter GaN nanowire with a depletion width of 110 nm for (a) m = 0, n = 1, (b) m = 0, n = 2, and (c) m = 3, n = 1, where a = 1 is the dimensionless nanowire radius and w = 0.55 is the dimensionless width of the Au/GaN depletion layer.
of nanowire diameter. The net effect is that the depletion region becomes more localized near the surface of the nanowire with increasing nanowire diameter. Consequently, higher modes have weight within the undepleted region of the nanowire, where the number of carriers is determined by the energy of these modes. This is borne out by the steady increase of photocurrent with increasing nanowire diameter up to ∼270 nm for all three wavelengths of light. Because of the finite size distribution of the Au NP, the frequency distribution of SPP is bound, which will impose an upward (lower) limit on the D
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(5) Mathur, S.; Barth, S.; Shen, H.; Pyun, J.-C.; Werner, U. Small 2005, 1, 713. (6) Huang, K.; Zhang, Q.; Yang, F.; He, D. Nano Res. 2010, 3, 281. (7) Calarco, R.; Marso, M.; Richter, T.; Aykanat, A. I.; Meijers, R.; Hart, A.; v.d.; Stoica, T.; Lüth, H. Nano Lett. 2005, 5, 981. (8) Wang, J.; Gudiksen, M. S.; Duan, X.; Cui, Y.; Lieber, C. M. Science 2001, 293, 1455. (9) Singh, A.; Li, X.; Protasenko, V.; Galantai, G.; Kuno, M.; Xing, H. G.; Jena, D. Nano Lett. 2007, 7, 2999. (10) Soci, C.; Zhang, A.; Xiang, B.; Dayeh, S. A.; Aplin, D. P. R.; Park, J.; Bao, X. Y.; Lo, Y. H.; Wang, D. Nano Lett. 2007, 7, 1003. (11) Soci, C.; Zhang, A.; Bao, X.-Y.; Kim, H.; Lo, Y.; Wang, D. J. Nanosci. Nanotechnol. 2010, 10, 1430. (12) Liu, K.; Sakurai, M.; Liao, M.; Aono, M. J. Phys. Chem. C 2010, 114, 19835. (13) Chen, M.-W.; Chen, C.-Y.; Lien, D.-H.; Ding, Y.; He, J.-H. Opt. Express 2010, 18, 14836. (14) Lu, M.-L.; Lin, T.-Y.; Weng, T.-M.; Chen, Y.-F. Opt. Express 2011, 19, 16266. (15) Hyun, J. K.; Lauhon, L. J. Nano Lett. 2011, 11, 2731. (16) Dobrokhotov, V.; McIlroy, D. N.; Norton, M. G.; Abuzir, A.; Yeh, W. J.; Stevenson, I.; Pouy, R.; Bochenek, J.; Cartwright, M.; Wang, L.; Dawson, J.; Beaux, M.; Berven, C. J. Appl. Phys. 2006, 99, 104302. (17) Turba, T.; Norton, M. G.; Niraula, I.; McIlroy, D. N. J. Nanopart. Res. 2009, 11, 2137. (18) LaLonde, A. D.; Norton, M. G.; Zhang, D.; Gangadean, D.; Alkhateeb, A.; Padmanabhan, R.; McIlroy, D. N. J. Mater. Res. 2005, 20, 3021. (19) Kim, J.-R.; So, H. M.; Park, J. W.; Kim, J.-J.; Kim, J.; Lee, C. J.; Lyu, S. C. Appl. Phys. Lett. 2002, 80, 3548. (20) Berven, C. A. IEEE Sens. J. 2008, 6, 930. (21) Dobrokhotov, V. V.; McIlroy, D. N.; Norton, M. G.; Berven, C. A. Nanotechnology 2006, 17, 4135. (22) Kolmakov, A.; Klenov, D. O.; Lilach, Y.; Stemmer, S.; Moskovits, M. Nano Lett. 2005, 5, 667. (23) Kind, Yan, H.; Messer, B.; Law, M.; Yang, P. Adv. Mater. 2002, 14, 158. (24) Lopez, F. J.; Hyun, J. K.; Givan, U.; Kim, I. S.; Holsteen, A. L.; Lauhon, L. J. Nano Lett. 2012, 12, 2266. (25) Zayats, A. V.; Smolyaninov, I. I.; Maradudin, A. A. Phys. Rep. 2005, 408, 131. (26) Derkacs, D.; Lim, S. H.; Matheu, P.; Mar, W.; Yu, E. T. Appl. Phys. Lett. 2006, 89, 093103. (27) Hägglund, C.; Zäch, M.; Petersson, G.; Kasemo, B. Appl. Phys. Lett. 2008, 92, 053110. (28) Liu, Y.; Zentgraf, T.; Bartal, G.; Zhang, X. Nano Lett. 2010, 10, 1991. (29) Seletskiy, D. V.; Hasselbeck, M. P.; Cederberg, J. G.; Katzenmeyer, A.; Toimil-Molares, M. E.; Léonard, F.; Talin, A. A.; Sheik-Bahae, M. Phys. Rev. B 2011, 84, 115421. (30) Murata, K.; Tanaka, H. Nat. Commun. 2010, 1, 16. ̌ M. E.; Rumyantsev, S. L.; Shur, M. Properties of (31) Levinshtein, Advanced Semiconductor Materials: GaN, AIN, InN, BN, SiC, SiGe; John Wiley & Sons: New York, 2001.
frequency (wavelength) of EM waves produced by SPP scattering. In order for these EM waves to propagate in the nanowire they will have to satisfy the boundary conditions defined by the diameter of the nanowire. Consequently, the photocurrent will oscillate between maxima and minima as a function of nanowire diameter, as seen in Figure 2. Furthermore, the oscillatory behavior of the photocurrent with increasing nanowire radius is stipulated by the redistribution of the intensity among the existing modes. Indeed, for some radii the maximum intensity corresponds to modes where the highest antinodes lie in the undepleted region of the nanowire. For other radii, the maximum intensity occurs in the modes where the highest antinodes lie in the depleted region. Hence, this intensity distribution is unique for each particular radius. Also, for each nanowire radii there are different numbers of allowed modes for a particular incident wavelength. The similarity of the curves in Figure 2 arises from the fact that the Au NPs define the SPP spectrum and the nanowire diameter dictates which EM modes are allowed. The only requirement of the light source is that it can excite a sufficient number of SPP states. Consequently, a well-defined pattern of the oscillations is difficult to quantify due to the size distribution of the Au NPs that produce a complex SPP density of states, where different wavelengths of light will excite different regions and spans of the SPP density of states. In summary, we have successfully fabricated and investigated the photocurrent of individual gallium nitride (80 nm ≤ d ≤ 400 nm) nanowire devices with and without decoration with Au NPs using three light sources, 405, 532, and 632.8 nm. Oscillations of the photocurrent of Au/GaN NWs are observed, which are not observed for bare GaN NWs. The oscillations are described in terms of the scattering of surface plasmon polaritons into allowed EM modes of the nanowire that have maximum intensities in the undepleted region of the nanowire. This study illustrates the unique opto-electric phenomena that can be realized through the integration of zero- and onedimensional nanostructures. The construction of nanowires with rectangular cross sections by micromachining would enable precise repeatability and could lead to the development of a new class of opto-electric devices.
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AUTHOR INFORMATION
Corresponding Author
*E-mail: (D.N.M.)
[email protected]; (J.P.S.) jencys@ vandals.uidaho.edu. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This research was supported by UI-BANTech (University of Idaho - Biomedical Applications of Nanotechnology) project, the UI-COS Dyess Faculty Fellowship, USDA (Grant 200934479-19833), and Office of Naval Research (Grant N0001410-1-0282).
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NOTE ADDED AFTER ASAP PUBLICATION This article was published ASAP on September 5, 2012. The first word in the title of the article has been changed. The correct version was published on September 6, 2012.
REFERENCES
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