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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 7 — Apr. 7, 2014
  • pp: 8396–8404
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Nanoscale heat transfer in direct nanopatterning into gold films by a nanosecond laser pulse

Yuanhai Lin, Tianrui Zhai, and Xinping Zhang  »View Author Affiliations


Optics Express, Vol. 22, Issue 7, pp. 8396-8404 (2014)
http://dx.doi.org/10.1364/OE.22.008396


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Abstract

We investigate nanoscale heat transfer and heat-flux overlapping effects in nanopatterning through interactions between interferogram produced by 5-ns laser pulses at 355 nm and gold films. These mechanisms played different roles in direct writing of gold nanolines with different periods. Continuous gold nanolines were produced for large periods, where heat-flux overlapping is too small to effect the laser-metal interactions. Thus, the heat-transfer distance and direct laser-ablation determined the width of resultant gold nanolines. However, gold nanolines consisting of isolated gold nanoparticles were produced for small periods, where the overlapped heat-flux exceeds the threshold for removing or melting gold films.

© 2014 Optical Society of America

1. Introduction

In this work, we demonstrate direct patterning of gold nanoline arrays into continuous gold films through single-shot exposing to the interference pattern of a single laser pulse at 355 nm, where the whole process is accomplished within a time scale of 5 ns. This not only enables driect writing of metallic photonic structures, but also reveals the electromagnetic thermal dynamics involved in the interaction between the interferogram and the gold film. Gold nanolines with different widths and different compositions have been produced at different periods, which were found dependent on the laser intensity threshold for direct ablation, the heat transfer distance, and the overlapping of the heat fluxes from the adjacent bright interference fringes. As has been reported [11

11. R. Kelly and A. Miotello, “Comments on explosive mechanisms of laser sputtering,” Appl. Surf. Sci. 96, 205–215 (1996). [CrossRef]

13

13. S. K. Sundaram and E. Mazur, “Inducing and probing non-thermal transitions in semiconductors using femtosecond laser pulses,” Nat. Mater. 1(4), 217–224 (2002). [CrossRef] [PubMed]

], thermal processes dominate laser ablation, however, a non-thermal or indirect thermal effect is also involved in the laser-matter interactions, which is referred to as explosion-like phase sputtering. However, considering gold films thinner than 20 nm, high conductivity of the gold, a single-pulse interaction within 5 ns, this explosive process is much weaker than the direct ablation and it is not addressed particularly in this work.

2. Direct pattering of gold nanolines into thin films within nanoseconds

Gold films with different thicknesses of 6, 12, 18 and 25 nm were first thermally evaporated onto silica substrates that are coated with a layer of indium tin oxide (ITO) as thick as 200 nm, as shown in Fig. 1(a)
Fig. 1 Schematic illustration of single-pulse single-shot interference ablation on gold films. (a) The sample consisting of gold film thermally evaporated onto the ITO-coated silica substrate. (b) Interference ablation geometry using 355-nm laser pulses with a large separation angle α1 between the two laser beams. (c) The resultant grating structures produced by the geometry in (b), which have a small period of Λ1 with each gold nanoline consisting of gold nanoparticles with a diameter of WP. (d) Interference ablation geometry using a small separation angle α2 between the two laser beams. (e) The resultant grating structures produced by the geometry shown in (d), which have a large period of Λ2 with each gold nanoline consisting of continuous gold films with a width of WP.
. The ITO layer acts as the waveguide in the investigation of the optical properties of the resultant structures in response to the Fano coupling between the plasmon and waveguide resonance modes. However, the thickness of the thermally deposited gold films was optimized to about 18 nm after a series of experiments, which was employed in the practical fabrication process as will be described in the following context. The optimized pulse energy means complete removal of the gold within the bright fringes with continuous gold nanolines remained within the dark fringes. A frequency-tripled solid-state laser at 355 nm is used as UV laser source in the interfernece ablation scheme, which has a pulse length of about 5 ns, a direct output pulse energy of 60 mJ, and a repeition rate adjustable from 1 to 100 Hz. However, single-pulse and single-shot exposure scheme has been employed in the practical fabrication process. The UV laser pulse is split into two beams before they are overlapped again onto the gold film with a separation angle of α, as shown in Figs. 1(b) and 2(d)
Fig. 2 The scanning electronic microscope (SEM) images of the grating structures consisting of periodically arranged gold nanolines with different periods: (a) Λ = 350 nm, (b) Λ = 450 nm, (c) Λ = 550 nm, (d) Λ = 750 nm, (e) Λ = 850 nm, and (f) Λ = 1000 nm. WP denotes the practical width of the gold nanolines or the diameter of the gold nanoparticles.
. The period of the directly patterned plasmonic gratings consisting of gold nanolines is determined by Λ=λ/2sin(α/2), where λ = 355 nm is the wavelength of the UV laser pulse. It is understandable that larger α corresponds to a smaller grating period.

Experimental results found that grating lines consisting of isolated gold nanoparticles have been produced when α is larger than 38 degrees (α1) and the grating period (Λ1) is smaller than 550 nm, as shown in Fig. 1(c), whereas, the grating lines become continuous when α is smaller than 25 degrees (α2) and the grating period (Λ2) is larger than 750 nm, as shown in Fig. 1(d). In Fig. 1, WP denotes the width of the gold nanolines, which is also equal to the diameter of the gold nanoparticles that are aligned into the grating nanolines. Thus, depending on the periods of the gratings, gold nanolines consisting of continuous gold film or isolated gold nanoparticles have been obtained, which is found to be determined by the threshold laser intensities for removing and melting the gold films and the heat-transfer processes due to the interaction between UV laser pulses and the gold films. This is verified by the experimental results shown in Fig. 2.

Figure 2 shows the SEM images of a series of fabrication results of gold-nanoline gratings with different periods (Λ). Gold films with a thickness of about 18 nm and a total pulse energy of about 40 mJ have been employed for all of the fabrications in Fig. 2. The laser beams have been sent to an area of about 5 mm in diameter on the overlap. Figures 2(a)-2(c) show the SEM images of the fabricated structures with periods of 350, 450, and 550 nm, where isolated gold nanoparticles, instead of continuous films, were produced to constitute of the gold nanolines. When the grating period is increased from 350 to 450 nm, the size of the gold nanoparticles that constitute the nanolines is increased roughly from 70 nm to 110 nm in mean diameter. Clearly, the periodicity for Λ = 350 nm is much weaker than that for Λ = 450 nm. However, the gold nanoparticles become smaller again with their diameters reduced to as small as 90 nm when the grating period is increased further to Λ = 550 nm, while the gold nanoparticles are distributed in a wider range within each gold nanoline. This range is estimated to be about 200 nm and it is equivalent to the width of the grating lines. When the grating period is increased to more than 750 nm, continuous gold films are observed in the gold nanolines of the gratings, as shown in Figs. 2(d)-2(f), where the bright areas are remaining gold films after interference ablation and the dark areas correspond to the exposed ITO. For Λ = 750, 850, and 1000 nm, the width of the gold nanolines are easily and much more precisely measured to be WP = 366, 408, and 507 nm, respectively.

Figure 3(a)
Fig. 3 (a) The AFM image of the grating consisting of continuous gold films with a period of Λ = 850 nm. (b) The cross-section measurement on the gratings at a position marked by the horizontal red line in (a).
demonstrates the atomic force microscopic (AFM) image of the grating consisting of continuous gold films with a period of 850 nm, corresponding to the result in Fig. 2(e). Within the bright fringes, most of the gold has been removed, leaving some gold nanoparticles on the ITO surface. In these locations, the AFM image actually shows the morphology of the ITO surface. Within the dark fringes, continuous gold films remain to form grating lines. We can resolve approximately 18-nm film thickness for these gold lines, according to the cross-section measurement in Fig. 3(b). Due to the 18-nm thickness, the gold films are also modulated by the morphology of the ITO layer. Furthermore, gold nanoparticles in spherical shapes with an average size of about 90 nm are observed on the edges of the grating lines, which have been produced by thermal processes investigated in the following sections.

3. Scaling the thermal transfer distance defined by the UV interference pattern

To understand the mechanisms that determine the composition and the width of the gold nanolines, heat-transfer effects for the interaction between UV laser pulses and gold films needs to be investigated. These mechanisms are important not only for the fabrication of plasmonic photonic structures through interference ablation, but also for supplying general physics for laser-induced electromagnetic thermal effects in metallic thin films. We define effective heat transfer distance XT, threshold laser intensity It for the direct removal of the gold films, direct removal line-width WD, and threshold line-width Wt in the analysis of the interaction mechanisms. Effective heat transfer distance here means that the gold film is ablated within this distance due to transferred heat from the center area of the bright fringes although the laser intensity is lower than the threshold at the local site. Threshold laser intensity (It) means the lowest laser intensity required for the direct ablation process and the threshold line-width (Wt) is the width of the dark fringes below the threshold intensity, implying that:

WD+Wt=Λ.
(1)

For the interference pattern with different periods, the peak laser intensity at the center of the bright fringes is constant in case the pulse energy is kept constant. Therefore, it is reasonable to assume a constant heat transfer distance (XT) for all of the fabrications. Thus, the practical width of the gold nanolines may be determined by the grating period (Λ), the direct removal line-width (WD), and the heat transfer distance (XT), which is calculated by:
WP=ΛWD2XT.
(2)
However, according to Eq. (1), ΛWD=Wt, therefore,

WP=Wt2XT.
(3)

Thus, the value of XT can be evaluated by comparing the calculated intensity distribution over the interference fringes with the measured width of the gold nanolines, as shown in Fig. 4
Fig. 4 Quantitative evaluation on the heat transfer distance (XT) on the gold film using a comparison between the calculated laser intensity distribution over the interference fringes and the measured gold nanoline widths (WP). This is characterized by the threshold laser intensity for direct ablation It, direct removal width WD, and the threshold-defined gold nano-line width Wt=ΛWD.
. It can be found in Fig. 2 that continuous gold nanolines are produced only when the period is larger than 750 nm, where the practical line-width may be measured directly and precisely. Therefore, the heat transfer distance is evaluated using the experimental data on the structures with Λ = 750, 850, and 1000 nm, as illustrated in Fig. 4.

Figure 4(a) shows the calculation results of laser intensity distribution over the interference fringes for periods of Λ1 = 1000 nm, Λ2 = 850, and Λ3 = 750 nm, corresponding to a separation angle between the two interference arms of α = 20.4, 24.1, and 27.3 degrees, respectively, for the interference ablation scheme. Considering that the overlapping area between the two laser beams or the interaction area between the laser beam and the gold film is enlarged by a factor of 1/cos(α/2)and the laser intensity is reduced by such a factor, we have corrected the laser intensity in the calculation results in Fig. 4. The practically measured gold-nanoline widths are marked by WP1, WP2, WP3, respectively. The correspondingly direct-removal/threshold line-widths are denoted by WD1/Wt1, WD2/Wt2, WD3/Wt3, which are determined by cross between interference fringes and level of the threshold laser intensity (the dashed line). According to Fig. 4(a), we have Λ1=WD1+Wt1, Λ2=WD2+Wt2, and Λ3=WD3+Wt3. XT denotes the heat transfer distance, which is constant for all of the three grating periods. Therefore, we can determine XT by:
XT=Wt1WP1=Wt2WP2=Wt3WP3
(4)
or

XT=Λ1WD1WP1=Λ2WD2WP2=Λ3WD3WP3.
(5)

In practical operation, we need to level the threshold laser intensity vertically in Fig. 4(a), so that for each experimentally measured WP and theoretically evaluated WD or Wt, a constant XT may be found. This not only determines the value of XT, but also characterizes the threshold laser intensity for the direct removal of the gold within the bright fringes.

Figure 4(b) shows the plots of the width of the gold nanolines obtained from practical measurements and threshold as a function of the grating periods. The difference between these two curves corresponds to the double values of XT, where a simple calculation found 2XT = 96.2 nm, 2XT = 104.2 nm, 2XT = 90.4 nm. Therefore, the value of XT may be determined to be 45-52 nm for the system studied here. In fact, this heat transfer distance also leads to the direct removal of the gold film and formation of gold nanoparticles on the edges of the continuous gold nanolines, as shown in Figs. 2(d)-2(f).

We noticed that the adhesive force between gold and the ITO glass substrate is unavoidably involved in the ablation process. However, the gold film has much stronger absorption of UV laser and much higher thermal conductivity than the ITO glass, in particular, the gold and ITO layers have much different melting point and much different thermal expansion performance. Thus, ablation of the gold film involves rapid and dramatic phase transitions, leading to much stronger interactions than the adhesive force mechanism. Furthermore, the threshold laser intensity (It) defined in Fig. 4 corresponds to the direct removal of the gold from the substrate. Therefore, the adhesive force are already included in the characterization of the laser-induced thermal effects.

4. Spatial overlapping of the heat-flux distribution at small periods of the interference patterns

In fact, the transfer distance XT is still not large enough for the heat to go across the dark fringes for gratings with periods smaller than 550 nm and result in total melting of gold within the dark fringes, which can be verified by analysis on Figs. 2(a)-2(c) using the same approach as illustrated in Fig. 4. In other words, the heat transfer distance is not enough to explain the fabrication results in Figs. 2(a)-2(c), where gold nanolines were produced to consist of nanoparticles instead of continuous films. Thus, a further mechanism due to the overlapping between the spatially distributed heat fluxes from the adjacent bright fringes has to be taken into account for the direct writing of gratings with periods smaller than 550 nm.

The spatial distribution of heat flux in thin films has been characterized theoretically using the so-called ballistic-diffusive equation [14

14. G. Chen, “Ballistic-diffusive heat-conduction equations,” Phys. Rev. Lett. 86(11), 2297–2300 (2001). [CrossRef] [PubMed]

]. Adopting the line-shape of such a spatial distribution function, we are able to present a qualitative study on the interaction between gold films and the interference pattern. We consider that for different incident angles, the laser intensity distributions over the interference patterns are all sine functions with approximately equal amplitudes, as shown in Fig. 4. Furthermore, a single laser pulse as short as 5 ns has been employed in the fabrication process and for a gold film with a thickness of 18 nm the heat conduction behaves in the same dynamics for different incident angles. Therefore, it is reasonable to assume a same line-shape of the function to describe the heat flux in the approximate evaluations.

As illustrated schematically in Fig. 5(a)
Fig. 5 Schematic illustration of the heat-flux overlapping effect. It, HD, and HM denote the threshold laser intensity for direct ablation, the threshold heat flux for direct removal of the gold, and that for melting the gold, respectively. R(X) and L(X) denote the heat-flux function induced by the bright fringes on the right and left sides, respectively. H(X)=R(X)+L(X)is the overlapped heat-flux function. F(X) is the laser intensity distribution over the two adjacent bright fringes.
, the heat flux distributions have almost no spatial overlap for the adjacent bright fringes, where the solid blue circles denote the heat flux induced by the bright fringe on the right R(X) as a function of the spatial coordinate X, the solid green circles denote that induced by the bright fringe on the left L(X), the solid red circles denote the overlapped heat flux distribution H(X)=R(X)+L(X), and the solid black curve denotes the intensity distribution of the interference fringes F(X). We also defined the threshold heat fluxes for direct removal (HR) and for melting (HM) the gold films. It is understandable that HR correspond to the threshold laser intensity (It) for direct removal. In Fig. 5(a), the separation between the two bright fringes is so large that the overlapped heat flux may not induce additional processes to exceed the removal and melting thresholds. In other words, the direct writing process is not modified by the heat-flux overlapping effect for large-period patterning, corresponding to the fabrication results in Figs. 2(d)-2(f). This also validate our investigations in section 3 without the heat-flux overlapping effect included.

With reducing the grating period, the “overlap” becomes larger. In Fig. 5(b), the overlapped heat flux already exceeds slightly the melting threshold even at the lowest level of the curve (red circles), implying that the gold film within the dark fringes becomes molten completely although it is not removed. In this case, the gold film is molten into nanoparticles that are distributed within relatively wide nanolines. This corresponds to the fabrication results in Fig. 2(c), where relatively small gold nanoparticles with a mean diameter of about 90 nm are produced with relatively wide grating lines. As the grating period is reduced further, the overlap between adjacent heat-flux functions becomes larger, so that the overlapped heat flux extends the direct removal width and reduces the remaining range defined by melting and removal thresholds. Thus, a small range on the function of overlapped heat flux remains between the HR and HM lines, as shown in Fig. 5(c). As a result, relatively narrow grating lines consisting of large gold nanoparticles (~110 nm in mean diameter) aligned into single rows are produced, as verified by Fig. 2(b).

Further reduction in the grating period leads to more strongly overlapped heat flux, which even exceeds the direct removal threshold HR across the width of the dark fringes, as shown in Fig. 5(d). This leads to the removal of the gold film within the dark fringes, so that very little amount of gold is left. As is verified by the fabrication result in Fig. 2(a), much smaller gold nanoparticles (~70 nm in mean diameter) with considerably reduced amount are produced to form grating lines, where the periodicity becomes much weaker. Therefore, the heat-flux overlapping effect is a reasonable mechanism for understanding the direct patterning process into small-period structures.

It should be noted that the heat-flux description in Fig. 5 is a qualitative analysis. However, the well-established functions in [14

14. G. Chen, “Ballistic-diffusive heat-conduction equations,” Phys. Rev. Lett. 86(11), 2297–2300 (2001). [CrossRef] [PubMed]

] ensures validness and reliability of the proposed mechanisms. These data explained concisely why gold nanolines consisting of continuous films were produced at larger periods than 750 nm and those consisting of nanodots were produced at smaller periods than 550 nm.

5. Conclusions

In conclusion, we evaluated the electromagnetic heat transfer and heat-flux overlapping effects in the interaction between the interferogram and the gold films using direct nanopatterning by single-shot exposure to a UV laser pulse as short as 5 ns. Periodical arrays of gold nanolines were produced with different widths and different compositions, depending on combined mechanisms: (1) Direct removal of the gold for laser intensities above a specific threshold within the bright fringes. This leaves gold on the substrate within the dark fringes. (2) Heat transfer from the “hot” spots defined by the bright fringes into surrounding “cold” areas. This leads to further removal or melting of the gold in areas close to the hot spots and below the direct removal threshold. (3) Heat-flux overlapping between adjacent bright fringes. This defines two thresholds due to thermal effects for removal and melting of the gold within the dark fringes, respectively, where the former is consistent with the direct removal threshold of the laser intensity. Experimental results showed that the mechanism (3) takes effect only for interference periods smaller than 550 nm, whereas, for larger periods than 750 nm, this kind of overlapping is too small to influence the direct patterning process. As a result, gold nanolines consisting of continuous films are produced for periods larger than 750 nm and those consisting of queued gold nanoparticles are produced for periods smaller than 550 nm. The experimental investigations involved in this work not only provide insights into physics for the electromagnetic thermal interaction between UV laser pulses and metal films, but also introduce approaches for direct writing of photonic nanostructures into continuous gold films.

Acknowledgments

We acknowledge the 973 program (2013CB922404) and the National Natural Science Foundation of China (11274031, 11104007) for the support.

References and links

1.

J. P. McDonald, V. R. Mistry, K. E. Ray, and S. M. Yalisove, “Femtosecond pulsed laser direct write production of nano- and microfluidic channels,” Appl. Phys. Lett. 88(18), 183113 (2006). [CrossRef]

2.

X. Yin, N. Fang, X. Zhang, I. B. Martini, and B. J. Schwartz, “Near-field two-photon nanolithography using an apertureless optical probe,” Appl. Phys. Lett. 81(19), 3663–3665 (2002). [CrossRef]

3.

M. Svalgaard, “Direct writing of planar waveguide power splitters and directional couplers using a focused ultraviolet laser beam,” Electron. Lett. 33(20), 1694–1695 (1997). [CrossRef]

4.

T. Tavera, N. Pérez, A. Rodríguez, P. Yurrita, S. M. Olaizola, and E. Castano, “Periodic patterning of silicon by direct nanosecond laser interference ablation,” Appl. Surf. Sci. 258(3), 1175–1180 (2011). [CrossRef]

5.

T. R. Zhai, Y. H. Lin, H. M. Liu, S. F. Feng, and X. P. Zhang, “Nanoscale tensile stress approach for the direct writing of plasmonic nanostructures,” Opt. Express 21(21), 24490–24496 (2013). [CrossRef] [PubMed]

6.

G. Raschke, S. Kowarik, T. Franzl, C. Sönnichsen, T. A. Klar, J. Feldmann, and K. Kürzinger, “Biomolecular recognition based on single gold nanoparticle light scattering,” Nano Lett. 3(7), 935–938 (2003). [CrossRef]

7.

Y. Cui, J. Xu, K. Hung Fung, Y. Jin, A. Kumar, S. He, and N. X. Fang, “A thin film broadband absorber based on multi-sized nanoantennas,” Appl. Phys. Lett. 99(25), 253101 (2011). [CrossRef]

8.

C. Reinhardt, S. Passinger, B. N. Chichkov, W. Dickson, G. A. Wurtz, P. Evans, and A. V. Zayats, “Restructuring and modification of metallic nanorod arrays using femtosecond laser direct writing,” Appl. Phys. Lett. 89(23), 231117 (2006). [CrossRef]

9.

A. Radke, T. Gissibl, T. Klotzbücher, P. V. Braun, and H. Giessen, “Three-dimensional bichiral plasmonic crystals fabricated by direct laser writing and electroless silver plating,” Adv. Mater. 23(27), 3018–3021 (2011). [CrossRef] [PubMed]

10.

Z. G. Pang and X. P. Zhang, “Direct writing of large-area plasmonic photonic crystals using single-shot interference ablation,” Nanotechnology 22(14), 145303 (2011). [CrossRef] [PubMed]

11.

R. Kelly and A. Miotello, “Comments on explosive mechanisms of laser sputtering,” Appl. Surf. Sci. 96, 205–215 (1996). [CrossRef]

12.

J. M. Fishburn, M. J. Withford, D. W. Coutts, and J. A. Piper, “Method for determination of the volume of material ejected as molten droplets during visible nanosecond ablation,” Appl. Opt. 43(35), 6473–6476 (2004). [CrossRef] [PubMed]

13.

S. K. Sundaram and E. Mazur, “Inducing and probing non-thermal transitions in semiconductors using femtosecond laser pulses,” Nat. Mater. 1(4), 217–224 (2002). [CrossRef] [PubMed]

14.

G. Chen, “Ballistic-diffusive heat-conduction equations,” Phys. Rev. Lett. 86(11), 2297–2300 (2001). [CrossRef] [PubMed]

OCIS Codes
(140.6810) Lasers and laser optics : Thermal effects
(220.4241) Optical design and fabrication : Nanostructure fabrication
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Laser Microfabrication

History
Original Manuscript: February 18, 2014
Revised Manuscript: March 22, 2014
Manuscript Accepted: March 24, 2014
Published: April 1, 2014

Citation
Yuanhai Lin, Tianrui Zhai, and Xinping Zhang, "Nanoscale heat transfer in direct nanopatterning into gold films by a nanosecond laser pulse," Opt. Express 22, 8396-8404 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-7-8396


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References

  1. J. P. McDonald, V. R. Mistry, K. E. Ray, S. M. Yalisove, “Femtosecond pulsed laser direct write production of nano- and microfluidic channels,” Appl. Phys. Lett. 88(18), 183113 (2006). [CrossRef]
  2. X. Yin, N. Fang, X. Zhang, I. B. Martini, B. J. Schwartz, “Near-field two-photon nanolithography using an apertureless optical probe,” Appl. Phys. Lett. 81(19), 3663–3665 (2002). [CrossRef]
  3. M. Svalgaard, “Direct writing of planar waveguide power splitters and directional couplers using a focused ultraviolet laser beam,” Electron. Lett. 33(20), 1694–1695 (1997). [CrossRef]
  4. T. Tavera, N. Pérez, A. Rodríguez, P. Yurrita, S. M. Olaizola, E. Castano, “Periodic patterning of silicon by direct nanosecond laser interference ablation,” Appl. Surf. Sci. 258(3), 1175–1180 (2011). [CrossRef]
  5. T. R. Zhai, Y. H. Lin, H. M. Liu, S. F. Feng, X. P. Zhang, “Nanoscale tensile stress approach for the direct writing of plasmonic nanostructures,” Opt. Express 21(21), 24490–24496 (2013). [CrossRef] [PubMed]
  6. G. Raschke, S. Kowarik, T. Franzl, C. Sönnichsen, T. A. Klar, J. Feldmann, K. Kürzinger, “Biomolecular recognition based on single gold nanoparticle light scattering,” Nano Lett. 3(7), 935–938 (2003). [CrossRef]
  7. Y. Cui, J. Xu, K. Hung Fung, Y. Jin, A. Kumar, S. He, N. X. Fang, “A thin film broadband absorber based on multi-sized nanoantennas,” Appl. Phys. Lett. 99(25), 253101 (2011). [CrossRef]
  8. C. Reinhardt, S. Passinger, B. N. Chichkov, W. Dickson, G. A. Wurtz, P. Evans, A. V. Zayats, “Restructuring and modification of metallic nanorod arrays using femtosecond laser direct writing,” Appl. Phys. Lett. 89(23), 231117 (2006). [CrossRef]
  9. A. Radke, T. Gissibl, T. Klotzbücher, P. V. Braun, H. Giessen, “Three-dimensional bichiral plasmonic crystals fabricated by direct laser writing and electroless silver plating,” Adv. Mater. 23(27), 3018–3021 (2011). [CrossRef] [PubMed]
  10. Z. G. Pang, X. P. Zhang, “Direct writing of large-area plasmonic photonic crystals using single-shot interference ablation,” Nanotechnology 22(14), 145303 (2011). [CrossRef] [PubMed]
  11. R. Kelly, A. Miotello, “Comments on explosive mechanisms of laser sputtering,” Appl. Surf. Sci. 96, 205–215 (1996). [CrossRef]
  12. J. M. Fishburn, M. J. Withford, D. W. Coutts, J. A. Piper, “Method for determination of the volume of material ejected as molten droplets during visible nanosecond ablation,” Appl. Opt. 43(35), 6473–6476 (2004). [CrossRef] [PubMed]
  13. S. K. Sundaram, E. Mazur, “Inducing and probing non-thermal transitions in semiconductors using femtosecond laser pulses,” Nat. Mater. 1(4), 217–224 (2002). [CrossRef] [PubMed]
  14. G. Chen, “Ballistic-diffusive heat-conduction equations,” Phys. Rev. Lett. 86(11), 2297–2300 (2001). [CrossRef] [PubMed]

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