1. Introduction

Although typically considered as tools for microstructure generation, lasers also provide a rich pool of nanostructure-promoting effects [1–3]. An interesting example of this is the formation of so-called laser-induced periodic surface structures (LIPSS), a phenomenon that occurs as a consequence of light-matter feedback mechanisms creating a pattern of periodically oscillating light intensity on the surface of solids [4–6]. The periodicity Λ of such photonic fringe patterns, henceforth abbreviated as PFP, depends largely on parameters such as the wavelength λ and the pulse width of the laser as well as the angle of incidence θ and the refractive index η of the affected material. In case of nanosecond lasers, as utilized in this study, the fringe pattern periodicity can be approximated using the equation Λ = λ∙[Re(η) – sinθ)]⁻¹, where Re(η) is the real part of the refractive index [7,8]. The formation of so called low spatial frequency LIPSS (LSFL) is commonly accepted to result from interference of incident laser wavefronts with surface plasmon polaritons (SPPs) exited upon irradiation [9–12]. LFSL formation can be predicted by the Sipe-Theory which uses the surface roughness of materials as a basis for simulation [13]. SPPs exited on semiconductor and metal surfaces feature traverse magnetic polarization. This implies that interference with incident polarized plane waves forms PFPs in orthogonal direction to the laser polarization, a fact that corresponds to experimental observations [10–12,14].

Materials subjected to PFPs react with certain transformations that depend on specific material properties or rather the complexity of the stimulated system. Besides morphological changes the repertoire of potential effects includes spatially selective phase separations and chemical segregations [15]. Transformations like these were shown to be the result of optically induced thermal gradients of sufficient magnitude to melt the surface of a material in regions where the PFP intensity peaks. Thermal gradients are, however, not the only driving force that causes the formation of LIPSS. Spatially controlled photochemical reactions have also been demonstrated to be a promising way to exploit the potential of PFPs for practical applications [16]. All these investigations show that the formation of LIPSS can be understood as the result of certain transformations triggered by periodically varying optical flux densities in the near field of solids. The example of photochemical LIPSS formations demonstrates a pattern formation process which is directly mediated by photons rather than thermal gradients. It is thus reasonable to raise the question whether photonic interactions with materials have a direct influence on LIPSS-formation.

The present study addresses this question on the example of a model system comprising randomly distributed gold nanoparticles on silicon. PFPs are demonstrated to reorganize the system by a process based on mass transport across the silicon wafer. Different stages of pattern maturity provide insights into the mechanisms of PFP-stimulated pattern formation. The first stages are shown to be governed by directed assembly and concomitant fusion of gold nanoparticles to gold nanowires. Excessive stimulation eventually leads to the fragmentation of as-generated gold nanowires, a process of self-organization driven by the Rayleigh Plateau instability of liquefied gold nanowires. PFP-directed assembly is also demonstrated to provide the opportunity to rotate existing gold nanowire arrays by specific angles. The process features certain similarities to the rotation of suspended objects by optical tweezers. However, the degree of mechanistic relatedness between these two phenomena leaves room for interpretation.

2. Experimental procedure

In a typical experiment, a silicon wafer (P525, n-type, 1-0-0, R = 800-1600 Ω, Siltronic AG, Germany) is coated with a gold film of 5 nm thickness using a vacuum coater system (Auto 306, Edwards, UK). Subsequent heat treatment at 250 °C for 24 h in a muffle furnace (L08/14 Nabertherm, Germany) leads to spinodal dewetting of the gold thin film. This self-organization process finally results in the formation of gold nanoparticles which are statistically distributed over the wafer surface [Fig. 1(a)] [17].

 

Fig. 1 (a) SEM picture of silicon wafer after thermally induced dewetting of Au thin film. (b) Gold nanoparticles formed after 35 P. (c) Commencing formation of periodic gold nanostructures in orthogonal orientation to the laser polarization (green arrow). (d) Early stage of gold nanowire formation after 250 P. (e) Alignment and merging of gold nanowires after 320 P. (f) Formation of continuous gold nanowires and removal of residual gold nanoparticles from line interspaces after 450 P.

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As-prepared samples are irradiated with a nanosecond-pulsed laser emitting linearly polarized light at a wavelength λ = 532 nm and a pulse width τ = 5 ns (Explorer XP 532-5, Newport, USA). The laser beam is focused to an effective spot size of 30 μm diameter by an F-theta lens (f-163-532, Rodenstock, Germany) and scanned over the samples with a line spacing of 3 μm using a galvanometer scan head (SCANgine 14-532, Scanlab, Germany). Depending on the scan speed irradiated zones are subjected to a certain number of overlapping laser pulses, henceforth abbreviated as P. A suitable condition for the generation of PFPs in the model system is identified at a laser fluence of φ = 1.63 J/cm² and a pulse repetition rate of ν = 100 kHz. Appendix A provides additional process-related details.

3. PFP-induced pattern generation

In response to stimulation with PFPs Au-particles on the wafer surface initially undergo a loss in average particle size from about 80 nm to about 20 nm when 35 P are applied [Fig. 1(b)]. First signs of pattern formation can be observed after 225 P by means of particles agglomerating in a stripe-like manner [Fig. 1(c)]. Recurrent laser stimulation leads to continuous structure refinements and eventually results in continuous gold nanowires featuring a periodicity of about 500 nm [Fig. 1(d)-1(f)].

Excessive stimulation leads to a degradation of pattern quality. The concomitant destabilization of formerly well-defined gold nanowires starts with the formation of corrugations at 640 P and finally ends with the fragmentation of former line arrays [Fig. 2].

 

Fig. 2 Rayleigh-Plateau instability of liquid gold nanowires (a) Starting formation of corrugations in gold nanowires after stimulation with 640 P. (b) Partial break up into fragments of about 800 nm length at 900 P. (c) Almost complete fragmentation of former gold nanowires after 1500 P.

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Mechanistically, this process bears striking similarity to the Rayleigh-Plateau instability (RPI) which indicates that a jet of falling liquid will break up into droplets satisfying the equation λ ≈9.02 R₀, where λ is the fastest growing wavelength of fragmentation in a jet of radius R₀ [18,19]. Accordingly, a transiently liquefied gold nanowire of 180 ± 10 nm diameter is expected to undulate in a wavelength of 812 ± 45 nm. Experimentally, λ is observed to fall in the range between 780 and 820 nm. This is very close to the value expected theoretically thus indicating RPI to be the underlying mechanism of gold nanowire fragmentation. One could argue that RPI is a macroscopic phenomenon; however, it was demonstrated to exist on the nanoscale as well [20,21]. In the given case, the mere fragmentation of gold nanowires demonstrates that optical flux densities in peak regions of PFPs are evidently high enough to induce the transient liquefaction of gold. Due to the high surface tension of liquid gold such rivulets break up into droplets striving to minimize their surface [22]. The self-organization process resulting thereof is almost unaffected by PFP-induced forces because the two effects cannot directly counteract one another for geometric reasons. This statement is supported by a survey of the sequential development of pattern maturity states. In order to gain a better understanding of competing pattern formation mechanisms emergent upon PFP-stimulation Fast Fourier Transformation (FFT) was applied as a measure for pattern quality. In practice, SEM images of respective gold patterns were transferred into the reciprocal space using FFT and evaluated with respect to pattern periodicity, pattern orientation and pattern defects [Fig. 3(a)-3(c)].

 

Fig. 3 Numerical analysis of pattern quality (a) SEM image taken from a high quality array of gold nanowires on silicon. (b) Fast Fourier Transformation (FFT) of the SEM image; area of interest marked in red. (c) Enlarged view on area of interest and determination of measuring point used for the analysis of pattern quality. (d) Interdependence between pattern quality and the number of applied laser pulses P. The best pattern quality achieved is normalized to 1 and represents gold nanowires on Si generated with 450 P.

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A comparative evaluation is achieved by an indicator for pattern quality extracted from a region of interest (red) which includes feature sizes down to 300 nm in real space (6.66 x 6.66 μm⁻¹). The quality indicator was determined by means of gray scale values extracted from different regions in FFTs. It was defined to be the ratio of the gray scale value of the first order reflex and the average gray scale value of the region of interest; see Appendix B for details. For instance, gold nanowire arrays generated with 450 P [Fig. 1(f) and 3(a)] yield a quality indicator of 120.2 which is the highest achieved in this study. This maximum value was taken as the basis for normalization in order to display the interdependence between the number of applied laser stimuli (P) and the pattern quality in a more convenient way [Fig. 3(d)]. Accordingly, the pattern quality initially increases exponentially upon iterative PFP-stimulation but decays hyperbolically after passing a maximum at 450 P. The different nature of these functions clearly shows that the overall process of pattern formation is governed by two competing mechanisms. Firstly, PFPs promote the formation of gold nanowires, a process that can be described as directed assembly, and secondly, optical heating by PFPs leads to the liquefaction of as-generated nanowires thus favoring RPI which is a process of self-organization.

4. Considerations about the mechanisms behind LIPSS formation

Apparently, the process of nanowire formation requires lateral mass transport to occur thus raising the question of the driving force behind it. As mentioned above, thermal gradients have already been identified to be a driving force for PFP-stimulated pattern formation. Depending on the affected system such thermal stimulation may induce phase segregations, chemical separations and surface reshaping [15]. Mass movement across a surface may be another effect initiated by thermal gradients; however, reports referring to thermally driven mass movement induced by PFPs are not found in the literature. This may be due to the fact that the underlying mechanisms of thermal mass transport are hardly tangible neither experimentally nor theoretically as the formation of LIPSS is a fast and nonlinear process running under harsh conditions. Direct measurements of thermal gradients are thus almost impossible. Simulation could be a solution to this problem but underlying mathematical models would be required to handle fast-proceeding and highly nonlinear light-matter-interactions. In consequence, the mechanisms behind LIPSS-formation remain nebulous, even though thermal gradients appear to be a likely driving force. It should, however, be noted that thermal gradients are not the only structure directing effect of PFP-stimulated pattern formation. For instance, PFPs have also been demonstrated to trigger spatial selective photochemical reactions on surfaces [16]. A process like this requires locally varying photonic flux densities in close proximity to the surface. It is thus reasonable to address the question whether direct photonic interactions play a role in the process of LIPSS formation. In the given example, PFPs may also be interpreted as a special type of optical tweezers that forces objects such as gold nanoparticles into regions where the fringe pattern intensity peaks. To pursue this question, the principal feasibility of light driven transport is assessed on the example of the system under investigation.

5. Optical trapping as a potential driving force behind LIPSS-formation

Metallic objects are considered poor candidates for optical trapping because they reflect light, a property which counteracts the magnitude of optical gradient forces. One exception to this are metallic objects featuring diameters by far smaller than the laser wavelength used for optical trapping. Such metallic Rayleigh particles feature scattering cross-sections similar to those of dielectrics but their polarizability is by far greater thus favoring high trapping forces [23,24]. Due to its relevance for practical applications optical control over gold nanoparticles in particular is well investigated [25–28]. Objects spanning the size range from Mie-particles down to quantum dots have been successfully trapped using optical tweezers [29–31]. By default, optical trapping is performed on suspended particles which are drawn to the focal point of a tightly focused laser beam by forces in the order of 10⁻¹² N [32–34]. Compared to that, the movement of particles across a surface must be expected to require higher forces than those delivered by standard optical tweezers. It is known that the trapping forces of optical tweezers largely depend on parameters like the laser wavelength, the irradiated power or rather the maximum flux density of an optical trap as well as its intensity distribution. For this reason, the experimental set-up utilized here was chosen in a way that tunes each of these parameters to optimum performance. First of all, the laser wavelength of 532 nm overlaps almost perfectly with the plasmon resonance peak of gold nanoparticles in the given size range [35]. The mode of optical trapping can thus be expected resonant which, compared to non-resonant trapping, yields higher particle polarizability, a factor that increases the trapping force [36]. In addition to that, photonic flux densities delivered by a nanosecond pulsed laser exceed those of commonly used continuous wave lasers by far. Transient trapping forces generated by pulsed optical tweezers were shown to be about one order of magnitude higher (in the order of 10⁻⁹ N) than those of cw-lasers-based optical tweezers [37]. Peak gradient forces induced by pulsed lasers are evidently high enough to overcome binding forces between particles and surfaces. For instance, Ambardekar and Li successfully demonstrated the movement of polystyrene microbeads stuck to surfaces using pulsed laser optical tweezers [38]. Analogous to this, the movement of gold nanoparticles across silicon appears to be possible provided that optical gradients of sufficient magnitude can be generated in close proximity to the surface. The laser-stimulated self-construction of PFPs at gas-solid interfaces represents an elegant solution for the practical realization of massive optical gradients in near-surface regions. Figure 4 illustrates the successful generation of PFPs (green) in the model system schematically.

 

Fig. 4 Model of gold nanowire formation by PFP-stimulated optical trapping of gold nanoparticles on silicon.

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Since a nanosecond pulsed laser is used for PFP generation the optical power at peak positions of PFPs can reach several kilowatts under given irradiation conditions. Compared to this, optical tweezers based on cw-lasers are typically operated with optical powers in the range of several hundred milliwatts. The very combination of resonant trapping, near diffraction limited focusing and high-power stimulation can thus be assumed to induce optical gradient forces of sufficient magnitude for the movement of gold nanoparticles over silicon. It must, however, be noted that such harsh conditions also promote rapid heating of gold nanoparticles, a side effect which is normally not desired to occur upon optical trapping [39]. Contrary to that, elevated temperatures would contribute decisively to the formation process of gold nanowires as gold nanoparticles are not only concentrated but also concomitantly fused in regions where the photonic flux density peaks (red).

6. PFP-induced rotation of gold nanowire arrays

In order to explore the relatedness between PFPs and optical tweezers an experiment was conducted which is commonly known to demonstrate the performance of optical tweezers: The rotation of objects around their own axis. We found that a manipulation of this kind can be achieved by resumed stimulation of gold nanowires with PFPs orientated in another direction with respect to the alignment of the existing pattern. Figure 5(a) illustrates this principle on the example of a pattern rotation by 90 degree. The rotation of PFPs is put into practice by a simple rotation of the laser polarization. Stimulation with 200 P results in rotated gold nanostructures whose shapes differ with the distance from the center of the laser spot. This inhomogeneity is caused by the Gaussian intensity profile of the laser beam. In the center of the PFP-affected zone the former array of gold nanowires is transformed into orthogonally aligned nanostructures which look very much like patterns generated out of randomly distributed gold nanoparticles by stimulation with 250 P. Further similarities include that the pattern quality peaks at 400 P and then decreases upon excessive stimulation due to nanowire fragmentation [Fig. 5(b)-5(d)]. The finding indicates that gold nanowires are actually not rotated but rather reconstructed in orthogonal orientation, a mechanism that is considered to be the result of non-gradual stimulus rotation. On the one hand, this demonstrates the structure directing power of PFPs impressively, but, on the other hand, the experimental result does not allow conclusions to be drawn concerning the question whether optical trapping or rather thermal gradients are the driving force behind this transformation.

 

Fig. 5 Rotation of gold nanowire arrays (a) Sketch of orthogonal PFP-stimulation in a single laser spot of Gaussian intensity profile: structure directing force gradients are rotated by 90 deg with respect to already existing gold nanowires on Si. (b) Orthogonal directing stimulation with 200 P results in pattern rotation by 90 degree in a spot-like area. (c) 400 P result in rotated gold nanowires located in the center of the laser spot. (d) Iterative stimulation with 600 P leads to the fragmentation of gold nanowires.

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7. Conclusion

PFPs have been demonstrated to reorganize an initially chaotic system of randomly distributed gold nanoparticles on silicon into well-defined patterns of periodic gold nanostructures. The opportunity to utilize directed assembly and self-organization in a process that is essentially simple to initiate makes the introduced concept attractive for practical applications. Besides the model system investigated here we expect the principle to be applicable to other materials as well. Some issues must, however, be addresses before it can be exploited for practical applications. Most notably, this includes the unsolved question of the driving force behind the process of nanowire formation. Thermal gradients are commonly accepted as the structure directing effect but the potential influence of optical gradient forces cannot be ruled out categorically. Since photonic gradients induce thermal gradients it is considerably difficult to distinguish the influences of the two effects in a separated manner. Future experimental approaches towards this question could make use of the fact that certain materials react specifically to thermal or optical stimulation, respectively.

Appendix A: Generation of extended LIPSS patterns

LIPSS generation is a laser-based process and thus typically covering areas the size of a laser spot footprint which makes homogeneous pattern formation on extended areas initially difficult. In order to overcome this problem a dynamic laser scanning process was employed that facilitates LIPSS modifications on areas by far greater than a laser spot footprint. A Nd:YVO₄ DPSS nanosecond laser (Explorer XP 532-5, Newport, USA) emitting a wavelength of 532 nm in spatial mode TEM₀₀ (M² < 1.1) at a pulse repetition rate of 100 kHz and a pulse width of 5 ns was scanned over Au/Si-substrates in a meandering pattern as illustrated in Fig. 6(a).

 

Fig. 6 Dynamic LIPSS generation (a) Typical laser scan profile used for homogeneous irradiation of extended surface areas on Au/Si substrates. (b) Temporal course of irradiated intensity (I) exemplified for the red point in the scan field.

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Since the effective laser spot diameter of 30 μm (FWHM) is greater than the line spacing of 3 μm each point (e.g. the red one) on the irradiated surface is affected by an optical intensity flow whose temporal course is sketched in Fig. 6(b). The transient flow of energy input results from the Gaussian intensity profile of the laser spot whereas its time interval depends on the x-dimension of the scan field and the line scan speed. Keeping the line spacing constant at 3 μm, the line scan speed is the decisive parameter by which the number of laser pulses (visualized as vertical lines in the intensity envelopes of passing laser spots in Fig. 6(b)) incident on a certain point of the scan field is controlled. The number of overlapping laser pulses (P) which is the characteristic value to be found in LIPSS studies, can be derived statistically. In the present study P is expressed as the statistic number of fully overlapping laser pulses incident on an area of 706 μm² which corresponds to the footprint of a single laser spot of 30 μm diameter FWHM. In practice, P is calculated as the quotient of the total number of laser pulses incident on a scan field of dimension A and the area covered by a laser spot footprint.

Appendix B: Quality determination of LIPSS patterns

In search of process conditions enabling for the generation of high quality gold nanowires on Si, critical parameters such as irradiation conditions and precursor set up have continuously been optimized. With regard to laser-induced pattern formation on precursor substrates, two laser parameters appeared to be of major importance: the pulse energy and the number of overlapping laser pulses. Both parameters were systematically screened in batch experiments. Surface modifications generated under diverse irradiation conditions have been examined by SEM. In order to ensure objective evaluations of the nanowire quality SEM pictures were transferred into the reciprocal space using Fast-Fourier transformation. Fourier-transformed images include frequency information in x and y-direction thus enabling the determination of pattern periodicities, pattern orientations and pattern defects. Figure 7 shows a SEM picture taken from gold nanowires generated at optimum conditions (400 P, φ = 1.63 J/cm², as indicated above) and its corresponding FFT. The first order reflex corresponding to gold nanowires is located at a position of about 2 μm⁻¹ from the center of the plot thus indicating a pattern periodicity of about 500 nm. Higher orders result from smaller distances in real space and are attributed to the line width or rather the line-sharpness of the pattern. The sickle-shaped deformation of reflexes is caused by angular deviations of single lines from the predominant LIPSS orientation. An angular deviation smaller than 3.5° was analyzed in thecase of high quality LIPSS (400 P, φ = 1.63 J/cm²). The comparative evaluation of laser-generated patterns is performed by means of a quality indicator Q which is extracted from FFTs of SEM images. Q is defined to be the quotient of averaged gray scale values taken from the first order reflex and a section of 6.66 x 6.66 μm⁻¹ (region of interest including objects down to 300 nm in real space) around the center of the FFT-plot [Fig. 7(c)]. The first order reflex of high quality gold nanowires features a gray scale value of 6.01 whereas the average gray scale value in the region of interest is 0.05. Calculating the quotient of both values yields a value of 120.2 which is the highest achieved in the survey. This maximum value was taken as the basis for normalization to 1 in order to display the results of pattern quality optimization in a more convenient way. Further examples of generated patterns and their corresponding FTTs and quality indicators are given in Fig. 8.

 

Fig. 7 Determination of LIPSS-quality (a) SEM picture of high quality Au/Si-LIPSS generated by 450 P at φ = 1.63 J/cm² (b) FFT-plot of the SEM-image (c) region of interest (6.66 x 6.66 μm⁻¹) for quality evaluation of laser generated patterns.

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Fig. 8 Quality evaluation of patterns created under different conditions (a) pattern generated by dynamic irradiation of already existing LIPSS with 800 P at φ = 0.95 J/cm² under orthogonal directing laser polarization (b) LIPSS created with 320 P at φ = 1.63 J/cm² (c) LIPSS created with 900 P at φ = 1.63 J/cm².

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