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Abstract
The article describes the results of finite-difference time-domain (FDTD) mathematical modeling of electric field strength distribution near the gold laser-induced periodic surface structures (LIPSS). Both theoretical and experimental results have been described for two fabricated morphologies: round «hill-like» and grating structures. The structures were fabricated by using a femtosecond Yb-fiber laser with a wavelength of λ=1032 nm, pulse duration τ=280 fs, and repetition rate υ=25 kHz. Morphological properties of the surfaces have been investigated by means of scanning electron microscopy (SEM). The plasmonic activity was analyzed by means of the surface-enhanced Raman spectroscopy (SERS) technique. FDTD-calculated electric field values were converted into the electromagnetic field enhancement coefficient and the theoretical SERS intensity. The prospects of the theoretical approach for LIPSS to evaluate optimal field amplification and light scattering parameters has been shown. The presented approach could be applied as a basis for performing the methods of controlled synthesis for LIPPS.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The field of laser manufacturing of plasmon-active nanoscale periodic structures on metal surfaces is being carried out today actively [1–3]. It is perspective to implement the light harvesting [4] and creation the structures with certain optical properties [5]. During last decades, periodic structures nano-fabrication has formed a new scientific direction, known as LIPSS [6], which appeared to become a perspective research field. Authors in [7] discussed in detail the mechanisms of LIPSS formation using a high repetition rate femtosecond laser beam radiation at λ=1030 nm for titanium oxides. The paper [8] performs a fast and reliable method for fabrication of polarization modifying devices using a femtosecond laser. Surfaces were studied using scanning electron microscopy (SEM) and atomic-force microscopy (AFM). Combined with optical properties characterization, the possibility of periodical surfaces controlled fabrication was shown. LIPSS are widely used for fundamental [9] and practical applications [10]. The effect of plasmon resonances induced by laser excitation near the nanostructured surfaces [11] are being actively studied during last decades. Plasmonic LIPSS can be applied for metamaterials fabrication [12], biosensing, optical trapping. One of the main problems in the development of new nanostructured surfaces is the answer to the question of whether plasmon oscillations can be induced on the surface of the structure being created. The theoretical approach or model focused on LIPSS morphological and optical properties determination can be extremely useful to solve such problems. One of the methods used to simulate electric field disturbances is the FDTD method. It allows estimation both the electric field strength near the surface and the strength-related quantities [13]. The method is used to perform simulations of both colloidal particles and surfaces on a nanoscale size. This paper performs a study of new LIPSS along with flexible FDTD simulation method for their optical properties obtaining with experimental data comparison.
2. Materials and methods
2.1. Femtosecond gold nanostructures fabrication
As a first step, gold films were prepared by electrochemical deposition on an anodized titanium surface [14] in the gilding electrolyte. The electrolyte was prepared as follows: 5 g of K4[Fe(CN)6] was dissolved in 200 ml of distilled water, then the solution was placed on a magnetic stirrer at 240 rpm, t=30°C. The solution of 20% HAuCl4 (V=3 ml) was added drop by drop to a 6 g of K2CO3 and 1 g of KSCN was added after 15 min. The solution was heated at constant stirring for a 1 hour and then cooled to room temperature. The electrochemical deposition of gold on the anodized titanium surface was carried out in the potentiostatic mode at a current density of 5 mA/cm2. A gold plate has 99.9% purity and was used as an anode. After gold plating process, the sample was washed in distilled water and dried. After drying, the gold plate had a characteristic shine and it was easily removed from the titanium substrate for further laser exposure. The thickness of the resulting film, according to Faraday's law [15], was 100 µm. As a second step, femtosecond LIPSS fabricating was performed. The single-mode femtosecond laser (Avesta TETA-25/30 laser system, Russia) (pulse duration τ=280 fs, repetition rate υ=25 kHz) operating at λ=1032 nm with horizontal linear polarization of laser beam was used for LIPSS formation on gold plates. The gold plate was mounted on a motorized positioner 8 MTF-102LS05 (Standa, Lithuania), controlled by XILab software. Two types of geometry of the structuring were created: round «hill-like» and grating. We have designated «round «hill-like»» structures as «circles» as it were fabricated as circles on the gold surface. The structures have been fabricated at the following technical conditions: energy fluence was E=4 J/cm2; laser spot size was 20 µm; the power density for one pulse with pulse duration of τ=280 fs was P=5 TW/cm2; the number of pulses per one µm was n=25 and n=500 in the grating structures fabrication process and in the circle structures respectively. The average speed scanning during LIPSS fabrication was 1000 and 50 µm/s for grating and circles, respectively. The morphology of gold LIPSS was investigated by means of Zeiss Cross Beam-540 (FIB-SEM) electron microscope. SEM images were taken from the surface for circles and grating.
2.2. FDTD simulation process
After surfaces fabrication, the FDTD-based simulation was performed. Simulation algorithm was based on experimental morphology of fabricated surfaces. Models were created based on the obtained experimental SEM images of the surfaces. The modeling was carried out using the Lumerical FDTD Solutions software package (v.8.19.1584, Lumerical Inc.). The main modeling algorithm was described in detail in [13]. However, some modifications have been performed to adjust it for flat surfaces modeling. The result algorithm consisted of five main steps and was performed as follows:
- 1) The computational domain, mesh resolution, and boundary conditions were set. The domain used a rectangular grid in the Cartesian system. The basic values for modeling (The physical material properties and geometry of the objects, electric and magnetic fields) were calculated at each point of the grid separately. Then, additional clarifying mesh for modeling was set. The size of the counting area of the additional grid was set at the value of the grid step: dx, dy, dz = 5.8 nm. To maintain accuracy, the meshing algorithm generated a smaller mesh with a high index (in order to maintain a constant number of mesh points per certain wavelength).
- 2) A body with specified optical and geometric parameters was placed inside the computational domain. Next, the optical and geometric parameters of the body were set. The material database takes into account the values of such a parameter as the real and imaginary parts of the dielectric constant, which depends on the radiation frequency. We have used experimental values for modeling taken from ellipsometry data: Re(ε) = 1.56; Im(ε) = 0.52. We created a rectangular gold plate as a substrate for the rough surface. Further, geometric objects of various shapes were applied to this surface.
- 3) The parameters for the radiation source were set as a next step. Our study involved a total field/scattered field (TFSF) source and it was suitable to study scattering of small particles illuminated by a plane wave. The TFSF source divided the computational area into two separate areas: (a) the general field area, which included the sum of the incident field wave plus the scattered field and (b) the scattered field area, which included only the scattered field. The TFSF source was an extended source. It is important to note that the physical field is the total field, and the separation into the incident and scattered fields requires careful interpretation. For particles in a homogeneous medium, we used p-polarized plane wave in our simulations. Standard simulation parameters were set: the travel time of a plane-polarized wave through the working area as 1000 fs and the temperature of 300°K
- 4) In order to provide us with the final information on a 2D slice form, the plane of the monitor was set. We used XZ and YZ field monitors in the frequency domain, which allowed us to collect a field profile in this domain and provide simulation results in a certain spatial domain for the FDTD solver. The monitor planes were parallel to the plane of the XY model surface (Fig. 4(b) and 5(b)) and correlated with p-polarized wave direction. The E values obtained on the XY surface were recalculated into the SERS and EF values in these parallel planes in a small region (about 26 nm) near where E reaches its maximum, to find the maximum possible values of EF in a «hot spot».
The energy parameters based on E were collected from the monitor data. It should be noted, that that the field values might differ at different points on the surface of our model; we chose points on the surface between the “bumps” of geometric objects, where, in theory, the maximum value of plasmon resonance should occur.
- 5) As a final step, we calculated values of the E field in our simulation. It was recalculated into the SERS intensity and |E|4 coefficient using FDTD Lumerical scripts. The effective SERS enhancement was defined as |E/E0|4, where E is the local maximum electric field and E0 is the input source for electric field amplitude in linear simulations. Under proper conditions, localized surface plasmons and surface plasmon polaritons (SPP) can occur on rough surfaces. As described above, we used the TFSF source to simulate the electric field on a rough surface and find the maximum possible EF and intensity of the SERS signal.
2.3. SERS experiments
In order to carry out SERS experiments, Centaur U (LTD «NanoScanTechnology», Russia) spectrometer was used. The spectrometer was equipped with three different laser sources: 632.8 nm He-Ne laser (37 mW), 532 nm and 473 nm diode-pumped solid-state (DPSS) lasers (45 mW). We used lasers operated at 532 nm and 632.8 nm to correspond the excitation with plasmon maximum for gold structures and to avoid fluorescence of R6G on the surfaces, respectively. The optical scheme of the spectrometer included an Olympus BX41 microscope (Olympus, Japan) with a 100×(NA 0.9) objective to perform beam positioning and scattered photons collection. The spectrometer monochromator had a focal length of 266 mm, 1200 g/mm holographic diffraction grating and was equipped with a 1024 × 256 pixels CCD thermoelectric cooled detector (Andor Tech., UK). Freshly prepared solutions of R6G (10−5 M) was added drop by drop on prepared surfaces, dried at room temperature and placed in the spectrometer holder. The laser beam was positioned manually using a USB Video Camera (Olympus, Japan) and the laserspot from the Raman spectrometer was focused on the surfaces. The spot was positioned on the center of the circle or grating after the laser action. The size of the laser spot varied from 1 × 25 µm to 1×30 µm depending on the laser power used. To prevent sample destruction and best signal-to-noise ratio achievement, the laser power embedded to the sample was manually adjusted from 5 to 37 mW for He-Ne excitation source and from 5 to 45 mW for DPSS lasers. The edge filters were applied to eliminate Rayleigh scattering. Raman spectra were recorded in a wavenumber «fingerprint» range for organics 600 cm−1 and 1750cm−1 with the spectral resolution of 2.5 cm−1. The unit was calibrated before the assessment of each series of specimens with silicon standard (Horiba, Japan) at a static spectrum centered at 520.1 cm−1 for 1 s. All spectral data were saved after the registration as .txt files for further assessment.
3. Results and discussions
3.1. Circle geometry
In the first series of laser structures fabricating, the moving of the positioner with gold plate was around the circle (with diameter of 1 mm). XILab software (v.1.14.12, Standa) with lab-created scripts were used to set a scanning speed as 50 µm/s, scanning step equal to 1 µm and laser fluence E=4 J/cm2. The structures were self-organized along the laser path beam as a result. The fragments of these structures forming inside/on the circle are presented in Fig. 1. Analyzing Fig. 1(a), it is possible to distinguish surfaces of different morphology on the periphery and on the inner side wall of the path beam. We suggested different mechanisms being responsible for the formation of a particular structure. Thus, the formation of periodic structures at the inner side wall of the ring is due to s-state polarization of E vector of incident radiation (Fig. 1(b)-scheme). During the laser exposure the E vector always directs perpendicular to the inner side wall of the ring. The forming of such hill-like structures with spatially periodic of 10 µm also is due to interference of the incident and scattered radiation.
Fig. 1. SEM image of the LIPSS in circle geometry on the gold plate (a) with scheme of the scanning (b)
Height analysis demonstrates changes in the relief of the structures (Fig. 2(a)), it can be assumed that the hill-type periodic structures are repeated with a period of 10 µm. It should be noted, that the average scanning speed in the structuring process was 50 µm/s, with pulse frequency of 25 kHz, so there were 90 pulses per area of 30 µm. However, considering the width of the beam had a diameter of 20 µm and the scanning step length was 1 µm, therefore each sub-area of the beam path was exposed by large number of pulses (more than 500 pulses) during the laser pulse. This fact also determines the formation of the structures on the inner side wall of the circle beam path with a period of 10 µm. It is due to the repeated laser radiation exposure with a constant s-polarization of E vector relative to the gold plate plane with moving step of 1 µm, small clusters were formed (Fig. 2(b)), consisting of hill-type structures generally. The maximum relief height (Fig. 2(a)) was 400 nm, the average height of each periodic structure was approximately 200 nm. Considering the cluster of small particles on the side wall of the path beam (Fig. 2(d)) according to the surface profile, we can assume that a 250 × 200 nm cluster had an average relief height of ≈300 nm. Figures 1(a), 2(e) show that structuring of the material occurring at the periphery of the laser path beam was different. Thus, Fig. 2(d) demonstrates the presence of dendrite-like structures consisting of accumulations of gold nanoparticles (NPs) after laser surface scribing. The formation of such spherical clusters with a diameter of up to 200 nm on the peripheral region of the ring was due to the droplet formation mechanism [16,17]. For structures formed at the periphery, the maximum height could amount to 600 nm (Fig. 2(e)). The size of such cluster consisting of gold NPs could amount to 1 ÷ 2 µm.
Fig. 2. SEM images of the LIPSS in circle geometry on the gold plate: the inner side wall of the circle (b); near the path beam (d) and the color landforms of the structures (a,c,e).
3.2. Grating geometry
In the second series of laser structures fabricating, the moving of the positioner with gold plate was along linear trajectory in the perpendicular and parallel direction relative to the polarization Es vector (Fig. 3(a)). The speed scanning was 1000 µm/s with scanning step equal to 2 µm and laser fluence E=4 J/cm2. The spot size of the laser beam was ≈ 20 µm and the ripple formation on the gold surface under laser exposure during 1 s in one point is present on Fig. 3(a) (scheme-inset). Thus, laser exposure time per one line with 25 pulses/µm was 625 ms. The structures obtained at this surface scribing regime is shown in the Fig. 3(c). Figure 3(c) illustrates gold clusters with an average size of ≈300 nm formed on the periphery of the laser path beam. The formation of such constant structures was associated with the processes of laser evaporation of material from the surface and its subsequent deposition near the laser path. Agglomeration of structures occurred near the surface at temperatures close to the melting point of gold. The height of such clusters varied in 200 ÷ 400 nm range on the sample investigated area (Fig. 3(d)). It should be noted that the laser scribing speed of the grating structuring was 100 µm/s. The laser pulse duration per one line (Fig. 3(a)) was 0.625 s. During this time, gold clusters were formed by the laser exposure (with the frequency of 25 kHz and a pulse duration of 280 fs) (Fig. 3(c)) settling near the groove extends at a distance of 10 µm from the edge. According to the analysis of the surface relief (Fig. 3(a,(b))) the formation of 40 µm-smooth hillocks in the intervals between the grooves of the lasers path beam was revealed (Fig. 3(a)). Based on the analysis of the images shown in Figs. 1–3, at the given parameters of laser structuring, micro- and nanostructures can be formed on the gold surface, on which the processes of plasmon energy conversion could be observed [18,19]. These processes were further simulated by the FDTD method on nanoscale areas of the investigated surfaces.
Fig. 3. SEM images of the LIPSS in grating geometry on the gold plate with scheme of the scanning process and ripple structures of the spot beam (inset): (a) – in 100 µm scale and (c) – in 300 nm scale and the color landforms of the structures (b,d).
3.3. FDTD simulation Results and SERS
The simulation of plasmon fields distribution on the studied structured surfaces is complex task due to the relief features of the surfaces. We developed and used two models, corresponding to the morphology of gold surfaces after fs-laser structuring process. We use morphology corresponding with SEM images presented in Fig. 2(d) for «circle» and Fig. 3(c) for «grating». The most appropriate different structural elements such as cylinders, spherical segments and sharp cones were chosen to form the surface in the modeling area. For «circle» (Fig. 4(a)) and «grating» (Fig. 5(a)) surface base size in the simulation area was set as follows: x – 200 nm, y – 400 nm, z –10 nm. In case of «circles» the surface consisted of large (“L”), middle (“M”) and small (“S”) cylinders with spherical segments on their top. “M”-cylinders were placed between the “L”-cylinders, while “S”-cylinders were placed along the periphery. Sizes of the modeling morphological elements are described in detail in Table 1.
Fig. 4. FDTD model area with «circles» surface geometry (a) and electric field strength distribution (b).
Fig. 5. FDTD model area with «grating» surface geometry (a) and electric field strength distribution (b).
Table 1. Morphology parameters for «circles» surface geometry
In case «grating» (Fig. 5(a)) the surface consisted of “L”-cylinders with spherical segments on the top. Segments of ellipsoid of revolution were added into the system between “L”-cylinders. Cones were placed along the periphery as the third element. The parameters of modeling objects are described in detail in Table 2.
Table 2. Morphology parameters for «grating» surface geometry
The simulation results were used to determine the magnitude of the electrical disturbance and theoretical SERS enhancement near the surface. 2D images reflect «hot-spots» for «circles» (Fig. 4(b)) and «grating» geometry (Fig. 5(b)). The electrical field disturbance was recalculated to the SERS enhancement factor. It was shown that the adding of sharp cones into the modeling area slightly increased the theoretical SERS signal in the selected area.
The maximum overall calculated enhancement factor (EF) was 103 ÷ 104, depending on the position of the monitor (Table 3). Implementation sharp-cone structures into the simulation area did not result in significant E enhancement, although overall, the predicted SERS signal strength increased. The greatest perturbation of the electric field arose between cylinder dimers on the surface of the structures in both cases. Taking into account the above-mentioned fact, for better substances surface adsorption and for them to reach hot-spots resulting in high SERS enhancement factors achievement, clustered surfaces should be fabricated.
Table 3. Results of FDTD simulations and experimental SERS intensity
Photoprocesses enhancement near the metal surfaces can be implemented by surface plasmons and evaluated with scattering and fluorescence-based spectroscopy methods [20,21]. We used SERS on R6G molecules to estimate Raman scattering EF. Figure 6(a) shows R6G SERS spectra for grating-like geometry structuring in the «сrossroads» (intersection area) (Fig. 6(b)) and «channels» (inside the laser path beam area) (Fig. 6(a)) in the structured area. SERS signal did not differ significantly, implementing SERS enhancement up to 2.7 · 103.
Fig. 6. SERS spectra for grating type structures with different positioning of laser beam: in the groove after laser beam passaging (a), in the «crossroads» after the laser beam passaging (b). ND filter was applied for both cases, decreasing intensity of laser beam in 100 times. λex = 532 nm
From the other hand, for circles type structures, difference in the SERS signal depending on the laser beam positioning has been detected. In case of laser spot positioning between two circles (Fig. 1(a)), the EF SERS is 4.97 times higher (Fig. 7(a) and Fig. 7(b)) compared with one for the laser spot positioned in the inner side wall of the laser beam path. The maximum enhancement obtained was 1.12 · 104 for clustered surface (Fig. 2(d)).
Fig. 7. SERS spectra for circles with different positioning of laser beam: between two circles in the sample (a) and in the inner side wall after laser beam passaging (b). ND filter was applied for both cases, decreasing intensity of laser beam in 100 times. λex = 632.8 nm
4. Conclusions
A flexible FDTD-based mathematical approach for modeling of electric field strength distribution near the gold LIPSS manufactured surfaces has been performed. Calculations were in good agreement with experimental data. Two LIPSS morphologies have been fabricated and analyzed: circles and grating. We have manually created surface models using different geometry elements. Morphological properties of surfaces have been investigated and described. Surface enhanced Raman spectroscopy (SERS) technique has been used in order to analyze each type of surfaces. It was shown that the greater SERS EF were implemented in clustered surfaces. The prospects of the theoretical approach for LIPSS to evaluate optimal field amplification and light scattering parameters have been shown. The presented approach could be applied as a basis for performing methods of LIPSS controlled synthesis and other surface fabrication methods.
Funding
Ministry of Science and Higher Education of the Russian Federation (FZWM-2020-0003).
Disclosures
The authors declare no conflicts of interest.
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