1. Introduction

Scientists from various research fields are currently concentrating research efforts on gaining a more profound understanding of plasmonic effects by metal nanoparticles [1–3]. Close to the plasmon resonance, scattering and absorption by the particles, as well as the near-field effects, are enhanced [4]. The plasmonic resonance is very sensitive to characteristics of the particle configuration [5]. By increasing the size of the particle or the refractive index of surrounding media, the resonance peak is red-shifted. Metal nanoparticles at the interface between two materials scatter preferably into the medium with higher refractive index [6]. Furthermore, single particle effects are modified by interactions between particles [7–9]. Deeper insight is needed to tune the plasmonic resonance via shape, size, material and arrangement of the particles for particular applications [1]. Besides near-field effects, large optical cross-sections are utilized to improve devices such as biological sensors, Raman spectrometers and solar cells [3, 10]. Strong near-field enhancements close to the particles can be applied to amplify non-linear processes like upconversion [11, 12].

In particular, the efficiency of thin silicon solar cells, which only weakly absorb near-band-gap light, can be enhanced by increased light scattering [7, 13]. As silicon exhibits a relatively high refractive index [14], plasmonic nanoparticles placed on the front or rear side of the silicon film yield light trapping due to preferential scattering [3]. Light trapping results in a path length increase and, thereby, absorption enhancement in the silicon layer [15], provided that parasitic absorption by the particles is low [16]. To this end, particles should be fabricated such that resonant absorption in the metal occurs at wavelengths which cannot be used by a silicon solar cell [17]. Ideally, the nanoparticles strongly scatter but weakly absorb light in the spectral range of 900 nm to 1200 nm. This can be achieved because resonant scattering and absorption do not necessarily occur in the same spectral region.

In order to meet the demands of these applications, the fabrication of controllable and reproducible particle configurations on large areas is essential. In literature, annealing of thin metal layers has been used to randomly structure substrates [18, 19]. This method is effective, but prevents exact control of particle features and configurations. Uniformly shaped metal particles can be conveniently fabricated by nanoimprint lithography (NIL), which requires a master structure [20] and a lift-off process [21]. By electron beam lithography, masters for the production of various nanoparticles can be precisely defined [22]. However, the throughput of this method is very low so that it is not suitable for structuring large areas [23].

With the help of laser interference lithography (LIL), areas of up to $\text{1}\text{.2×1}\text{.2}{\text{m}}^2$ [24] can be homogeneously patterned by structures with grating spacings between 200 nm and 100 µm [25]. These masters are transferred to flexible films or rigid substrates with areas of up to $\text{200×200}{\text{mm}}^2$ by NIL [24, 26]. In a previous work, we presented round silver and platinum particles with diameter 600 nm and showed first tests on 200 nm large silver particles arranged in a crossed grating [27]. Those tests revealed how difficult it is to reproducibly process such small particles. Noble metals are chosen as they are more resistant to oxidation and corrosion. Silver nanoparticles show a particularly high scattering and low absorption in the wavelength range between 500 nm and 2500 nm [28], which is advantageous for use in solar cells.

In this paper, the process chain for the controlled production of round and elliptic silver particles that are arranged in crossed and hexagonal gratings, respectively, and have a diameter of around 200 nm is presented. These particles can be fabricated on glass as well as on silicon substrates. The absorbance spectra of both particle arrangements at a glass-air interface are investigated. Experimental results obtained with Fourier spectrometer analysis are compared to simulations performed with rigorous coupled wave analysis (RCWA) [29].

2. Fabrication and simulation methods

The process chain starts with the fabrication of a master structure by LIL and electroplating. Flexible silicone stamps can be repeatedly molded from the master. Subsequently, metal nanoparticles covering a substrate are obtained by NIL, etching, metallization and a lift-off (see Fig. 1 (a)).

 

Fig. 1 (a) Overview of the process chain for the fabrication of uniform metal nanoparticles. The master (I) is produced by laser interference lithography and electroplating in order to replicate silicone stamps (II). Resist covering a substrate is structured by nanoimprint lithography with the help of the silicone stamp and UV light (III). After residual layer etching (IV), metallizing (V) and lifting off the resist (VI), only metal nanoparticles remain on the substrate. The grating spacing of the particle arrangement can be adjusted by changing the half-angle θ between the two beams in the laser interference lithography setup (b). The sample is exposed twice and turned by α = 90° or α = 60° in order to obtain a crossed or hexagonal grating.

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LIL, appointing the composition of the nanoparticles, was performed as described in [24, 25]. First, the laser beam is divided into two beams by a beam splitter (Fig. 1 (b)). With the help of mirrors and lenses, these beams are then separated by several meters and expanded in order to homogeneously expose an area of $\text{7}\text{.5×7}\text{.5}{\text{cm}}^2$. When superposing those two beams, the photographic plate is exposed by a line interference pattern. Crossed and hexagonal gratings can be obtained by turning the sample by α = 90° or α = 60°, respectively, before a second exposure. The grating spacing D is controlled by the half-angle θ between the beams. Photographic plates were fabricated by coating glass substrates with an absorbing layer and the positive photoresist MicroChemicals AZ MiR 701. Photoresist layers were 300 nm thick. Additionally, several microns of an absorbing layer at the back of the glass substrate prevented standing wave effects. Each exposure had a mean dose of about 50 mW/cm² and was developed in Clariant AZ 400 K Developer diluted with water (for 120 s with dilution ratio 1 to 6). Nickel shims of the photoresist structure with area $\text{5×5}c{\text{m}}^2$ were produced by electroplating at temicon GmbH [30].

Based on the master structure, silicone stamps consisting of hard-polydimethylsiloxane (hPDMS) and polydimethylsiloxane (PDMS) bonded to a glass substrate were molded [26, 31]. Substrates spin coated with about 200 nm of the resist mr-UVCur06 [32] were imprinted by the stamp and cured under at least 700 mJ/cm² of ultraviolet (UV) light. Due to the transparency of the stamp in the UV spectral region, non-transparent substrates can be structured. Homogeneous pressure of 0.6 mbar was applied to the stamp. For the later lift-off, a sacrificial layer, also acting as adhesion promoter, was used.

In the next step, the residual resist layer of the imprinted pattern and the sacrificial layer underneath were removed. Reactive ion etching (RIE) is appropriate because dosage is exactly controllable [33]. The physical contribution leads to an anisotropic removal of the residual layer. Sulfur hexafluoride was applied as etching gas since for the use of oxygen a corrugation of the resist was experienced. After etching the resist, silver was sputtered onto the sample such that the holes in the resist were completely metallized. The thickness of the silver layer was optimized with respect to particle quality and lift-off. Thicker layers resulted in lower surface roughness and porosity of the silver particles. However, only silver layers that were up to 30 nm thick allowed for the lift-off as the dissolver could diffuse to the sacrificial layer. Silver layers of 15 to 30 nm thickness demonstrated low particle porosity while allowing lift-off. After the lift-off, during which the sample was dipped in an ultrasonic bath of solvent N-Methyl-2-pyrrolidone at 40°C for several minutes, only silver nanoparticles remained on the substrate. When using higher temperatures of the solvent, the silver layer started to form unwanted clusters and voids.

Each process step was controlled by scanning electron microscopy (SEM) and atomic force microscopy (AFM), allowing for accurate measurements of structure depths, residual resist layers and particle sizes. With the help of a Fourier spectrometer incorporating an integrating sphere, reflectance and transmittance spectra of the fabricated metal particle arrays were measured.

Simulations of periodically arranged metal nanoparticles with a well-defined shape on the front or rear side of a substrate can be performed using RCWA [29], a Fourier modal method. When using this approach, the system is divided into three regions in the z-direction (see Fig. 2 (a)). Region I and III are semi-infinite, isotropic, homogeneous and non-absorbing. In contrast, region II can consist of several layers containing absorbing materials with realistic dielectric functions. In the z-direction, the dielectric function has to be constant in each layer but in x- and y-direction it can be periodically modulated.

 

Fig. 2 (a) Cross-section of the system simulated by RCWA (not to scale). The back of a glass substrate is structured by cylindrical silver particles. Light is incident from the top along the z-direction, indicated by vector k_inc. The electric field of TM-polarized light is defined to point along the minor axis of the ellipse. Region I and III are semi-infinite, non-absorbing, isotropic and homogeneous. The real refractive indices of substrate and region I are equal to avoid reflections at the top surface of the substrate. (b) Rectangular unit cell of elliptic particles arranged in a hexagonal grating. It consists of two particles, which are approximated by $N$ = 5 cuboids.

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Reflections at the top surface of the substrate are prevented by using the real refractive index of the substrate in region I. One unit cell is defined (see Fig. 2 (b)) and subject to periodic boundaries in x- and y-direction. Maxwell’s equations [34] are solved by using the Floquet-Bloch theorem for periodic surface gratings [35] and Rayleigh expansions in regions I and III. Boundary conditions at the interfaces lead to the electromagnetic field in region II. In order to solve Maxwell’s equations exactly, infinitely many expansion coefficients need to be determined. However, in practice, the series are cut and only a limited number M of positive and negative diffraction orders is taken into account in x- and y- direction. Since the magnitude of evanescent diffraction modes declines with higher orders and the series converges, the resulting error can be kept small.

The Reticolo Code 2D [36] written in MATLAB was used to simulate the interaction of light with different configurations of plasmonic particles. Rounded structures are coded by a staircase approximation using $N$ cuboids that lead to $4\times N$steps of the pattern (see Fig. 2 (b)). It was found that $N$ = 5 approximates round or elliptic cross sections of particles well. As shown in Fig. 2 (b), the unit cell of a hexagonal grating contains two particles. The side lengths of the rectangular cell, describing a grating with spacing D = 300 nm, are 2D = 600 nm and $2D/\surd 3=$346.4 nm. Crossed gratings are described by one particle in a square cell with side lengths D = 300 nm. Light is incident along the z-direction and therefore perpendicularly to the surface structured by nanoparticles (see Fig. 2 (a)). As a result, the definition of transverse-electric-polarized (TE-polarized) and transverse-magnetic-polarized (TM-polarized) light is arbitrary. The electric field of TE-polarized light E_TE is chosen to point along the y-axis, that of TM-polarized light E_TM along the x-axis. The increase of computation time is of the order $O(M^3).$ On the basis of convergence analyses, M = 20 was chosen. At this number of diffraction modes, the peak position is very reliable whereas the peak height and shape does not fully converge.

In order to compare simulated and measured absorption A, reflection R and transmission T of the modelled structure have to be outputted since they are related by [37]

3. Results and discussion

With the help of the described LIL, steep photoresist structures with grating spacing D = 300 nm and pillar height of about 250 nm were obtained (Fig. 3 (a)).

 

Fig. 3 SEM pictures of (a) photoresist structured by LIL, (b) imprinted resist after etching, (c) round silver particles arranged in a crossed grating on glass and (d) elliptic silver particles arranged in a hexagonal grating on silicon. In each case the grating spacing measures 300 nm. The photoresist pillars are arranged in a hexagonal grating on a glass substrate and about 250 nm high. Subsequent to etching the imprinted and cross-linked resist, a structure depth of about 120 nm remains. The round particles on a glass substrate exhibit a diameter of about 200 nm, whereas the axes of the elliptic particles on silicon measure approx. 240 nm and 140 nm. In both cases, the particles have a height of around 15 nm.

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The round pillars measure about 180 nm in diameter; the axes of the elliptic pillars are about 150 nm and 250 nm long. Small saddles between the pillars stabilize the resist on the glass substrate. Based on these photoresist structures, nickel shims with holes around 250 nm deep were formed.

Due to the combination of the flexible stamp material PDMS and a hard shell of hPDMS, imprinting holes that are about 200 nm deep and wide into the imprint resist is feasible. AFM measurements revealed that a layer of about 50 nm of residual resist remains in the holes. Figure 3 (b) shows resist imprinted by the crossed structure on a glass substrate after RIE. Although the resist is corrugated by etching, the steep resist faces and a height of about 120 nm remain. Subsequent to metallization and lift-off, disk shaped silver nanoparticles with round or elliptic cross-sections cover the glass or silicon substrate (see Fig. 3 (c) and (d)). From AFM measurements, we find the round particles have a diameter of about 200 nm and the axes of the elliptic particles are 140 nm and 240 nm long. Depending on the sputtering time, particles with a height of 15 to 30 nm are conveniently fabricated.

Reflectance and transmittance spectra of nanoparticles covering 1 mm thick glass substrates were measured by Fourier spectroscopy. Using Eq. (1), the absorptance spectra of round and elliptic particles, shown by solid lines in Fig. 4(a) and Fig. 5(a), can be deduced. It is important to note that the characterized round and elliptic particles are about 30 nm and 15 nm high, respectively. Whereas the round particles show only one plasmonic resonance peak at wavelength λ = 750 nm, which is independent of polarization of incident light, elliptic particles exhibit two resonance peaks. If the electric field of incident light points along the minor axis of the elliptic particles (defined as TM-polarized), resonance occurs at around λ = 900 nm. In contrast, light with an electric field parallel to the major axis generates an absorptance peak at about λ = 1200 nm. Consequently, the position of the resonance peak of elliptic particles strongly depends on the polarization of incident light. This can be qualitatively explained by the fact that resonances of light polarized along the two differently long axes of the elliptic particle are comparable to resonances in two dipole antennas with different lengths. However, for such rather large particles the dipole approximation is certainly not accurate.

 

Fig. 4 (a) Absorptance spectra of fabricated (solid line) and simulated (dashed line) round silver nanoparticles with height h = 30 nm arranged in a crossed grating on a 1 mm thick glass substrate. Plasmon resonance is apparent at around λ = 750 nm. (b) Simulated system of round silver particles arranged in a crossed grating. Porosity of silver is not taken into account.

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The experimental data were compared to theoretical results obtained with RCWA. The particle configurations for the modeling were based on dimensions measured by AFM. Round particles arranged in a crossed grating with spacing D = 300 nm were approximated by circular cylinders with diameter d = 200 nm and height h = 30 nm at the back of a 1 mm thick glass substrate (see Fig. 4 (b)). Analogously, elliptic cylinders with h = 15 nm as well as minor and major axes d₁ = 140 nm and d₂ = 240 nm, respectively, describe the elliptic particles arranged in a hexagonal grating with D = 300 nm (see Fig. 5 (b)). In the case of elliptic particles, the electric field of TM-polarized light points along the minor axis. In addition to the geometry, material characteristics crucially influence the plasmon resonance.

 

Fig. 5 (a) Absorptance spectra of fabricated (solid line) and simulated (dashed line) elliptic silver nanoparticles with height h = 15 nm arranged in a hexagonal grating on a 1 mm thick glass substrate. The simulated peaks are blue-shifted in comparison to the experimental data as porosity is not taken into account. (b) Simulated system of elliptic silver particles arranged in a hexagonal grating. (c) Absorptance spectra of the simulated and fabricated particles as shown in Fig. 5 (a), but with the consideration of porosity. The porosity of silver is taken into consideration by Bruggeman’s effective medium theory [38] in the simulations. Simulated as well as measured plasmon resonances occur at around λ = 900 nm or λ = 1200 nm depending on the polarization of incident light. (d) Real and imaginary part of the refractive index of silver [39] without and with consideration of porosity.

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The refractive index data of glass and silver were taken from Palik’s book on optical constants [39]. In the semi-infinite region I, only the real part of the refractive index of glass is used (see Sec. 2). By the dashed lines in Figs. 4 (a) and 5 (a), simulated absorptance spectra of the round and elliptic particles are presented. A comparison to the measured data reveals good agreement of the plasmonic resonance peaks in case of the round 30 nm thick particles. Simulated and measured spectra of the round particles exhibit local maxima and minima below λ = 500 nm. This effect results from propagating diffraction orders in the crossed grating at small wavelengths.

In contrast to the spectra of the 30 nm thick round particles, both simulated resonance peaks of the elliptic 15 nm thick particles are blue-shifted in comparison to the experimental data. This observation suggests that for thin metal particles porosity has to be considered. Therefore, Bruggeman’s effective medium theory [38] was applied to Palik’s silver data for modelling the 15 nm thick elliptic particles. A mixture of 80% silver and 20% air with refractive index n = 1 was assumed. As shown in Fig. 5 (c), the consideration of porosity red-shifts both resonance peaks such that experimental and simulated data conform well. Real and imaginary parts of the refractive index of silver with and without the consideration of porosity are presented in Fig. 5 (d). Qualitatively, the red-shift due to porosity can be understood as a damping effect. Due to porosity, the conductivity of the metal decreases such that the oscillation of the electron plasma in the metal particle is damped. Consequently, the resonance wavelength increases.

Especially the spectral range of the plasmon resonance can be predicted well by RCWA. Some differences between measured and simulated data, however, can be observed. As an example, side maxima are apparent in the simulated spectrum of round particles around λ = 500 nm. Furthermore, the simulated resonance peaks of the elliptic particles arising from the different polarizations are further separated than the corresponding measured maxima. Additionally, the simulated peaks in the case of TM-polarized light incident on the elliptic particles show two maxima.

On the one hand, those phenomena presumably result from the difficulty to precisely model geometry and material of the fabricated nanoparticle arrays as well as the half-infinite real refractive index of glass in region I (see Sec. 2), which excludes multiple reflections. On the other hand, numeric inaccuracies need to be considered. Comparisons to calculations by finite element method suggest that the side maxima result from numeric inaccuracies as they only occur when using RCWA.

4. Conclusion and outlook

With the help of laser interference lithography, metal nanoparticles with defined size and shape can be fabricated on large areas. In this paper, we have presented a process chain for producing round or elliptic silver particles with a diameter of about 200 nm covering $\text{5×5}{\text{cm}}^2$of glass or silicon substrates. Spectrally selective plasmon resonances of manufactured particles could be confirmed by rigorous coupled wave analysis. Results from experiment and simulation showed a dependency of the plasmon resonance in elliptic particles on the polarization of incident light. Additionally, a strong impact of the metal porosity on the resonance is observed.

As our process works equally well on silicon as on glass, it is part of ongoing investigations to integrate such particles into silicon solar cells. First experimental and simulative analyses have demonstrated that parasitic absorption by silver particles of such size is small compared to their gain. Nevertheless, other metals such as aluminum should also be taken into consideration [40]. In addition, the presented process could be applied to structure areas of $\text{20×20}{\text{cm}}^2$with the help of a Roller-NIL tool [24].