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Abstract
Nanoporous gold is a three-dimensional bulk material that is percolated with a random network of nanometer-sized ligaments and made by selective corrosion of bimetallic alloys. It has intriguing geometric, catalytic, and optical properties that have fascinated scientists for many decades. When such a material is made into the form of small, 100-nm-sized particles, so-called nanosponges emerge that offer much flexibility in controlling their geometric, electronic, and optical properties. Importantly, these particles act as an antenna for light that can efficiently localize optical fields on a deep subwavelength scale in certain hotspots at the particle surface. This makes such nanosponges an interesting platform for plasmonic sensing, photocatalysis, and surface-enhanced Raman spectroscopy. Since the optical properties of these nanosponges can be controlled to a large degree by tuning their geometry and/or composition, they have attracted increasing attention in recent years. Here, we provide a concise overview of the current state of the art in this field, covering their fabrication, computational modeling, and specifically the linear and nonlinear optical properties of individual and hybrid nanosponges, for example, plasmon localization in randomly disordered hotspots with a size ${\lt}10\;{\rm{nm}}$ and a long lifetime with an exceptionally high Purcell factor. The resulting nonlinear optical and photoemission properties are discussed for individual and hybrid nanosponges. The results presented have strong implications for further applications of such nanosponges in photonics and photocatalysis.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. INTRODUCTION
The optical properties of metallic nanoparticles have been comprehensively studied for more than a hundred years and open the way to a wealth of fascinating optical and photonic applications of rapidly increasing technological importance [1]. One of their elementary optical properties, localized surface plasmons [2], reflects the coupling of longitudinal, collective charge oscillations of the delocalized electrons inside the metal to the surrounding electromagnetic field. The resulting highly localized optical field enhancement has been used, for example, for the implementation of efficient spectroscopy methods [3,4], the development of new, ultrafast electron sources [5–9], and DNA sequencing [10,11]. A material of particular interest is nanoporous gold [12], which is produced when bulk gold is perforated with a three-dimensional (3D), randomly disordered network of pores with ligament diameters of 10 nm to 100 nm. Nanoporous gold naturally combines highly interesting properties such as a high surface-to-volume ratio, a large density of high-index facets, and exceptional optical properties. At the metal surface of the pores, incident light is coupled to surface plasmons. Their multiple scattering within the porous networks results in the localization of surface plasmons in certain nanometer-sized hotspots, similar to the Anderson localization of waves in other disordered media [13,14]. The subwavelength spatial localization of surface plasmons [15] and the resulting giant fluctuations in local optical fields have received much attention [16,17] due to resulting pronounced enhancements of local optical nonlinearities [18] and their potential for surface-enhanced Raman sensing [19,20]. For an overview, we refer the reader to the textbook by V. Shalaev [21].
In recent years, the focus of research on nanoporous gold has shifted toward real-world applications of these materials. Of particular relevance are their applications in catalysis. The first experimental results regarding the catalytic potential of nanoporous gold were published in 2006 by Zielasek et al. [22] and only shortly thereafter by Xu et al. [23]. Both groups studied the catalytic oxidation of carbon monoxide (CO) and demonstrated high catalytic activity at low temperatures. Nanoporous gold was used to build efficient catalytic converters [24–26] and was introduced as an efficient catalyst for methanol electro-oxidation [24].
Photocatalytic applications of nanoporous gold take advantage of both its unique photonic and catalytic properties [27,28], whose interplay is, however, at present only poorly understood. Nugraha et al. [27], e.g., explained the superior photodegradation of metanil yellow via mesoporous gold nanoparticles by the fact that the strong plasmon-enhanced electric fields are spatially co-localized along concave/convex features. These step edges and kinks in the atomic structure generate numerous catalytic active sites [25,27]. More microscopic investigations into local optical field enhancements, their statistical properties, and their connection to the catalytic activity are, however, needed to make progress in this direction. The present review focuses on the increased field strength, the presence of higher harmonics, and the increased emission of electrons at curved gold surfaces, all of which may influence photocatalysis.
Nanoporous gold has found applications in a broad variety of fields, including sensing devices [29,30], supercapacitors [31], precise actuators [32,33], heat-mediated light-to-mechanical kill switches [34], and ultrasound-powered nanowire motors [35]. A recent review of nanoporous gold in sensing devices [36] addresses the connections between structural properties and optical response in some detail.
In addition, several new methods have been developed to fabricate nanoporous gold in the form of finite-sized particles with diameters in the 100 nm range and extensive tunable geometry and composition, including methods based on the dealloying of gold-silver thin films [37,38] and others based on wet-chemical synthesis [39,40].
This has triggered substantial renewed experimental and theoretical interest in these particles’ nanoscopic optical properties, since the particles act as efficient nanoscale antennas with greatly enhanced coupling of far-field light to localized plasmonic hotspots. In particular, efficient plasmon localization in sub-10-nm-sized hotspots with comparatively long plasmon lifetimes has been demonstrated experimentally [41–43]. This results in plasmonic modes with large field enhancements and exceptionally large Purcell factors, which makes such nanosponges interesting nonlinear optical light and photoemission sources and promising nanoscale resonators for exploring the strong coupling of quantum emitters to surface plasmons, with optical properties that can be widely tuned by varying the porosity or composition of the nanosponges. It is the aim of this paper to give an overview of the current state of the art of the research on such nanoporous gold nanosponges.
The review is structured as follows. In Section 2, we discuss fabrication methods for such nanoparticles. Then existing methods for computer-aided generation of nanosponge geometries are discussed and summarized in Section 3. Such methods are important to complement and extend the experimental study of nanoporous particles. Following this, we review experiments and theory on the optical properties of gold nanosponges in both the linear (see Subsection 4.A) and the nonlinear (see Subsection 4.B) regime. Finally, the results are summarized in Section 5, and possible further research areas are discussed in Section 6.
2. FABRICATION
Gold as a material has fascinated humans since the dawn of time. Also, the dealloying process that underlies the fabrication of nanoporous gold has a history that goes back hundreds of years, since South American metal workers used it for the dissolution of copper for copper/gold alloys [44,45]. Nevertheless, its basic structure was not discovered until the second part of the 20th century, and the first atomistic model for its structure was brought forward only in 2001 [46].
There exist different possibilities for the production of nanoporous gold. In most cases, an alloy of gold with another material such as silver, aluminum, palladium, platinum, or copper serves as the starting material [47,48], and the fabrication is based on either chemical or electrochemical dealloying. By combining this process with advanced fabrication methods, very different structures can be made from nanoporous gold, such as disks [49–52], tubes [53], spheres [54], particles [55,56], wires [57,58], or even bowls [59].
In the present work, we focus mainly on elliptically shaped nanoporous particles of finite size. Such particles are also referred to as “nanosponges” due to the obvious similarity.
A successful manufacturing process for forming randomly distributed nanosponges is shown schematically in Fig. 1(a). Initially, two thin layers of gold and the material to be alloyed (such as silver) are deposited on a substrate. Annealing initializes a dewetting process whereby nanoparticles of the gold alloy form on the surface (solid-state dewetting [61]). The alloying metal is less noble and is then removed from the alloy nanoparticles, resulting in a porous gold skeleton.
Fig. 1. (a) Schematic representation of the manufacturing process of nanoporous gold nanosponges; (b)–(g) results for different layer thicknesses of the bilayer; (c), (f) the alloyed particles are shown after dewetting; (d), (g) scanning electron microscopy (SEM) images of the final nanosponges after dealloying. Reproduced from Ref. [60] with permission from the Royal Society of Chemistry.
By adjusting the process parameters, such as dealloying time and temperature, the pore size can be tailored [38,62]. The overall particle size can be adjusted over a wide range from just tens of nanometers to micrometers by varying the thickness of the bilayer for the dewetting process, as shown in Figs. 1(b)–1(g). Examples of nanosponges showing different combinations of pore and particle sizes can be seen in Fig. 2. The nanoporous gold is not stable thermally, and a further thermal annealing of the as-prepared nanosponges will lead to coarsening of pore size, which can be hindered by a passivation layer [62,63]. The thermodynamics of the dealloying process were investigated in detail by Li et al. [55], and the influence of surface passivation and annealing on porosity, morphology, and optical properties has been extensively studied by Kosinova et al. [64]. Here also the correlation between the optical absorbance spectra and the particle morphology and microstructure has been investigated, and it has been shown that a broad absorption peak in the infrared region can be associated with thin gold ligaments.
Fig. 2. SEM images of gold nanosponges with different pore and particle sizes. From left to right, the pore size visibly increases. Reprinted with permission from Rao et al., ACS Appl. Mater. Interfaces 9, 6273–6281 (2017) [62]. Copyright 2017 American Chemical Society, https://doi.org/10.1021/acsami.6b13602.
In addition to randomly positioned nanosponges, periodically ordered arrays of nanosponges can also be produced by combining the presented solid-state dewetting process with nanostructuring techniques. For example, pyramidal pit-shaped structures can be fabricated using nanoimprint lithography in combination with a subsequent wet etching process using a potassium hydroxide solution (KOH) on a silicon substrate. The individual steps of the fabrication process are shown in Fig. 3 and described in detail in Ref. [37]. Once the structures are created in the substrate, the gold-silver bilayers are deposited. After the solid-state dewetting process, ordered arrays of alloy nanoparticles are formed. Subsequently, after dealloying, the nanosponges are formed in the individual pits. Thus, the creation of nanosponges in precisely selected regions of the substrate is possible and offers a new pathway to fabrication sensing devices with (sub-)micrometer dimensions. Exemplary pyramidal structures filled with a gold-silver alloy are shown together with pictures of dealloyed particles in Fig. 4 on the left. Scanning electron microscopy (SEM) images of the produced arrays of nanosponges are shown on the right side of Fig. 4.
Fig. 3. Schematic representation of the process of the fabrication of ordered arrays of nanoporous nanosponges. A conventional (100) oriented silicon wafer serves as the starting material. An oxide layer is applied, which is later used as masking material. Nanoimprint lithography is used to create a structured mask of photoresist on the oxide layer. Subsequently, the oxide is structured by reactive ion etching. Next the photoresist is removed and the remaining structured oxide layer is used as a masking material for the subsequent KOH etching process. During the KOH etching, pyramidal pit structures are formed. Then the remaining oxide layer is removed and a complete oxide layer is created using thermal oxidation. The silver-gold bilayer is then deposited onto this oxide layer. Thereafter, the annealing step is performed to achieve dewetting. In the final step, the particles are dealloyed. Images reproduced from Ref. [37].
Fig. 4. Left: SEM images of gold nanosponges (a) before and (b) after dealloying. Right: False color SEM images of ordered nanosponge arrays. Images reproduced from Ref. [37].
Further information on the fabrication process, including on how to tailor process parameters to achieve desired geometrical properties, is available in the references [37,38,61]. By using other nanopattering techniques, dealloyed nanoporous gold nanoparticles can be achieved in various other shapes. For example, Ref. [49] and Ref. [58] describe fabrication processes resulting in nanoporous gold disks and nanoporous gold wires, respectively.
It is worth mentioning that there are a variety of different fabrication methods seperate from dealloying that also result in porous gold nanoparticles, such as wet-chemical synthesis [39,40] or laser ablation [65]. However, the structure of the nanoparticles resulting from these methods differs substantially from the structure of the nanoparticles resulting from the solid-state dewetting and dealloying method discussed here. For example, nanoparticles resulting from wet-chemical synthesis generally show comparatively fewer pores, while nanoparticles generated by laser ablation are more akin to buckled porous films. The properties of such particles are not as well researched as the particles considered here, and it is not obvious—but worth exploring—how transferable results are from one class of particles to another.
3. COMPUTER-AIDED CREATION OF THREE-DIMENSIONAL NANOSPONGE GEOMETRIES
Computer simulations are essential for uncovering the properties of nanoporous gold [46] and of gold nanosponges [66–68]. As is discussed in more detail below in Section 4, the optical properties of gold nanosponges depend strongly on their internal geometry. Like human fingerprints, the individual gold nanosponges are similar but differ in details. To model common features and to explore the range of variations, a realistic representation of the complex 3D geometry of individual nanosponges is required for most purposes. Such modeling must in turn be calibrated by comparison with experiments.
Fig. 5. (a), (b) Linear light spectra of two individual gold nanosponges for different polarization states of the linearly polarized incident light. SEM images of the nanosponge are shown on the left, along with an arrow indicating the direction of ${0^ \circ}$ polarization. The corresponding polarization-resolved spectra are shown on the right. (c), (d) Simulated polarization-resolved scattering spectra based on a simplified geometry creation algorithm in which small, randomly arranged spherical air voids are cut out of a larger gold half-sphere; (c) reasonable agreement with the experimental data is reached when assuming that the entire gold volume is filled with air voids, while (d) less pronounced anisotropies appear for nanosponge structures for which only the surface layer is perforated. Images adapted from Ref. [71]. ITO, indium-doped tin oxide.
SEM images can only reveal the surface topology of the nanosponges, and thus more sophisticated techniques are required to reconstruct the 3D geometry. A powerful method for this purpose is focused ion beam (FIB) tomography. In FIB tomography, the nanosponge is cut into many two-dimensional slices, and cross-sectional SEM images of these slices are recorded and combined to assemble a full 3D model of the nanosponge geometry [68,69]. This provides a powerful tool for the investigation of the local structure on the nanoscale but is both complex and time-consuming. Therefore, other approaches to creating artificial gold nanosponge geometries in computer-aided processes are desirable. This is highly relevant from a materials science point of view, since the generation of accurate 3D geometries is challenging yet essential for realistic microscopic modeling of the functional properties of such nanosponges.
Relevant approaches can be broadly divided into two different classes. First, geometries can be created from purely geometric considerations. Second, geometries can be created from a physical point of view. Methods from this second class are common in the investigation of nanoporous gold, where kinetic Monte Carlo or molecular dynamics simulations have been used to great effect [46,70]. The physically motivated methods, however, are difficult to apply to gold nanosponges due to the finite mesoscopic size, which implies that edge effects that define the structure of the surface cannot be neglected. In the investigation of nanoporous gold, unit cells need to be considered that are much smaller than typical nanosponge geometries, but for the aforementioned reason, the surface region should be modeled explicitly. Therefore, no fully physically motivated methods for the creation of finite-sized nanosponge geometries have been reported so far. All geometry creation algorithms for the generation of nanosponge geometries utilized so far are thus based, more or less, on purely geometrical considerations or a combination of geometrical and physical methods.
Depending on the complexity of the chosen geometry creation method, different geometric properties are targeted. The first developed method consists of creating a half-ellipsoid and simply removing spherical “pores” from its volume [71,72]. By varying the amount and size of the cut-out pores, the porosity of the final geometry can easily be tuned. Some example geometries are shown in Fig. 5, together with calculated scattering cross-sectional spectra, which will be compared to experimentally measured spectra in Subsection 4.A. While the method can thus reproduce the dimensions and the porosity of the nanosponge, the surface and topology of the generated structures show little resemblance to those of real fabricated nanosponges. Some improvement can be achieved by choosing a suitable spatial arrangement of the spheres that are carved out of the gold, as shown in Fig. 6 on the left. Nanosponge geometries obtained in this way were regularly used for subsequent simulations, and most of the theoretical calculations of nanosponge properties so far are based on this or similar methods. However, as discussed later in more detail, the geometry plays a central role in determining the optical properties, and it is therefore not clear how applicable predictions obtained from such simple models are to real experimental nanosponges, resulting in the need for more accurate geometry generation methods.
Fig. 6. Left: Comparison of different algorithms for generating nanosponge geometries. (a) SEM image of an experimental nanosponge, (b) cross section and (d) top view of a geometry created from correlated random numbers in Fourier space, (c) a geometry created by cutting out Poisson-sampled spheres from a larger sphere. Right: Comparison of the radially averaged autocorrelation functions for an experimental nanosponge (black curve), a nanosponge made by subtracting spheres from the geometry (red curve), and a nanosponge generated using correlated random numbers in the Fourier space (blue curve). Image taken from the dissertation thesis of Felix Schwarz [73].
A more sophisticated method developed by Schwarz and Runge [66] is based on reproducing the radially averaged autocorrelation of the nanosponge geometry. Examples of autocorrelation functions are shown on the right in Fig. 6. To artificially create a nanosponge with a specific correlation, smoothly varying correlated random numbers are distributed over a 3D grid in the Fourier space and are transformed back to real space. Then every voxel whose value exceeds a threshold value is filled with gold. Finally, any freestanding particles are removed. This results in much more realistic nanosponge geometries. By tuning the exact correlation of the random numbers, any sensible autocorrelation of the thereby generated nanosponge can be created. To achieve this, uncorrelated random numbers in Fourier space are multiplied by a suitable amplitude function $A(k)$. An amplitude function that reproduces the experimentally measured autocorrelation functions well is given in Ref. [66] as
Fig. 7. Comparison of the structures of nanosponges with different porosity reconstructed using focused ion beam (FIB) tomography and phase-field simulations. Left: Geometries of two nanosponges reconstructed using FIB tomography. The geometries of the nanosponges are measured by repeatedly performing FIB cutting and taking SEM images of each individual slice. The 3D geometry is then reconstructed from the obtained image stack. Right: Geometries of two nanosponges obtained using phase-field simulations. The parameters of the simulations were chosen to produce geometries with similar averaged geometric properties compared to the experimentally measured nanosponges. Images taken from Ref. [68].
To compensate for these discrepancies, another method for nanosponge generation based on phase-field methods was introduced [68]. In this case, the following time-dependent Cahn–Hilliard equation is solved to calculate the geometric shape of the air/gold interface of the gold nanosponge, imitating the dealloying process [74]:
Here, $\phi$ is the phase-field function, ranging from ${-}1$ to 1. The parameters $\sigma$, ${{\epsilon }_{pf}}$, and $\chi$ define the interfacial tension, interfacial width, and mobility of the interface, respectively. Even though the use of the Cahn–Hilliard equation is physically motivated, the goal is not to model the dealloying process and the dynamics in detail. This keeps the method efficient despite its high accuracy. Examples of the resulting geometries are shown in Fig. 7. Their direct comparison to the geometries that have been reconstructed via FIB tomography shows that such phase-field simulations can be a very powerful tool in faithfully reconstructing 3D nanosponge geometries based on models with a clear physical background. We believe that this is an efficient and promising approach for providing a microscopic understanding of the optical properties of such nanosponges as well as their (photo-)catalytic performance. Work along this direction is ongoing in our groups and will be discussed in more detail in the future.
4. OPTICAL PROPERTIES
The optical properties of gold nanosponges are, arguably, their most spectacular characteristic and the subject of most of the current research in the field. They are crucial for many of the envisioned applications of nanosponges, in particular for potential applications in photocatalysis or nanosensing. Both the linear and nonlinear optical properties of nanosponges have been studied in great detail. In particular, the localization of light in nanometer-sized hotspots at the nanosponge surface has received attention. This localization is the origin of locally enhanced optical nonlinearities in both isolated nanosponges and nanosponges filled with various types of quantum emitters, a field of study that has progressed significantly over the past five years. In this section, we will first discuss the linear optical properties and the underlying theory. Subsequently, different nonlinear optical processes in nanosponges, including plasmon-enhanced photoemission, are discussed, and the state of the art in understanding the coupling of nanosponges to quantum emitters is reviewed.
Fig. 8. Left: Experimentally measured polarization anisotropy in the scattering spectra (red circles) and photoluminescence (PL) spectra (blue squares) of single gold nanosponges as a function of the average particle size. The exact definition of the quantity measuring the spectrally integrated “anisotropy” is given in Ref. [72]. Small particles show similar anisotropy in PL and scattering, while for larger particles, the anisotropy is more pronounced in the light-scattering spectra. Light blue and red shading is intended as a guide to the eye. Right: Calculated electric-field distribution of a simplified nanosponge geometry for excitation (a), (c), (e) via an external far-field wave and (b), (d), (f) by an internal dipole, mimicking electron–hole recombination inside the nanosponge. The nanosponge geometries increase in size from top to bottom. It is evident that for large particles, less and less parts of the particle can be excited at once, especially from inside the nanosponge. Reprinted with permission from Vidal et al., Nano Lett. 18, 1269–1273 (2018) [72]. Copyright 2018 American Chemical Society, https://doi.org/10.1021/acs.nanolett.7b04875.
A. Linear Optical Properties of Individual Gold Nanosponges
The most commonly investigated optical properties of gold nanosponges are their light-scattering cross sections. Ensembles of nanosponges show a broad and featureless scattering spectrum that extends all the way from the visible ($\sim 600 \; {\rm nm}$) to the near-infrared ($\sim 2000 \; {\rm nm}$) [42]. The center wavelength of such spectra largely depends on the average size of the nanosponges and can be tuned toward the blue by reducing the nanoparticle diameter. Since such spectra are largely governed by the size and geometry fluctuations of the nanosponges within the ensemble, they do not give much insight into the microscopic optical properties of nanosponges. More meaningful tools are far-field light-scattering spectra of individual nanosponges, particularly spectra recorded for different polarization states of the incident light, since they give insight into geometry-induced anisotropies.
Polarization-resolved scattering spectra of individual gold nanosponges recorded by Vidal et al. [71] are shown in Fig. 5. These spectra are quite broad, extending over more than 300 nm, show multiple peaks, and have a complex structure and polarization dependence. Moreover, the spectra vary strongly from nanosponge to nanosponge, suggesting that the complex inner geometry plays a significant role in determining the optical properties. For reference, a solid gold nanosphere with the same diameter would simply show a much narrower polarization-independent peak, as is well-known from Mie theory [75–77]. Computer simulations have been carried out to understand these observations. These simulations are based on the most simple geometry-creation model, carving out randomly distributed spherical air voids from a bulk gold half-sphere. It is evident in Fig. 5(d) that the spectra cannot be understood by assuming that only the topmost layer of the gold half-sphere is filled with air voids. Only if the bulk volume is perforated is reasonable agreement with the experiment obtained. This is a first indication that the complete 3D structure of the nanoparticle plays a fundamental role in its optical properties.
The polarization anisotropy of both the photoluminescence (PL) and the scattering spectra of individual nanosponges was studied in detail by Vidal et al. [72]. The results are shown in Fig. 8 on the left. To quantify the anisotropy in both types of measurements, Vidal et al. integrated the squared difference in spectral intensities for two different polarization angles of the incident light (${0^ \circ}$ and ${80^ \circ}$) over a somehow ad hoc chosen spectral region and with an ad hoc choice of the considered polarizations. Nonetheless, evidently, for sufficiently large nanosponge sizes, the anisotropy that is observed in the scattering spectra (red circles) is much larger than that in the PL spectra (blue squares). The authors rationalized this observation based on the following considerations: PL in gold is caused by the local recombination of generated electron–hole pairs, which excite nearby plasmonic resonances. For small enough nanosponges, this coupling to plasmonic excitations can delocalize the emitted light, so the PL from a localized plasmonic hotspot can couple to the entire ensemble of localized and delocalized resonant plasmonic modes of the nanosponge. This is no longer possible for large nanosponges, where light localization due to multiple coherent scattering of surface plasmons is so pronounced that the PL emission remains localized in a small region of the nanosponge. This results in a largely “far-field-like” emission pattern with a low polarization anisotropy. Thus, for large nanosponges, the recombination of electron–hole pairs leads to a PL emission that remains localized within a finite region of the nanosponge, forming an unpolarized background. In coherent light scattering, however, the far-field light couples primarily to delocalized, dipolar plasmon excitations with large dipole moments and pronounced anisotropy, as dictated by the elliptical geometry of the particle. Vidal et al. further support this argument using computer simulations carried out on simple geometries that are shown in Fig. 8 on the right [72]. Far-field excitation results in coupling to localized hotspots that are spread across the entire surface of the nanosponge. PL emission is mimicked by localized dipole excitation, and the resulting field distribution is delocalized across the surface for small nanosponges, but is localized to a finite region for larger nanosponges.
Finite-difference time domain (FDTD) simulations, carefully compared to single-particle surface-enhanced Raman spectra (SERS) [39], suggest the relevance of field localization to the optical properties of the nanosponges. Extinction spectra calculated for gold spheres with different numbers of air pores, as shown in Fig. 9, reveal a characteristic transition in spectral line shape. In the absence of pores, the spectra are governed by the dipolar and quadrupolar resonances of the spheroid. With an increasing number of pores, the spectrum broadens and redshifts, largely suppressing the quadrupolar resonance. A large increase in local field enhancement $\langle | {E/{E_0}} |\rangle$, spatially averaged over the surface of the nanosponge, is induced by the presence of the pores in the gold nanosponge. The simulations predicted average field enhancements of the order of 3. However, the nanosponges investigated are geometrically quite different from the typical porous nanosponges, and it is not conclusively clarified to what extent the results are transferable.
Fig. 9. (a) Calculated extinction spectra of spherical gold particles for different numbers of pores, (b) calculated extinction cross sections at the dipole and quadrupole resonance wavelengths (upper panel) and the plasmon resonance wavelengths (lower panel) of the gold particles with a varying number of pores. (c), (d) Calculated, spatially averaged linear and nonlinear near-field enhancements (c) $\langle {| {E/{E_0}} |^2}\rangle$ and (d) $\langle {| {E/{E_0}} |^4}\rangle$ for porous (orange) and solid (green) gold nanoparticles. Reprinted with permission from Zhang et al., J. Phys. Chem. Lett. 5, 370–374 (2014) [39]. Copyright 2014 American Chemical Society, https://doi.org/10.1021/jz402795x.
Definite experimental evidence of the existence of localized hotspots in nanosponges was provided by Zhong et al. [42] using the technique of scattering-type scanning near-field optical microscopy (s-SNOM). The s-SNOM technique overcomes the diffraction limit by using evanescent waves for optical spectroscopy [78–80]. In s-SNOM, laser light is focused to the apex of a sharp, usually metallic probe tip, and the scattered light is measured in the far field. The interaction between the sample and the light that is localized at the apex of the probe tip locally enhances light scattering [9]. A periodic oscillation of the tip-sample distance at kilohertz frequencies and an amplitude of a few tens of nanometers results in a modulation of the light-scattering intensity that can be used to discriminate the local optical near field at the probe apex, enhanced by the tip-sample coupling, from the spatially less resolved light-scattering background. Using this technique, both the local topography of the sample and maps of the field enhancement factor can be obtained, as in atomic force microscopy (AFM). This information can be directly compared to the local near-field enhancement induced by the tip-sample coupling. Example near-field images for different excitation wavelengths ranging from 720 nm to 840 nm are shown in Fig. 10. Several aspects of these measurements are relevant. First, it can be see that there is a faint background scattering intensity at essentially all points of the sample. The far-field excitation light couples to the delocalized dipole resonance of the nanosponge, and this results in a certain electric field amplitude everywhere on the sample surface. This background field is overlaid with pronounced, spatially highly localized field enhancements in certain hotspots that are spatially and spectrally well separated. Importantly, different hotspots dominate the field enhancement at different wavelengths, pointing to spectrally sharp resonances of individual hotspots.
Fig. 10. Optical near-field scattering images of a single gold nanosponge. The data are recorded for monochromatic excitation of the tip-sample region at various wavelengths ranging from 720 nm to 840 nm. The scattering signal is recorded at the third harmonic of the tip oscillation frequency to discriminate local near-field contrast against less spatially resolved background scattering. The data show enhanced light scattering from randomly distributed and spatially highly localized hotspot modes. Different hotspots are excited at each of the laser wavelengths, evidencing the spectral sharpness of the different localized modes. The bottom-right image is the AFM error signal of the sample topographies used to correct drift and track the evolution of hotspot modes for different imaging scans. Reprinted with permission from Zhong et al., Nano Lett. 18, 4957–4964 (2018) [42]. Copyright 2018 American Chemical Society, https://doi.org/10.1021/acs.nanolett.8b01785.
More quantitative information can be obtained by taking cross sections through this set of measurements, as shown in Fig. 11. It can be seen that the hotspots are spatially highly localized in regions with a size of around 10 nm. The individual hotspot resonances are spectrally surprisingly sharp and have linewidths of only 20 nm or even less. The spectra are reasonably well described by a Lorentzian line shape. They show no sign of the inhomogeneous broadening that is inevitable in ensemble studies. This indicates that they indeed reflect the spectra of individual hotspots. An analysis of the distance suggests that the hotspot-induced near-field enhancement rapidly decays with tip-sample distance, suggesting decay lengths of around 3 nm. To obtain a statistically significant measure of the mode localization, histograms were created to determine the probability of finding a normalized scattering intensity $I/\langle I\rangle$, as shown in Fig. 11(d). Marked deviations from Gaussian statistics are found, with a long, slowly decaying tail at large $I/\langle I\rangle$ values. This long tail is dominated by localized modes with strong field amplitudes. For the analysis of the histograms, they were compared to a single-parameter-scaling model of light transport through multiply scattering non-absorbing media [81]. The data were normalized using a single scaling (Thouless) parameter, $g = 0.4$. This supports the conclusion that the plasmonic excitations of the studied nanosponge samples are spatially strongly localized with intensity fluctuations similar to those of the strong localization regime ($g \lt 1$) of Anderson localization [13]. The use of $g$ for any disordered system is very common in the community, although it is well defined only under rather restrictive conditions. For this reason, $g$ as a measure of mode localization should be interpreted more as a heuristic mean than as a proven fact, but is nonetheless considered helpful.
Fig. 11. (a), (b) Representative cross sections of the near-field light-scattering signals shown in Fig. 10 at selected wavelengths of (a) 740 nm and (b) 760 nm. The data reveal optical near-field localization in hotspots with an $\sim 10 \; {\rm nm}$ diameter. (c) Near-field scattering spectra of individual hotspots, recorded at the third harmonic ($3f$) of the tip modulation frequency (open circles). The red lines show resonances with a Lorentzian line shape, with linewidths of only 15 nm to 25 nm. The quality factor of those hotspots can exceed 40. (d) Histogram of the $3f$ scattering intensity from a single nanosponge, averaged over measurements taken at different excitation wavelengths. The data are normalized to the average scattering intensity. Strongly non-Gaussian statistics reveal pronounced fluctuations of the local near-field intensity. The red line shows a fit based on a single-parameter scaling model with $g = 0.4$. (e) Histogram of the near-field intensity distribution taken from finite-difference time domain (FDTD) calculations (open circles) and fit to the same model with $g = 0.4$ (red line). Reprinted with permission from Zhong et al., Nano Lett. 18, 4957–4964 (2018) [42]. Copyright 2018 American Chemical Society, https://doi.org/10.1021/acs.nanolett.8b01785.
To understand this complex linear optical response of the nanosponges, the system can be thought of as a randomly disordered plasmonic system. The roughly elliptical shape of the nanosponge leads to a broad polarization-dependent dipole mode, as is already known from solid nanoparticles. The many holes and fine ligaments lead to multiple random scatterings of delocalized plasmonic modes. The interference of all these plasmon waves then leads to localized plasmonic modes. Both the broad dipole mode and the local resonances can be understood within the framework of localized surface plasmon resonance, as presented in the following simple model. Consider a spherical particle under the influence of an external incident wave. If the particle is much smaller than the wavelength of the incident wave, the electrical potential $\varphi$ on the surface can be considered to be constant. On the exterior of the particle, the following relationship results for the electrical potential $\varphi$ [82,83]:
Comparison with the well-known potential of a dipole provides the following equation for the polarizability $\alpha$:
It is clear that the polarizability becomes particularly large if $\varepsilon + 2{\varepsilon _m} = 0$. This equation is known as the Fröhlich condition [83]. The factor 2 in the denominator is characteristic of a spherical particle. An analogous calculation for the diagonal elements of the polarizability tensor of an ellipsoid yields
Another way to model the optical response of a nanosponge is to ignore the complicated geometry and to describe the nanosponge using an effective medium theory. In this approximation, the nanosponge is modeled as a solid ellipsoidal region made out of an effective medium with an adapted permittivity but no internal structure [84]. A wide range of possible models for the calculation of the properties of the effective medium exist; see, e.g., Choy’s book [85] for an overview. The use of effective medium theories for describing nanoporous metals has been described in some detail by Koya et al. [86]. Here, the well-known Maxwell Garnett and Bruggeman theories are used to explain the general ideas of description using an effective medium. In the Maxwell Garnett theory, the permittivity of the effective medium is given by the simple equation [87]
Fig. 12. Optical absorption (left) and scattering (right) cross sections for typical experimentally studied coarse (c)- and fine (f)-pored nanosponges (${S_{{\rm{c/f,ref}}}}$). In addition, the spectra based on the Maxwell Garnett theory are shown (${S_{{\rm{c/f,MG}}}}$). Using the Bruggemann theory, very similar spectra are obtained (not shown). Solid lines show the spectra of a solid gold nanosponge (${S_{{\rm{c/f,solid}}}}$). Image reproduced from Ref. [68].
Fig. 13. Top row shows rendered images of nanosponges that are cut in half (left, original nanosponge geometry; middle, half-filled with an effective medium; right, nanosponge almost completely filled with an effective medium). The middle row shows the simulated field intensity on a cut plane parallel to the substrate. The white area in the center shows the region that has been replaced with an effective medium from the center outward, with the length given signifying the thickness of the shell that has been left untouched. In the bottom row, the same cut plane as in the middle row is shown. In this case, the entire nanosponge is replaced with an effective medium, except for a conical section of the angle given. Images reproduced from the dissertation thesis of Felix Schwarz [73].
The process of coupling the external field to the strongly localized modes can now be considered in more detail. We find it helpful to think of the optical response as involving two parts. One part of the optical response is characterized by a broad dipole mode, with the exact spectral response determined by the global parameters of the nanosponge, i.e., composition, porosity, size, and aspect ratio. The external field couples well to this dipole mode; the second part of the optical response is that the dipole mode couples well to a multitude of localized and complex-shaped plasmonic modes. These hotspots are spatially and spectrally well separated and show a comparatively long lifetime. However, a direct coupling between the external field and the local modes is unlikely, and thus they can be thought of as rather dark surface modes [66]. This means that the energy is gradually transferred from the external field into the dipole mode and finally into the localized plasmonic modes.
The result of this plasmon localization is a pronounced local field enhancement. This is of immediate interest for applications, since any quantum emitter placed in a volume of the localized mode will experience a large Purcell effect, i.e., a pronounced increase in the radiative damping rate of the emitter due to the enhanced local density of optical states in the hotspot region. The related Purcell factor can be calculated by [89,90]
where ${V_M}$ is the (quasi-)mode volume of the hotspot and $Q$ is its quality factor, i.e., the ratio of the resonance frequency and linewidth of the mode. The narrow spectral linewidth of the hotspot modes of less than 20 nm results in surprisingly high $Q$ values of more than 40. The consequences of these high $Q$ values and the small mode volumes of the order of $1000\;{\rm{n}}{{\rm{m}}^3}$ are large Purcell factors in the order of $1 \times 10^6$ [42,91].The narrow light scattering suggested long hotspot lifetimes of around 10 fs to 20 fs, which are significantly enhanced compared to the very short electric field decay time of the dipole mode of bulk nanoparticles of similar size [41,43]. The first evidence of these long lifetimes was provided in time-resolved photoemission experiments by Hergert et al. [41]. The FDTD simulations reproduced here in Fig. 14 convincingly support these experimental findings. They show a very rapid decay of the plasmonic field in the region outside the hotspots, essentially following the time profile of the far-field excitation pulse. Inside the hotspots, however, the localized near field at the surface of the nanosponge persists far beyond the excitation pulse, decaying on a time scale of a few tens of femtoseconds.
Fig. 14. (a) Calculated field intensity distribution and resonance wavelengths of the localized modes from a model of a nanosponge. The diameter of each circle corresponds to the amplitude of the dominating mode found via harmonic inversion at that specific point. The wavelength of the dominating mode is depicted by the displayed color code. (b) The local field intensity on a logarithmic scale for a nanosponge, calculated along a cross section through a plane parallel to the substrate, 5 nm above the substrate, and at a time delay of 120 fs after the arrival of the excitation pulse. (c) The time-dependent field intensity calculated along a circle close to the surface of the nanosponge [see white dashed line in (b)]. The $y$ axis indicates the position on the circle. The maximum of the incident pulse is at 0 fs. Images reproduced from Ref. [41].
One promising application that was recognized early on was the use of gold nanosponges as material for single-particle SERS, as shown, for example, by Yan et al. [92]. They investigated the SERS enhancement by gold nanosponges for various chemicals relevant in the food industry, such as the compound Butter Yellow, a potential carcinogen that is sometimes illegally used as food coloring. Their results are shown in Fig. 15. They discovered a significant enhancement of the SERS signal linked to the existence of strong near-field enhancement. Furthermore, they demonstrated the excellent tunability of the gold nanosponge system by using cyclic electroless deposition of silver on as-prepared gold nanosponges to produce gold–silver hybrid nanosponges that further enhanced the SERS signal. References [39,93,94] cover the use of SERS with gold nanosponges created by different processes and thus displaying different optical behavior in more detail. Another promising characterization method, cathodoluminescence nanoscopy, has shown success in probing field localization in disordered silver plasmonic networks [95]. However, similar investigations on gold nanosponges have not yet been carried out. Results from cathodoluminescence measurements could complement and be compared to the s-SNOM measurements reviewed above.
Fig. 15. Top: (a) Surface-enhanced Raman spectroscopy (SERS) signals of the compound Butter Yellow recorded using various different gold–silver hybrid nanosponges. Spectrum (1) shows the background signal, (2) is the signal of the gold nanosponges with silver, and (3)–(5) are signals of gold–silver hybrid nanosponges after one, three, or six cycles of Ag deposition. Spectrum (6) corresponds to the SERS spectrum measured on powder. (b) Integrated peak area of the band around $1410\;{\rm{c}}{{\rm{m}}^{- 1}}$. Bottom left: SEM images of nanosponges (NSs) after various cycles of silver deposition. Bottom right: Scanning transmission electron microscopy (STEM) and selected area electron diffraction (SAED) images of hybrid nanosponges, showing clear separation of gold and silver regions. Reprinted with permission from Yan et al., Chem. Mater. 28, 7673–7682 (2016) [92]. Copyright 2016 American Chemical Society, https://doi.org/10.1021/acs.chemmater.6b02637.
B. Nonlinear Optics
Due to the strong localization of the electromagnetic field and the resulting strong field enhancement, nanosponges are ideal for studying nonlinear optical phenomena or exploiting them for applications. While extreme field localization and enhancement can be achieved by specifically designed geometries [96,97], the field enhancement in such custom-designed antennas usually occurs only in a narrow spectral region, which is highly dependent on the exact shape of the geometry. Nanosponges offer the unique advantage of field localizations occurring in many randomly distributed hotspots at the same time, covering a very broad spectral region. This negates the need for highly precise manufacturing of structures.
Fig. 16. Nonlinear photoemission from single gold nanosponges. (a) Photoelectron count as a function of the electric field strength of the exciting few-cycle laser pulses at 1700 nm for three different nanosponges (black, blue, red). The lines show fits to a multiphoton emission model, and the resulting order of the nonlinearity $n$ is indicated. (b) Photoelectron count from a single gold nanosponge (blue circles) as a function of the time delay between a phase-locked pair of few-cycle excitation pulses at 1700 nm. The solid black line shows the time resolution of the experiment, and the inset shows the same data on a logarithmic scale highlighting the persistent photoemission for delay times beyond 20 fs. Plasmon hotspot lifetimes of 20 fs are deduced. Images taken from Ref. [41].
Fig. 17. Interferometric photoelectron emission from individual hotspots of a single gold nanosponge. (a) SEM image of a single gold nanosponge, (b) photoemission electron microscope images of the nanosponge with its contour indicated by dashed ellipses, recorded at different time delays of the few-cycle pulse pair. Electron emission from three well-defined localized plasmonic hotspots is observed, which can be selectively excited by tuning the time delay. An analysis of time dynamics of the PEEM images reveals hotspot dephasing times of 17 fs, 13 fs, and 10 fs, respectively, for the three investigated hotspots. Images taken from Ref. [43].
A particularly fascinating nonlinear effect is light-induced electron photoemission. In the plasmonic hotspots, the local field is so high that efficient multiphoton photoemission can be induced by light with a photon energy that is far below the work function of gold (i.e., ${\lt}4.5\;{\rm{eV}}$). Hergert et al. [41] report this process with an order of nonlinearity $n$ of up to 7 when using few-cycle driving pulses centered at 1600 nm, i.e., a photon energy of 0.77 eV. Slight variations in $n$ point either to spatial variations in the local work function or to a local transient heating of the electron gas inside the metal by the short and intense excitation pulse. The experimental measurements are shown in Fig. 16. Information about the lifetime of the plasmonic modes of the nanosponge can now be extracted by performing the photoemission experiment with a phase-locked pair of few-cycle excitation pulses and varying the time delay between the pulse pair. The experimental data (blue circles) reveal a burst of photoemission during the pulse overlap, while the emission signal quickly vanishes when the delay increases beyond 15 fs. However, a careful inspection of the data, plotting the emission signal on a logarithmic intensity scale, reveals persistent photoemission even for longer delay times with a signal level that is much larger than expected from an instantaneous nonlinear response function of the sample (black line). A quantitative data analysis reveals plasmon hotspot lifetimes of 20 fs, corresponding to decay times of the plasmonic field of 40 fs. When using a photoelectron emission microscope (PEEM) to spatially resolve the nonlinear photoemission [91], the photoemission from individual hotspots is clearly resolved, as shown in Fig. 17, and it can be seen be that the hotspots that contribute to the photoemission can be selectively controlled by varying the time delay between the pair of excitation pulses. This is understandable, since the optical spectrum of a phase-locked pulse pair has a comb-like structure with a fringe spacing that is controlled by the interpulse delay. Thus, the selective excitation of individual hotspots is switched on or off by coherently controlling the interpulse delay. From a theoretical point of view, the photoemission process occurs according to the following pathway: The far field couples to the broad dipole mode, which in turn couples to the many localized hotspots possessing the enormous field enhancement necessary for such highly nonlinear processes. The strong plasmonic field locally heats up the electron gas in the hotspot region and creates a highly nonequilibrium charge carrier distribution inside the metal. For few-cycle excitation, as in the case of the discussed experiments, the distribution of the electron gas is highly nonthermal, while thermal distributions with electron temperatures of several thousand degres Kelvin are reached after a few femtoseconds. As is discussed later in Section 6, highly energetic charge carriers are a crucial component of many photocatalytic reactions, and the presence of multiphoton electron photoemission from localized hotspots is a strong indication of the presence of such highly energetic carriers.
Fig. 18. (a) Image of a gold nanosponge that is infiltrated with zinc oxide (ZnO) and the resulting second harmonic (SH) generation; (b) schematic representation of the few-level energy structure depicting the occurrence of the SH from the infiltrated nanosponges ($|SP\rangle$, surface plasmon hotspot; $|1\rangle$, ZnO exciton); (c) cross-sectional TEM images of the nanosponges. (d) Laser spectrum centered at 890 nm used for the excitation (left); electric field profile of the pulses obtained by interferometric frequency-resolved autocorrelation measurements (right). Reprinted with permission from Yi et al., ACS Photon. 6, 2779–2787 (2019) [91]. Copyright 2019 American Chemical Society, https://doi.org/10.1021/acsphotonics.9b00791.
Evidently, such nonlinear emission processes are highly sensitive to the local field enhancement in the plasmonic hotspot that drives the nonlinear emission. This raises the interesting question of how this field enhancement is affected by coupling the plasmon fields to quantum emitters infiltrated into the nanopores of the gold nanosponges. The first experiments addressing this question have recently been reported. The generation of second or higher harmonics has been studied in detail by Yi et al. [91].
Fig. 19. Nonlinear optical spectra from (a) bare gold and (b) gold/ZnO hybrid nanosponges recorded as a function of the orientation $\theta$ of a linearly polarized, phase-locked pair of 8 fs pulses. Pronounced interference stripes reflect the temporal coherence between the pair of nonlinear emission pulses and allow us to separate SH and two-photon luminescence (TPL) via Fourier filtering. The spectrally integrated intensities (open circles) of the TH emission are shown in the top panels. While the coherent TH intensity is reduced upon ZnO infiltration, SH emission is largely enhanced in the spectral region of the ZnO exciton (390 nm). Reprinted with permission from Yi et al., ACS Photon. 6, 2779–2787 (2019) [91]. Copyright 2019 American Chemical Society, https://doi.org/10.1021/acsphotonics.9b00791.
The measurement setup is as follows. Two few-femtosecond phase-locked laser pulses excite the nanoparticle and high-frequency photons are measured. The effect of filling the nanosponges with ZnO, a large-bandgap semiconductor known for its sharp excitonic resonance, on both second-harmonic (SH) and third-harmonic (TH) generation is investigated. The use of phase-locked pulse pairs allows the separation of coherent (SH, TH) from incoherent (e.g., two-photon photoluminescence [TPL]) signals. Cross-sectional transmission electron microscopy (TEM) images of such an infiltrated nanosponge are shown in Fig. 18(a), and the recorded nonlinear optical spectra are shown in Fig. 19. Interestingly, it is observed that the TH, mostly emitted from the bulk of the percolated gold nanosponge, is significantly reduced upon infiltration. This suggests that the insertion of a high-refractive-index material into the air voids actually reduces the local field amplitude at the surface and, thus, diminishes the nonlinear signal. In contrast, the SH emission, however, is found to be significantly enhanced by ZnO inclusion. This enhancement is most pronounced in the spectral region of the ZnO exciton emission ($\sim 390\; {\rm nm}$). It is not a priori clear what the microscopic mechanism underlying this SH enhancement is. Direct laser-induced SH emission from ZnO can safely be ruled out, since nonlinear measurements on zinc oxides, without the presence of the nanosponge nanoresonator, yield basically negligible SH emission. Two additional pathways appear reasonable. The local hotspot field could drive plasmonic SH emission, and the SH field then induces one-photon absorption in the excitonic layer. Alternatively, the off-resonant, yet locally strongly enhanced, hotspot field could induce two-photon absorption in ZnO. The two possible pathways could be distinguished by means of time-resolved studies of the SH emission from hybrid metal/semiconductor nanosponges like those recently reported by Zhong et al. [43], who used interferometric frequency-resolved auto-correlation (IFRAC) measurements to study the nonlinear response of individual gold nanosponges with and without ZnO infiltration. In these measurements, the sample was excited with a pair of phase-locked 6 fs pulses with a center wavelength of around 800 nm. The induced nonlinear emission was spectrally dispersed, and SH emission spectra were recorded as a function of the time delay between the pulse pair. Their results are summarized in Fig. 20. As explained in more detail in the original paper, a Fourier transform of the measurement results creates a two-dimensional map that correlates the excitation frequency of the broadband laser pulses with the frequency of the induced nonlinear emission signal. A signal along the diagonal (dashed line) in this map is the sign of hotspot-enhanced SH emission. In the region around the ZnO emission (${\sim}4.8\;{\rm{f}}{{\rm{s}}^{- 1}}$), however, a splitting of the signal into two peaks is observed. This is a characteristic signature of a nonlinear, sum-frequency process: the excitation laser first couples to the surface plasmon hotspot resonance, and the locally enhanced plasmon field then drives two-photon absorption in the ZnO inclusion. Through detailed comparison to time-dependent density matrix simulations of a few-level quantum system, Zhong et al. convincingly showed that the recorded IFRAC maps are indeed distinctly different from those expected for the alternative process in which the nonlinear signal is generated in the plasmonic hotspot and ZnO is excited by a one-photon absorption process.
Fig. 20. Interferometric frequency-resolved autocorrelation (IFRAC) traces reveal quantum pathways of nonlinear plasmon–exciton coupling. (a) Fourier-transformed fundamental band of IFRAC traces of a gold nanosponge infiltrated with ZnO. The map correlates the frequency of the optical excitation of the system (vertical arrows) to the frequency of the generated nonlinear emission signals (horizontal arrows). The signal is symmetric with respect to the diagonal line with a slope of 2, indicating a second-order nonlinear process. The split signal at the exciton frequency shows that the excitonic emission is generated by a sum-frequency process in which the excitation laser first couples to the surface plasmon hotspot resonance, and the locally enhanced plasmonic field then drives two-photon absorption in the ZnO inclusion. The nonlinear plasmonic emission signal at the diagonal line corresponds to SH generation from localized hotspots. (b) Simulated fundamental band map using a nonlinear plasmon–exciton coupling model, reproducing the features of the experiment well. (c) Schematic illustration of nonlinear plasmon–exciton coupling. Few-cycle pulses excite several plasmonic hotspot modes with distinct resonance frequencies at the surface of the hybrid nanosponge (bottom inset shows a transmission electron microscopy image; scale bar: 20 nm), generating a nonlinear plasmonic polarization. (d) Simulated electric fields of the three emission pathways for a coupled hotspot–exciton system from a single plasmonic hotspot. Images taken from Ref. [43].
In essence, Zhong et al. were able to demonstrate an interesting pathway toward efficient nonlinear optics with random plasmonic nanoresonators, infiltrated with quantum emitters. The far field couples to the broad dipole mode of the plasmonic antenna, which couples to the many localized plasmonic hotspots, which couple individually to the exciton modes in the ZnO inclusions, driving multiphoton absorption in the inserted quantum emitter. This not only sheds new light on the interesting nonlinear optical processes of such hybrid nanosponges but also demonstrates the detailed insight that can be gained into the dynamics of coherent energy transfer processes in nanostructures from time-resolved nonlinear optical experiments.
Using a gold–silicon hybrid nanosponge created by laser ablation, Larin et al. [98–100] have shown SH generation as well as stable white-light PL. As opposed to the ZnO previously discussed, silicon nanospheres show some white-light PL on their own. Remarkably, upon their inclusion in a gold nanosponge, the PL was enhanced up to 20 times. While Larin et al. did not analyze the underlying processes in depth, they propose the following mechanism: hot electrons and holes generated in the gold regions tunnel into silicon, where they recombine, thereby enhancing the white-light PL.
5. SUMMARY
Much has been learned during the past decade about the geometrical and, in particular, the optical properties of gold nanosponges. They exhibit many intriguing morphological and optical properties. Their optical properties emerge out of a unique combination of a quasi-zero-dimensional nanoparticle and its 3D, randomly disordered interior structure. The main optical features can be understood by considering the nanosponge as a combination of a large plasmonic dipole antenna, with properties defined by the shape and composition of the entire particle, coupled to many plasmonic hotspots caused by the chaotic local ligament geometry. These hotspots are highly localized and available over the entire optical region and lead to strong field enhancements. Using the different methods available for manufacturing gold nanosponges, the geometric properties like porosity, ligament size, or total particle size can be tuned over a wide range. The optical properties, however, do not depend to a large degree on a precisely engineered geometrical arrangement, but emerge out of the disordered structure, which can be tailored to the respective target application by varying the individual process parameters.
6. FUTURE OF THE FIELD
Despite the significant progress made in the understanding of the optical properties of gold nanosponges, many important questions remain. For example, it is still not known exactly how the optical response depends on the local chaotic structure. In a similar vein, it is not yet known if reliable predictions of, e.g., the average optical response of an ensemble can be made without knowledge of the exact geometry of each nanosponge, for example, from looking at easily accessible global parameters like filling fraction, aspect ratios, or the number of pores. With recent advances in the detailed analysis of the geometry—for example, via FIB tomography—and the constant improvement in the computer-assisted generation of nanosponge geometries, further insights are foreseeable.
Many avenues of future research remain. Gold nanosponges serve as an ideal system for the investigation of nonlinear or quantum optical phenomena. In particular, their combination with different filling materials opens up wide fields of research and promises interesting applications. On the manufacturing side, the integration of nanoporous nanosponges into microelectromechanical systems (MEMS) or other larger-scale systems (for example, through their combination with conventional microstructuring techniques) remains an underdeveloped topic that could lead to the design of more efficient sensors.
While the optical and morphological properties of gold nanosponges have been investigated in great depth and have been understood to a considerable extent during recent years, an exciting potential application has been widely overlooked: photocatalysis. Nanoporous gold has attracted much attention for its catalytic activity regarding the oxidation of CO. This process became better understood after the seminal paper of Fujita et al. [25]. Using scanning transmission electron microscopy (STEM) and high-resolution TEM, they showed that the enormously enhanced catalytic activity of nanoporous gold can be traced to the existence of high-Miller-index facets, steps, and kinks on its surface. The atoms located at such sites obviously possess less bonds compared to atoms in the bulk or on close-packed surface sites and are thus much more chemically active. These sites are generally located near highly convex or concave regions.
However, many more possible applications open up when we consider the effects of localized surface plasmon resonance as we move toward highly efficient photocatalysis [101]. Just as there exist a large number of reaction pathways, there also exist a variety of plasmon-induced photocatalysis pathways. The simplest pathway is related to the increased temperature in the plasmonic particle, caused by the increased light absorbance and the resulting ohmic losses near the plasmon resonance frequency. A more interesting pathway is related to the enhancement of the electromagnetic field, as discussed earlier. The most fascinating pathway, in our opinion, may come from the generation of highly energetic charge carriers, so-called hot carriers, caused by the decay of the plasmon resonances. This process can enhance the reactivity of the considered reaction either directly or indirectly; i.e., the reaction can occur on the nanoparticle itself or the generated charge carriers can be transferred to, e.g., a substrate or adsorbate of a different material [102]. Theoretical calculations by Manjavacas et al. [103] have shown that hot carrier generation follows the absorbance cross section of the plasmonic resonance very closely and that many-body effects can be largely neglected. They have also uncovered that there exists a trade-off between the number of charge carriers generated and their energy distribution. Accordingly, they have defined a figure of merit for hot electron generation ${{\mathbb{N}}_{e}}(\epsilon )$:
We end with a slightly philosophical remark. It is a truism that “disorder is robust against disorder.” This simple observation summarizes not only the 5000-year history of glass, but also the optical and the photocatalytic properties of nanosponges: whatever happens, whatever the experimental conditions are, there are always some spots providing almost “ideal” conditions—for example, for a strong localization or photocatalytic reaction—irrespective of what is meant by “ideal.” However, it remains an open question to be explored in the ways outlined here as to what degree the hotspots for field enhancement and for, e.g., catalytic activity coincide. To conclude, nanoporous gold nanosponges are a fascinating system both for the investigation of nonlinear optics and for various practial applications, and their future looks bright.
Funding
Deutsche Forschungsgemeinschaft (LI 580/12, RU 1383/5, SCHA 632/24, SPP1839 ‘Tailored Disorder’); Niedersächsisches Ministerium für Wissenschaft und Kultur (DyNano); Volkswagen Foundation (SMART).
Acknowledgment
We thank Petra Gross, Germann Hergert, Anke Korte, Jan Vogelsang, Juemin Yi, and Jinhui Zhong from the University of Oldenburg, as well as David Leipold, Yong Yan, Wenye Rao, and Hauke-Lars Honig from the Technische Universität Ilmenau, for their invaluable contributions to different stages of this research. C. L. gratefully acknowledges financial support from the Niedersächsische Ministerium für Kultur und Wissenschaft (“DyNano”) and the Volkswagen Foundation (SMART).
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analyzed in the presented research.
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