Exploiting eutectic formation and phase separation to produce plasmonic metamaterials

Surface plasmons (SPs) and surface plasmon polaritons (SPPs) are nonlinear many-body excitations that couple light with the electron density of states of a material, in particular, metals.¹ The nonlinear nature of SPs and SPPs can be used for frequency doubling of light (second harmonic generation)^2,3 and the formation of evanescent waves that enhance the Raman signature of molecules on a surface (surface enhanced Raman spectroscopy),^4,5 to name a few. More recently, plasmonics are being utilized in metalenses, a two-dimensional lens that mitigates aberrations and stigmatisms associated with traditional 3D lenses.⁶ The future of metalens technology rests on the shoulders of the materials science community to develop new plasmonic materials that have a broader suite of capabilities and superior nonlinear responses. To address this challenge, we report on our efforts to develop highly active gold plasmonic mesostructures by exploiting the unique kinetics of the gold–silicon eutectic.^7,8 The process produces unique mesoscopic polyhedron structures, which we refer to as Au pyramids, which have unique bulk and surface morphologies that we will show are highly efficient at absorbing visible and subsequent conversion into SPPs. These structures have been previously reported^9,10 on and, therefore, we do no claim to be the first to observe them. However, in previous studies, demonstrative proof of certain steps in the process of their formation was unavailable and relied instead on logical conjecture, modeling, or a combination of both to bridge the gaps. Herein, we report experimental findings that conclusively verify the hypotheses previously put forward. In addition, we are reporting a previously unobserved surface morphology consisting of chevron-like surface channels that only occurs when the Au pyramids have dimensions on the order of tens of micrometers. We are also reporting for the first time the surface plasmon polariton spectrum of these novel mesostructures and their ability to produce polarized reflected light. The polarization of the reflected light is attributed to the chevron morphology of the larger pyramids.

Samples were prepared by a magnetron sputter deposition head sputtering a 25 nm thick Au film at room temperature with 10 mTorr of argon onto RCA cleaned Si(100) substrates with a native oxide. Due to the room temperature deposition of this film, the film is amorphous and observes no long-range ordering. The thickness of the film and the native oxide creates a rough film with no preferential pinning of the gold atoms covering the entire substrate.¹¹ A deposition rate of 1.25 nm/s was calibrated using a Bruker MMRC DektakXT stylus profilometer. Samples were annealed in a custom-built vacuum chamber that had a base pressure of 50 mTorr. The system was back filled with air to a pressure of 150 ± 5 mTorr, at which time the sample temperature was ramped up at a rate of ∼23 °C/min until it reached its maximum temperature of 700 °C, where it was soaked for 30 min. At the end of the soaking cycle, the heater was turned off and the sample was allowed to cool to room temperature, where the cooling rate to 300 °C was ∼20 °C/min, and 300 °C is below the Au–Si eutectic melting point. The chamber pressure was maintained at 150 mTorr during the cooldown phase of growth.

The optical data for this investigation were obtained using a microscope with a long-range focal point 50× objective. This objective allowed for spectral sampling from a single pyramid. The light source was a tungsten filament white light. The light was delivered to the surface of a single pyramid with the use of a single fiber optic cable in a custom build jig that allowed for both specular and non-specular measurements to be taken. The scattered light was then collected through the objective and analyzed with a QEPro Ocean Optics spectrometer.

This process produces well-defined circular delineated zones with diameters in the range of 500–1000 μm. Similar behavior has been observed for Au films on Si.^9,12 Scanning electron microscopy (SEM) micrographs of these zones reveal the formation of mesoscopic polyhedron Au structures,¹³ which are referred to as meso-pyramids or simply pyramids. All SEM microphases presented in this study were obtained in secondary electron mode. The SEM micrograph in Fig. 1(a) is of one such delineation zone consisting of a large pyramid (20 × 25 μm²) surrounded by a distribution of many smaller pyramids, typically <10 μm on a side. We believe that this is the first observation of pyramids of this size. Note that all of the pyramids in Fig. 1(a) are aligned in the same direction, specifically, parallel to the [001] and [010] directions of the Si(100) surface, which has been previously reported.^7,13–15 Furthermore, a delineation zone may contain a single pyramid or many, as in the case of Fig. 1(a). Displayed in Fig. 1(b) is a high-resolution SEM micrograph of a large Au pyramid (23.6 × 26.3 μm²) that clearly reveals its unique surface morphology. The height of these pyramids can range from 2 to 5 μm. These data were obtained with the use of an Atomic Force Microscopy (AFM) microscope in the tapping mode. The base of the observed pyramids is much larger than the height. They pyramid like geometry can be well observed with SEM micrographs that are taken at an angle with respect to the horizontal plane. The angle of the facets on these pyramids will be a function of the ratio between the base and the height. There is a wide range of angles due to the variation in size of the pyramids. However, a pyramidal-like geometry can been seen in all of the observed structures. The surface topography of a pyramid consists of channels that cut into their surface and plateaus bordered by channels. The surface of the pyramid in Fig. 1(b) consists of many long channels that cut into the surface and are on the order of 1 μm in width and as long as 10 μm. The surface channels radiate on average outward from the center to the perimeter of the pyramid. This type of surface morphology is only observed for taller pyramids with heights on the order of tens of micrometers. Au pyramids that have a height less than ∼5 μm have cavities, as opposed to surface channels. Both morphologies are a consequence of diffusion of Si and will be addressed shortly.

Surface texturing of Au structures supported on Si have been attributed to the formation of an Au–Si eutectic phase and subsequent phase separation of Au and Si.^16–19 Furthermore, Lindner et al.²⁰ observed similar texturing of the Au catalyst on the tip of a Si nanowire, where in this case the Au–Si eutectic²¹ provides the Si for the Si nanowire forming below. Their results suggest that the texturing of the Au surfaces²² in their studies correspond to channels, similar to our findings. However, this is indirect evidence. In an effort to conclusively verify that the channels in the Au pyramid in Fig. 1(b) are due to phase separation of the Au–Si eutectic and subsequent diffusion of Si out of the pyramid,²³ the pyramid formation was aborted by turning off the sample heater prior to reaching the maximum temperature of 700 °C and rapidly quenched. Typically, this involved turning off the sample heater once it reached 400 °C. Consequently, these experimental runs excluded any soaking of the sample, where soaking is defined as the amount of time that the system was held at the target temperature. An SEM micrograph of a representative example of a partially formed Au pyramid is presented in Fig. 1(c). The surface is solid but with light and dark contrasting regions, as opposed to channels like in Fig. 1(b). The contrast arises from differences in electron scattering associated with the different Z numbers of Au and Si. Energy dispersive spectroscopy (EDS) was performed on dark (SP1) and light (SP2) regions of the pyramid of Fig. 1(c) to obtain the relative normalized ratios of gold to silicon. The EDS scans were performed at an energy level of 5 keV, relatively low energy to sample near the surface of the pyramids. The interactive depth of the x rays for SP1 and SP2 are 100 and 300 nm, respectively. The probe depths are well below the typical thicknesses of the pyramids of 6 μm (typically > 2 μm protruding above the surface and 4 μm below the surface). This is well below the total height of the pyramid. The EDS of SP1 in Fig. 1(c) indicates a normalized atomic composition of 95.4% Si and 4.6% Au, while the EDS of SP2 indicates a composition of 6.4% Si and 93.6% Au. Note that EDS analysis of pyramids similar to that in Fig. 1(b) had the following normalized atomic composition: channels 85.7% Au and 14.3% Si and intact regions 98.1% Au and 1.9% Si, where the higher Si content of the channels is consistent with them previously being filled with Si. Note that contributions from regions adjacent to or below SP1 and SP2 may give rise to the dilute concentrations of Si in Au or Au in Si reported above. The main conclusion of the EDS analysis is that the channels in the surface of the Au pyramids are the result of phase separation of the eutectic, where the formation of Si rich regions are precursors to the cavities that form when Si vertically diffuses from the pyramid to the Si substrate (see below). The shape of the Si rich regions in Fig. 1(c) are exactly the same as the morphology of the Au catalysts at the tips of Si nanowires reported by Munford et al.¹⁵ and supports our conclusions that phase separation of the eutectic occurs, followed by diffusion to the Si substrate, in Lindner's case, to the underlying Si nanowire. The rippled tracks on the surface of the pyramid in Fig. 1(c) are an interesting artifact of an aborted pyramid formation but are presently beyond the scope of this work.

The surface morphology of the pyramid in Fig. 1(b) is typical of pyramids with heights >5 μm. For these taller pyramids, randomly aligned voids are replaced by interconnected surface channels that have an average alignment relative to the symmetry plane of a face of the pyramid that is defined as the line connecting the middle of the base of the face to the apex of the pyramid. Channels to the left of the symmetry plane have an average clockwise rotation of 30° and those to the right have an average counterclockwise rotation of 30°. Note that the surface channels produce Au plateaus on the surface with the same orientation. The effects of the orientation of these plateaus on the optical properties of the pyramids will be discussed shortly. We believe that the diffusion of Si out of the taller pyramids is a combination of Si diffusion in the interior vertically back into the substrate and Si diffusion parallel to the surface of the pyramids either toward the edges and back into the substrate or to cavities that vertically extend to the bottom of the pyramid.

Cross-sectional SEM of the Au pyramids was performed to better understand the formation of the Au–Si eutectic, as well as the subsequent formation of the Au pyramids and their alignment with the Si substrate. The samples were cast in resin, cut, and polished. A cross-sectional SEM image of a pyramid is displayed in Fig. 2(a). Note that >50% of the volume of the pyramid is subsurface. This indicates that Si is scavenged from the substrate and that the mechanism of their formation is surface diffusion of Au^24,25 concomitant with dissolving of and incorporation of Si into the Au–Si eutectic.²⁶ Au is soluble in Si above the liquidus line. The phase diagram of the Au–Si eutectic indicates that the Au–Si ally can exist in liquid and solid phases for a broad range of temperatures.²¹ The mechanism for Au diffusion into Si has been explained by Wilcox and LaChapelle.²⁴ Figure 2(b) is a high-resolution EDS map of the pyramid/Si interface, where green corresponds to Au and purple to Si. The pyramid is predominantly comprised of Au with small quantities of Si, consistent with the analysis in Fig. 1. More importantly, a 200 nm boundary layer with a rapidly increasing concentration of Si exists at the pyramid/Si interface, which is consistent with Si reincorporation into the Si substrate, i.e., the final phase of pyramid formation.

The question of the indexing of the pyramids to the Si(100) lattice is intriguing and to date an open question. Specifically, does indexing occur during the formation of the eutectic or as Si is driven from the Au pyramid? To definitively answer this question, we performed experiments using Au layers with thicknesses less than 20 nm, where thin Au layers allow us to image the foundation upon which the pyramids form. Displayed in Fig. 2(c) is a SEM image of early stages of pyramid formation. It is apparent that the Au–Si eutectic forms by scavenging Si from the substrate preferentially in the $001¯$ direction, which produces a rectangular trough with walls in the [100] ([$1¯00$]) and [010] and ([$01¯0$]) directions. It can, therefore, be concluded that the indexing of the Au pyramids occurs at the initial phase of their formation and is a consequence of preferential etching in the $001¯$ direction and the formation of a rectangular profile, which obviously corresponds to the minimum free energy configuration of the system.²⁷ This redeposition of silicon back to the substrate is the lowest energy configuration for this system post annealing. The minimum energy to maintain the eutectic is lost during the cooldown phase of the growth process. These scavenged locations serve as nucleation points for the pyramids, where Matthews et al.¹² have developed a diffusion model for this system that takes into account the flux associated with Au–Si alloying.^28–30 The nucleation point for pyramid growth is hypothesized to be a pinhole defect in the native oxide layer on the surface of the silicon substrate.³¹ The silicon oxide layer acts as a barrier to diffusion to the gold in the eutectic during annealing. It has been well established that gold will readily diffuse into silicon.^32–34 

The unique polyhedron shape and surface topology of these pyramids makes them a well-suited material for research into surface plasmon polaritons (SPPs), where SPP optoelectronic devices are being of great interest to the scientific and engineering communities. For instance, a subwavelength nanodevice takes advantage of the dual nature of SPP having a photonic component as well as an electronic component that allow them to be focused in volumes below the diffraction limit.³⁵ The naturally occurring surface plateaus on the surface of the pyramids created by Si diffusion to the substrate should be ideal structures for launching SPPs. These plateaus occur due to the channels that form during the eutectic phase separation. These regions are devoid of the material, i.e., voids in the structure. This is the postphase separation of the Au–Si eutectic. There will be trace amounts of silicon in these regions as can be seen in the elemental map in Fig. 2(b); these regions are primarily gold. Note that the lithographic formation of polyhedron structures is already being explored for use as metalenses. Our ability to produce this unique texturing using thin films and annealing processes greatly reduces the cost and waste in metalenses fabrication. Scattering spectra (non-specular reflection) of an Au pyramid, similar to the one in Fig. 1(b), is displayed in Fig. 3(a), which was acquired using an unpolarized broad spectrum light source. The spectrum reveals two strong absorption bands at 550 and 650 nm. These correspond to transitions from the d-band to the sp-band in the conduction band at the X and L zone centers of the Au Brillouin zone.³⁶ The locations of the SPP modes in Fig. 3(a) have a one to one correspondence to the photoluminescence modes of Au nanorods reported by Imura et al.³⁷ Note that the observation of two SPP modes of Au is typically only observed with nanohole arrays.^38–41 Based on the cross-sectional SEM of the Au pyramids in Fig. 2, one can assume that the scattering from the surface of the pyramids is due to the Au plateaus on the surface of the pyramid created between two neighboring surface channels. Based on the plasmonic properties of Au nanorods³⁷ and Au nanohole arrays^38–41 and their similarity to the scattering spectrum of the Au pyramids, we propose that the plateaus on the pyramid surface and their alignment of 30° relative to the mirror plane of the pyramid face produce the scattering spectrum in Fig. 3(a). Specifically, the scattering spectrum is a function of the large aspect ratio of the plateaus and their alignment to one another. In effect, the surface texturing of each pyramid is a natural 2D quasiperiodic plasmonic array. The spacing between aligned plateaus ranges from 200 to 500 nm and, therefore, on the order of the wavelength of visible light, ergo, perfectly capable of producing collective optical effects of scattered light.

The plasmonic array produced by the plateaus can be approximated either as the superposition of two parallel gratings offset from one another by 60° or more coarsely as an array of chevrons aligned along the mirror plane of the face of the pyramid. Both of these configurations have been used in a variety of metaoptics designs.^42–48 The superposition of the two orientations of the plateaus on the pyramids will produce linearly polarized light, where the polarization vector is parallel to the mirror plane of the pyramid face. Assuming the scattered light from each side of the mirror plane of the pyramid face are in phase, the superposition of the two polarized wavefronts, $n^net$⁠, is defined as

where $y^$ is parallel to the base of the pyramid face and $z^$ is parallel to the mirror plane. In order to test this hypothesis, specular reflection measurements were conducted on the Au pyramids. Displayed in Fig. 3(b) is a representative specular reflectivity spectrum. The spectrum exhibits what appear to be four absorption bands, i.e., four SPP modes. However, this is not the case since the wavelength spacing between the peaks or valleys is a constant value of 50 nm. Consequently, the peaks and valleys derive from interference phenomena. It has been determined that they are beats arising from interference within the spectrometer itself. This was confirmed by the removal of the fiber optic cable from the experimental setup, coupling the spectrometer directly to our microscope. The observation of beats in Fig. 3(b) is a verification that reflection of light by the Au pyramids produces polarized light. The pyramids, therefore, are multifunctional in that they are strong SPP structures as well as polarizers. We hypothesize that the latter capability will produce additional interesting optical phenomena that is worthy of further investigation. To directly verify that the reflected light is polarized, the light source was passed through a polarizer and the intensity of multiple regions of the spectrum in Fig. 3(a) were measured as a function of polarization angle. The scattered light intensity as a function of the angle of polarization is displayed in Fig. 4. The maxima occur when the polarization is parallel to the mirror plane of the face of the pyramid (θ = 0 and π/2). An excellent fit of the experimental data is obtained with a sinusoidal function (red curve in Fig. 4). The surface of the pyramids produces p-polarized light parallel to the mirror plane of the faces of the pyramid. The results in Fig. 4 demonstrate that light scattering off the pyramid produces polarized light and that maximum scattering of polarized light occurs for a polarization parallel to the mirror planes of the faces of the pyramids, i.e., p-polarized light.

In summary, mesoscopic Au polyhedron structures (pyramids) with unique nanoscale texturing were produced by annealing a 25 nm Au thin film on a Si [100] substrate and are products of the formation of an Au–Si eutectic, Au diffusion, and subsequent phase separation of the eutectic.⁴⁹ Greater than 50% of the pyramid is subsurface. The indexing of the pyramids to one another along the [001] and [010] directions of the Si(100) surface is due to eutectic formation-induced preferential etching of the Si substrate. The pyramids have a sponge-like structure due to the reabsorption of Si into the substrate upon cooling. This morphology extends to the surface and, in the case of large pyramids, produces a chevron-like surface topology that is well suited for launching surface plasmon polaritons, as determined by scattering spectroscopy (non-specular reflectivity). In addition to launching SPP, the chevrons produce polarized light for specular reflection. The simplicity of the process and modest cost of production lends itself to the development of new technology, such as SPP sensors,⁵⁰ light polarizing optical elements, and metaoptics.⁵¹ 

Funding was provided by the Office of Naval Research (No. N00014-20-1-2433). Images were obtained from Venture One Electron Microcopy lab. The authors especially thank Lisa Whitworth and Brent Johnson. The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.