Large area single crystal gold of single nanometer thickness for nanophotonics

Two-dimensional single crystal metals, in which the behavior of highly confined optical modes is intertwined with quantum phenomena, are highly sought after for next-generation technologies. Here, we report large area (>104 μm2), single crystal two-dimensional gold flakes (2DGFs) with thicknesses down to a single nanometer level, employing an atomic-level precision chemical etching approach. The decrease of the thickness down to such scales leads to the quantization of the electronic states, endowing 2DGFs with quantum-confinement-augmented optical nonlinearity, particularly leading to more than two orders of magnitude enhancement in harmonic generation compared with their thick polycrystalline counterparts. The nanometer-scale thickness and single crystal quality makes 2DGFs a promising platform for realizing plasmonic nanostructures with nanoscale optical confinement. This is demonstrated by patterning 2DGFs into nanoribbon arrays, exhibiting strongly confined near infrared plasmonic resonances with high quality factors. The developed 2DGFs provide an emerging platform for nanophotonic research and open up opportunities for applications in ultrathin plasmonic, optoelectronic and quantum devices.

However, as-fabricated gold films have a granular polycrystalline structure that can affect their performance in many applications (e.g., due to the electron scattering losses introduced by surface roughness and grain boundaries [39][40][41][42] ).In addition, it is difficult to detach them from the substrates due to the existence of adhesion/seeding layers, which greatly limits their flexibility for fundamental studies and applications (e.g., integration with other structures and devices).
Here, we introduce an atomic-level-precision etching (ALPE) approach to circumvent the lateral size-thickness relation in wet-chemical approaches, enabling the fabrication of large-area, freestanding single-crystal 2D gold with thicknesses down to a single-nanometer level.Large-area atomically-smooth gold flakes (Supplementary Fig. 1) were first synthesized on a substrate (e.g., mica) 22,42 as the starting structures.Then, they were immersed into a cysteamine solution to initiate chemical etching.During this process, gold atoms on the surface of the gold flakes were etched monolayer-by-monolayer via the formation of soluble gold-thiolate complexes to transform them into substrate-supported 2D gold flakes (2DGFs, Fig. 1a).Figure 1b presents optical micrographs of the etching of a gold flake with its thickness decreasing from 32 to 1.9 nm (accompanied by a visible increase in transmission), while its lateral size remaining almost unchanged.The etching rate was estimated to be ~0.2 nm/min (Fig. 1c) and is dependent on the concentration of the cysteamine.This indicates the crucial ability to control the thickness of the 2DGF at an atomic-level precision, which is difficult for conventional wet-chemical approaches and is of great importance for the precise engineering of properties of the 2DGF 5,6,10,13 .
Because of the absence of adhesive layers, as-fabricated 2DGFs are freestanding, as evidenced by the optical micrograph of a 2.8-nm-thick 2DGF folded on itself (Fig. 1d).
The lateral size of the 2DGF is determined by the size of the initial gold flakes, which can be at a 100s-μm scale (Supplementary Fig. 2).Its area is at least five orders of magnitude larger than that of 2D gold of similar thicknesses obtained with other methods 24,29 .Such a large area makes it possible to exploit 2DGFs for applications in fundamental studies and the construction of ultrathin metal-based structures and devices.The ALPE approach can be applied to spatially localized areas to create micro/nanostructures (see Supplementary Fig. 3).As an example, Figure 1e shows an optical micrograph of a gold flake locally etched to implement a concentric ring pattern, whose thickness is about 10 nm less than that of the surrounding area (Fig. 1f).The ALPE approach can also be applied for the fabrication of 2D silver and copper flakes (Supplementary Fig. 4), showing applicability of this approach to other metals.Atomic force microscopy (AFM) and transmission electron microscopy (TEM) were used to characterize the surface morphology and crystalline structure of as-fabricated 2DGFs.The AFM image of a typical 2DGF (Fig. 2a) shows that it has a thickness of 1.9 nm and an atomically smooth surface with a root-mean-square roughness of ~0.3 nm.This reveals the uniform atomic monolayer-bymonolayer etching characteristic of the approach that can retain the excellent surface quality and thickness uniformity of the initial flake, which is important for obtaining large-area 2DGFs.The highresolution TEM images of the surface of a 3.7-nm-thick 2DGF (Fig. 2b) show highly periodic lattice fringes with an interplanar spacing of ~0.24 nm (inset).The single-crystal property of the 2DGF was confirmed by the electron diffraction pattern (Fig. 2c), showing a hexagonal close-packed structure with a <0001> crystal orientation.Figure 2d (and Supplementary Fig. 5) further presents a cross-sectional TEM image of a 2DGF (see Methods for details), in which 10 atomic planes of gold can be clearly observed (Fig. 2e).2DGFs with such a large area is stable under ambient conditions for at least 6 months (Supplementary Fig. 6).g, Scanning electron microscopy image of a 3.8-nm-thick 2DGF suspended across a groove.h, Optical micrograph of a rolled-up 3.6-nm-thick 2DGF.The dashed line shows the outline of the original 2DGF (inset).i, Thickness-dependent sheet resistance of 2DGFs and sputered gold films (the latter is conductive only for thicknesses larger than the percolation thickness of ~7 nm).Inset, optical micrograph of a Hall-bar structure fabricated with a 5.4-nm-thick 2DGF.
Because of their large area, excellent structural quality and freestanding nature, the 2DGFs can be readily manipulated and transfer-printed onto diverse substrates (see Methods and Supplementary Fig. 7), greatly expanding their flexibility for fundamental studies and applications.As an example, three pieces of 2DGFs were sequentially transfer-printed to form a stacked multilayer structure (Supplementary Fig. 8a).In another example, a 2DGF was transfer-printed onto a WS 2 monolayer to form an ultrathin metal-semiconductor heterostructure (Fig. 2f).Due to its ultrathin thickness, the 2DGF is transparent, thus, the underlying WS 2 monolayer and its photoluminescence excited through the 2DGF (inset) can be clearly seen.Compared to conventional deposition approaches, the transfer printing of 2DGFs provides a gentle and damage-free approach for metal integration, which is especially attractive for delicate materials such as 2D semiconductors and organic molecules 43 .Transfer printing of 2DGFs onto a groove (Fig. 2g) and the curved sidewall of an optical microfiber (Supplementary Fig. 8b) were also demonstrated; either of the systems is difficult to realize with conventional deposition approaches.Furthermore, the 2DGF can be rolled up into a microtube structure with a diameter of ~2 μm (Fig. 2h) 44 , showing its excellent mechanical flexibility and the potential for introducing a strain to further engineer its electric and optical properties 45 .Electric properties of the 2DGFs were investigated by using a four-probe approach based on a Hall-bar structure (inset of Fig. 2i, see Methods and Supplementary Fig. 9 for details).With the decrease of the thickness from 9 to 1.4 nm, the sheet resistance of 2DGFs increases from ~9 to 530 Ω per square (Ω/sq) (solid dots, Fig. 2i).By contrast, sputtered gold films are only conductive for thicknesses larger than the percolation threshold of ~7 nm, their sheet resistance increases quickly from ~31 to 61 Ω/sq when the film thickness decreases from 9 to 7 nm (hollow dots, Fig. 2i).The pronounced decrease in the sheet resistance of 2DGFs can be attributed to their high crystal quality and excellent surface smoothness.The decrease in the thickness endows 2DGFs with intriguing optical properties.Transmission and reflection spectra of 2DGFs with different thicknesses were compared to sputtered gold film counterparts (Fig. 3a).Due to the presence of electrically unconnected gold islands in the investigated sputtered gold films, a dip (peak) in transmittance (reflectance) around 650 nm, that red-shifts and widens with increasing thickness, can be observed (dashed lines) as a signature of the excitation of localized surface plasmon (LSP) modes of the gold islands 10 .By contrast, these dips/peaks are absent in the transmission and reflection spectra for 2DGFs with thickness down to 2.5 nm (solid lines), further indicating the excellent continuity of 2DGFs.Benefitting from the outstanding crystalline quality and surface smoothness, 2DGFs have a much higher transmittance compared with that of sputtered gold films with the same thickness.Particularly, for the 2.5-nm-thick 2DGF, the transmittance around 600 nm reaches a value of ~91%.
As the thickness of 2DGFs approaches few nanometers, quantization of the electronic energy in the out-of-plane direction becomes important 5 (Supplementary Fig. 10), which makes a crucial impact on the nonlinear optical response of 2DGFs 6,14,46,47 .Under pulsed laser excitation at 1550-nm wavelength (see Methods and Supplementary Fig. 11), the nonlinear emission spectra from both 2DGFs with various thicknesses and a 200-nm-thick sputtered gold film feature narrow peaks at 775 and 516.7 nm (Fig. 3b), which corresponds to the second-harmonic generation (SHG) and third-harmonic generation (THG) signals, respectively.The SHG and THG intensities from the 2DGFs are much higher than those from the sputtered gold film, and are strongly dependent on the thickness.With the decrease of the thickness, they increase nonmonotonously, exhibiting very sharp oscillations with thickness (Fig. 3c).
The SHG and THG intensities are enhanced by ~500 and 250 times for the 2DGFs with thicknesses of 5 and 7 nm, respectively.This can be explained by quantization of the electronic energy levels of the 2DGFs so that the optical transitions excited by photons with a fixed energy between the intersubband levels are in and out of resonance as the thickness changes, resulting in the resonant enhancement 6,[46][47][48] .
The resonances occur at different thicknesses of gold for SHG and THG processes and agree well with the simulation results (Supplementary Fig. 12a,b) based on the quantum electrostatic model 6 (see Methods).It is worth noting that the measured thickness-dependent THG is observed on a broad underlying background, which can be attributed to the contribution from interband transitions in the 2DGFs with quantized electronic states 46 (see Methods and Supplementary Fig. 12c).The SHG intensity from 2DGFs under the excitation with 800-nm laser pulses (Fig. 3d, inset) also exhibits the thicknessdependent oscillatory behavior (Supplementary Fig. 13).In addition to the SHG signal, a broad multiphoton photoluminescence (MPPL) background is also observed, identified by typical excitation power dependences (Supplementary Fig. 14).With the decrease of the gold thickness from 30 to 2 nm, the spectrally integrated MPPL intensity increases by ~2200 times (Fig. 3d).The enhancement is so high because in bulk gold MPPL is an extremely inefficient process, as the momentum of the photon is too small to satisfy momentum conservation of the involved intraband transition in the sp conduction band 49 .Benefiting from the thickness-dependent quantization of the energy levels, intersubband transitions in 2DGFs do not require an additional momentum, which greatly boosts the MPPL efficiency 49 .
Due to the strong thickness dependence of the nonlinear optical properties, the ALPE approach can be used to locally engineer the optical nonlinearity of gold flakes.As an example, a logo of Zhejiang University was etched into a 36-nm-thick gold flake (Fig. 3e), with its thickness locally modified with a 28-nm step.Under the excitation with 800-nm laser pulses, the logo was observed in the MPPL image taken with a 575-630 nm bandpass filter as a red emission pattern on a completely dark background (Fig. 3f), revealing significantly enhanced MPPL in the thinner logo region compared to a thicker surrounding.This is particularly important for the applications in which high local optical nonlinearity is required without the integration of other, e.g.technologically incompatible, materials.
The excellent crystal quality, atomically-smooth surface and 100s-μm lateral size of 2DGFs enable the realization of low-loss plasmonic nanostructures with extreme optical confinement 8,10,11,50,51 .To implement a typical plasmonic nanostructure supporting LSP resonances, 2DGFs were patterned into nanoribbon arrays using the local etching approach (Fig. 4a).First, nanoribbon arrays with a fixed width (w = 100 nm) and period (p = 3w) were fabricated using 2DGFs with thicknesses of 7, 5 and 3 nm.Figure 4b shows an example of an as-fabricated nanoribbon array with a thickness of 3 nm, featuring a smooth surface and having no visible defects.In marked contrast, for nanoribbon arrays fabricated using sputtered gold films (see Methods), the nanoribbons are quite rough and become discontinuous when the thickness is less than ~7 nm (Fig. 4c).As a result, there is no observable LSP mode in their transmission spectra (Fig. 4d, solid lines), however, strong resonance dips due to the excitation of a dipolar LSP mode in each of the nanoribbons can be observed for the nanoribbon arrays fabricated using 2DGFs (Fig. 4d, dashed lines).The resonance dip is red shifted dramatically from 767 to 1115 nm with the decrease of the nanoribbon thickness from 7 to 3 nm by only 4 nm, showing an unprecedented versatility in the plasmonic response as a consequence of the ultrathin thickness.The quality factor for the plasmonic mode of the nanoribbon array with 3-nm thickness is up to ~5, which can be attributed to the greatly reduced electron scattering losses in the ultrasmooth single-crystal 2DGFs 10,50 .The resonance wavelength of the plasmonic modes in the ultrathin nanoribbons can also be tuned by changing their width (Fig. 4e, solid lines).With the decrease of the nanoribbon width from 100 to 75 nm (t = 2.5 nm, p = 3w), the resonance dip is blue shifted from 1264 to 951 nm.Numerically simulated transmission through the gold nanoribbon arrays (see Methods) confirms the experimental results (Fig. 4e, dashed lines).fabricated with 2DGFs (dashed lines) and sputtered gold films (solid lines) for various nanoribbon thicknesses (w = 100 nm).e, Measured (solid lines) and calculated (dashed lines) transmittance of nanoribbon arrays fabricated with 2DGFs for various nanoribbon widths (t = 2.5 nm).f, Numerically calculated space-integrated near-field intensities confined within an area extending by a distance d outside the nanoribbons made from a 2.5-nm-thick 2DGF and a 30-nm-thick sputtered gold film.The insets show the corresponding near-field intensity distributions of the nanoribbons having the same resonance wavelength of 970 nm.
Despite similar plasmonic resonances can be obtained in nanoribbon arrays fabricated using sputtered gold films with larger thicknesses (e.g., 30 nm, see Supplementary Fig. 15), nanoribbon arrays with an ultrathin thickness enabled by the 2DGFs, as shown in Fig. 4f, provide attractive advantages including tighter optical field confinement around the nanoribbon (cf., red and black lines), larger localfield enhancement (~20 times higher) and smaller footprint (~5 times reduction in width).Compared with plasmons in graphene and other 2D semiconductors which usually lie at mid-infrared frequencies 52 , 2DGFs with a much higher free electron density allows the realization of extremely-confined plasmons operating in the technologically appealing near-infrared spectral range 10,50 .Large-area freestanding 2DGFs, merging low-loss extremely-confined plasmons with the significantly quantum-confinementaugmented optical nonlinearity, allow the access to the regime of extreme light-matter interactions for fundamental studies 8,11,14,51 as well as the realization of ultrathin nanophotonic devices including ultrafast optical modulators 9,10 and high-sensitivity optical sensors 52 .
Using an ALPE approach, we have successfully fabricated freestanding single-crystal 2DGFs with dimensions extending over a 100s-μm scale and thicknesses down to a single-nanometer level, which has unique properties including significantly quantum-confinement-augmented optical nonlinearity, plasmon-enabled extreme light confinement, low sheet resistance and high mechanical flexibility.The thickness of 2DGFs can be further pushed down to a sub-nanometer level by optimizing the etching conditions (Supplementary Fig. 16).Large-area freestanding 2DGFs provide an emerging platform for fundamental research in various disciplines, such as physics, electronics, chemistry and mechanics, and promises many unique opportunities in the development of ultrathin optoelectronic, photonic and quantum devices.2176-2179 (2002).
measurements (Fig. 3b), laser pulses generated from a Ti:sapphire femtosecond laser (Mai Tai HP, Spectra-Physics) with a central wavelength of 1550 nm (~140-fs pulse width, 80-MHz repetition rate) was used for the excitation.A 20× objective (0.7 NA, Nikon) was used to focus the p-polarized incident pulses (800-mW average power) onto the samples (at a fixed incident angle of ~30° and a spot size of ~20 μm) and collect the reflective spectra of the nonlinear emission.After passing through a 950 nm short-pass filter blocking the reflected excitation laser pulses, the nonlinaer emission was directed into a charge-coupled device (CCD) camera (DS-Fi3, Nikon) and a spectrometer (Shamrock SR-750, Andor) for imaging and spectral analysis, repectively.For the SHG and MPPL measurements (Fig. 3d), laser pulses generated from a Ti:sapphire femtosecond laser (Mai Tai HP, Spectra-Physics) with a central wavelength of 800 nm (~100-fs pulse width, 80-MHz repetition rate) were used for the excitation.A 50× objective (0.8 NA, Nikon) was used to focus the p-polarized incident pulses (5-mW average power) onto the samples (at a fixed incident angle of ~30° and a spot size of ~1 μm) and collect the reflective spectra of the nonlinear emission.After passing through a 700 nm short-pass filter blocking the reflected excitation laser pulses, the nonlinaer emission was directed into a CCD camera and a spectrometer (QE Pro, Ocean Insight) for imaging and spectral analysis, repectively.
To avoid the impact of surface roughness on the nonlinear emission measurement, the 200-nmthick sputtered gold film used for comparison was fabricated using a template stripping method to obtain an atomically smooth surface.Firstly, a gold film with a thickness of 200 nm was deposited onto a cleaned silicon substrate by magnetron sputtering at a base pressure of 5×10 -6 Torr at a deposition rate of 0.2 nm/s.Secondly, a droplet (10 μL) of epoxy glue (EPO-TEK 301-2) was admitted onto the gold film, followed by the placement of a cleaned glass substrate on the top.Thirdly, the structure was transferred onto a hot plate to cure the epoxy under 80 °C for 3 h, and then was slowly cooled down to monolayer of (3-aminopropyl)trimethoxysilane instead before the deposition of gold 42 .Then, gold films with various thicknesses were deposited on the substrates under a base pressure of ~5×10 -6 Torr at a rate of 0.2 nm/s (DISCOVERY-635, DENTON), which was followed by a lift-off process to obtains the nanoribbon arrays.
Numerical simulations for nanoribbon arrays.Transmission through gold nanoribbon arrays was numerically simulated using the finite element method (COMSOL Multiphysics software).The nanoribbon arrays were illuminated with a plane wave at normal incidence.Due to the invariance of the numerical problem in one of the directions, its dimensionality was reduced to 2D.Taking advantage of the symmetry of the structure, a unit cell of the array was modelled with periodic boundary conditions set on its sides.Perfectly matched layers were introduced at the top and bottom of the simulation domain to ensure the absence of back-reflection.The nanoribbon was set to have a rectangular crosssection with the width  and thickness , both of which were varied.In the case of 2DGFs the singlecrystal permittivity from Olmon et al. was taken, while in the polycrystalline case data from Johnson and Christy was used.Additionally, to take into account additional losses related to the thicknessdependent electron scattering on the nanoribbon boundaries, the permittivities in both cases were corrected using the Fuchs theory.The refractive index of a mica substrate was taken to be 1.53.
UK EPSRC CPLAS project EP/W017075/1, Zhejiang Provincial Natural Science Foundation of China (Grant LDT23F04015F05) and Fundamental Research Funds for the Central Universities (226-2022-00147).The data access statement: all the data supporting this research are presented in full in the results section and supplementary materials.

Figure 1 |
Figure 1 | Fabrication of 2DGFs.a, Schematic illustration of the ALPE approach for fabricating 2DGFs.b, Optical

Figure 2 |
Figure 2 | Structural and electric properties.a, AFM image of a 1.9-nm-thick 2DGF.b, Planar TEM image of a 3.7-

Figure 4 |
Figure 4 | 2DGFs for low-loss nanoplasmonics.a, Schematic illustration of patterning of a 2DGF into a nanoribbon . G. & Xia, Y. N. Shape-controlled synthesis of gold and silver nanoparticles.Science 298,