1. Introduction

Historically, metals have always played a special role in electrodynamics and optics. Due to their ability to effectively reflect electromagnetic waves, they are widely used in the manufacture of mirrors, diffraction gratings, polarizers, waveguides, etc. At the beginning of the 20th century, it was discovered that metal surfaces can not only effectively reflect the light, but also provide the propagation of surface electromagnetic waves [1]—surface plasmons. Depending on the design of the metal—dielectric structure both localized surface plasmon (in metal clusters or sub-wavelength holes inside metals) and delocalized surface plasmons—surface plasmon polariton (on an extended flat metal-dielectric interface) could be observed [2].

Basically, plasmonic effects have been used by mankind for many centuries. Localized plasmon in silver and gold nanoclusters in glass provide extraordinary brightness and lifetime of the colored stained-glass windows of medieval cathedrals [3]. The famous Lycurgus Cup (changing its color depending on the lighting), made in the IV century A.D. in Rome and now kept in the British Museum, also had been made of glass with metallic plasmonic nanoclusters [4, 5]. However, despite its long history, major study and truly vigorous applications of plasmonic effects [6–9] have started just a few decades ago due to recent revolutionary progress in nanotechnologies.

A detailed review of the achievements in plasmonics is beyond the scope of this review. The authors will mention here only such breakthrough applications as creating markers used in decoding the human genome [10], enhancing the organic semiconductors luminescence [11], the implementation of media with a negative refractive index [8], major improvements in photo detectors efficiency [12] and light-emitting diodes [13], control of liquid crystal and magneto-optical layers [14, 15], modulation of the terahertz range radiation [16], etc. Due to the subwavelength light concentration in metal nanostructures, localized surface plasmon resonance is used to enhance optical spectroscopy [17], to make progress on nonlinear optics [18, 19], light emission [20], refractive index sensing [21–28]. To cover research on plasmonic sensors in the last two decades, several review articles on this topic have been published [29–31]. However, the wide practical implementation of plasmonic devices is still limited by materials and nanofabrication issues: high losses in metals, degradation of optical characteristics during nanopatterning processes, extremely high requirements on the accuracy of nanoscale elements, imperfect structure and the thin films morphology. Until present, high losses in plasmonic thin films still remain one of the key problems. That is why over the past 60 years the research community has paid particular attention to the choice of low-loss material and thin films synthesis methods to provide superior plasmonic properties and the possibility of precise nanostructures fabrication.

This review is devoted to thin film synthesis and characterization of silver, which is primus inter pares among plasmonic materials, because of the lowest ohmic losses. The paper is organized as follows. First of all, the authors briefly describe frontier plasmonic devices and their performance versus plasmonic thin film properties. Then, the authors summarize the best published plasmonic films characteristics for various devices and discuss the requirements for the "dream film". Next, the comparison of silver films optical properties (losses) extracted via spectroscopic ellipsometry follows. Then, the authors consider silver thin films characterization techniques and discuss important metrological issues. In section 6 the last six decades in silver films advances synthesis techniques are considered. Prospective view on fabrication advances and conclusions are placed in the last section.

2. Frontier plasmonic devices: surface plasmon type—challenges—thin film issues

Losses in plasmonic devices are generally determined by: ohmic losses in metals, grain boundaries scattering, radiative-scattering and in-plane plasmon scattering (in case of plasmon propagation). The ohmic losses depend only on the optical characteristics of the metal: the real and imaginary parts of the dielectric constant (${\epsilon }^{\prime },{\epsilon }^{″}$). Scattering in the plasmon propagation plane and radiation are largely determined by the roughness of film and the nanostructures quality, as well as by root mean square (RMS) height and the lateral correlation length of the metal surface. Reduction of all types of losses can be achieved by precise engineering of the thin films. Standard polycrystalline films have inferior optical properties compared to epitaxial ones [32–40] due to worse material purity, a large number of grain boundaries, a non-ideal structure, a rough surface, and defective interfaces. Moreover, a typical grain size in case of polycrystalline plasmonic metal films (on the order of 10-100 nm [41, 42]) is comparable to the size of the devices critical dimensions, which (in addition to to losses) is resulted in etching defects along the grain boundaries [43]. For single-crystalline films, these negative effects are almost leveled out [32–40]. In the first part of review, the authors stress to summarize or to imagine the ideal properties of thin films for various plasmonic approaches. One of the main parameters of plasmonic films is optical performance, which can be represented by the quality factor [44] for various types of devices (Fig. 1).

 

Fig. 1 Main plasmonic effects based device types. a) Reprinted with permission from [45]. Copyright (2014) American Chemical Society. b) Reprinted by permission from [the Licensor]: [Nature] [Nature Nanotechnology] [46], [COPYRIGHT] (2013). c) Reprinted from [47] with permission from AAAS. d) Reprinted from [48], with the permission of AIP Publishing. e) Reprinted with permission from [49]. Copyright 2015Optical Society of America. f) Reprinted from [50], Copyright (2014), with permission from Elsevier. g) Pictures is used from [51], Attribution 4.0 International. h) Reprinted figure with permission from [52] Copyright (2014) by the American Physical Society. i) Reprinted with permission from [53]. Copyright (2017) American Chemical Society. j) Reprinted by permission from [the Licensor]: [Nature] [Nature Photonics][54], [COPYRIGHT] (2012). k) Reprinted with permission from [55]. Copyright (2018) American Chemical Society. l) Reprinted with permission from [56]. Copyright 2007 Optical Society of America.

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To fabricate "dream" film for high Q-factor plasmonic devices one have to minimize the imaginary part of the film dielectric constant${\epsilon }^{″}$ and to maximize the absolute value of the real part of the film dielectric constant$\left|{\epsilon }^{\prime }\right|$. From this point of view, single-crystalline films are better than polycrystalline ones because of its better ratio between the imaginary and real parts of the dielectric constant [32–35, 57, 58]. The exception for this rule are, perhaps, quantum emitters with plasmonic resonators [59, 55], whose Q-factor saturates starting from value of 100 approximately [60]. For such devices, utilizing the plasmonic structures, i.e resonators, instead of photonic ones allows to increase the Purcell coefficient (the ratio of the spontaneous emission time in a homogeneous medium to the spontaneous emission time in a nanoenvironment), which is the ratio between the quality factor of the resonator and its volume [61]. On the other hand, it was found that for the ultra high-Q plasmonic resonators fabrication and their effective coupling to light sources [55], the film surface roughness comes to the fore (the best results were obtained for RMS values <0.5 nm). The film roughness (sub-nm RMS value) is also one of the key factor which helps to improve, for example, surface plasmon - polariton waves (SPP) propagation length [62, 63], or the quality of hyperlenses and metamaterials [64]. The critical value for these devices RMS roughness has to be lower than 1.0 nm.

In addition to the serious requirements to film optical properties and surface quality, requirements to film thickness and thickness nonuniformity may vary by orders of magnitude for different types of devices. Continuous films with the thicknesses of 5-20 nm are used, for example, in waveguide applications to implement the long-range surface plasmons regime [65–72]. Special deposition techniques (wetting layers, ion-assisted deposition, etc) are required to form such ultrathin silver film. Unfortunately, these techniques are limited for the dedicated approaches, leading to dramatic optical properties degradation of deposited films in case of improper application. Thickness of the most widely used films in plasmonics is usually varies from 30 to 300 nm, however, thicker films (> 1 μm) are also required. For example, visible-frequency hyperbolic metasurfaces or light sources resonators fabrication [57, 73] utilize up to several micrometer silver thin films. Therefore, a wide range of specific technologies is required to deposit silver films of various thicknesses and well controlled structural, morphological and optical properties.

It is well known that the growth kinetics and following properties of metal films are determined by the substrate (or sublayer) crystalline structure and surface condition. At the same time, for a large class of plasmonic devices, for example, metal—insulator—metal (MIM) waveguides [74, 75, 66], insulator—metal—insulator (IMI) waveguides, metamaterials [56, 64, 76], and hyperlenses [56, 64, 77] metal—dielectric multilayer structures are widely used. In case of multilayer structures, amorphous and lattice-mismatched substrates the epitaxial growth of metals is almost impossible. New materials, nanofabrication and nanopatterning methods are needed to ensure the high optical quality of such films and multilayer structures. [57, 78]. Another well-known technological problem of the multilayer stacks practical application is the high quality nanopatterning [79]. It is often impossible to utilize standard litho—etch nanopatterning techniques for multilayer structures due to etch gases incompatibility for different thin films in stack, high aspect ratios with tight critical dimensions and low line edge roughness (LER) for required devices nanostructures [64]. Complicated multi-step plasma etch processes utilizing mixture of gases are required for multilayer structures patterning. A strong plasma-chemical treatment may both negatively affect the optical properties of thin films and even destruct films (lead to discontinuous films). On the other hand, there are problems with the nanoscale feature fabrication and significant restrictions on the substrates surface pretreatment and deposition parameters (temperatures, reactive gases, ion treatment effects, etc). The very similar situation can be observed in case of plasmonic nanoparticle arrays high-quality manufacturing, which are critical for LSPR-based devices, for example. These devices are usually fabricated by means of self-assembly (film annealing or deposition at elevated temperatures of the substrate [80]) or litho—etch and nanoimprint methods [81]. Here, with nanoimprint the plasmonic film is deposited on the polymer, which imposes serious restrictions on the deposition parameters and, therefore, limits the devices quality factor. In summary, the compromise solution between plasmonic material synthesis techniques and well defined nanoscale structures fabrication have to be found for each high-Q application.

From the other hand, most of the plasmonic structures discussed above are widely used in optical biosensing and environmental sensing applications. In the vast majority of sensing applications [21–24, 28–30, 82] a transparent substrates are required to illuminate the sensor surface with the analyte, which is supplied in liquid or gaseous form from the top side. Such configuration limits the variety of substrates to the transparent ones in visible and near-IR wavelength range (fused silica, borofloat, sapphire, etc), leading to metallic thin films with mostly polycrystalline or nanocrystalline structure.

At the first glance, there are a lot of contradictory specific requirements for the "dream" plasmonic films. We summarized the reported data for the plasmonic films, which were used by research community to create novel plasmonic devices (Table 1). Based on the provided data, one can conclude that most plasmonic devices require continuous thin silver films with ultra-low losses, extremely low surface roughness, single-crystalline structure and extremely long SPP propagation length. At the same time, it is necessary to provide the deposition of films (from ultrathin to optically thick), which are well compatible with nanopatterning on various substrates.

Table 1. Frontier plasmonic applications versus thin film requirements

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3. Silver as a golden material platform for plasmonics

After decades of noble metal-based plasmonic films and nanostructures intensive studies, the authors of [83, 84] still suggested new plasmonic materials offering some technological and physical advantages. Actually, transition metal nitrides (TMNs) are shown to exhibit plasmonic properties starting from the visible range – the situation when the real part of the dielectric function${\epsilon }^{\prime }$ becomes negative, while transparent conducting oxides (TCOs) are plasmonic materials in the infrared range. Moreover, provided that TCOs have five time smaller losses (magnitudes of the imaginary part of epsilon${\epsilon }^{″}$) than silver, the authors outline that the considered oxides have a potential for applications of plasmonics. As an advantage of the nitrides, the fabrication of defect-free crystalline layers with small surface roughness possibility is discussed. Among other advantages, as discussed in [83], the nitrides are proved to be the CMOS-compatible materials [85] and can compete gold and silver in plasmonic properties since the Drude-damping in the noble metals increases by many times due to imperfections such as roughness and grain boundary scattering [86].Another recent review [87] deals with an analysis of the wide range of available plasmonic and phononic materials for mid-IR wavelengths. Here, stating again that CMOS compatibility is essential and ruling out Au and Ag, the authors classify various plasmonic applications and give their outlook on the potential use of materials as TMNs, TCOs, silicides and doped semiconductors (InSb, InAs and Si); also, properties of materials with phononic resonances in the mid-IR, such as GaN, GaP, SiC, and the perovskite SrTiO₃ are reviewed. It is worth mentioning that binary CMOS-compatible TiN/Au (or other) films and nanostructures can be considered where the best features are combined.

Nevertheless, silver is thought to be the best material for plasmonics in the visible and near-IR range [32, 35, 57, 88]. Unfortunately, still there are well-known challenges in silver films fabrication and characterization. Accurate simulation and, therefore, design of possible perspective applications is impossible without retrieving the thin silver film dielectric function which is itself non-trivial and challenging task. For example, the authors of [89] reasonably doubt the results obtained in air because of the silver sulphide unavoidably formed at the Ag/air interface and state that the realistic dielectric function can be retrieved in measurements at ultra-high vacuum or for buried/protected surfaces. Figure 2(a) adopted from [90] illustrates a 60-year span of some works devoted to the studing of the dielectric function of silver samples fabricated in several ways, measured in the visible and IR ranges by various methods and at different conditions.

The authors of [90] demonstrate results on a template-stripped silver films over a broad spectral range. They discuss different contributions (influence of grain boundaries, defect scattering, and surface oxidation) on magnitudes of ε(Ag), and show that, on the contrary to${\epsilon }^{\prime }$, the values of${\epsilon }^{″}$ fluctuate over one order of magnitude (see Fig. 2(b)) [89]. The attention is paid to the features of relaxation time at low energies, outlining intrinsic and extrinsic contributions to the electron dumping in different samples and at different conditions (temperature, grain size and orientation). In conclusion, the authors claim that "Measurements as a function of temperature and purity, and with controlled sample morphology, are needed to discriminate the various mechanisms responsible for damping". Apart from that, more direct methods, such as energy and momentum resolved photoemission may be required in combination with spectroscopic ellipsometry for understanding the realistic dielectric function of silver.

On the other hand, the optical characteristics of Ag films can be not only worse than the bulk ones, but also exceed them when optimizing the films structure. been experimentally confirmed that the SPP propagation length is significantly increased with the use of the films with single-crystalline structure [32, 58, 88, 91], while the roughness reduction decreases optical losses and improves plasmonic properties [63, 92]. The graph (Fig. 2(b)) shows the experimentally measured silver films dielectric permittivity (imaginary part) from some well-known research articles in the plasmonic community.

 

Fig. 2 a) Six decades of dielectric function measurements of Ag covering different spectral regions, with in part inconsistent results mostly notably in the visible/UV spectral range. Figure is reprinted with permission from [90] Copyright (2015) by the American Physical Society and is supplemented with new results. b) Measurements of the imaginary part of the dielectric function of silver from some well-known research articles in the plasmonic community

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Despite the excellent experimentally measured${\epsilon }^{″}$ values, which are close to the theoretical (zero) values for silver, till the present there is a big gap between the experimental and theoretical values of SPP propagation length. It could be explained by the high complexity of the real and imaginary parts of dielectric permittivity retrival as well as of SPP propagation measurements, especially for the sub-100 nm thick films. Therefore, in many cases it is difficult to compare correctly the experimentally measured data for silver films, the well defined metrology procedure should be proposed and approved in the plasmonic community.

4. The "dream" silver film: characterization techniques and metrology issues

A wide range of papers is devoted to the silver films deposition [32–34, 36–39, 93–100], but their proper comparison is often limited due to insufficient data. A full set of characteristics for plasmonic films should include information on the surface quality, crystalline structure, substrate—film and film—ambient interfaces, thickness, optical and plasmonic properties. In the following, the authors shortly overview typical characterization techniques and plasmonic thin films metrology issues. A complete overview of the mentioned methods capabilities and details for measuring plasmonic films is beyond the scope of this review. In this section, the authors proposed the set of plasmonic thin films characterization techniques, which allows the reader to quickly evaluate the film practical value for various plasmonic devices, and provide useful recommendations on typical characterization recipes.

4.1. Surface roughness and morphology

Typical methods for the surface morphology characterization are scanning electron microscopy (SEM), stylus profilometry (SP) and optical profilometry, atomic force microscopy (AFM) and scanning tunneling microscopy (STM). The optimization or development of a novel thin film deposition processes is often associated with hundreds of samples fabrication and precise analysis. SEM and profilometry are very fast and effective methods for carrying out express analysis, which allow visualizing and classifying of a large number of samples in a short time. After such an express analysis, the best samples or sets of samples could be analyzed using the more time-consuming AFM (Figs. 3(a), 3(b)) and STM (Figs. 3(c), 3(d)) methods. Therein one should use STM mainly for analyzing the initial film growth stages and surface reconstruction at the substrate preparation process steps [37–39, 96, 97, 101]. The main method used to measure the film surface roughness is the atomic force microscopy [34, 36–38, 95, 101]. The AFM results are dependent on a variety of parameters, including scan area, force, cantilever bend measurement accuracy, material and diameter of the probe tip, scanning speed and the anti-vibration and anti-noise systems perfection.

 

Fig. 3 a, b) AFM images of single-crystalline and polycrystalline Ag films. Reprinted with permission from [102]. Copyright 2015 Optical Society of America. c, d) STM images of Ag films. Reprinted figure with permission from [103] Copyright (2009) by the American Physical Society.

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Taking into account the plasmonic devices typical footprint and possible local factors influencing thin film growth, for practically useful characterization it is necessary to perform AFM measurements both on a relatively small (few square micrometers) and larger (several thousands of square micrometers) areas. In the standard case the small AFM scan is measured over 2.5x2.5 μm² area with a pretty low scanning speed (down to to 2 nm/s) to ensure the best image quality [32, 58, 93]. The scan like this could be done in tens of minutes depending on recipe. Using AFM scans with the smaller areas (for example, smaller than 1x1 μm²) can lead to an incorrect (very local) characterization of the surface quality, which is not applicable to the majority of plasmonic devices. AFM scans of a larger area (50x50 μm²) performed with a higher scanning speed (at a rate of 100 nm/s) makes it possible to fairly estimate the global roughness and the surface continuity (the lack of voids and pits) in an area corresponding to the typical plasmonic elements dimensions [47, 48, 53]. Typical quantitative parameter for the surface roughness is the root mean square roughness. After many experiment the authors can summarize that the ultra-high resolution AFM scans for the silver films (and other soft metals) with sub-nm-roughness, as well as for sensitive island films, should be performed using probes with less than 2 nm radius, in the only single scan regime, semi-contact mode and with the loading force about tens nN.

For the initial express analysis, the authors recommend to use stylus profilometry, which results are independent on the thin film optical properties. Stylus profiler directly records the deviation of vertical position of the stylus that is in contact with the surface and moves along it. Modern systems can provide repeatability on a vertical scale up to units of angstroms at a scanning speed of up to tens of microns per second. As a result of hundreds measurements, the authors experimentally found the direct correspondence between the AFM and SP RMS roughness values down to 0.7-1.0 nm. For smoother surfaces with better roughness (<1 nm), there is no direct quantitative matching of the results and AFM measurements are much more accurate for sure. However, the possibility of a qualitative sample comparison according to the results of SP roughness measurements in most cases is preserved. It becomes more important and useful when the number of samples start growing rapidly, because SP measurements are much quicker than AFM ones. For soft metal films like silver, the authors recommend using a stylus with a tip less than 40 nm radius, a stylus force less than 0.05 mg (to eliminate the effect on the measured metal surface) and a minimum scanning speed of about 2μm/s. The authors have experimentally approved that silver films are not damaged when measured with the specified recipe.

Another particularly effective and useful express method for analyzing the thin film surface is scanning electron microscopy (SEM) [32, 93, 98]. SEM is based on the interaction of a focused electron beam with a surface and allows one to qualitatively estimate the surface topography and morphology. The most important advantage of this method is that it quickly allows getting images (with area ranging from square millimeters to square micrometers) with resolution up to fractions of a nanometer. To visualize the metal film surface, the authors recommend to use an accelerating voltage in the 1 kV to 5 kV range and a beam current in the 100 pA to 400 pA range (depending on the atomic mass of the metal). To assess the "global" quality of metal films, one can use SEM images with a minimum magnification of 3 kX for estimating the film continuity, the presence of large growth defects and particles, the quality of the substrate and the material. Moreover, SEM images with a maximum magnification of 35-50 kX make it possible to evaluate the crystallite size, surface quality, and the nanodefects presence. Having obtained a certain skills, in most cases, one can evaluate the silver film quality immediately after the SEM.

4.2. Crystalline structure and interfaces

To estimate thin films crystal structure electron backscatter diffraction (EBSD) and reflection high-energy electron diffraction (RHEED) methods could be used. The EBSD detector provides detection of single grains orientation with a resolution up to tens of nanometers based on Kikuchi lines at individual points. This method allows determining the film orientation and the crystallite size (Figs. 4(a), 4(b)), suitable for both polycrystalline and single-crystalline films [32, 93]. Such measurements take a relatively long time (up to several hours for a high quality scan), have a rather low resolution (not better than 20 nm) and could be acquired from a relatively small/local area about of 5x5 μm² (hardware limited by detector resolution and sensitivity). This method is extremely useful for characterizing the film properties with a nano- and polycrystalline structure and a crystallite size down to approximately 20 nm. The RHEED method, in which the electron beam falls at a sliding angle, interacts with the surface and is detected, allows conclusions to be drawn about the crystalline structure and lattice parameters of the sample surface small region. This method allows the qualitative assessment of the surface structural perfection and is mainly used for in-situ control of epitaxial film layer-by-layer growth with atomic accuracy analyzing diffraction beam intensity oscillations [33, 37, 38].

 

Fig. 4 a,b) EBSD images of polycrystalline silver films with different grain sizes c-f) XRD Structural characterization of a 35-nm Si (111) / Ag (111) film [104].

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The basic methods to determine the thin film crystalline structure are X-ray diffraction (XRD) in combination with transmission electron microscopy (TEM). The XRD method allows accurate quantitative characterization of the film crystalline structure on a relatively large (submillimeter) sample area. The TEM method supplement this information with precise measurements of the lattice parameters, information about interfaces and chemical composition. In case of XRD the sample crystalline structure cause a beam of incident X-rays to diffract from crystallographic planes of atoms into many specific directions. By measuring the angles and intensities of these diffracted beams, one can produce a three-dimensional picture of the density of electrons within the crystal. From this electron density, the mean positions of the atoms in the crystal can be determined, as well as their chemical bonds, their crystallographic disorder and various other information. To give an overall characteristic of the film crystalline structure, it is necessary to measure the rocking curves in three geometries (2theta, phi, omega) and fit the model parameters to the experimental reflectometry curve (Figs. 4(c)–4(f)) [32, 38, 39, 93, 98, 100, 101]. Silver "dream" plasmonic film should have the only substrate and film reflexes (of the corresponding orientation) on the 2theta and phi curves (without parasitic reflexes), and also provide a FWHM value of the XRD ω-scan less than 0.3° (the less the better film quality). With correct measurements and model selection, the results of film thickness extraction and roughness from XRD data should be in good agreement with the profilometry/ellipsometry/SEM/TEM and AFM data respectively.

 

Fig. 5 TEM micrograph of Ag thin film on Si a) Reprinted with permission from [99]. Copyright (2017) American Chemical Society. b) Reprinted with permission from [36]. Copyright [2014], American Vacuum Society. c)EDS mapping of Ag thin film on Si substrate

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TEM analysis detects electrons that pass through an ultrathin (usually less than 100 nm) sample, which requires the use of special sample preparation methods for creating nanoscale lamellae. Such lamellae are usually manufactured using focused ion beams (FIB) and precision ion etching, which can cause a non-uniform sample thickness, degradation and oxidation of the layers, contamination of the surface with gallium and a material sputtered by FIB. TEM provides the rigorous information about the substrate—film interface, allows visualization of the transition layer, lattice parameters and chemical composition at an atomic level (Fig. 5) [98, 99]. The method has atomic resolution (sub-100 pm) and is extremely local (tens of nanometers for atomic resolution). The visual TEM image processing is carried out by the Fourier analysis method, which allows obtaining the atomic positioning grids and extracting the sample crystal lattices. For high-quality single-crystalline silver films, the result of such extraction is usually Fourier-patterns that include only two lattice constants (substrate and film) of given orientations.

4.3. Film thickness

Accurate thickness measurement is extremely important for plasmonic films not only from the device design aspect, but it also plays an essential role in the film optical properties retrieval. For sub-50 nm thick silver films during ellipsometry data processing a change in film thickness in range of ± 1-2 nm leads to an error in the optical properties retrieving of tens and hundreds percents. At the same time, it is necessary to make a neat characterization and take into account the substrate—film interfaces (0.1-2 nm due to the intermixing layer presence) and the substrate—ambient interfaces (0.1–2 nm due to film roughness, surface reactions and adsorbants), which have effective optical properties that are different both from the substrate and film properties. Considering these factors, even for bulk homogeneous (valid not for all film growth methods) silver films, accurate measurement of the sub-50 nm silver film thickness becomes a difficult task. Therefore, to measure such silver film thickness, direct and indirect measurement results obtained using the methods of stylus profilometry, AFM, SEM cross section, SEM Energy-dispersive X-ray spectroscopy, TEM and Auger surface analysis can be used.

The most accurate direct method for retrieving film thickness is measuring the formed step height using stylus profilometry or AFM. Depending on the film adhesion level, the step can be formed by scribing (weak adhesion) or etching (strong adhesion). In the case of weak adhesion and hard substrate (like silicon, sapphire, etc.), which could not been damaged by tool, scribing gives excellent step height measurement results. With the epitaxial growth of silver on Si (111), for example, the film—substrateadhesion is very high and the step height measurement is possible only after etching. However, the litho—etch steps can damage not only the substrate, but also uncontrollably (plasma, temperature, etc.) affect the film. Therefore, it is necessary to carefully choose the step formation technique in the case of etching. Silver film thickness measurement with stylus profilometry is very fast, precise and repeatable (in the order of fraction of nanometers), thus it can be used for routine measurements of a large number of samples. Such measurements for metal films are usually made with a low speed 20-50 μ

m/s and with a small force on the stylus (<0.05 mg) [93]. At the same time with the step height measurement using the methods of profilometry and AFM, the substrate roughness and the film thickness can be measured. Another option for indirect thickness measurement is the SEM detector Energy-dispersive X-ray spectroscopy result processing, which allows one to retrieve the film thickness on the energy of reflected electrons when the size of the pear-shaped emission volume varies. Typical parameters for measuring the silver film thickness are 5 kV and 5–10 nA.

Combined SEM and TEM measurements on the sample cleavage make it possible to specify the thickness of the films and to obtain comprehensive information about the structure and chemical composition of substrate—film and film—ambient interfaces. It should be noted that even ultra-high resolution SEM does not allow measuring the silver film thickness on the cleavage with the required (for further accurate optical properties extraction) accuracy.

4.4. Optical and plasmonic properties

The main method for thin plasmonic films optical characteristics determining is spectroscopic ellipsometry [105]. First, one should measure ellipsometric parametersΨ and δ in a certain range of wavelengths at several light incidence angles on a sample. Reflection coefficients of s- and p-polarization (r_s and r_p, respectively) are related to theΨ and δ ratio and could be calculated by the following relation:

The processes of a coherent electromagnetic wave interaction with a film can be divided into bulk processes (phase incursion, exponential decay, volume scattering, etc.) and surface processes (refraction, reflection, scattering on the surface, etc.). To describe most bulk processes (including scattering), it is enough to use the dielectric permittivity, while to describe the interaction with the surface, it is necessary to additionally introduce transition layers and/or special non-Maxwellian boundary conditions [106, 107]. Attempts to describe the electromagnetic wave interaction with a film and to determine the dielectric permittivity of ab initio materials, based on its structure, have been made for two centuries. The first most comprehensive approach was proposed by Ewald and Oseen, who showed that when a wave falls from a vacuum onto a half space filled with periodically distributed dipoles, two waves appear in this half space—the first one dampens the falling one, that allows to introduce the term "refractive index" of such a dipole medium [108, 109]. This approach is now called the extinction theorem. It is important to note that with this approach, the dipoles located inside and near the surface are in a different effective field and, therefore, their dipole moment is different. To describe these surface dipoles, it was proposed to use a transition layer [106, 107]. In other words, even for ideal atomically smooth films, it is necessary to introduce a transition layer. Modern research and calculations from first principles [110] confirm the presence of transition layers with a thickness of several lattice periods, which is especially important for thin films when the thickness is comparable to several effective thicknesses of the surface layers and in terms of homogenization there is "not enough volume" to say about bulk characteristics such as dielectric permittivity.

Another problem of thin film ellipsometry is related to the instability of solving the inverse problem for almost transparent structures [111, 112]. Ellipsometry allows characterization of angstrom-thin layers, but interconnectedness of the film optical constants and its geometrical thickness, intrinsic for all methods measuring optical thickness of coatings, poses at times difficult problem of data elaboration, especially for ultra-thin films. Indeed, since the film is thin, even noticeable changes in its dielectric permittivity do not significantly change the transmission and reflection coefficients. The frequency relations of the transmission and reflection coefficients are smooth, slowly varying functions without any features (resonances). Therefore, even small, inherent errors in measuring the transmission and reflection coefficients lead to large errors in the dielectric constant. As a rule, for the regularization of this task, the parameters are retrieved in accordance with some semiempirical model of dispersion relation [113]. The Drude-Lorenz model and its modifications [114–116], the Tauc-Lorentz model [117] and the Brendel model [118] are most often used. At the same time, for the most realistic retrieving, the film thickness used in the model should be determined in advance by other methods (see section 4.3). For inhomogeneous film the introduced effective dielectric constant even more strongly depend on film thickness. This dependence is also called as "thickness dispersion" [119]. Particularly it was proposed to use the transmittance spectra in order to verify retrieved dielectric constant for Ag film from 4.7 nm to 21.5 nm thick.

Taking into account the metrology issues of determining the plasmonic films dielectric properties, the most promising are hybrid methods which are the combination of ellipsometry and resonant measurements (see [111, 112] and reference therein). Surface plasmon resonance (SPR) was exploited for the study of the optical constants of ultra-thin layers in attenuated total reflectance (ATR) setups [120–122]. This technique uses the exceptional sensitivity of surface plasmons, which are collective electron oscillations at the interface between a conductor and a dielectric. The SP electric field decays exponentially from the metal—dielectric interface into both media, and its decay depth of dozens of nanometers "probes" the materials adjacent to the metal—dielectric interface.

One of the resonance methods used to characterize metallic films is the measurement of the SPP propagation length. To implement it, a special topology is created (Fig. 6(b)), which represents slits in the metal film for plasmon excitation and located at equal distances from each other grooves, etched to half of the film thickness depth [32, 35, 58] for plasmon detection. When a plasmon passes through grooves, part of its energy is lost and scattered by radiation, the intensity of which can be detected in the far field with an optical microscope using a CCD camera.

 

Fig. 6 a, b) Real and imaginary part of dielectric permittivity of Ag thin film energy dependence extracted from SE measurements [104] c) Schematic of the propagation distance setup d) Optical microscopy of SPP: optical image of the Ag film surface with nanostructures created by a focused-ion-beam lithography and optical image of the Ag film surface when SPP is excited by a laser radiation. Figures 6(c) and 6(d) are reprinted with permission from [58]. Copyright2018 Optical Society of America.

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As another method for measuring the SPP propagation length, scanning probe microscopy can be used to study plasmon properties directly on the metal surface with a nanometer resolution. SNOM with uncoated optical fiber probes makes it possible to probe the plasmon field directly above the surface [123]. This method can be used both for detection and for the excitation of plasmons [124, 125] and therefore for measuring the SPP propagation length.

As another resonant method for determining the silver film plasmonic properties one can use a Q-factors of the resonator structures (consisting of nanoholes arrays) comparison. Figure 7 is an SEM illustration of the 100 nm-thick silver films possible realizations and structural features at their nanostructuring by the e-beam lithography and dry etch. Images from (a) for polycrystalline, (b) PCBG [42, 126] (c) single-crystalline silver films correspondingly. Zero-order transmission spectra of these films are shown in plot (d), illustrating the peaks related to the Fano resonances that can vary in intensity by one order of magnitude (see$\lambda \approx$ 850 nm). Actually, the RMS > 1,5 nm and polycrystalline structure of sample (a) causes a weaker light coupling to plasmonic surface wave at the silver/air interface and even absence of the resonance from the spectrum-see curve for sample (a) at$\lambda \approx$580 nm. The structural perfection and high optical Q-factor of nanostructures are evident primarily for the quality of deposited silver films – their single-crystalline structure.

 

Fig. 7 SEM images of possible realizations of the 100 nm-thick silver films and structural features at their nanostructuring by the e-beam lithography: (a) for polycrystalline, (b) PCBG [42] (c) single-crystalline silver films (d) Zero-order transmission spectra of these films

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The silver films discussed in Fig. 7(c) are single-crystalline and atomically smooth this is why retrieving of realistic ε is thought to be possible. The latter means that single-crystalline films are good candidates for ellipsometric retrieval that always suffer from uncertainties when accounting the roughness in the fitting model.

Summarizing the above it should be noted that characterization of plasmonic films optical properties, specially for sub-50 nm thick silver films, should be carried out by a hybrid method combining elements of ellipsometry and one of the resonant methods for determining the dielectric permittivity or functional plasmonic properties of the film. Such a combination makes it possible to avoid incorrect interpretation of ellipsometry data caused by the complexity of taking into account film structural features, roughness, interfaces and transition layers, as well as mathematical problems of solving the inverse problem.

5. Plasmonic metal films characterization summary and the silver "dream" plasmonic film

As a result of the characterization techniques for metal thin films review (including silver thin films), the authors conclude that to evaluate the main film properties and plasmonic performance, it is necessary to make a certain measurement set with characteristic parameters (Table 2). The authors do not claim that characterization method list is the only possible and comprehensive, but it does provide a sufficient set of relevant data for most of the plasmonic devices designing tasks. At the same time, it contains the necessary data set for assessing the plasmonic films key parameters. In the table the authors also specified the best published values of different silver films parameters from various films and named the resulting set the silver "dream" plasmonic film.

Table 2. Characterization techniques summary and the silver "dream" plasmonic film

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6. Thin film deposition methods

For thin silver films deposition, both vacuum and wet deposition methods are used. Vacuum deposition methods are more common, large-scale fabrication and nanopatterning compatible. According to physical principles, vacuum deposition methods are divided into physical vapor deposition (PVD) and chemical vapor deposition (CVD). PVD are processes in which a material goes from a solid phase to a vapor phase and then back to a solid thin film condensed phase. In CVD processes, precursors in the gaseous phase are fed to the substrate; they react on the surface of the substrate and form a thin film. The authors analyzed the key publications devoted to silver films deposition by various methods over the past 60 years and presented film parameters in Table 3. Considering each of the deposition methods, the authors tried to distinguish silver films with the best-published parameters, describe their deposition parameters and recommendations for optimizing the deposition processes.

Table 3. 60 year history of silver thin film deposition

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6.1. Resistive thermal evaporation

Resistive thermal evaporation is one of the easiest and the very first methods which was used in the community to deposit silver thin films [62, 100, 101, 127–129]. Despite the fact that evaporation occurs from the entire area of the material (duty process) and the base vacuum usually does not exceed${10}^{-7}$ Torr, resistive thermal evaporation provides high deposition rates and, therefore, pure films deposition. In 1972, P. B. Johnson and R. W. Christy used this method in a classical paper – one of the first full-scale thin metal films optical constants research. Published silver optical characteristics correspond to the averaged values measured for two polycrystalline films with thickness of 30.4 nm and 37.5 nm deposited at a rate of 60 Å/s [127]. In many further published papers silver films optical properties are compared to this JC data.

For thermal evaporation method the critical parameters influencing the film quality are the base vacuum and the deposition rate. By improving the base vacuum from${10}^{-6}$ to${10}^{-8}$ Torr range it is possible to decrease the polycrystalline film roughness by several times, down to sub-0.5 nm values [62]. By using the high deposition rates (tens of Å/s) the surface roughness can be reduced [127] and film grains size can be increased from tens [41, 42] to hundreds of nanometers [62], which positively affects the optical properties (reduces losses) to the level of values published in JC [127]. Very high deposition rates can effectively increase the nucleation density, prevent three dimensional island growth, and decrease the deposition time, that leads to better effective local vacuum and, consequently, to purer films.

It is also possible to deposit single-crystalline silver films by means of resistive thermal evaporation at elevated substrate temperatures in the$200-{800}^{\circ }$C range [100, 101, 128, 129] by resistive thermal evaporation. This helps to increase a mean free path of adatoms on a substrate surface, which is resulted in larger grains growth. At the same time, a well-known problem of a silver surface dewetting during deposition on a lattice-matched substrates under elevated temperatures (above${100}^{\circ }$C) leads to discontinuous silver films (Figs. 8(a), 8(b)). This could be the reason of three dimensional growth, discontinuous films or films with pinholes growth, even for optically thick silver films (50-300 nm). By optimizing the deposition recipe [101] it is possible to evaporate single-crystalline films (with a thickness of about 300 nm) with either reduced films RMS roughness (1.3 nm over an area of 2.5x2.5 μm²) or improved crystalline structure (FWHM =${0.2}^{\circ }$ for 2θ scan). For thinner (200 nm thickness) silver films, in another paper [130] the single-crystalline silver film with 0.43 nm RMS roughness were deposited at high rates and elevated temperatures on a mica substrates (Fig. 8(c)). The experimentally measured SPP propagation length (in the wavelength range 550 – 700 nm) for bare Ag films was 50 μm, for the single-layer and double-layer graphene-protected Ag films it was 28 μm and 23 μm respectively.

 

Fig. 8 a, b) Silver films dewetting substrates SEM images. Figure 6(b) is used from [131], Attribution 4.0 International. c) AFM image of a silver film with pinholes on a mica substrate. Reprinted with permission from [130]. Copyright (2017) American Chemical Society.

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Another method of improving the silver films surface morphology is a template-stripping of deposited films on a carrier substrate. In [62] 300 nm thick silver films were deposited on native-oxide-coated Si wafers with the high deposition rate at room temperature and then were template-stripped. For such films, the imaginary part of the dielectric permittivity is close to the JC data [127] for wavelengths of 400–650 nm as measured by ellipsometry, their plasmonic properties characterization was not described.

There is no data on high-quality single-crystalline silver films deposited using resistive thermal evaporation for plasmonic applications. The best optical properties for the thermal evaporated silver thin films [62] were obtained for polycrystalline films deposited at high rates (tens of Angstroms per second) and relatively high vacuum (better than$\sim 3\cdot {10}^{-8}$ Torr). These films optical properties correspond to the JC data for small thicknesses only (sub-50 nm thick), but the overall films are far from the silver "dream" plasmonic film.

6.2. Electron beam thermal evaporation

E-beam evaporation is also based on a material thermal evaporation, but provides more process control than resistive thermal evaporation and is widely used to deposit silver films [36, 86, 95, 132, 133]. In contrast to resistive thermal evaporation the only small part of the material is locally melted during e-beam evaporation leading to much better films purity and vacuum. All the rules described above for resistive thermal evaporation are valid and work well for e-beam evaporation. However, e-beam evaporation is less common for single-crystalline silver films deposition, because of dewetting effect under elevated temperatures, so that single-crystalline plates with regular pinholes [95] occur. To deposit continuous single-crystalline silver films with improved optical properties room-temperature deposition with the following annealing [36] was used. Using this method the 200 nm-thick silver films on Si (100) with high crystallinity (FWHM parameter of the XRD ω

-scan is$\sim {0.3}^{\circ }$) and sub-0.5 nm surface roughness over 1x1 μm² area (Figs. 9(a), 9(b)) were deposited. The films imaginary part of the dielectric permittivity, measured for such films, was close to the JC [127] data for wavelengths of 400 - 650 nm as measured by ellipsometry, their plasmonic properties characterization was not described.

The work [58] describes single-crystalline silver films e-beam evaporation using high vacuum tool and the two-step growth approach named the SCULL process (Single-crystalline Continuous Ultra-flat Low-loss Low-cost). The fundamental idea of the process involves a growth of an effective underlying layer under elevated temperature (first step), followed by a single-crystalline film growth under room temperature (second step) in the same vacuum cycle. The SCULL process allows to preciselly control adatoms mobility, nucleation and growth processes to deposit 100 nm-thick continuous single-crystalline silver films with high crystallinity (the FWHM parameter of the ω-scan XRD is 0.244°) and atomically (Fig. 9(c)) flat surface (RMS roughness measured over a 2.5x2.5 μm² and 90x90 μm² area is 0.18 nm and 0.51 nm respectively). The experimentally measured SPP propagation length for these films is almost 200 μm, which corresponds to theoretically limited values for silver films.

 

Fig. 9 1x1 μm² bird-view AFM images of the Ag films: (a) as-grown, (b) RTA at${340}^{\circ }$C. Reprinted with permission from [36]. Copyright [2014], American Vacuum Society. (c) 2.5x2.5 μm² bird-view AFM images of the SCULL Ag films. Reprinted with permission from [58]. Copyright 2018 Optical Society of America.

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There is the technique to deposit ultrathin silver films using sublayers which change the initial conditions of nucleation and crystallization. For example, a few nanometer thick germanium sublayer [132, 133] reducesthe silver percolation threshold from 11 nm to 6 nm (Fig. 10) [133] and improve the surface roughness to 0.22 nm. However, sublayers application makes the growth of single-crystalline films impossible and dramatically decrease optical properties. The imaginary part of the dielectric permittivity of the silver films with the 1 nm-thick germanium sublayer is several times larger than the measured by JC [127]. The pressure treatment [134] of the deposited silver film was reported as a possible technique to improve the surface roughness down to RMS <1 nm, but the other parameters of these films were not described.

 

Fig. 10 Comparison between a Ag layer with (b) and without (a) a Ge wetting layer. Reprinted with permission from [133]. Copyright 2010 Optical Society of America. AFM image of Ag layer with (c) and without (d) a Ge wetting layer. Reprinted with permission from [132]. Copyright (2008) American Chemical Society.

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The e-beam evaporation is quite promising method to deposit high-quality silver films with controlled crystalline structure, morphology, optical and plasmonic properties, since it provides a wide range of the process instruments like high and ultra-high vacuum conditions, high purity deposited material, wide range of deposition rates, heating and cooling of the substrates. Physical and optical properties of the e-beam evaporated single-crystalline silver films deposited using the SCULL process [58], are very close to the silver "dream" plasmonic film.

6.3. Molecular beam epitaxy

Molecular beam epitaxy (MBE) is the ultrahigh vacuum deposition method, which is mainly used to grow high-quality epitaxial films with extremely low growth rates. Numerous works are reported on single-crystalline silver films deposition using ultrahigh vacuum MBE tools [33–35, 37–40, 73, 98]. The typical base pressure in epitaxial processes is about${10}^{-10}$ Torr and better, which makes it possible to drastically reduce the deposition rate with a guaranteed quality (no reactions with residual gases in a vacuum chamber) of deposited silver films. This is very important for silver films usage, because they are extremely reactive and sensitive to residual gases in the vacuum chamber.

One of the commonly used MBE deposition processes for single-crystalline silver films is the 2-step growth process [33–35, 37–39]. The process involves the low temperature deposition of a few nanometer-thick film (with a deposition rate about of 0.016 Å/s) followed by its annealing by heating to room temperature. The resulting film is obtained under ultra-high vacuum conditions (about of${10}^{-10}$ Torr), but still has continuity defects (voids and pits). Single-crystalline silver films with a thickness up to 45 nm and a surface roughness of 0.36 nm were demonstrated [34, 35, 37], which were obtained by iterative repetition of a 2-step process with deposition of only a few nanometer thick films on each many-hours cycle (due to cooling and heating). The research of these films revealed that they degrade and change their structure over time [33], capping MgO thin films are used to protect silver. The measured values of the dielectric permittivity imaginary part for 45 nm film are better than the values obtained by JC [127] in the range of 420-680 nm. The experimentally measured SPP propagation lengths are 22 ± 5 μm (for 632 nm) and 42 ± 3 μm (for 880 nm), which are much lower than the theoretically predicted values for silver.

To avoid the dewetting effect (and 3D islands formation) and obtain continuous silver single-crystalline films with the thickness from 20 nm to 300 nm, it was also proposed to use the MBE method with atypically high deposition rates of about 0.5 - 5 Å/s [73, 98]. A complete characterization is given by the authors for a 300 nm silver film, that was deposited at room temperature, annealed and capped with aluminum oxide layer [73]. A good crystallinity of the 300 nm thick Ag film with the value of the XRD ω-scan FWHM parameter$\sim {0.2}^{\circ }$ and a root mean square roughness 0.42 nm (2x2 μm²) was demonstrated. The dielectric permittivity imaginary part is lower than the values obtained by JC [127] in the range of 420-680 nm, and the measured SPP propagation length was 120 μm (for a wavelength of 700 nm), which is only slightly worse than calculated for JC [127] silver optical constants.

Molecular beam epitaxy is one of the most promising techniques for epitaxial thin films growth. The best plasmonic properties for this method were obtained for 300 nm thick single-crystalline silver films [73] deposited at room temperature with the following annealing. For thinner (<50 nm) films deposition, it is possible to use a 2-step synthesis process [33, 35, 37–39]. In both methods, silver single-crystalline films are capped with protective ultrathin films of transparent oxides (MgO or Al₂

O₃).

6.4. Magnetron sputtering

The magnetron sputtering is one of the most commonly used methods for the thin silver films deposition [32, 57, 135–138]. For this method, the higher kinetic energy of the adatoms and high deposition rates give more possibilities to control the film growth kinetics. This provides more efficient structure control during the polycrystalline silver films deposition and allows to decrease the deposition temperature of single-crystalline films to reduce the dewetting effect. Magnetron sputtering with a high rate (>10 Å/s) allows to obtain silver single-crystalline films with the thickness from 100 nm [32] to 1200 nm [57]. Low RMS roughness values (0.3 nm) for thinner films (100 nm) were obtained in [57], that is better than for thicker (1200 nm) films (0.9 nm) with high crystallinity (rocking curve Ag peak FWHM better than${0.2}^{\circ }$). Measured optical characteristics for these films are close to JC [127], and, in a number of ranges, even the best in comparison. The measured SPP propagation length on the deposited films was 90 μm [32] (for a wavelength of 780 nm). The possibility of single-crystalline films template-stripping to transfer these films on non lattice-matched substrates [139] was also reported.

Polycrystalline films deposited by magnetron sputtering have a small grain size, worse purity, and, correspondingly, worse optical characteristics than films deposited by thermal evaporation [135, 136]. On the other hand, the possibilities to deposit continuous ultrathin polycrystalline films (down to 5-6 nm) using aluminum doping in the process of co-sputtering [137] or using sublayers, i. e. AZO [138], were shown with magnetron sputtering method. But it is hard to estimate the applicability of these films, because their dielectric permittivity and plasmonic properties have not been studied.

Magnetron sputtering is an extremely promising method for the plasmonic silver films deposition, both for ultrathin polycrystalline films and for the optically thick single-crystalline ones, since it provides wide control over the film growth energy. For these methods, a number of deposition parameters of single-crystalline silver films with roughness, crystalline structure, and optical properties close to silver "dream" plasmonic film were demonstrated. The open question for magnetron sputtered silver films is the relatively small SPP propagation length.

6.5. Chemical techniques for silver deposition

A detailed review of chemical methods is beyond the scope of this article, however, we present the key results below. Chemical methods for the silver deposition from the gaseous phase are less common than physical methods. However, a number of works are encountered with attempts to deposit continuous films [140–142]. A particular difficulty arises when it is necessary to produce a continuous film, because for chemical deposition methods it is necessary to use elevated temperatures of the substrate, at which the maximum dewetting effect exhibits.

One of the most promising methods for the silver thin films synthesis by chemical deposition in vacuum is the atomic layer deposition (ALD). A number of papers is published with various processes of silver films deposition using plasma assisted [140], plasma assisted at atmospheric pressure [141] and thermal [142] ALD processes. Thermal processes do not allow the deposition of a continuous film even at a thickness of more than 100 nm. For most plasma assisted ALD processes, the resulting films have a very high roughness. The ALD process at atmospheric pressure with plasma assistance to deposit continuous 30 nm-thick silver films was demonstrated at a substrate temperature of 120 ° C and 80 nm-thick molybdenum seed layer (Figs. 11(a), 11(b)). Optical characteristics of these films in the visible range are close to the JC results (Figs. 11(c), 11(d)) [141], but the data on the film roughness, crystalline structure and plasmonic properties are not presented.

 

Fig. 11 (a, b) SEM micrographs of plasma-enhanced spatial-ALD Ag films deposited for 2250 cycles (30 nm) at 120 °C, grown on a plasma pre-treated 80 nm Mo seed layer. (c, d) Representation of the dielectric-function data for Ag: deposited for 2250 cycles (30 nm). Figures 11(a)–11(d) republished with permission of [Electrochemical Society], from [141] permission conveyed through Copyright Clearance Center, Inc. Giant colloidal silver single crystals SEM images: (e) figure is used from [91], Attribution 4.0 International (f) Adapted with permission from [143]. Copyright (2016) American Chemical Society. (g) The predicted propagation length using the JC Ag data calculated by the eigenmode method for an air/5 nm-Al₂O₃/Ag planar structure, and the error bars are from the JC data. Reprinted with permission from [143]. Copyright (2016) American Chemical Society.

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Chemical methods are less common for the silver continuous films synthesis [144, 145], but they are actively used to produce individual colloidal plateau crystals [143]. The parameters of the obtained colloidal giant crystals are extremely attractive for high performance plasmonic applications. Record values were reached for giant crystals synthesized using the colloidal chemistry [91]: the measured SPP propagation length of about 130 μm (for 780 nm wavelength) and parameter FWHM of the XRD 2θ scan is 0.05 (Figs. 11(e)–11(g)). Such colloidal techniques are very promising for silver-based plasmonic devices fabrication. However, the use of these methods requires solving a serious technological challenge of incompatibility with standard nanopatterning methods.

7. Conclusion and outlook

Over the course of decades the plasmonic community has been focused on the research and development of the thin film material platform with ultra-low optical losses and superior plasmonic performance. Unique optoelectronic devices utilizing plasmonic effects will open new frontiers in quantum optics and quantum information science, if a novel ultra-low loss plasmonic material platform is developed. Despite the great progress in alternative plasmonic materials [44, 83], silver is by far potentially the best material for the most low-loss plasmonic applications in the visible and near-IR range [32, 35, 57, 58, 88]. However, the extensive application of silver-based plasmonic devices is still discredited due to low-loss thin films and nanofabrication issues: high losses, optical properties degradation over time and while nanopatterning, crystalline structure and morphology imperfections, and significantly worse plasmonic properties compared to theoretically predicted values.

Most of the high performance plasmonic devices need continuous silver films with sub-0.5 nm surface roughness, preferably of a single-crystalline structure or micrometers-scale grains size, the best achievable optical properties (the lower ε’(ω) and ε”(ω), the better) and SPP propagation length (at least more than 200 μm at 780 nm wavelegth) to be implemented. The authors name the film with mentioned above set of properties the silver "dream" plasmonic film. Moreover, various plasmonic applications require the use of extremely high optical quality silver films with a thickness from several nanometers to several micrometers on crystalline (silicon, GaAs, sapphire, etc) and non-crystalline (fused quartz, borofloat, etc) substrates. Synthesis of low-loss silver films with a sub-100 nm thickness is impeded by well-known problem of silver-substrate dewetting [62] at high growth temperatures (more than 100°

C), while the quality of thicker silver films can suffer from various process imperfections [95, 101, 130]. Nowadays there is no publications on a standard approach for ultra-thin (for waveguides, modulators, hyperlenses, etc) and thin (for nanolasers, single-photon emitters, photovoltaics, hyperbolic surfaces, etc) high quality silver films synthesis. Finally, the development of the synthesis technology of the described state-of-art "dream" films is associated with an ultra-precise characterization of their properties, the values of which lie near the accuracy limit of the most modern metrological devices [32, 35, 57, 58, 88], that is also a freestanding important and complex task. Here we highlighted the well-known ultra-high quality plasmonic film metrology issues and proposed the standard approach (with practical insights) for their properties characterization.

The first class of silver plasmonic films from deposition point of view is ultrathin and thin sub-15 nm thick silver films. In case of such films without special substrate preparation and deposition techniques it is difficult to deposit continuous films (it means to overcome the percolation threshold from island to solid film formation) even at room temperature [133, 132]. One of the critical parameters of such films for a number of plasmonic devices, including hyperlenses and long-range plasmonic waveguide, is a root mean square surface roughness, which should be less than 1 nm. Ultrathin wetting sub-layers, for example germanium [133, 132], are usually used to fulfill this condition and ensure the continuity of silver films with sub-10nm thicknesses, but which, however, significantly impair their optical and plasmonic properties.

The polycrystalline and single-crystalline thin silver films with the thickness in range from 15 to 2000 nm are mainly used for the majority of plasmonic devices. Many papers demonstrate higher optical and plasmonic performance of single-crystalline films compared to polycrystalline ones [32, 35, 57]. Herewith, nanocrystalline silver films (low temperature processes) are used in even fewer number of papers, since many grain boundaries increases losses dramatically. It should also be mentioned that the single-crystalline films deposition processes on transparent substrates (which are often used in optics) are scarcely encountered, except mica substrates, which are nontechnological and have anisotropic optical properties. Optical properties, plasmonic performance and nanopaterning compatibility of polycrystalline films can be significantly improved by improving the silver purity and smoothing surface roughness (with high deposition rates processes [62, 127]), as well as by increasing the film grain size leading to reducing the number of grain boundaries respectively [32, 42]. A cheap approach of high quality plasmonic films deposition on substrates, which are incompatible with single-crystalline silver film growth, is the template-stripping technology (a film transfer from the growth-substrate to carrier substrate). In this case optical adhesives [62] are used to glue and transfer the plasmonic film to the carrier substrate. The application of optical adhesives makes it difficult to use template-stripping with both standard nanopatterning techniques and in case of good film growth-substrate adhesion. At the same time, the above-described silver films deposition methods do not allow to get perfect optical and plasmonic silver film properties (so called "dream" film).

Several methods were published for single-crystalline silver films deposition using resistive thermal evaporation [62, 100, 101, 127–129], magnetron sputtering [32, 57, 135–138], electron-beam evaporation [36, 86, 95, 132, 133] and molecular beam epitaxy [33–35, 37–40, 73, 98]. The best published results in terms of physical, optical and plasmonic properties are obtained for single-crystalline silver films deposited using molecular beam epitaxy [33–35, 37, 38, 73] and electron-beam evaporation [58] techniques. The method to deposit continuous single-crystalline silver films with thickness ranging from 20 nm to 300 nm using the UHV MBE under 10⁻¹⁰ Torr vacuum conditions was recently described [73].To deposit such films the authors suggested to use the untypically high (for MBE method) deposition rates of the order of 0.5–5 Å/c. A complete characterization is given by the authors for the 300 nm thick silver film deposited at room temperature, followed by 500°C annealing, capping with an ultrathin aluminum film and its oxidation to form a protective aluminum oxide layer [73]. A good crystallinity of the 300 nm thick Ag film (with a FWHM value of the XRD$\omega -scan \approx {0.2}^{\circ }$) and a root mean square roughness of 0.42 nm (2x2 μm²) were shown. The imaginary part of the dielectric constant is lower than the values published by JC [127] in the range of 420–680 nm and the measured SPP propagation length is 120 μm (at a wavelength of 700 nm), which is just slightly worse than calculated value for JC optical constants [127] for silver.

There is the another approach [58] of single-crystalline silver films deposition using high vacuum e-beam evaporation (under 5$\cdot$10⁻⁸ vacuum conditions) and the two-step growth process named the SCULL process (Single-crystalline Continuous Ultra-flat Low-loss Low-cost). The fundamental idea of the process involves the growth of an island silver layer under elevated temperature (first step), followed by a single-crystalline film growth under room temperature (second step) in the same vacuum cycle. The SCULL process allows to precisely control adatoms mobility, nucleation and growth processes to deposit 35–100 nm-thick continuous single-crystalline silver films with high crystallinity (FWHM value of the XRD ω-scan 0.244°) and atomically flat surface (RMS roughness measured over a 2.5x2.5 μm² and 90x90 μm² area is 0.18 nm and 0.51 nm respectively). The experimentally measured SPP propagation length for these films is almost 200 μm (at a wavelength of 780 nm), which corresponds to theoretically limited values for silver films.

Both described approaches make it possible to deposit single-crystalline silver thin films which are very close to the silver "dream" film and theoretically predicted experimental plasmonic performance. The next steps on the way to novel silver-based applications are single-crystalline silver degradation mechanisms investigation, capping methods development (if needed), nanoscale features patterning techniques and silver integration into multilayer technologies. The revolutionary improvements in growth of single-crystalline silver thin films can be extended to the increasingly important noble (Au, Pt, Pd, etc), lightweight (primarily Al) and refractory (Nb, W, Ti, etc) metals, with a particular focus on quantum artificial systems performance through improved material growth and nanofabrication, particularly in attempts to achieve atomical quality of nanoscale features. Reaching the performance demands for these applications requires continued basic research as well as reengineering of already designed devices. Finally, many quantum electronics, information security, artificial intelligence and biomedicine practical application would benefit greatly from theoretically limited extremely high-quality metals with atomic level of imperfection. The required technological toolkit is in place, therefore it is the right time to dedicate resources to scalability, optimization and applicability of these achievements to real devices.