Optical Characteristics of Silver Thin Films from Island to Percolation in the Ultra-Wide Infrared Spectral Range

Abstract

Silver (Ag) thin films have garnered significant attention due to their unique optical properties. This paper systematically investigates the optical characteristics of Ag films prepared using the electron beam evaporation method. The investigation was conducted using spectroscopic ellipsometry and covers a broad wavelength range of 1679 nm to 36 µm (0.738–0.034 eV), spanning from near-infrared to far-infrared regions. Optical and dispersion models were developed to analyze the impacts of Ag nanostructures on the complex refractive indices, dielectric functions, and reflectance. The results indicate that Ag particles and coalescence films exhibit non-metallic and low absorption properties, while Ag percolation and continuous films present a typical Drude model. The reflectance of Ag films increases as the film coverage ratio increases, and it can reach close to 100% in continuous film. Additionally, a non-destructive, non-contact, and vacuum-free means of confirming the percolation threshold of Ag films was proposed based on the slope of the imaginary part curve. This work is useful to guide simulations and provide a basis for the applications of Ag films in different fields.

1. Introduction

Silver (Ag) thin films have been extensively investigated for several decades due to their unique optical properties. As a low-loss plasmonic material, Ag possesses significant application potential in extraordinary optical transmission [1], coherent microscopy [2], and photovoltaic absorption enhancement [3]. Additionally, Ag nanostructures can be used in molecule detection [4], photothermal therapy [5], and cancer treatment [6,7]. Moreover, Ag thin films can be used in antibacterial coatings [8], drug delivery systems [9], the photodegradation of hormones [10], and biosensors [11]. The optical properties of Ag thin films play an extremely important role in these applications. Thus, most previous investigations mainly concentrated on the surface plasmon polaritons (SPPs) of Ag films in the visible and near-infrared (VIS-NIR) regions [12,13,14,15,16,17,18,19,20,21,22]. By contrast, little attention has been paid to the optical characteristics of Ag thin films in the mid-infrared (MIR) and far-infrared (FIR) regions. Ag films also show high utilization value in the IR band. For instance, nanoparticle (NP) films deposited on zinc oxide (ZnO) nanoplates can improve the FIR optical properties of ZnO [23]. This will further enhance the potential use of ZnO in various optical devices. Percolated films are utilized as the metal layer of low-emissivity multilayer coatings to save energy [24]. Continuous films are significant for many optical systems, such as space telescopes, owing to their high and wide intrinsic reflectivity [25]. Briefly, the optical properties of Ag thin films play a critical role in their applications across various fields, and their surface coverage or nanostructure is a key determinant. Therefore, investigating the optical characteristics of Ag thin films from island to percolation in the IR spectral range is highly significant.

Relatively few reports have been published on the IR optical properties of Ag semicontinuous films. The transmittance and reflection spectra of Ag semicontinuous films were investigated in the MIR region using a Fourier transform infrared (FTIR) spectrometer [26,27,28]. However, the current literature is deficient in the examination of the optical constants and dielectric functions of Ag semicontinuous films. Spectroscopic ellipsometry (SE) is a robust measuring method that can be employed to analyze the optical responses of thin-film materials with exceptionally high detection sensitivity. The SE data obtained from the measurements contain valuable information regarding the interaction of electromagnetic waves with materials. Once the appropriate thickness is determined, the optical constants and dielectric functions can be accurately calculated. For Ag continuous films which are optically opaque, accurate values for the dielectric functions are needed in the IR spectral range because many important parameters are sensitively linked to small variations of the dielectric functions [29]. In 2015, a comprehensive measurement of the dielectric function of Ag opaque films was performed using SE in the energy range of 0.05–0.73 eV [30]. This is the widest measurement range used to study the optical properties of Ag continuous films. More recently, the reflectance of commercially available Ag mirror coatings was presented from 2.4 to 20 µm utilizing an FTIR spectrometer [31]. To our knowledge, there are still limited experimental studies conducted on the optical properties of Ag thin films in the FIR region.

In this work, Ag thin films from island to percolation were deposited on silicon (Si) substrates through the electron beam evaporation (EBE) (DE Technology, Beijing, China) method. The crystal structures and surface topographies of Ag films were inspected through X-ray diffraction (XRD) (Bruker, Billerica, MA, USA) and field-emission scanning electron microscopy (FESEM) (Zeiss, Oberkochen, Baden-Wurtberg, Germany), respectively. The ellipsometric parameters of Ag films were systemically investigated from the NIR to FIR region using SE (J. A. Woollam, Lincoln, NE, USA), covering the broad wavelength range of 1679 nm–36 µm (0.738–0.034 eV). The optical constants and dielectric functions of the films were obtained by analyzing the ellipsometric parameters. The reflectance of the films was calculated from the optical constants. In addition, a new way of confirming the percolation threshold of Ag thin films was put forward. The experimental results obtained from this work can inform researchers who are working with Ag as an infrared optical material.

2. Materials and Methods

A series of Ag films were evaporated via EBE at a rate of approximately 1 Å/s. The substrates utilized in the experiment were single-side polished Si wafers (99.99% purity) with a thickness of 350 µm. Ag particles (99.999% purity) with a diameter of 1–3 cm were used as evaporation target materials. Prior to deposition, the Si wafers underwent three ultrasonic cleaning rounds, with each lasting 5 min. Then, the Si wafers were dried with nitrogen. During the whole deposition process, the high voltage of the electron gun was set to 9.5 kV, and the electron beam was selected as 30 mA. Environmental pressure for thin film growth was maintained at a level lower than 6.7 × 10⁻⁴ Pa. Two quartz sensors placed within the vacuum chamber were utilized to monitor the deposition rate and film thickness. Ag films from island to percolation were obtained by controlling the evaporation time. The structure and crystalline characters of Ag films were investigated through XRD, covering an angle range of 20 to 60° with a precision of 0.02°. The surface topographies of Ag films were viewed with FESEM. The evaluation of average particle size and surface coverage of Ag films was conducted based on the analysis of FESEM images. The ellipsometric parameters Ψ and ∆ were determined with a variable-angle SE at incident angles of 65, 70, and 75° within the spectral range of 0.034–0.738 eV. During measurement, a long testing time of 4 h was taken to reduce noise. The dielectric functions and the thicknesses of Ag films were determined by extracting data from optical and dispersion models using WVASE (Wvase 32) software. The reflectance of the films was calculated from the optical constants.

3. Results and Discussion

3.1. Crystal Structure of Ag Films

Six Ag film samples with different nanostructures were obtained by controlling evaporation times. The samples were labeled S1–S6. Figure 1 displays the XRD patterns of Ag films. The XRD feature could not be obtained for sample S1 due to its extremely small particle size. In the 2θ scan (20°–60°), samples S2–S6 exhibit two obvious diffraction peaks at angles of 38.3 and 44.5°, corresponding to the crystal planes (111) and (200) of Ag. This indicates that Ag films S2–S6 are well crystallized and face-centered cubic (fcc) structures. Additionally, with increasing evaporation time, there is a noticeable enhancement in peak intensity, while the full width at half-maximum (FWHM) shows a reduction. This phenomenon is attributed to the growth of grain size in Ag films.

3.2. Surface Morphologies of Ag Films

The surface topographies of Ag films observed with FESEM are displayed in Figure 2. As deposition time increases, the grain size of Ag films increases, which supports the results of XRD. Normally, a metal film grown via physical vapor deposition evolves in several stages. Initially, the growth of the Ag film follows a Volmer–Weber mode to minimize the surface free energy, which is related to interface formation [32]. This leads to the formation of three-dimensional islands, as displayed in Figure 2a,b. Ag island NPs are randomly distributed on the Si substrate. The morphology and density of these particles are mainly determined by the substrate material, surface temperature, and the film deposition rate [33]. With increasing growth time, the islands start to agglomerate (Figure 2c) and ultimately shape a percolated network (Figure 2d,e). At this moment, called the percolation threshold, the film undergoes a transition from an insulator to a conductor [34]. Finally, a continuous film forms (Figure 2f) across the whole substrate, growing in a layer-by-layer mode. The particle size distribution of Ag NP films was determined by examining and measuring each individual particle based on the results obtained from FESEM images. As Figure 2g–i show, the estimated average diameters of S1, S2, and S3 were found to be 15, 24, and 35 nm, respectively. The coverage ratios of Ag films, as evaluated from FESEM images, are displayed in Figure 3 in blue.

3.3. Model Building and Parameter Fitting

The ellipsometry measurements of Ag films were carried out from 0.034 to 0.738 eV, while varying the incident angles at 65, 70, and 75°. Figure 4 displays the experimental and fitted results at an incident angle of 65°. The ellipsometric parameters Ψ and Δ are expressed as

$$\rho =\mathrm{t}\mathrm{a}\mathrm{n}\Psi \mathrm{e}\mathrm{x}\mathrm{p}(\mathrm{i}\Delta )=\frac{r_{\mathrm{p}}}{r_{\mathrm{s}}},$$

(1)

where r_p and r_s are the complex reflection coefficients for parallel and perpendicular polarizations, respectively.

The optical and structural information of Ag films can be extracted by analyzing the ellipsometric parameters. The inset in Figure 4 shows the optical models of Ag films. It is widely known that the optical characteristics of metals are influenced by both free and bound electrons. The free electron contribution to the dielectric function is significantly enhanced as the frequency decreases. In the energy range of 0.034–0.738 eV, the Drude model is a good choice for fitting ellipsometric parameters. However, a simple Drude model is not suitable for describing island films below the percolation threshold. For S1 and S2, Ag NPs randomly distribute on the Si substrate. The effective medium approximation (EMA) dispersion model is commonly employed for analyzing the optical characteristics of composite materials comprising multiple components. Thus, a three-layer optical model (air/Ag + void/substrate) and an EMA dispersion model were applied for ellipsometric analysis. The EMA model is given by [35]

$$\frac{{\epsilon }_{\mathrm{eff}}-1}{{\epsilon }_{\mathrm{eff}}+2}=f\cdot \frac{{\epsilon }_{\mathrm{Ag}}-1}{{\epsilon }_{\mathrm{Ag}}+2},$$

(2)

where ε_eff represents the dielectric function of the composite layer consisting of Ag and voids, ε_Ag denotes the dielectric function of Ag, and the parameter f indicates the proportion of volume occupied by Ag. To simplify the optical model, surface roughness is ignored because the detection wavelength is much larger than the particle size. According to the structural features, a three-layer optical model (air/Ag film/substrate) was proposed to fit S3–S6. Shortly before the percolation threshold, the ellipsometric data are better modeled by the Lorentz oscillator dispersion model for S3, which is expressed by [36]

$$\epsilon =1+{\displaystyle \sum _j\frac{C_{\mathrm{j}}}{{\omega }_{\mathrm{j}}^2-\omega (\omega +\mathrm{i}{\gamma }_{\mathrm{j}})}},$$

(3)

where C_j, ω_j, and γ_j are the strength parameter, resonant frequency, and damping factor of different oscillators, respectively. After the percolation threshold, the Drude model was chosen to describe the dielectric response of S4–S6. The formula is as follows [36]

$$\epsilon ={\epsilon }_{\infty }-\frac{{\omega }_{\mathrm{p}}^2}{{\omega }^2+\mathrm{i}\omega \gamma },$$

(4)

where ε_∞ is the dielectric function of high-lying interband transition, ω_p is the unscreened plasma frequency, and γ is the plasmon damping constant.

In Figure 4, the fitted curves are in fairly good agreement with the measured ones, demonstrating that the fitting results are reliable and reasonable. Additionally, the thicknesses of samples obtained via SE are exhibited in Figure 3 in magenta.

3.4. Refractive Indices and Extinction Coefficients of Ag Films

The refractive indices (n) and extinction coefficients (k) of Ag thin films within the energy range of 0.034–0.738 eV are presented in Figure 5. With the increase in photon energy, both n and k of S1–S3 increased, while the behavior of S4–S6 is the opposite. Additionally, the values of n are greater than those of k for S1–S3 and less than those of k for S4–S6. This indicates that Ag particles and coalescence films show non-metallic properties. Ag percolation films exhibit anomalous dispersion characteristics, which is the nature of metals. The optical constants spectra also show that n and k increase with film coverage, suggesting that the reflectivity and absorption increase as the film coverage increases.

3.5. Dielectric Functions of Ag Films

Figure 6a,b show the dielectric functions’ real part (ε₁) and imaginary part (ε₂) of Ag films from 0.034 to 0.738 eV in the logarithmic scale. Figure 6c displays the trends of ε₁ and ε₂ at different energies. The percolation threshold can be identified from where the ε₁ falls below zero in the IR region [37]. In the measured energy region, the ε₁ is positive for S1–S3 and negative for S4–S6, which further confirms that the percolation threshold exists between the coverage of 66 and 79.6%. Below the percolation threshold, ε₁ tends to increase with particle size due to the influence of SPR in the VIS-NIR region. Above the percolation threshold, Ag samples exhibit a typical Drude model and free electron action, indicating that the properties of the metallic state increase as the film thickness increases. It can be observed from the ε₂ that isolated Ag NP films S1–S2 show almost no absorption in the whole spectrum. The obvious absorption effect occurs from S3 onwards. The free electron concentration increases with film thickness, and Ag percolation films S4–S6 exhibit strong absorption properties, suggesting that the optical response of Ag films is dominated by the intraband transition of free electrons. Remarkably, the absorption of S6 is weaker than that of S4 and S5 when the energy is higher than 0.35 eV. As the energy is reduced to 0.35 eV, the absorption shows rapid growth and begins to accelerate. These phenomena reveal that the dielectric responses of S4 and S5 in the MIR region are affected by the resonance absorption in the VIS-NIR region. Additionally, the slope of the ε₂ curve is positive before the percolation threshold and negative after the percolation threshold, which can also be regarded as a signal for identifying the percolation threshold of Ag film. Moreover, the dielectric functions found by Yang et al. [30] in the energy region of 0.05–0.73 eV are displayed for comparison with the results for the continuous film S6 in our work, as Figure 7 shows. The two sets of data exhibit good consistency in the same band. This comparison demonstrates that the preparation and testing of the sample are reliable.

3.6. Reflectance of Ag Films

The reflectance of Ag film was calculated from the n and k using the following formula [36]:

$$R=\frac{{\left(n-1\right)}^2+k^2}{{\left(n+1\right)}^2+k^2},$$

(5)

Figure 8 presents the reflectance curves of Ag films in the energy range of 0.034–0.738 eV. The reflectance of Ag film increases as the film coverage ratio increases and exhibits a significant difference in particle films and percolation films, indicating the free electron concentration increases. Moreover, the reflectance of the continuous film S6 is close to 100% in the whole measured region.

4. Conclusions

Ag thin films ranging from island to percolation were fabricated on Si substrates using the EBE method. Films prepared using physical methods typically exhibit excellent crystal quality and can form stable chemical bonds with the substrate or functional layer, making them highly advantageous in photoelectric and photovoltaic devices. The crystal structure of Ag films was identified as fcc through XRD. The growth process of Ag films was revealed with FESEM images. The Ag particle film transforms into a network film and ultimately evolves into a continuous film. The optical properties of these films were systemically studied using SE from 0.034 to 0.738 eV. The optical constants and dielectric functions of the Ag films were obtained by analyzing the ellipsometric parameters. In the measured energy range, Ag particle and coalescence films present non-metallic and low absorption properties, while percolation and continuous films show a typical Drude model, revealing that the increase in free electron concentration and the optical response of Ag films are dominated by the intraband transition of free electrons. In addition, the dielectric responses of Ag films in the MIR region are impacted by resonance absorption in the VIS-NIR region. Moreover, the determination of the percolation threshold can be achieved by examining the slope of the ε₂ curve in the IR region, which is positive before the threshold and negative after it. Furthermore, the reflectance of the films was computed based on the optical constants, revealing a noticeable disparity in particle films and percolation films as the film coverage ratio increases. The reflectance of Ag films generally increases with an increasing film coverage ratio. Beyond the percolation threshold, the reflectance of Ag films in the IR region is boosted by the increase in free electron concentration, with the reflectance reaching near 100% in continuous films. This investigation provides a foundation for the utilization of Ag films across diverse fields.