1. Introduction

All-dielectric nanostructures attract now the growing attention in the design and fabrication of the series of innovative photonic devices, such as, e.g., invisibility cloaks [1], optically magnetized dielectric metamaterials [2] and epsilon-near-zero guiding systems [3]. A substantial part of this trend is stipulated by the progress in physics and technology of inhomogeneous thin films, widely used as optical filters [4], antireflection coatings [5] and transition layers between two media with different refractive indices [6]. Traditionally the design of these devices was based on the multilayer structures with steeply alternating high $n_h$ and low $n_l$ refraction indices. To the contrary, this paper is devoted to the design of all-dielectric nanostructures with technologically controlled smooth spatial distributions of refractive indices, varied at the nanometric scale. The continuous spatial changes of the chemical components with low and high refractive indices in the nanofilms provides the spatial distributions of their optical and mechanical properties. The optical properties of complex structures with specified continuous spatial variations of the refractive index, so-called gradient metamaterials, fabricated from the dielectrics without free carriers, are determined, unlike the metallic films, by the displacement currents. The ability of gradient metamaterials to govern the propagation of electromagnetic waves on and below the wavelength scales accompanied by low losses and weakened scattering, gives the rise to the series of unusual physical effects. Some of these effects open up the new avenues in the elaboration of transparent miniaturized sub-wavelength all-dielectric systems, forming the controllable reflectance and transmittance spectra of wave flows in any prescribed spectral range.

Consider the controlled distribution of refractive index along the direction $z$ across the gradient dielectric nanofilm$n\left(z\right)$. This gradient can be formed by continuous variations of chemical composition of the film. Formation of dielectric structures with prescribed distributions of $n\left(z\right)$ is now a challenging task, important for several problems of nanophotonics [7]. There are several ways to provide such $n\left(z\right)$ [8]. One of the first technologies, elaborated for fabrication of these structures, was based on the reduction of refractive index of glass due to embedding of air-filled pores into the glass. This continuously graded porosity can produce a smooth variation of the refractive index with distance from the glass surface. The widely known method of fabricating optical thin film nanostructures with porosity variation along z-direction is glancing-angle deposition on a rotated substrate with electron beam evaporation of a source material in high vacuum [9,10]. These porous media can have a very low refractive index, approaching to unity, e.g., $n = 1.05$ [11], however, they can display a notable loss in transmission due to scattering of light from the embedded pores; moreover, the effect of pores results in the worsening of their mechanical properties and stability against environmental factors. Typical methods of obtaining non-porous gradient optical films rely on physical vapor deposition (PVD), including ion-assisted PVD, of multiple source materials or plasma-enhanced chemical vapor deposition (PE-CVD) from gas precursors [7]. Another method of modification of refractive index is connected with the deposition of inhomogeneous thin films of SiO_xN_y by laser ablation of a Si₃N₄ target in an oxygen gas medium. The refractive index of the deposited material can be tailored at any value from 1.47 (SiO₂) to 2.3 (Si₃N₄) due to smooth changes of oxygen pressure [12]. Pulsed laser deposition is a low temperature technique for producing of such films. However, the small sizes of samples produced by this technique and presence of droplets reduce its applicability to the fabrication of practical optical devices. More preferable technique is based on ion sputtering of silicon target in the atomic state (without droplets) in the gas medium from mixture O₂ + N₂ [13]. The current index value of SiO_xN_y layer on the substrate is determined by the variable gas medium content. Unlike these methods the control of n can be carried out by regulation of ratio of quantities of the deposited source materials. This approach is known to be realized with highest precision by magnetron sputtering [8]. In magnetron sputtering a magnetic field is used to confine a gas discharge plasma above the target, which, being a discharge cathode, is kept at a negative voltage. This causes ions from the plasma to bombard the target and the atoms ejected from the target are deposited on the substrate to be coated.

Two main approaches to practical realization of magnetron sputtering can be stressed out:

The first approach is a traditional one, but it is characterized by low deposition rate and strong RF interference with the deposition apparatus. To the contrary, the second variant with lower frequencies (named as middle frequencies – MF, related to the tens of kHz) and higher deposition rate attracts the greatest attention. MF ensures the stable arc-less sputtering discharge in reactive gas medium (due to the periodical electrical recharging of dielectric films arising on the metal targets in reactive gas). Being used in a suitable low pressure environment magnetron sputtering can produce high quality coatings [8,14]. The limiting case of this approach, presented by a direct current (DC) power supply, was used for deposition of homogeneous thin films of titanium nitride TiN on the glass substrate [15].

Unlike these researches, our paper is focused on the fabrication of gradient dielectric periodical nanostructures by means of magnetron sputtering from Si and Ta targets in the oxygen environment and probing of unusual transparency properties of the obtained structures in visible and near infrared spectral ranges. Chapter 2 presents the technology of reactive magnetron sputtering of gradient nanostructures with the complex profile of refractive index. The potential of these structures for creation of new optical interfaces with prescribed dispersion and broadband antireflection coatings is illustrated in Chapter 3 by the experiments, visualizing their non-Fresnel transmittance spectra. The X-ray reflectometry for non-destroying control of refractive index profile $n\left(z\right)$ in the sputtered gradient nanofilms is described in Chapter 4. In conclusion (Chapter 5) the merits and shortcomings of all-dielectric nanogradient miniaturized dispersive elements are considered.

2. Reactive pulse magnetron sputtering: devices and procedures

The technology of reactive magnetron sputtering of nanofilms is based on the coordinated operating regime of a pair of magnetrons and programmable movement of substrate. To realize this technology an automatic computer-controlled magnetron sputtering set-up operating in the MF (22 kHz) pulsed regime has been used (Fig. 1).It comprises two magnetrons (M1, M2) for sputtering, respectively, of two materials (e.g., Si and Ti or Ta). A substrate S is disposed on the substrate plane, which is arranged parallel to the plane of the magnetron sputtering targets. The substrate rotates around its own axis and its holder can change the substrate axis position determined by coordinates $X_1$ and $X_2$ accordingly to the computer control program.

 

Fig. 1 Set-up for deposition of nanogradient coatings from mixtures of two oxides. M1 and M2 – magnetrons with rectangular targets for sputtering of two materials (e.g., Si and Ta); S – rotating substrate, which can move along the main axis (bold line); the oval racetrack zones on the magnetron targets are the sputtered areas; the arrows from the racetracks show schematically the directions of propagation of the sputtered atoms.

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When both the magnetron plasma discharges are ignited and maintained in the working state, the target material atoms are sputtered due to plasma ion bombardment and fly away from the targets; then atoms from both of the targets are captured by the substrate surface, providing the formation of a thin film layer. So, the coating material is a mixture of two target materials. The substrate rotation is in need to obtain the coating thickness uniformity over the substrate surface. The substrate surface with the growing coating is constantly blown by activated oxygen (or other gas if necessary) to form the stoichiometric oxide coating. The coordinate–dependent refraction index of the growing coating is determined by the ratio of doses of captured atoms from two magnetron targets. Each dose can be evaluated as the product of sputtered atoms flow captured by substrate from one target and duration of substrate exposure by this flow. The exposure duration is the time period when the substrate is in the given position on the substrate plane over the magnetron target plane. This deposition procedure is based on the variation of the substrate position $X_1$ (or $X_2$) and the exposure duration under computer control, herein the powers of magnetron discharges and values of gas parameters in the deposition chamber remain constant. Such approach ensures the stable sputtering rates of both the magnetrons in reactive gas.

Before the elaboration of computer control program, the deposition process has to be calibrated: the coating deposition rate and the refraction index are experimentally determined for each possible substrate positions $X_1$ ($X_2$) at the given electrical powers of two magnetron discharges. Then, the computer control program describes step-by-step the trajectory and the time characteristic of substrate movement over the magnetron targets along the deposition system main axis (shown by the bold line in Fig. 1). To obtain the refractive index profile in the coating with the minimal value, corresponding to the index of SiO₂, and the maximum value, corresponding to the index of other metal oxides, the computer provides movement of the substrate step-by-step from the position over 1st magnetron (M1) with Si target ($X_1 = 0$) to the position over 2nd magnetron (M2) with metal target ($X_2 = 0$), then to the position over 1st magnetron, and so on, if a periodical gradient structure is in need. An example of the aforesaid calibration curve, presenting the calculated dependence of refractive index $n$ upon the distance $X_1$ along the trajectory of substrate’s motion is shown in Fig. 2.Values of $n$ from this curve were verified by means of ellipsometry of the single layer nanofilms after the process of its sputtering: thus, for example, the distances $X_1=160\text{mm}\left(240\text{mm}\right)$ and the corresponding ellipsometric parameters – angles $\delta =33.22°\left(47.22°\right)$ and phase shift $\varphi =7.9\left(10.32\right)$ proved to be related to the thicknesses of layer $d=114\text{nm}\left(116\text{nm}\right)$ and the values of refractive index $n=1.945\left(2.05\right)$ respectively; the discrepancy of these data with the relevant values on the calibration curve at Fig. 2 doesn’t exceed 1%. Thus, the computer program contains information on the duration of each exposure in each position of the substrate on the substrate plane over the magnetrons accordingly to the prescribed refractive index profile. The stability and reproduction of this deposition process are provided by the invariable regime of energy supply and constancy of gaseous parameters during the sputtering process. It means that the formation of designed profile of $n\left(z\right)$ is controlled by the law of substrate motion.

 

Fig. 2 Calibration curve of the magnetron sputtering system, shown in Fig. 1 (dependence of refraction index of deposited material from SiO₂ – Ta₂O₅ mixture against substrate position X₁).

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3. Design and fabrication of gradient optical nanocoatings

The set-up shown in Fig. 1 was used for magnetron sputtering of periodical transparent nanostructures containing several similar contiguous gradient layers with the predesigned profile of refractive index $n\left(z\right)$. This profile was produced by deposition of mixed oxides of silicon and tantalum due to sputtering of two targets (Si and Ta) accompanied by the appropriate movement of the substrate above the targets. Each layer was formed by coordinate–dependent content of SiO₂ and Ta₂O₅, providing the symmetric profile$n\left(z\right)=n_{0}U\left(z\right)$; here the dimensionless function $U\left(z\right)$ describes the coordinate dependence of refractive index inside each layer. A large family of continuous functions $U\left(z\right)$, perspective for the design of gradient nanofilms, is presented in [16]. All these functions are shown to ensure the exact analytical solutions of Maxwell equations in gradient dielectric media. These solutions, obtained beyond of the scope of any suppositions about smallness or slowness of variations of fields or media, are needed for analysis of wave phenomena in gradient metamaterial structures with sub-wavelength spatial scales, for which these suppositions become invalid. To pave the way to the experimental verification of transmittance spectra, calculated by means of these exact solutions, the simplest flexible non – monotonic distribution $U\left(z\right)$was chosen [16]:

 

Fig. 3 Profiles of normalized square of refractive index U(z) = n(z)/n₀ are plotted vs the normalized thickness of gradient nanolayer z/d; curves 1 and 2 relate to the profiles, providing negative (positive) dispersion of nanolayer.

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The gradient nanostructures with distribution (1) were fabricated, since these structures were shown to possess the strong heterogeneity–induced dispersion, ensuring in its turn the unusual transmittance spectra of the aforesaid structures [16]. The transmittance spectra of multilayer gradient nanostructures for the normal incidence of visible and near infrared radiation, containing several similar layers, characterized by the normalized distribution of refractive index (1), are considered below.

The calibration of the deposition apparatus and fabrication of the optical coating were fulfilled at the following magnetron operation conditions: the average current of both the magnetron discharges was 0.5 A (the discharge voltages were 380 V for Si target, M1, and 580 V for Ta target, M2), the total pressure of argon-oxygen gas mixture in the chamber was about 0.1 Pa. The substrate was prepared from quartz glass К8 with the refractive index $n_s=1.51$. The calibration had indicated that the minimal value of the refraction index ($n_m\approx 1.5$) was obtained when the substrate was above the magnetron M1 with Si target; the maximum value of the refraction index ($n\approx 2.1$) was obtained when the substrate was above the magnetron M2 with Ta target. The process duration for deposition of each gradient layer with thickness $d=140\text{nm}$ was about 1000 sec.

The three-layer structure, corresponding to the continuous distribution, Eq. (1), is depicted in the Fig. 4.Note that this profile is not continuous, but it is formed by broken lines, mimicking the profile (1). Formation of these small steps, stipulated by the technology of sputtering, will be discussed below in Chapter 4. Curves 1 and 2 in Fig. 5 present respectively the transmittance spectra for three layer structure, experimentally measured for the structure, shown in Fig. 4, and calculated for the structure, characterized by three layers with the profiles (1); the widths $d$ and the values $n_m$ and $n_s$ for both structures are equal. Both spectra reveal the range of strong dispersion in the visible range ($400 \text{nm} < \lambda < 650 \text{nm}$) and almost non-dispersive plateau close to the red edge of visible and near infrared spectral ranges. This periodical structure can be viewed as the model of broadband antireflection coating for the spectral range $650 \text{nm} < \lambda < 1000 \text{nm}$, the total thickness of this coating $D$ remaining sub-wavelength: $D = 3d = 420 \text{nm}$.

 

Fig. 4 Distribution of refractive index $n\left(z\right)$in the periodical three layer gradient Ta₂O₅ – SiO₂ – Ta₂O₅ nanocoating, period d = 140 nm.

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Fig. 5 Experimental (curve 1) and calculated (curve 2) transmission spectra of periodical gradient coating with refractive index profile shown in Fig. 3.

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Figure 6 illustrates the influence of the widths of gradient nanolayers on the transmittance of three layered structure. The increase of width $d$ from $d = 140 \text{nm}$ (curve 1) up to $d = 270 \text{nm}$ (curve 2) results in formation of spectrum with two maxima, separated by one minimum. The increase of $d$, other optical parameters of the structure ($n_0$, $n_m$ and$n_s$) remaining invariable, can be viewed as a weakening of optical heterogeneity; herein the trend to formation of oscillating spectra, inherent to transmittance of homogeneous transparent layers, is expressed better in this case, stipulating the oscillations in the spectrum 2; herein the near infrared spectral range is characterized by weakly dispersive almost constant high transmittance.

 

Fig. 6 Dependence of experimental transmittance spectra of three layer gradient nanostructures (n₀ = 2, n_m = 1.5) upon the layer’s width d; curves 1 and 2 relate to the values d = 140 nm and d = 270 nm respectively.

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Figure 7 exemplifies the experimentally measured dependence of transmission spectra upon the amount of gradient layers in nanostructure. Increase of amount of contiguous similar layers from 3 up to 11 is accompanied by deepening of minima of transmission coefficient from ${\left|T\right|}^2=0.45$ down to ${\left|T\right|}^2=0.05$; herein the transmittance in the range $600 \text{nm} < \lambda < 1000 \text{nm}$remains high, almost constant (${\left|T\right|}^2 = 0.9–0.95$) and weakly dependent upon the amount of layers, which means weak dependence upon the total thickness of structure. Note, that the well known minima, habitual for transmittance spectra of homogeneous layers with $m\lambda /4$ (m = 1, 2, 3…) thickness, don’t arise in these spectra. The phenomena, shown by spectra in the Fig. 5–Fig. 7, may become perspective for design and fabrication of new types of broadband antireflection coatings and frequency–selective interfaces.

 

Fig. 7 Transmittance spectra of multilayered gradient nanostructures, containing the m layers with the parameters n₀ = 2, n_m = 1.5, d = 145 nm; curves 1, 2, 3 and 4 relate to the amount of gradient layers m = 3, 5, 7 and 11 respectively.

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Note, that this behavior is stipulated by the technologically controlled heterogeneity–induced dispersion, inherent to the gradient dielectric layers. The agreement between the experimentally measured and calculated transmission spectra proves to be good, indicating the proximity of the sputtered refractive index profile and the predesigned one. Moreover, this closeness confirms the correctness of the deposition apparatus calibration.

4. Non-destroying control of sputtered optical coatings

The theoretical research of gradient optical media had revealed the decisive influence of shape and sizes of spatial distribution of refractive index $n\left(z\right)$ across the metamaterial layer on its reflectance and transmittance [16]. In a case of gradient coating, the useful information concerning the profile $n\left(z\right)$ can be obtained from the density profile $\rho \left(z\right)$ by means of Maxwell Garnett theory, linking the dielectric permittivity of an admixture of two dielectrics with the percentage and dielectric permittivity of each component constituting this admixture [17]. The percentage of each of these components can be evaluated from the measurements of density profile $\rho \left(z\right)$. To perform the non–destroying control of the profile $\rho \left(z\right)$ we had used the X-ray reflectometry (XRR) [18].

The XRR method was used for the characterization of gradient single layer Ta₂O₅ – SiO₂ –Ta₂O₅ with thickness 140 nm; the results are presented in Fig. 8.Grazing incidence XRR proves to be a powerful tool for subsurface analysis of the density profile in the depth range of 0.2-500 nm. XRR measurements were performed with D8 Discover (Bruker-AXS, Germany) multi-goal X-ray diffractometer equipped with a copper anode X-ray source. The high-resolution device contains the Göbel mirror coupled with the Ge (220) Bartels-type primary beam monochromator and a Ge(220) diffracted beam analyzer. With this configuration, the wavelength dispersion of the primary beam of $\Delta \lambda /\lambda \approx 7\times {10}^{–5}$ and the divergence of only 12 arcsec both for both primary and diffracted beams were achieved. The scattered beam contains both specular and diffuse components, but only the specular scattering is known to depend upon the density profile. The simulation procedure, based on Parrat's theory [19] and assumption, that the density gradient can be treated as a multilayer structure composed of thin slices with different densities, was used for fitting of the specular XRR data to the determination of density profile.

 

Fig. 8 Density profile of the single layer nanogradient Ta₂O₅ – SiO₂ – Ta₂O₅ coating, sputtered on the quartz substrate.

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Figure 8 depicts the measured depth profile $\rho \left(z\right)$ of the material density for the single layer of sputtered Ta₂O₅ – SiO₂ – Ta₂O₅ coating obtained by the grazing incidence of XRR was used to determine $\rho \left(z\right)$. The profile $\rho \left(z\right)$ proves to be formed by the layers of unequal thickness, separated by small step-like discontinuities of density. To derive the profile of refractive index $n\left(z\right)$ (Fig. 4) from the density profile $\rho \left(z\right)$ (Fig. 8) the effective medium theory [17] was used; herein the small step–like discontinuities on these profiles are correlated in the framework of Maxwell Garnett theory. It can be seen that the thickness of this layer matches the specified period $n\left(z\right)$; the position of minimal density corresponds to the position of minimal refractive index. The minimal refractive index corresponds to maximum concentration of silicon oxide in the coating material. Thin transition layer with thickness about 10 nm between the substrate and the first sputtered layer at the left side of Fig. 8 can be viewed as a result of diffusion of sputtered particles to the substrate. Thus, the measured profile $\rho \left(z\right)$ confirms the possibility to fabricate the optical nanogradient coating by means of pulse magnetron sputtering of metal targets in the reactive gas medium.

Comparison of the theoretical and experimental transmittance spectra in Fig. 5, related to three gradient layers, shows some discrepancy between the short–wavelength parts of these spectra; the similar discrepancy was found for the theoretical and experimental transmittance spectra for the seven layer nanostructure, containing the same layers. These discrepancies, independent upon the amount of layers, can be originated due to calculation of $n\left(z\right)$ in the framework of Maxwell Garnett model, dealing with the admixtures of particles without taking into account the possibility of formation of new microscopic structures from the sputtered particles inside the gradient layer. However, the spectroscopic researches of sputtered SiO₂ nanofilms had revealed the well expressed lines at the wavenumbers $k = 1040{\text{cm}}^{-1}$ and $k = 1320{\text{cm}}^{-1}$, belonging to the calculated infrared vibration spectra of nanoclusters (SiO₂)₃ (Fig. 9).This result permits one to pose the problem of an eventual cluster structure of SiO₂ films (Fig. 10) as well as the problem of contribution of nanoclusters to the dielectric permittivity of sputtered Ta₂O₅ – SiO₂ – Ta₂O₅ nanofilms under discussion. The research of conditions of possible formation of these clusters can give the rise to reconsideration of some habitual concepts determining the optical and mechanical properties of sputtered nanofilms.

 

Fig. 9 Vibration spectrum of nanoclusters (SiO₂)₃ in the infrared range; the intensity in the arbitrary units is plotted vs the frequency given in cm^–1.

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Fig. 10 Structure of the nanoclusters (SiO₂)₃.

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Thus, although the XRR is shown to reveal some difference between the prescribed design of continuous gradient structure and the measured density profile, this method seems to be useful for the qualitative monitoring of the layers with complex density and refraction distributions.

5. Conclusion

We have shown the perspectives of gradient dielectric nanostructures for elaboration of new types of optical coatings for control of radiation flows in the visible and near infrared spectral ranges. The following properties of such structures, demonstrated by the testing of fabricated multilayer gradient nanocoatings, have to be stressed out:

Side by side with these merits of reactive magnetron sputtering one has to mention several physical and technological problems, requesting the further elaboration: