Breaking the optical loss barrier in amorphous silicon across the full visible spectrum via dopant-controlled chemical vapor deposition

Abstract

The propagation of light in nanophotonic structures is governed by the refractive index and optical dispersion of constituent materials. However, the choice of dielectrics is often restricted within the transparency window. We introduce object-driven engineering of the process of silicon-based dielectric materials for metasurfaces: visibly transparent hydrogenated amorphous silicon (a-Si:H) with a high refractive index of 3.48 and oxygen-doped a-Si:H (a-SiO_x:H) exhibiting strong dispersion (Abbe number < 10). Both films are fabricated via chemical vapor deposition with precise control over atomic bonding and dopants, revealing the link between optical properties and the amorphous silicon network. We demonstrate the effectiveness of a-Si:H in metalenses with conversion efficiencies of 66.3, 92.0, and 97.0% at 450, 532, and 635 nanometers, respectively. In addition, a wavelength-decoupled a-SiO_x:H beam-splitter achieves a 3.67-fold steering intensity contrast between 450 and 635 nanometers. These materials broaden the dielectric design space and enhance the performance of nanophotonic devices across the visible spectrum.

Dopant-controlled, bandgap-engineered silicon enables low-loss, high-index properties for visible-range nanophotonic devices.

INTRODUCTION

In nanotechnology, the optical properties of materials are pivotal in determining the efficacy and functionality of nanophotonic devices, whose optical responses are restricted by refractive index (n), extinction coefficient (k), and optical dispersion of its consistent. These parameters shape light behavior within artificial nanostructures, governing phenomena like light confinement, wavefront manipulation, and electromagnetic wave guiding. For example, the spatial distributed n using artificial nanostructures determines the final wavefront shapes through light-matter interaction, yielding metalenses, diffractive optical components, and reflection coatings (1). Furthermore, wavelength-decoupled nanophotonic devices demand varied optical responses within a single static structure at the distinct wavelengths, driving need for diverse optical dispersions characteristics. Recently, the optical properties of materials have become crucial in defining the operating spectrum of integrated photonic circuits, thereby influencing their potential applications (2).

Despite the importance of optical properties, substantial constraints persist in the commercially available options for nanophotonic experts. While materials like hydrogenated amorphous silicon (a-Si:H), germanium (Ge), and lead telluride (PbTe) have been identified as optimal for the infrared region due to a fairly high n of 3.5, 3.9, and 5.8, respectively, the choices for materials in the visible spectrum are constrained to titanium dioxide (TiO₂) and silicon nitride (Si₃N₄), which exhibit n of 2.5 and 1.9 respectively. TiO₂ nanophotonic devices (3–5) have been demonstrated for dispersion-engineering for achromatic focusing with their high n at the visible; however, their time-consuming atomic-layer deposition process is incompatible with commercial complementary metal-oxide semiconductor (CMOS) process. In contrast, Si₃N₄ (6) have shown promise as low–optical loss materials with high reproducibility through plasma-enhanced chemical vapor deposition (PECVD); however, its lower n prohibit wavelength-decoupled optical properties, limiting efficiencies in achromatic lenses (7) and holographic display (8). For these reasons, various researchers have continuously explored using a-Si:H for visible optical devices, despite its absorption, to exploit a high n at visible frequencies.

Efforts to expand the range of optical material candidates through a-Si:H bandgap engineering have been extensive, often entailing the suppression of k by passivating dangling bonds with hydrogenation (9–11). Although some synthetic methods aimed at reducing k have been partially reported, evidence regarding of the relationship between the atomic configuration of Si and optical properties within the visible spectrum remains elusive. As a result, achieving reproducibility across different research groups has proven to be challenging, thereby hindering the commercialization of nanophotonic devices with bandgap-engineered dielectrics. Therefore, despite the promising a-Si:H applications [e.g., metalenses (12, 13), beam spreaders (14, 15), and beam splitters (9)], reports of their reproducibility have been confined to a few groups where the bandgap-engineered a-Si:H recipe has been established.

We introduce a-Si:H and oxygen-doped a-Si:H (a-SiO_x:H), synthesized via PECVD, offering high n and extensive optical dispersion. Precise control of deposition conditions enable the production of visibly transparent a-Si:H, which exhibits low optical losses at reduced substrate temperatures (T_s) and optimized chamber pressures (P_c), achieving a minimal k of 0.084 at the F-spectral line (486.1 nm) under conditions of T_s = 100 and P_c = 30 mtorr, while a-Si:H exhibits higher n (n = 2.674) compared to conventional dielectrics, such as TiO₂ (n = 2.52) and GaN (n = 2.53). In addition, oxygen (O) doping during PECVD enhances the optical dispersion of a-SiO_x:H, indicated by an Abbe number smaller than 10. To reveal atomic configuration, we conduct comprehensive atomic-level analyzes with Raman spectroscopy, secondary ion mass spectrometry (SIMS), and density functional theory (DFT).

RESULTS

Bandgap engineering of a-Si:H and a-SiO_x:H

Visibly transparent a-Si:H, and highly dispersive a-SiO_x:H are deposited using PECVD with following processes (Fig. 1, A and B)

$$\text{Si}{\mathrm{H}}_4\left(\mathrm{g}\right)+{\mathrm{H}}_2\left(\mathrm{g}\right)\rightleftarrows \mathrm{a}-\mathrm{S}:\mathrm{H}\left(\mathrm{s}\right)+{\mathrm{H}}_2\left(\mathrm{g}\right)$$ (1)

$$\text{Si}{\mathrm{H}}_4\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)+{\mathrm{H}}_2\left(\mathrm{g}\right)\rightleftarrows \mathrm{a}\mathtt{-}{\text{SiO}}_{\mathrm{x}}:\mathrm{H}\left(\mathrm{s}\right)+{\mathrm{H}}_2\left(\mathrm{g}\right)$$ (2)

Fig. 1. High-n and optical dispersion of dopant-controlled transparent amorphous silicon films.

(A) Visibly transparent a-Si:H and a-SiO_x:H films are synthesized using PECVD, varying gas concentrations, T_s and P_c. (B) Transparent a-Si:H is formed at specific P_c range. (C) Optical losses in a-SiO_x:H decrease with higher O₂ input during deposition at T_s = 200°C and P_c = 40 mtorr. (D) Plots of n_max and n_avg of dielectrics across visible wavelengths (400 to 700 nm). The inset shows the higher reflectivity of high-n materials compared to glass. The thickness of a-Si:H is 100 nm. (E) Dispersion and refractive index (n_F) of a-SiO_x:H at the Fraunhofer F-spectral line, with the lowest n_F under conditions of T_s = 200°C, P_c = 30 mtorr, and O₂ input rate = 3 SCCM. The inset displays a 100-nm-thick a-SiO_x:H film.

During these processes, hydrogen (H) and O are implanted on silicon (Si) networks, affecting average bonding length between adjacent Si atoms and range of Si disorder, influencing optical properties (see note S1, for growth mechanisms and H doping) (16–29). Also, by controlling stoichiometry of O in Si-typed films, their values of k are suppressed at visible frequencies.

To find visibly transparent a-Si:H, various chemical deposition conditions are constructed to find suppressed absorption at the visible frequencies. T_s and P_c are mainly manipulated, as they strongly influence the optical properties of a-Si:H films by changing their atomic bonding configurations (see note S2, for deposition conditions) (9). At lower temperature T_s (<200°C), a-Si:H has higher transparency than that deposited at higher T_s (> 250°C) (see the total optical dispersion of a-Si:H in fig. S1).

The optical absorption of a-Si:H can be further suppressed by doping O during the film growth (Fig. 1C). As input O₂ gas rate increases, the suppression of optical losses is enhanced. This phenomenon is attributed to the increasing proportion of SiO₂ matrix within the a-Si:H film. As predicted by effective medium theory, a higher proportion of SiO₂ leads to lower n and k at visible frequencies.

Obtained visibly transparent a-Si:H has higher n compared with that of conventional optical materials (Fig. 1D). Average refractive index (n_avg) of visibly transparent a-Si:H at the visible frequency (400 to 700 nm) reaches 3.02 with the maximum refractive index (n_max) of 3.48. These values exceed those of ZnSe, previously known as the material with the highest n among visibly transparent optical materials (n_avg = 2.70 and n_max = 2.97) excluding crystalline silicon (c-Si), whose substrate selection is limited by lattice constant.

The obtained visibly transparent a-SiO_x:H exhibit extremely large optical dispersion regardless of its relatively low n compared to a-Si:H (Fig. 1E). Optical dispersions are characterized with n at Fraunhofer F spectral line (486.1 nm) (n_F) and Abbe number (V) that is expressed as (n_D-1)/(n_F-n_C), where n_D and n_C are Fraunhofer D1 (587.6 nm) and C (656.3 nm) spectral lines, respectively. Small V means that optical materials exhibit large optical dispersion. In most optical dielectrics, values of V are in unproportional to n_F. However, our results show that O-doping induces large dispersion (V < 10) with a relatively lower n_F (~2.2) (see the total optical dispersion of a-SiO_x:H in fig. S2)

Atomic configuration of high-refractive index, visibly transparent a-Si:H

The optical properties of a-Si:H are strongly dependent on the T_s and P_c. Six different samples are analyzed at conditions of two T_s (100° and 300°C) and three P_c (20, 40, and 60 mtorr), with measured n and k. a-Si:H films deposited at 300°C exhibit higher n and k values compared to those deposited at 100°C, except for samples deposited at T_s = 100°C and P_c = 20 mtorr (Fig. 2A). In addition, all six silicon samples, regardless of T_s and P_c, have k values below 0.1 at a visible wavelength of 550 nm (Fig. 2B). Upon visual inspection, images of a-Si:H films deposited on glass wafer at T_s = 100°C and P_c = 40 mtorr exhibit greater transparency compared to those deposited at T_s = 300°C and P_c = 60 mtorr, attributed to their lower k values (Fig. 2C) (see note S3, for effects of T_s and P_c on a-Si:H films).

Fig. 2. Optical and structural characteristics of a-Si:H films.

(A) n and (B) k of a-Si:H films deposited at two T_s (100° and 300°C) and three P_c (20, 40, and 60 mtorr). (C) Comparative outdoor images showing the transparency of a-Si:H films with low k at T_s = 100°C and P_c = 40 mtorr versus high k at T_s = 300°C and P_c = 40 mtorr. Both films are deposited on 4-inch (approximately 10 cm) glass wafer with thicknesses of 100 nm. (D) and (E) Raman spectra indicate the presence of a-Si and nc-Si phases and bonding environments such as Si-H, Si-H₂, and O-SiH₂. (F) Schematic of composite films showing variations in (i) higher-n and (ii) lower-n. (G) DFT models of structures with varying H adhesion numbers (i) 1, (ii) 5, and (iii) 15 within the 212 Si atom matrix. (H) Variation in optical properties at 473 nm as determined by DFT, correlating with the number of H atoms.

Raman spectra has been conducted to reveal their atomic configuration including Si-Si bonding network, dopants, and voids in a-Si matrix. The Raman spectra show dominant peaks at 512 to 519 and 476 cm⁻¹, which support the existence of nanocrystalline (nc-Si) and amorphous Si (a-Si), respectively. Four samples, which are (i) T_s = 100°C, P_c = 20 mtorr; (ii) T_s = 300°C, P_c = 20 mtorr; (iii) T_s = 300°C, P_c = 40 mtorr; and, (iv) T_s = 300°C, P_c = 60 mtorr, contain nc-Si phases in a-Si matrix, while the other does not (Fig. 2D) (30, 31). Compared to c-Si and a-Si, whose transverse optical phonon mode are located at 521 and 480 cm⁻¹, respectively (32, 33), crystalline nanoparticles have red-shift and broadening of the bulk phonon mode of c-Si (34). This is because of broken translational symmetry of the crystal lattice with the presence of grain boundaries (33, 35). The findings from Raman spectra are consistent with the data obtained from x-ray diffraction (XRD) (see figs. S3 and S4, for untreated Raman spectra and XRD pattern, respectively).

In addition, all the samples exhibit Raman peaks from stretching vibrations of the monohydride (SiH), polyhydride (SiH₂), and oxidized hydride (O-SiH_x) at 2000, 2100, and 2250 cm⁻¹, respectively (Fig. 2E) (30). Raman peaks at 2100 cm⁻¹ represent clustered SiH₂ at the boundaries of nc-Si and internal surfaces of voids. Thus, strong Raman peak at 2100 cm⁻¹ implies that higher-n of a-Si:H films have porous material nature (Fig. 2F). The microstructure factor μ_void is calculated as following equations

$${\mathrm{\mu }}_{\text{void}}=\frac{\int I_{2100}\left(v\right)\mathit{d}v}{\int I_{2000}\left(v\right)\mathit{d}v+\int I_{2100}\left(v\right)\mathit{d}v}$$ (3)

where I₂₀₀₀ and I₂₁₀₀ denote Raman intensity peak intensity, and ν is wavenumbers. The integral has been conducted with Gaussian fitting of peak spectra. Films with relatively higher n, which are (i) T_s = 100°C, P_c = 20 mtorr; (ii) T_s = 300°C, P_c = 20 mtorr; (iii) T_s = 300°C, P_c = 40 mtorr; and, (iv) T_s = 300°C, P_c = 60 mtorr, exhibit μ_void > 0.75, while the other samples show μ_void < 0.69 (see note S4, for specific calculation of microstructure factor). In short, the whole samples have microvoid and the higher-n a-Si:H films have both nc-Si matrix and large void fraction. Furthermore, the peak at 2250 cm⁻¹ represents that O molecules are mixed into the silicon during growth.

To detect contamination of a-Si:H during deposition, SIMS has been conducted with the detection of Si, H, and, O ions (fig. S5). All six samples exhibit O contamination during the deposition, raising the possibility of either SiH₄ gas input line or chamber leakage. The findings from SIMS are consistent with the data obtained from Raman spectroscopy, suggesting a uniform distribution of O at various depths, indicative of a steady influx of O into the process chamber. These observations could potentially stem from chamber leakage, a phenomenon previously documented in (36, 37).

To discern that attachment of H influence the decrease of k, DFT calculation has been conducted. A-Si matrices with varying number of H atoms are modeled under periodic boundary conditions (Fig. 2G). Optical properties at the wavelength of 473 nm are numerically estimated depending on H atom counts from 1 to 70. In the simulation, the maximum n is observed in a-Si:H with 15 H atoms, with n steadily decreasing as the number of H atoms increased from 15 to 70 (Fig. 2H).

Moreover, our repeated-thickness measurements further support this trend. Under 40 mtorr and a 50-s deposition, the 200°C condition yielded an average thickness of 833.84 nm with an SD of 28.97 nm, reflecting the inherently more reactive and less stable growth environment at lower temperatures. Although this condition produces films with more favorable visible-range optical characteristics, such reactivity naturally leads to slightly larger variation. In contrast, the 300°C condition produced a tighter thickness distribution (725.7 nm with an SD of 8.33 nm) consistent with a more stable deposition regime. These observations suggest that low-temperature growth offers optical advantages through reduced absorption, but this benefit comes with a modest trade-off in deposition uniformity.

Atomic configuration of highly dispersive a-SiO_x:H

Larger dispersion of n has been achieved in a-SiO_x:H, and its magnitude is influenced by deposition conditions of T_s and P_c (Fig. 3, A and B). The influence of P_c contributed to substantial variations in the n of highly dispersive a-SiO_x:H. Values of n have been obtained ranging between 1.65 and 2.75 at P_c = 40 mtorr (Fig. 3A), while higher n (2.25 to 4.00) are obtained at P_c = 20 mtorr (Fig. 3B). Although the high-T_s (200°C) resulted in higher n compared to low-T_s (100°C), the influence of T_s was relatively smaller compared to P_c. In addition, we noted that a-SiO_x:H deposited at T_s = 200°C and P_c = 20 mtorr exhibit higher n of that of TiO₂ (3–5), which is typically used for highly efficient dielectric metasurfaces operating at the visible frequencies.

Fig. 3. Optical dispersion characteristics of a-SiO_x:H.

(A) and (B) Comparison of the n between conventional dielectrics and highly dispersive a-SiO_x:H deposited at P_c of 40 and 20 mtorr, with variations in T_s and input O₂ rates. a-SiO_x:H shows higher n at 20 mtorr compared to 40 mtorr. (C) Demonstrates the large optical dispersion of a-SiO_x:H at lower averaged n (n_avg). Raman spectra detailing the atomic configuration of a-SiO_x:H under deposition conditions at (D) T_s = 300°C and (E) 100°C. (F) Graphical illustration of atomic structures of a-SiO_x:H and comparison of optical properties between conventional HfO₂ and a-SiO_x:H, highlighting differences in n of 0.05 and 0.24, respectively, at the visible frequencies.

To compare optical dispersion with conventional dielectrics, we plotted the logarithm of the maximum difference in n within visible range (400 and 700 nm) against the n_avg within the same range (Fig. 3C). Conventional dielectrics included ZnS, ZrO₂, Si₃N₄, HfO₂, ZrO₂, ZnS, ZnSe, and TiO₂, and they compared with a-SiO_x:H, which are deposited at two P_c (20 and 40 mtorr), two T_s (100° and 200°C), and three input O₂ flow rate conditions [1, 2, and 3 standard cubic centimeter per minute (SCCM)]. Other conditions (P_c = 60 mtorr or T_s = 300°C) exhibit higher k than 0.1 at F-spectral line, so we do not consider them in this comparison. Both conventional dielectrics and a-SiO_x:H showed an increasing dispersion of n with increasing n_avg, but the slope for a-SiO_x:H is notably gentler. In short, it is noted that optical dispersion at lower n_avg is considerably larger in a-SiO_x:H compared to those of conventional dielectrics.

To elucidate the atomic configuration, Raman spectra have been conducted on deposited a-SiO_x:H. Comparisons are made between a-SiO_x:H deposited at high (300°C) (Fig. 3D) and low T_s (100°C) (Fig. 3E). Although a-SiO_x:H deposited at 300°C exhibited high k, rendering it opaque, our comparison followed the convention of separating high T_s (300°C) and low T_s (100°C) as seen in previous literature, being linear (9). Raman peaks around 2000 cm⁻¹ originating from Si-H bonds are close to 0 for a-SiO_x:H deposited at T_s = 300°C, indicating a difference from those deposited at 100°C. Given that visibly transparent a-Si:H exhibits Raman peaks at 2000 cm⁻¹, it can be speculated that the input O₂ removes Si-H bonds and forms other bonds at high T_s (300°C). This speculation is supported by the observation of higher O-SiH peaks under high input O₂ rates (3 SCCM) across all conditions. Conversely, at low T_s (100°C), SiH bonds remained intact, implying that SiH bonds are not dissociated in the plasma at low T_s (100°C). In addition, a-Si:H deposited at 40 mtorr overall showed higher ratios of SiH₂ and O-SiH compared to Si deposited at 20 mtorr.

From the Raman results and deposition conditions, evidence for highly dispersive a-SiO_x:H can be found (Fig. 3F). In general, H is known to attach to dangling bonds in silicon networks, forming long-range atomic Si order that related with crystalline phase. SiH₂ is known to form voids within the Si matrix. Within these results, higher SiH content is observed at low T_s, which can be interpreted as the formation of microvoids within the a-Si matrix. In short, adjusting deposition conditions toward obtaining high SiH and SiH₂, as indicated by the Raman results, can lead to the attainment of highly dispersive a-SiO_x:H.

Nanophotonic applications with the a-Si:H and a-SiO_x:H

To evaluate a-Si and a-SiO_x:H films, we have selected two deposition conditions of visibly transparent of a-Si:H (Fig. 4A) and highly dispersive a-SiO_x:H (Fig. 4B), whose n and optical dispersion have the maximum values, respectively. The visibly transparent a-Si:H is deposited at T_s = 200°C and P_c = 20 mtorr, while the a-SiO_x:H are deposited at T_s = 100°C, P_c = 50 mtorr, with an input O₂ rate of 3 SCCM. Both films exhibit lower k than that of c-Si (38) at the F-spectral line (486.1 nm) (Fig. 4C), and their k can be further optimized by adjusting n and dispersion trade-off.

Fig. 4. Nanophotonic applications with a-Si:H and a-SiO_x:H.

(A) n of visibly transparent a-Si:H and (B) largely dispersive a-SiO_x:H, both exhibiting maximum n_avg and V, respectively. (C) Comparison of k among the a-Si:H, a-SiO_x:H, and conventional c-Si, all showing k values below 0.1 at the F-spectral line (486.3 nm). (D) Schematic depicting phase manipulation in geometric metasurfaces; phases of transmitted right circularly polarized light (RCP) are adjusted in proportion to rotation angle (θ) of nanostructures under input left-circularly polarized light (LCP). (E) Analytically and (F) numerically max(η_meta) of geometric metasurfaces depending on variation in n and k. (G) Scanning electron microscopy (SEM) image of metalenses with a-Si:H. (H) a-SiO_x:H Beam-splitter, designed to steer red light (635 nm) while minimally scattering blue light (450 nm). P_x = 300 nm, P_y = 100 nm, W = 65 nm, and H = 750 nm; shown in (i) tilted, (ii) top, and (iii) side views. (I) Display of retarded phases at wavelengths of (i) 450 nm and (ii) 635 nm. (J) SEM images of a-SiO_x:H beam splitters, illustrating (i) top and (ii) tilted views.

To assess the effect of high n of a-Si:H on geometric metasurfaces, we conduct an analytical approach to approximate the maximum efficiencies of geometric metasurfaces (Fig. 4D). Geometric metasurfaces consist of anisotropic nanostructures that induce phase differences between two linearly polarized light, which are x- and y-polarized, allowing phase manipulation of transmitted circularly polarized light phase with polarization conversion. Using the transmission matrices, we derive the analytical maximum efficiencies, where nanostructures act as an ideal half-wave plate (see note S5, for derivation of the analytical maximum of conversion efficiency) (9, 39). The analytical maximum conversion efficiency is expressed as

$$\text{max}\left({\mathrm{\eta }}_{\text{meta}}\right)={\mathrm{e}}^{\frac{-2\mathrm{\pi }k}{n_y-1}}$$ (4)

where η_meta is a conversion efficiency of nanostructures, n_y is effective n of nanostructures along longer axis, and max(η_meta) is the analytical maximum efficiency. Although, the max(η_meta) exponentially decrease as increase k, the effect of absorption can be suppressed with the term of (n_y-1) (Fig. 4E). We computed the maximum cross-polarization efficiency for the measured n and k, observing a reduced impact of k in regions with higher n values (Fig. 4F). Despite differences observed between analytical and numerical maximum efficiencies due to the assumption of the minimum thickness, both the analytical and numerically calculated results corroborate the notion that high n suppresses the effect of k on the conversion efficiency.

Highly efficient metalenses have been achieved using the high-n, visibly transparent a-Si:H (Fig. 4G). The optimized anisotropic nanostructures exhibit η_meta values of 66.3, 92.0, and 97.0% at wavelengths of 450, 532, and 635 nm, respectively (see fig. S6 and note S6 for details of measurement setup and possible measurement errors). Experimentally measured efficiencies of 37, 84, and 61% are observed at wavelengths of 450, 532, and 635 nm, respectively, under a numerical aperture of 0.05.

In the case of a-SiO_x:H, its large optical dispersion can be used in truncated-waveguide metasurfaces, whose optical responses are wavelength dependent (Fig. 4H). By exploiting n differences at 450 and 635 nm, we have successfully achieved the 2π-phase coverage at 450 nm, whereas at 635 nm, full-phase retardation has not been attained (Fig. 4I). Using these wavelength-dependent scattering responses, we design truncated-metasurfaces from a-SiO_x:H. These metasurfaces direct 635-nm light at a specific angle while maintaining the propagation vector for 450-nm light under y-linearly polarized conditions. The beam splitter features eight discretized nanostructures, each with lengths and heights of 65 and 750 nm, respectively, and widths varying from 0 to 252 nm to match the target retarded phases. Rigorously coupled wave analysis has provided estimated diffraction efficiencies of 25.7% at 450 nm and 7% at 635 nm.

Experimentally, wavelength-decoupled beam splitters are fabricated using highly dispersive a-SiO_x:H films (Fig. 4J). The efficiencies measured for diffracted light at 450 and 635 nm are 12 and 3.6%, respectively. (See fig. S7 and note S7 for details of beam splitter measurement and possible measurement errors). Despite discrepancies between the simulated and measured efficiencies, which suggest minor alignment errors between the designed and fabricated structures, the measured beam-splitting contrast ratio of 3.33 closely aligns with the simulated value of 3.67.

DISCUSSION

This study explores the optical properties and atomic configurations of a-Si:H and a-SiO_x:H, synthesized using PECVD. By adjusting key deposition parameters, such as T_s and P_c, we have engineered the atomic structures for optimized bandgap, enhancing optical characteristics influenced by the presence of nanocrystalline phases, microvoids, and O contamination.

Unlike traditional optical materials that often require a trade-off between optical performance and fabrication compatibility, we optimize silicon-based materials with a focus on manufacturability. This approach enables both high fabrication feasibility and extended optical functionality for visible-wavelength nanophotonic devices. By optimizing dopants, we expand the optical range of Si materials with controllable dispersion while maintaining CMOS-compatible processability. Such tunable silicon-based dielectrics hold promise not only for scientific advances in high-index nanophotonics but also for emerging applications such as biointegrated optics and commercial extended reality technologies.

In the broader context, while innovative materials like particle-embedded resins (40, 41) and hybrid resin composites (42) have been proposed for nanophotonic applications through nanoimprinting processes, they face substantial challenges such as limited yield rates and control issues at larger wafer scales, which reduce device efficiency. In contrast, traditional materials like Si₃N₄, although useful for low-loss photonic circuits and chip-scale applications, often lack the necessary optical properties for broader bandwidth applications (2). Our object-driven engineering of silicon-based dielectric materials for metasurfaces, a-Si:H and a-SiO_x:H, with their enhanced optical dispersion and high transparency, offer superior alternatives, extending the potential applications across the nanophotonic spectrum and paving the way for more efficient and functional optical devices.

MATERIALS AND METHODS

Measuring optical properties of thin films using ellipsometry

The n and k were measured using ellipsometry, which extracts optical properties of films by analyzing polarization of reflected light. The reflected light is expressed as the complex Fresnel reflectance ratio ρ as follows

$$\mathrm{\rho }=\frac{E_{\mathrm{p}}}{E_{\mathrm{s}}}=\mathit{\text{tan}}\left(\mathrm{\psi }\right){\mathrm{e}}^{i\mathrm{\Delta }}$$ (5)

where E_p and E_s are the complex reflected amplitudes of the transverse magnetic and electric components of light, respectively; Ψ and Δ are parameterized values of the amplitude ratio and phase difference, respectively. The incident angle has been set as 75° when measuring ρ, which is suitable for maximizing E_p/E_s in high-n dielectrics. The experimentally measured ρ has been used to infer n, k, and thickness of films by fitting to the modeled Tauc-Lorentz dispersion, whose imaginary part (ε_i) is expressed as (43)

$${\mathrm{\epsilon }}_i\left(E\right)=\frac{A{E}_0\mathrm{\Gamma }{(E-E_g)}^2}{{(E^2-E_g)}^2+\mathrm{\Gamma }{E}^2}·\frac{1}{E}$$ (6)

where A is the Lorentz oscillator strength and is related to film density, E₀ is the Lorentz resonant energy at the peak position, Γ is the Lorentz broadening term that related with disorder in dielectric film, and E_g is the optical bandgap representing the onset of optical absorption through inter-band transitions. Using Kramers-Kronig relation, the real part of permittivity (ε_r) is obtained as the following form

$${\mathrm{\epsilon }}_{\mathrm{r}}\left(E\right)=\mathrm{\epsilon }(\infty )+\frac{2P}{\mathrm{\pi }}{\displaystyle \underset{E}{\overset{\infty }{\int }}}\frac{\mathrm{\xi }{\mathrm{\epsilon }}_i\left(\mathrm{\xi }\right)}{{\mathrm{\xi }}^2-E^2}\mathrm{d\xi }$$ (7)

where P denotes the Cauchy principal value encompassing the residues of the integral at poles situated in the lower half of the complex plane and along the real axis. Additional fitting procedures were applied using ellipsometry software (CompleteEASE with J. A. Woollam, M-2000) to account for film roughness. Following these steps, the optical properties of a-Si:H and a-SiO_x:H were determined.

Geometric optimization of nanostructures

Nanostructure geometric optimization was conducted on a-Si:H metalenses and a-SiO_x:H beam splitters using a self-developed rigorous coupled-wave analysis technique. The light source was situated within glass substrates, while nanostructures were monitored. Both x- and y-polarized light were inputted, and geometries were iteratively optimized to achieve the maximum conversion efficiency. Furthermore, Fourier modal method was used to compute diffracted beam efficiency.

Fabrication of a-Si:H and a-SiO_x:H metasurfaces

The fabrication process of the designed a-Si:H metalenses and a-SiO_x:H beam splitter involved conventional electron beam lithography techniques. Initially, a positive electron-beam resist (Microchem, ZEP520-A) was spin-coated onto the a-Si:H (or a-SiO_x:H) thin film deposited on a fused silica substrate at 2000 rpm for 1 min, followed by baking the sample at 180°C for 5 min. To prevent charge accumulation during subsequent processes, a conductive polymer (Showa Denko, Espacer 300Z) was spin-coated onto the sample at 2000 rpm for 1 min. The resist was then exposed to an electron beam according to the designed metasurface patterns using electron beam lithography equipment (Elionix, ELS-BODEN, 50 keV). Subsequently, the sample was submerged in a developer solution (ZED-50) at 0°C for 3 min to develop the exposed areas of the resist. A 65 nm-thick chromium (Cr) mask was deposited onto the sample using electron beam evaporation (KVT-E4000L, Korea Vacuum Tech.), followed by immersion in hot acetone (55°C) for 12 hours to retain the Cr pattern on the a-Si:H (or a-SiO_x:H) film. Last, inductively coupled plasma-reactive ion etching was used to etch the a-Si:H (or a-SiO_x:H) film along with the Cr mask, which was then removed using a specific Cr etchant (ETCR-300), completing the fabrication process.

Film characterization with XRD and Raman spectroscopy

The atomic structures of the a-Si:H and a-SiO_x:H films were examined using an x-ray diffractometer (Rigaku, D/MAX-2500/PC) with a substrate size of 1 cm by 1 cm. XRD measurements were conducted within an angular range of 10° to 50° to identify both nc- and a-Si peaks. Sequently, the a-Si:H films were analyzed using a Raman spectrometer (Horiba Jobin Yvon, LabRAM Aramis) with an excitation wavelength of 514 nm and a power of less than 1 mW.

DFT calculation of a-Si:H films

All computational simulations, including the structure optimization and optical absorption spectra, were performed by using the Vienna ab initio simulation package based on the DFT. The exchange-correlation effects were determined by using the generalized gradient approximation via the Perdew-Burke-Ernzerhof functional. The plane-wave cutoff energy was set to be 400 eV throughout the calculations. All calculations were converged with the criteria of 10⁻⁸ eV and 0.01 eV Å⁻¹ for energy and forces, respectively. The amorphous silica bulk structure from the previous paper (44) contained the 212 Si atoms, and the slab was modeled with dimensions of 16.5 Å by 16.2 Å by 31.3 Å in periodic simulation boxes containing a 15-Å vacuum layer. Because of the large computational costs, the Brillouin zone was sampled using k-grid meshes of 1 × 1 × 1 during the calculations. The independent-particle-approximation was used to calculate the optical properties of Si.

Supplementary Materials

This PDF file includes:

Supplementary Notes S1 to S7

Tables S1 to S4

Figs. S1 to S7