1. Introduction

Nanostructured optical metamaterials enable to control and manipulate the light at the subwavelength scale [1–4], thus exhibiting unique optical properties and functionalities, such as extraordinary spectral features (transmission/reflection/absorption), high field concentration and strong optical confinement. The metamaterial-based perfect absorber takes advantage of amplitude modulation and spectral engineering from elaborate structural design [5–8]. Specifically, when the light incident on material architecture, the material surface is engineered to minimize the electromagnetic impedance, thus rendering the intensity of both reflection and transmission are close to zero. However, a rather challenging for such perfect absorber is to conquer the large-area, high precision and costly nanofabrication techniques for massive industrial manufacturing and practical applications. Recently, the innovative utilization of continuous, lithography-free metal-insulator-metal (MIM) films are proposed to provide a potential solution [9,10]. Simplified planar film enjoys the advantage of simple fabrication steps without demanding any lithography or patterning process. Fundamentally, the MIM structure would confine strong penetrated optical field and give rise to high losses in both metallic film [9,11,12]. Nevertheless, such film-stacked perfect absorbers mostly convert the optical absorption to heat in metal (Ohmic loss), which lacks the capability of direct conversion from light to electricity for photovoltaics or photocurrents in solar cell functionalities. In addition, it also faces the difficulty to remain its perfect absorption performance irrelevant to light incidence angles or light polarization variation. Typically, perfect absorptivity spectrum is quite sensitive to the change of incidence angles or polarizations. Moreover, the geometry of conventional MIM coating is close to quarter-wavelength (∼λ/4), which is still bulky compared to metamaterial/metasurfaces-based counterpart [13,14].

In this work, we propose and report an ultrathin perfect absorber architecture for photovoltaic functionality with large view of angle window operating at visible frequencies. Based on a triple layer metal-semiconductor-metal (MSM) cavity with amorphous silicon (α-Si) and metallic film, the high optical index from α-Si dominates the majority of optical absorption and shrinks the optical cavity length to be deep-subwavelength scale to be ∼ λ/20 - λ/10. The top metallic boundary layer also reduces to be at several nanometers scale (∼ λ/100). Additionally, in contrast to the traditional MIM structure, the majority of optical absorption (∼89%) in MSM occurs in the α-silicon layer, which serves to convert to photocurrent and photovoltaics applications, rather than producing the heat loss in metallic layers of MIM. Distinctive from the traditional Fabry-Perot (FP) cavity with longer optical paths as well as thicker film stacks [15,16], here the proposed architecture is quite insensitive to the incident angle changes or polarization variations [17], which determines that the ultrathin MSM design could yield and robustly maintain the same perfect absorptive feature on bent or twisted flexible substrates. We believe the perfect absorber based on MSM architecture can easily find various promising applications, including photovoltaic [18–20], bio-sensors, solar cells [21–23], photodetectors [24–28], thermal bolometers, color filters, nano-imaging devices [29] and thermal emitters [30–32], etc.

2. Result and discussion

For the design of perfect absorbers, we chose the bottom metal layer thickness to be optically thick (h = 100 nm) in order to ensure zero transmission. The top layer must be optically thin to allow the coupling of the incident light into the MIM cavity and consequently getting trapped inside it with back and forth reflections from metals. The trapped light is partly absorbed in each pass during the multi-reflection process, eventually, leading to complete absorption. It is worth mentioning that the choice of α-Si is due to its wide use in today’s thin film solar cells [33], which comprise one of the most desired paths for the perfect absorption exploitation. Noble metal Ag is selected as the top layer material because of its relatively low absorption loss (the imaginary part of optical refractive index) and partial transparency. The representative geometry is schematically drawn in Fig. 1(a) with geometrical parameters of top Ag thickness t, middle α-Si thickness d, and bottom Ag thickness h. The simulated reflectance are obtained by performing the Finite-Difference Time-Domain (FDTD) method for planar MSM cavity in the visible-frequency regime. The optical constants for Ag and α-Si are retrieved from experimental data measured with an ellipsometer. For a sufficiently thick bottom metallic layer (> 100 nm), the transmission T is reduced to close to zero and thus the absorption A is simplified to A = 1 - R, where R represents for the refection spectrum. Figure 1(b) and 1(c) show the reflectance and absorption spectra as a function of top Ag thickness and middle α-Si thickness, respectively. As shown in Fig. 1(b), the reflectance dip is shifting from ∼ 550 nm continuously to ∼ 750 nm across the entire visible regime as the top Ag thickness t changes from 3 to 14 nm, and middle α-Si thickness d from 15 to 45 nm.

 

Fig. 1. (a) 3D schematic of the proposed MSM structure based on planar Ag/Si/Ag cavity. (b) Simulated reflection and (c) absorption spectra for MIM cavity with top Ag spacer thickness of t = 3 nm, 8 nm, 11 nm and 14 nm, and the core α-Si thickness of d = 15 nm, 25 nm, 35 nm and 45 nm, respectively.

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The absorption response is highly dependent on the structural parameters of the film stacks. As shown in Fig. 2(a)–2(d), when the core α-Si layer thickness d changes from 15 nm to 45 nm, the absorption resonance is subjected to wavelength redshift from ∼ 550 nm to ∼ 750 nm with narrower bandwidth of 124 nm to 89 nm, which is caused by the stronger metallic confinement for the resonant electric field. In order to achieve the maximum absorption peaks for different core layer thickness, it requires correspondingly different top metal thickness to meet the best matching impedance for perfect absorption condition. Specifically, when the silicon layer thickness is 15 nm, it demands the top Ag layer thickness to be ∼ 3 nm; On the other hand, when the silicon layer thickness is increased to 45 nm, the top Ag layer needs to increase to ∼ 14 nm thickness for meeting the perfect absorption case. Hence, we conclude that the α-Si spacer thickness mainly determines the absorption peak position and the thickness of the top Ag layer mainly determines the absorption bandwidth as well as the absorptive intensity. Therefore, the elaborate combination of specific thickness designs for both α-Si and top Ag layers enables the perfect absorber functionality across the entire visible frequency domain. Additionally, it is worth noting that the geometry scale of the proposed MSM is much thinner (∼ λ/20) than conventional MIM coating (∼ λ/4). Thanks to the high refractive index of α-Si, it significantly reduces the effective optical path in the MSM, thus leading to the deep-subwavelength thickness scale and ultrathin optical device potentials.

 

Fig. 2. Calculated absorption spectra as a function of the wavelength and top Ag film thickness t, for the cases of the amorphous silicon thickness of d = 15 nm, 25 nm, 35 nm, and 45 nm. The white point in each figure indicates the optimum value of t and the peak wavelength at the maximum absorption.

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To gain more insight of the perfect absorptive mechanism, we further elucidate the location where electromagnetic (EM) field absorption takes place and the functions of each stack layer. Corresponding to the film stack schematics (Fig. 3(a)), the total electric filed distribution inside the structure is calculated and depicted in Fig. 3(b) at the resonance wavelength of 625 nm. It is observed that a cavity resonance mode is formed owing to the back forth multi-reflection from the top and bottom metallic layers, and thus the incident light is subject to be trapped at the center of α-Si region. Hence, the high absorption efficiency is attributed to the constructed lossy FP-type resonance with metal and α-Si layers. To reveal the light absorption contribution from each film layer, the absorbed power distribution at the individual layer has been calculated (Fig. 3(c)). We calculated the absorption power as ${\textrm A}\;\sim\;{\bar{E}^2} \cdot \varepsilon ^{\prime\prime}(\omega )$, where ${\bar{E}^2}$ represents the penetrated electric field power and $ \varepsilon ^{\prime\prime}(\omega )$ represents the imaginary part of the material permittivity. The majority of light power consumption (∼ 89%) takes place in the core α-Si layer, as the dashed line in Fig. 3(c) shows the line plot of absorptivity trend inside the film stack. The optical absorption in the α-Si layer is calculated by comparing and subtracting the transmission power at the top and bottom boundary of the α-Si layer. The high absorption yield in α-Si rather than in the Ag layer is due to the confined stronger field in the FP cavity as well as stronger absorptive feature of α-Si than Ag. In contrast to the conventional MIM cavity where the optical absorption takes place at the boundary metallic layers, our proposed MSM enhances the optical field in the core layer and eventually absorbed in the core α-Si layer. Distinctive from Ohmic loss in metal which merely converts light to heat, the absorbed optical power in α-Si enables to optoelectronic conversion of photocurrent or photovoltaic with external bias device, enjoying much higher efficiency than thermal-photovoltaic applications. Therefore, it fundamentally makes the Ag/Si/Ag design stand out with significant potential in photovoltaics and solar cell applications.

 

Fig. 3. (a) 2D schematic of the MSM structure at the cross-section. (b) Electric field distribution over the cross-section of absorber and (c) absorbed power distribution at the peak wavelength of 625 nm for the case of top Ag film thickness t = 8 nm and the core α-Si layer thickness d = 25 nm.

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To visualize and emphasize the strong absorptive enhancement characteristics from MSM design, different film stacks with Ag, α-Si, and SiO₂ are calculated for comparison. Figure 4(a)–4(c) shows the absorptivity spectra for Ag/Si/Ag, Si/Ag, and Si/SiO₂ film stacks, respectively as depicted in the inset figures. The α-Si layer keeps at the same thickness in all the above cases for a fair comparison. The absorption enhancement was calculated by comparison between Ag/Si/Ag vs. Si/Ag (Fig. 4(d)) and Ag/Si/Ag vs. Si/SiO₂ (Fig. 4(e)), respectively. It reveals that the triple layered Ag/Si/Ag can provide as high as four folds of absorption enhancement comparing to single layer α-Si film on Ag substrate (Si/Ag), and 2.5 folds enhancement comparing to single layer α-Si film on a glass substrate (Si/SiO₂). Such considerable absorptivity enhancement results from the dual metallic film confinement for the penetrated light field. Particularly, the top ultrathin Ag film (3 - 14 nm) has a crucial impact on the absorption enhancement in the lossy FP cavity mode. It shows partially transparency for the penetrated light field, and resonantly couples with the bottom metal layer, thus enabling a strong field concentration and drastic absorption increment.

 

Fig. 4. Total absorption spectra for (a) triple film stack of Ag/Si/Ag, (b) dual film stack of Si/Ag, (c) dual film stack of Si/SiO₂. (d) Total absorption enhancement between Ag/Si/Ag vs. Si/Ag (without the top Ag film). (e) Total absorption enhancement between Ag/Si/Ag vs. Si/SiO₂ (without the top and bottom Ag films). The α-Si layer is set at the same thickness in all the above cases for a fair comparison. The substrate layer thickness remains at 100 nm for either Ag or SiO₂.

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Furthermore, for the ideal optical behavior of a perfect absorber device, the maximum absorptions are supposed to maintain the same for Omni-directional incidences as well as being insensitive to different polarization modes. However, most of the previous film stacks devices are highly sensitive to the change of oblique directional incidence. Particularly, for MIM-based optical absorber, the absorptive characteristics including the resonance amplitude and peak wavelength would vary corresponding to the effective optical length change at oblique incident cases. To examine the absorption response of our MSM structure for the off-normal incidence occasions, we calculated the absorption spectra from 0° to 60° oblique incidence for TM and TE polarization mode, respectively. Figure 5(a)–5(b) plot the contour map of the simulated absorptivity spectra for t = 8 nm and d = 25 nm. TM polarization corresponds to the electric field vector being parallel to the incident surface, and TE to the electric field vector perpendicular to the incidence surface. For both TE/TM polarization cases, the absorptivity intensity and resonance wavelengths surprisingly remain nearly the same between normal incidence and different oblique incidence cases of 0° – 60°. Specifically, for the TM polarization case, the absorption intensity almost keeps the same value of > 99% while the absorptivity peak slightly migrates a blueshift of ∼ 30 nm when the incident angle varies from 0° to large oblique incident angle of 60°. On the other hand, for the TE polarization occasion, the resonance wavelength almost remains the same (only 3 nm blueshift from 625 nm to 622 nm) and the absorptivity intensity slightly reduced ∼ 7.8%. The underlying angular-insensitive behaviors are sourced from the deep-subwavelength scale of the top Ag and core α-Si layer. When the film thickness is at the deep-subwavelength scale (λ/10 - λ/100) which is much thinner compared to the visible light wavelength, the additional phase shift, as well as the effective optical cavity path change could be neglected at the oblique incident case, even if at large oblique incident angle as high as 60°. Therefore, the optical absorptivity performance is irrelevant to the light oblique incidences due to the negligible propagation phase shift and effective optical length change in the ultrathin α-Si layer.

 

Fig. 5. Contour map of the simulated absorptivity spectral evolution for t = 8 nm and d = 25 nm under (a) TM polarization and (b) TE polarization illumination.

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To gain more insight on light propagation and spectral characteristics through the MSM coatings, we also conducted numerical modeling by TMM (Transfer Matrix Method) to verify the FDTD simulation results. From the TMM derived from the Maxwell equations in each individual material layer, the field within each layer could be treated as superposition of forward-traveling (transmitted) and backward-traveling (reflected) wave with wave number k and a transfer matrix could represent the propagation through interface or within medium. According to TMM, it can be described as:

We choose the structure with the top Ag spacer thickness of t = 8 nm and the core α-Si thickness of d = 25 nm to verify FDTD and TMM for the normal incidence as well as the wide-angle incidence cases, as shown in Fig. 6. It is observed that the absorption spectra show good consistency in terms of absorption amplitude, bandwidth as well as peak wavelength by using both FDTD and TMM modeling.

 

Fig. 6. Absorption spectral comparison between TMM modeling and FDTD simulations at (a) normal incidence; (b) oblique incident angle of 50° with TM polarization and (c) TE polarization.

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3. Conclusion

In conclusion, we systematically investigate a planar cavity with deep-subwavelength thin MSM film to realize perfect absorption functionality across the visible light regime. The strong light absorption yield benefits from the field enhancement effect in the core layer of constructed FP cavity as well as the large imaginary part of permittivity of α-Si layer. Distinctive from the conventional absorber based on plasmonic metamaterial or MIM, here the majority of the optical absorption concentrates at the core α-Si layer. It can be potentially utilized for optoelectronic conversion of photocurrents in solar cell and photovoltaic applications, rather than merely Ohmic loss in metallic layer. Because the ultrathin lossy α-Si layer (thickness = ∼ λ/20) induces a negligible resonant phase change, it gives rise to the extraordinary angular-insensitive characteristics (up to ± 60° oblique incidence angle) for both TM and TE polarizations. We believe that the ultrathin, lithography-free Omni-directional perfect absorber could hold great promise for diverse applications, such as solar cells, photovoltaics, photodetectors, thermal emitters, bio-spectroscopy, optical nano-imaging, and color filters.