Optics and Laser Technology 119 (2019) 105657
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Broadband light absorption with doped silicon for the terahertz frequency ⁎
T
Jun Wu , Xiayin Liu, Zhe Huang Department of Physics, Zhejiang University of Science and Technology, Hangzhou 310023, China
H I GH L IG H T S
terahertz absorber based on patterned doped silicon is investigated. • AThebroadband with absorption above 95% covers a large frequency range. • The bandwidth • polarization-insensitive absorption remains over large incident angle range.
A R T I C LE I N FO
A B S T R A C T
Keywords: Square array Broadband absorption Resonance Terahertz
The broadband absorption effect with patterned doped silicon for terahertz (THz) frequency is investigated. It is achieved by patterning the doped silicon substrate with a two-dimensional grating and covered by a layer of anti-reflective coating. The bandwidth with the polarization-insensitive absorption above 95% covers a frequency range of 0.79–4.115 THz. Moreover the broadband absorption performance can be maintained for the incident angle up to 70°. The electromagnetic field distributions at the resonant frequencies are illustrated to disclose the underlying mechanism of such broadband absorption phenomenon. Last, the influence of geometry parameters on the absorption performance is investigated to provide a guide for practical fabrication. It is hoped that the designed broadband absorber may found applications in the area of thermal emitter, cloaking and biosensor.
1. Introduction Broadband light absorption has been widely investigated during recent years because their wide applications in solar energy harvesting [1], thermal emissivity control [2] and thermal imaging [3], etc. To achieve broadband absorption, many approaches have been proposed, such as, the idea of multiple resonances [4–10], i.e. constructing a superlattice structure with each subunit resonance at overlapping frequencies, and anisotropic metamaterials structure [11–15]. Here the metamaterial absorbers are typically composed of a top periodic subwavelength metallic structure and a dielectric spacer layer backed with a bottom metallic mirror. However, these methods generally suffer from limited bandwidth or complicated design and fabrication process, which is not beneficial for practical application. On the other hand, doped silicon, as a highly lossy dielectric material, has been introduced into the area of THz devices during recent years [16–25]. Because complex patterns can be readily fabricated by conventional lithography technology, doped silicon becomes a promising candidate for broadband absorber at THz frequency. Pu [16] introduced the first design and characterization of a THz absorber based
⁎
on a binary grating on heavily doped silicon. Peng [17] employed a simple double-layered doped-silicon grating to realize an polarization independent THz perfect absorber with an absorptivity above 95% ranging from 0.59 to 2.58 THz. Zang [18] propose a simple periodical structure, composed of two 90 degree crossed dumbbell-shaped dopedsilicon grating arrays, which results in a absorption above 95% ranging from 0.92 THz to 2.4 THz. Shi [19] designed an absorber with a heavily doped silicon substrate and a two-dimensional grating. Lv [20] investigated the broadband polarization-insensitive absorption in the THz regime with surface relief grating on heavily phosphorus-doped silicon substrate surface. Cheng [21] designed an absorber comprising a planar array of cross-shaped structures defined by surface etching of doped silicon with the absorbance of over 90% from 0.67 to 1.78 THz. Yin [22] proposed an THz metamaterial absorber based on a patterned lossy silicon substrate, with which a large absorption efficiency of more than 95% from 0.9 to 2.5 THz was obtained up to a incident angle as large as 70°. In this paper, a broadband THz absorber, which consists of patterned square array of doped silicon substrate covered by a layer of anti-reflective coating, is designed and analyzed. The paper is arranged
Corresponding author. E-mail address:
[email protected] (J. Wu).
https://doi.org/10.1016/j.optlastec.2019.105657 Received 23 February 2019; Received in revised form 14 June 2019; Accepted 18 June 2019 0030-3992/ © 2019 Elsevier Ltd. All rights reserved.
Optics and Laser Technology 119 (2019) 105657
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Fig. 1. Configuration of the THz absorber consisting of a square array of doped silicon covered by a layer of anti-reflective coating: (a) 3D view and (b) cross-section view. Here, d = 64 μm, w = 36 μm, h1 = 20 μm, h2 = 48 μm and h3 = 250 μm.
as follows: Firstly, The optimized structure parameters are obtained by use of rigorous coupled-wave analysis (RCWA) [26] and then the absorption properties for light under normal incidence are calculated. Next, the electromagnetic field distributions at the resonant frequencies are illustrated to give a physical understanding of such broadband absorption effect. Furthermore, the angle sensitivity of broadband absorption performance for both TE and TM polarizations are investigated. Last, in Section 3, the influence of geometry parameters on the absorption performance is investigated and some considerations about real fabrication are presented. 2. Design and results Fig. 1 illustrates the structure of the broadband THz absorber, which consists of a continuous doped silicon slab and a square array of doped silicon particles covered by a dielectric anti-reflective coating. The absorber is assumed to be fabricated on a silica (SiO2) substrate. The lattice constant is denoted by d. The thickness of the doped silicon particles is h2 and its side lengths along the different axis are both w. The thickness of anti-reflective coating, doped silicon slab are h1 and h3, respectively. The refractive index of the dielectric anti-reflective coating (SiO2) is 1.45. The permittivity of doped silicon is given by Drude model [22]:
ε = ε∞ −
Fig. 2. Absorption spectra of broadband absorber for normally incident light.
larger frequencies. In comparison, the absorption of the proposed absorber is higher than that of the referenced planar structure in nearly the entire frequency range, which demonstrates the excellent absorption performance of the proposed absorber. To disclose the broadband absorption mechanism of such THz absorber, the electromagnetic field distributions at y = 0 plane for the three resonant frequencies are shown in Fig. 3, where they are calculated through their harmonic coefficients obtained by the RCWA and the constitutive relations in real space [26,27]. In these figures, the origin of the z-axis is located at the bottom surface of the doped silicon slab. For the first absorption peak, there is large electric field enhancement in the air gap between neighboring silicon particles, which leads to a large energy dissipated by the boundary silicon particles enclosing the air gap. The enhanced absorption can be attributed to the cavity mode resonance. The magnetic field intensity of |Hx|2 is enhanced in silicon particle array and the anti-reflective coating, while |Hz|2 is large at the edges of the silicon particle array. For the higher two frequencies, the electric field is strongly enhanced and concentrated in the silicon particle array, especially for the third resonant frequency. Thus, most of the light is absorbed by the silicon particle array and the enhanced absorption results from the guided mode resonance of silicon particle array. For the second and the third peak, magnetic field intensity |Hx|2 is also concentrated in the silicon particle array. In contrast, the |Hz|2 is large at the edges of the silicon particle array for the second peak while it is mainly concentrated in the silicon particle array for the third resonant peak. For the analysis above, the absorption performance is only considered for normally incident light. However, to meet actual applications, the broadband absorption performance should be maintained for a wide range of incident angle. To characterize this problem, we show
ωp2 ω2
+ iγω
(1)
where ε∞ = 11.7 is the high frequency limiting value of the dielectric function, ωp = 2π × 5.22 THz is the plasma frequency and γ = 2π × 1.32 THz is the collision frequency [22]. All materials were assumed to be nonmagnetic (μ = μ0). The simulated absorption spectra under normally incident light is shown in Fig. 2. The absorbance is calculated using A(λ) = 1 − R (λ) − T(λ), where R(λ) and T(λ) are the reflection and transmission spectra, respectively, which are both achieved by the RCWA. Because of the symmetry of square array, the spectral responses at normal incidence for TE and TM polarizations are the same. Thus the absorption spectra are only shown for TE polarization. For comparison, a referenced thin-film planar absorber, which consists of a doped silicon slab with a thickness of 298 nm (equal to the thicknesses of doped silicon slab plus doped silicon particles shown in Fig. 1) placed on a SiO2 substrate, is also presented. As clearly shown in Fig. 2, for the case of the proposed absorber, there are three main close peaks in the spectral range, which results in a broadband polarization-insensitive absorption with absorbance above 95% in the frequency range of 0.79–4.115 THz. Besides, there are some small absorption peaks at frequency range of 4–5 THz, which makes the broadband absorption can be expanded to 2
Optics and Laser Technology 119 (2019) 105657
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Fig. 3. Electric field distributions |Ey|2 for f0 = (a) 1.01 THz, (d) 2.535 THz, and (g) 3.57 THz. Magnetic field distributions |Hx|2 for f0 = (a) 1.01 THz, (d) 2.535 THz, and (g) 3.57 THz. Magnetic field distributions |Hz|2 for f0 = (a) 1.01 THz, (d) 2.535 THz, and (g) 3.57 THz.
Fig. 4. Absorption as a function of frequency and the angle of incidence for (a) TE polarization and (b) TM polarization.
incident angle is less than 61° (70°). This demonstrates that the designed broadband THz absorber can be operated in a large incident angle range. Moreover, though the symmetry is lost with the incident angle gradually departing from normally incident, the absorber still exhibits excellent polarization insensitivity, which is beneficial for real applications.
the absorbance as a function of frequency and the incident angle for TE and TM polarizations in Fig. 4(a) and (b), respectively. In general, the broadband absorption performance gradually becomes worse with the increasing of incident angle for both polarizations. As shown in Fig. 4(a), the absorption of TE polarization remains above 90% (80%) at frequencies of 0.91–4.7 THz (0.93–5 THz) for incident angles up to 61° (70°). In contrast, for TM polarization, the absorption is higher than 90% (80%) at frequencies of 1.02–4.49 THz (1.04–5 THz) when the 3
Optics and Laser Technology 119 (2019) 105657
J. Wu, et al.
Fig. 5. Absorption spectra for different (a) d, (b) w, (c) h1, and (d) h2. The basic structure parameters are the same as in Fig. 1.
3. Discussion
absorber may contain coating on the silicon walls. However, the addition of this anti-reflective coating on the silicon walls will not lower the absorption performance, since it also provides anti-reflection effect along the silicon walls, such concept have already been employed in the design of solar cells [28].
In order to provide useful guide for the practical manufacturing, the influence of geometric parameters on the absorption spectra is investigated in this section. In Fig. 5, we show the absorption spectra as a function of lattice constant d, width of doped silicon particles w, thickness of anti-reflective coating h1 and thickness of doped silicon particles h2. The basic parameters for all plots are obtained from Fig. 1(a), unless otherwise specified. From Fig. 5(a), it is found that the absorption spectra become better at short and long frequencies with the decreasing and increasing of period, respectively. It is worth noting that the first absorption peak shows a large change while the second and the third peaks change a little with the variation of period. Fig. 5(b) indicates that as w decreases or increases, the absorption spectra become better at long and short frequencies. When the thicknesses of anti-reflective coating and doped silicon particles change, their influence on the absorption spectra is about the same as w, as clearly shown in Fig. 5(c) and (d). In general, with the geometric parameters deviating from the optimized values, the absorption spectra gradually become worse. However, the bandwidth with absorbance above 90% can be maintained with the geometric parameters confined within a large range. As a whole, the proposed broadband THz absorber possesses large parameter tolerance, which can be easily fabricated by conventional lithography technology at low cost. Though a theoretical design have been proposed and investigated in this work, the absorber can be fabricated by using conventional microfabrication techniques involving photolithography, deep-reactive ion etching and coating technology. It should be noted here that in all the above simulations, it was assumed that the anti-reflective coating is covering only array of doped silicon particle and the gaps between them, not the silicon walls, as depicted in Fig. 1. The actual fabricated
4. Conclusion In conclusion, a broadband THz absorber, which consists of patterned square array of doped silicon slab covered by a layer of antireflective coating, is designed and investigated. The absorber exhibits above 95% polarization-insensitive absorption across a frequency range of 0.79–4.115 THz for light under normal incidence. Besides, the polarization-insensitive absorption is higher than 90% (80%) at frequencies of 1.02–4.49 THz (1.04–5 THz) for the incident angle up 61° (70°). By investigating the distributions of electromagnetic field at the resonant frequencies, it is found that the broadband absorption behaviors can be attributed to the hybridization of cavity mode resonance and guided mode resonance of silicon particle array. In addition, the influence of geometry parameters on the absorption performance and some considerations about real fabrication are discussed, which demonstrates that the proposed absorber possesses large parameter tolerance and thus is beneficial for practical manufacturing. It is believed that the designed broadband THz absorber should found potential applications in the area of photonics and optoelectronics.
Acknowledgements The authors acknowledge the support of National Natural Science Foundation of China (61405217 and 11604299). 4
Optics and Laser Technology 119 (2019) 105657
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