Paper 17
Paper 17
https://doi.org/10.1007/s11468-024-02427-w
RESEARCH
Abstract
Present report focuses on the design and optical perfect absorption/reflection properties of novel plasmonic metasurface
made of square array of Si3N4 hemi-spheres on flat Si3N4 surface. The whole structure is sandwiched between flat gold layer
and top gold coating. Theoretical study using Finite Difference Time Domain (FDTD) computation shows multiple near
perfect absorptions (80–100%) with narrow line width (~ 50 nm) between 550 to 1500 nm. Four distinct absorption peaks
(or reflection dips) are observed at 1020 nm (A1), 888 nm (A2), 614 nm (A3), 740 nm (A4) which can be manipulated by
varying structural parameters such as period, hemi-sphere diameter and top gold coating thickness. These multiple absorp-
tions arise due to electric dipolar resonance, magnetic resonance, excitation of various surface plasmon modes (such as
(1,0); (2,0); (1,1)) and cavity mode, as evident from near-field analysis. With appropriate structural parameters, multiband
well resolved near perfect absorptions are achieved at desired wavelengths. The proposed metasurface is insensitive to the
polarization of excitation beam, and has relatively large launch angle tolerance (~ 20°), making it suitable for optical and
optoelectronic device integration.
Keywords Plasmonic metasurface · Si3N4 hemi-spheres in square lattice · visible-near-infrared (Vis-NIR) wavelengths ·
multiband absorber · FDTD computation
                                                                                                                             Vol.:(0123456789)
                                                                                                                                   Plasmonics
hemi-spheres array and strong multi-resonant absorption                  resonances, ωo = plasma frequency, Γ = collision frequency,
characteristics in the visible-NIR regime have not been                  ωn = resonance frequency, S = strength, εr,∞ = dielectric
investigated. Nevertheless, simpler designed structures                  constants at infinite frequency, and εr = relative dielectric
are favoured over complex geometry. Therefore, design of                 constant) [61]. The resonance details for S   i3N4 (Characteristics
simpler absorbing metasurface made of Si3N4 and study of                and Influenceve) are as follows: n = 1, ωo = 14.5808 × 1015 rad/s,
their multi-resonant absorption characteristics seem to be not           S = strength = 2.954315, Γ = 7.292 × 1 0 13 rad/s,
only attractive but also have fundamental and technological              ω1 = 14.5808 × 1015 rad/s, εr,∞ = 1 (as available in optiwave
importance. The present study focuses on the design of                   FDTD master library (OPTIWAVE is used for computation)).
plasmonic metasurface made of Si3N4 hemi-spheres array                  Excitation source is a Gaussian modulated continuous wave (for
on flat S
         i3N4 surface, and study of its optical absorption/             broad band excitation) with peak wavelength of 750 nm, time
reflection characteristics in the visible-NIR regime using               off-set of 4 × 10–15 s and half width of 1 × 10–15 s [61]. Linear-x
FDTD computation. Multiple absorption peaks between                      polarization is set for excitation beam (due to structural
500 to 1500 nm are achieved whose strengths approach                     symmetry, linear-y polarization excitation will give same results
to ~100%.                                                                as that for linear-x). For angle dependent study launch angle is
                                                                         varied from 0 to 30 degrees. Periods ( Px and P   y) of 600 nm are
                                                                         set along X − Y − directions. PBC (periodic boundary
FDTD Computation Details of the Absorptive                               conditions) along X-Y and APML (anisotropic perfectly
Metasurface                                                              matched layers) along Z direction are applied. Time step of
                                                                         5000 and appropriate mesh size (10 cells per wavelength) are
 Schematic representation (three-dimensional (3D) and two-               set [61]. To detect reflection, a monitor is placed at a distance
 dimensional (2D)) of Au coated square array of hemi-sphere              (away from the top surface) greater than Fresnel’s limit.
 plasmonic absorptive metasurface (unit cell) is shown in Fig. 1.        Similarly, transmission is detected using a monitor placed at the
The proposed metasurface consists of (from bottom side): (a) a           back side of the metasurface.
SiO2 substrate (refractive index (μ) 1.5 (fixed)) of thickness 200
 nm at the bottom (h1), (b) a 100 nm thick gold (Au) layer ( h2) on
 the supportive S   iO2 layer, (c) a 150 nm thick flat S
                                                         i3N4 (≡ SiN)   Results and Discussions
 layer (h3), (d) S
                   i3N4 hemi-sphere square array on the top of the
 flat Si3N4 layer, (e) a top gold coating (25 nm (or 50 nm)) ( h4),    Absorption Characteristics and Influence of Au
 and (f) top SiN coating (if required). A suggestive approach to         Coating and Hemi‑sphere Size
 fabricate the proposed metasurface is mentioned after the
 conclusion section (note-1). Hemi-sphere has radius Rh                 Absorption/reflection spectra of the hemi-sphere arrayed
typically in the range of 100 nm to 175 nm. Unit cell period is          metasurface are shown in the Fig. 2. Structural parameters
set to 600 nm (along X: Px = 600 nm, and along Y: Py = 600             of the metasurface are as set: period = 600 nm, h 4 = 25 nm,
 nm). Gold (Au) is considered to be Lorentz − Drude (LD)                 and hemi-sphere diameter = 200 nm, 250 nm, 300 nm and
                                       s 𝜔2o
 dispersive (εr = 𝜀r,∞ + n 𝜔2 −𝜔n2 +j𝜔Γ      , here n = number of        350 nm. Absorption spectrum (A(λ)) is obtained from the
                              ∑
                                    n     n
relation, A(λ) = 1 − R(λ). Here, T(λ) = 0 is considered due    absorption spectra of metasurface with hemi-sphere diam-
to the fact that 100 nm thick gold layer is thick enough to    eter of 200 nm, 250 nm, 300 nm and 350 nm are shown.
block the transmission. For the case of hemi-sphere diam-      For 200 nm sphere diameter, three distinct absorption peaks
eter of 200 nm, three absorption peaks are observed at 932     are observed at 895 nm (A1), 807 nm (A2) and 642 nm
nm (A1), 864 nm (A2), and 630 nm (A3) with absorption          (A3). The absorption peaks, A1 and A2 are blue-shifted
strength of 80%, 100% and 55%, respectively (Fig. 2(a)).       by 37 nm and 57 nm, respectively in comparison to the
When diameter changes to 250 nm, the absorption peaks are      absorption peak A1 and A2 for the case of 25 nm top gold
red-shifted to 963 nm, 860 nm, and 625 nm, respectively.       coating. Moreover, A1 and A2 peak absorption strengths
While absorption strengths of A1 and A2 remain same but        significantly reduce to 25% and 37% from 80 and 100%,
with lesser overlap, the A3 absorption strength increases      respectively. Absorption strength of A3 peak at 642 nm is
to 85%. Further increase in diameter (300 nm) shows more       significantly increased to 91%. Similar trend is observed
red-shifts in the peak position. The characteristic peaks      for the other cases (hemi-sphere diameter: 250 nm, 300 nm
are now observed at 996 nm, 868 nm and 630 nm. A new           and 350 nm). Absorption peak positions and strengths in
peak is appeared at 730 nm (A4) with absorption strength       all these cases are summarized in Table 1. It is noticeable
of ~ 73%. A1, A2 and A3 peak absorption strengths increase     that numbers of resonant peaks are less in this case (50 nm
to 80%, 99% and 98%. Widths of A2 and A3 peaks increase        to gold) compared thinner coating (25 nm). This is espe-
too. When diameter changes to 350 nm red-shifted resonant      cially observed for metasurface with higher hemi-sphere
peaks are observed at 1020 nm (A1), 888 nm (A2), 614 nm        diameter. In general, to achieve multiple resonances with
(A3), 740 nm (A4). A newly appeared peak at 1157 nm            stronger absorption characteristics thinner top gold coat-
shows absorption strength of ~ 40%. Absorption strengths       ing (less than 30 nm (skin depth of gold)) is more effec-
of A2, A3, A4 are > 90% and comparable to each other.          tive than thicker one. Due to thin coating, there is a chance
It is noteworthy that with higher hemi-sphere diameter,        of surface plasmon excitation on both the dielectric sides
the absorption peaks are observed to be stronger and well      of gold. Furthermore, due to thinner metal layer plasmon
resolved. To understand absorption characteristics and fab-    modes can overlap and make resonance broad. For thicker
rication tolerance, top gold thickness dependence is studied   gold coating top surface reflection will be more, and only
in details. Top gold thickness is increased from 25 to 50      SPR related to gold-air interface can be excited (without
nm keeping all other parameters unchanged. In the Fig. 3,      further top SiN coating).
                                                                                                                              Plasmonics
   Double layer top coating with Au followed by SiN is                  at 1200 nm and 1156 nm), 1052 nm (A2), 971 nm (A4)
employed to study further influence on the absorption/                  and 855 nm (A3). The respective absorption strength
reflection characteristics. On the top of the gold (25 nm)              reaches to 90% (doublet absorption strength: 100% and
layer, SiN coating is applied. Thickness is varied, as if,              92%), 92%, 92% and 100%. At 250 nm SiN coating, fur-
gold coated SiN hemi-sphere is embedded in SiN layer                    ther red-shift is seen. It is noticeable here that the dou-
(either side) (see Fig. 1: metasurface in 2D after top SiN              blet becomes broad and appeared to be single peak at
coating). Metasurface period and hemi-sphere diam-                      1240 nm with absorption strength ~ 99%. Peak at 1070
eter are kept fixed at 600 nm and 300 nm, respectively.                 nm shows absorption of about 82%. Two peaks at 975 nm
These are typically set due to the fact that distinct multi-            (absorption: 85%) and 925 nm (absorption 100%) overlap
resonant absorptions are seen in this case. The spectrum                making resonance very broad. The SiN-Au-SiN struc-
with zero (0) top SiN coating (only 25 nm top gold coat-                ture makes the resonant peak to split into symmetric and
ing case) are re-plotted in Fig. 4(a) for easy comparison.              antisymmetric modes (doublet). These peaks are closely
When 200 nm top SiN coating is applied, a significant                   separated making the resonant absorption broad. Finally,
enhancement in the absorption (> 90%) is seen, espe-                    for very thick SiN coating (300 nm thick), absorption
cially for A1 and A4 peak (Fig. 4(b)). All the absorption               peaks show reduction in absorption strength. Absorption
peaks are red-shifted to 1175 nm (a doublet (A1): peaks                 contrast reduces too.
Table 1  Resonant peak wavelength (nm) and absorption strength (% absorption) for the metasurface with 600 nm period
Hemi-sphere         Absorption peak wavelength (λ (nm)) and strength (%A)
diameter (nm)
                    A1                            A2                             A3                              A4
                    h4 = 25 nm       h4 = 50 nm   h4 = 25 nm      h4 = 50 nm     h4 = 25 nm      h4 = 50 nm      h4 = 25 nm   h4 = 50 nm
                    λ (%A)
200                 932 (80)         895 (25)     864 (100)       807 (37)       630 (55)        642 (91)        -            -
250                 963 (80)         930 (25)     860 (100)       807 (50)       625 (85)        650 (98)        -            -
300                 996 (80)         960 (25)     868 (99)        807 (68)       630 (98)        675 (90)        730 (73)     -
350                 1020 (91)        1000 (20)    888 (99)        807 (85)       614 (91)        700 (88)        740 (75)     -
Plasmonics
Table 2  Peak wavelength,        Period (nm) Hemi-sphere Resonant peak wavelength (nm)
absorption strength for                      diameter (nm) (Au coating of 25 nm + final top layer SiN coating of 200 nm)
different periods. Hemi-sphere
diameter = 300 nm (fixed)                                    A1 (%A)           A2 (%A)         A3 (%A)                       A4 (%A)
                                 600          300            1211 (90),        1050 (90)       975 (90)                      852 (100)
                                                              1158 (100)
                                                              (doublet)
                                 700          300            1263 (100)        1160 (90)       897 (100), 852 (85) (doublet) -
                                 800          300            1372 (85)         1242 (90)       961 (82), 930 (80)            859 (100)
                                                                                               (doublet)
                                 500          300            1116 (95)         1004 (95),      646 (99)                      -
                                                                                919 (80)
                                                                                (doublet)
Fig. 7  Electric (Ex) and magnetic (Hy) near-field distributions (upper   lengths are 855 nm, 972 nm, 1052 nm and 1154 nm. Various field
and lower panels) of hemi-spheres square arrayed metasurface excited        components are as labelled in the Figure. Scale bars represent relative
by linear-x polarized light. Upper panel: excitation wavelengths are        field strengths
632 nm, 732 nm, 866 nm and 997 nm. Lower panel: excitation wave-
Absorption/Reflection Characteristics:                                      absorption peak wavelengths. For the first case, there are
Near‑field Analysis                                                         four strong absorption peaks at 632 nm, 732 nm, 866 nm,
                                                                            997 nm, while, in the second case, peaks are at 855 nm, 972
Near-field distribution is studied to unveil mechanism of                   nm, 1052 nm, 1154 nm. At lower wavelengths the electric
multi-resonant absorption characteristics observed for the                  near-fields (Ex, X–Z plane) are predominately confined at
hemi-spheres arrayed metasurface. Two cases are consid-                     the gold-air interface of the hemi-sphere dome as shown in
ered: (a) top gold coating = 25 nm, and (b) top gold coating                the upper panel of Fig. 7. Field confinement is also seen
(25 nm thick) followed by SiN coating (200 nm thick).                       within the S
                                                                                        i3N4 dielectric region, especially for 632 nm and
Structural period is fixed at 600 nm, and hemi-sphere diam-                 866 nm excitations. At 997 nm excitation, entire field is
eter is set to 300 nm. Single wavelength excitation is carried              confined within the S  i3N4 region under hemi-sphere dome.
out for both the cases (normal incidence and linear-x polar-                Magnetic near-field (Hy) is confined weakly except for 997
ized light). Wavelengths are set according to resonant                      nm excitation (upper panel: lower row). The near-field
                                                                                                                                 Plasmonics
 confinement is caused by the electric dipole resonance with           strength of ~ 80–100% and narrow line width of ~ 50 nm.
 effective resonating wavelength, λres = 2μLeff = 600 nm.              Distinct absorption peak position and strength can be
 Here, μ = refractive index of air, Leff = dipolar length = diam-     manipulated by varying structural parameters, such as,
 eter of the hemi-sphere. However, plasmonic excitation                period, hemi-sphere diameter and top gold coating thick-
 (grating coupling: square array of hemi-sphere) at the                ness. These multiple absorptions arise due to electric dipo-
Si3N4-gold interface can not be ruled out completely. For             lar resonance, magnetic resonance, excitation of various
 plasmon assisted absorption signature, we need to calculate           surface plasmon modes (such as (1,0); (2,0); (1,1)) and
 resonating wavelength
                     � 𝜀which   can be estimated from the rela-        cavity mode, as evident from near-field analysis. With
 tion, 𝜆res = √ 2 2 𝜀 +𝜀 , where, εd, εm are dielectric per-
                P        d 𝜀m
                                                                       appropriate structural parameters, well resolved near perfect
               m +n
                                                                       absorption peaks can be obtained at desired range. Moreo-
                         d   m
35. Li X, Tang S, Ding F, Zhong S, Yang Y, Jiang T, Zhou J (2019)              Conf Promising Electronic Technologies (ICPET). IEEE Xplore
    Switchable multifunctional terahertz metasurfaces employing                2021:108–111. https://doi.org/10.1109/ICPET51420.2020.00029
    vanadium dioxide. Sci Rep 9:5454                                     54.   An L, Ali ST, Sondergarrd T, Norgaard J, Tsao YC, Pedersen
36. Song Z, Zhang J (2020) Achieving broadband absorption and                  K (2015) Optimization of TiAlN/TiAlON/Si3N4 solar absorber
    polarization conversion with a vanadium dioxide metasurface                coatings. Sol Energy 118:410–418
    in the same terahertz frequencies. Opt Exp 28:12487–12497            55.   Zhao X, Chen C, Li A, Duan G, Zhang X (2019) Implementing
37. He J, Zhang M, Shu S, Yan Y, Wang M (2020) V           O 2 based          infrared metamaterial perfect absorbers using dispersive dielec-
    dynamic tunable absorber and its application in switchable                 tric spacers. Opt Express 27:1727–1739
    control and real-time color display in the visible region. Opt       56.   Wang Y, Li X, Wu S, Hu C, Liu Y (2024) Design of metamate-
    Exp 28:37590–37599                                                         rial perfect absorbers in the long-wave infrared region. Phys
38. Song Z, Chen A, Zhang J (2020) Terahertz switching between                 Chem Chem Phys 26:551–557
    broadband absorption and narrowband absorption. Opt Exp              57.   Bauters JF, Heck MJR, John D, Dai D, Tien M-C, Barton JS,
    28:2037–2044                                                               Leinse A, Heideman RG, Blumenthal DJ, Bowers JE (2011)
39. Sun M, Taha M, Walia S, Bhaskaran M, Sriram S, Shieh W,                    Ultra-low-loss high-aspect-ratio Si3N4 waveguides. Opt
    Unnithan RR (2018) A photonic switch based on a hybrid com-                Express 19:3163
    bination of metallic nanoholes and phase-change vanadium             58.   Krückel CJ, Fülöp A, Ye Z, Andrekson PA, Torres-Company V
    dioxide. Sci Rep 8:11106                                                   (2017) Optical bandgap engineering in nonlinear silicon nitride
40. Mandal P, Rao ChN (2017) Period- and cavity-depth-dependent                waveguides. Opt Express 25:15370
    plasmonic metamaterial perfect absorber at visible frequency:        59.   Sabaruddin NR, Tan YM, Chao C-TC, Kooh MRR, Chau Y-FC
    design rule. J Nanophotonics 11:036003                                     (2024) High Sensitivity of Metasurface-Based Five-Band
41. Jiang J, Xu Y, Li Y, Ren L, Chen F, Cheng S, Yang W, Ma C,                 Terahertz Absorber. Plasmonics 19:481–493
    Wang Z, Zhou X (2022) Triple-band perfect absorber based on          60.   Chao C-TC, Kooh MRR, Lim CM, Thotagamuge R, Mahadi
    the gold-Al2O3-grating structure in visible and near-infrared              AH, Chau Y-FC (2023) Visible-Range Multiple-Channel
    wavelength range. Opt Quant Electron 54:43                                 Metal-Shell Rod-Shaped Narrowband Plasmonic Metamate-
42. Pech-May NW, Lauster T, Retsch M (2021) Design of Mul-                     rial Absorber for Refractive Index and Temperature Sensing.
    timodal Absorption in the Mid-IR: A Metal Dielectric Metal                 Micromachines 14:340
    Approach. ACS Appl Mater Interfaces 13:1921–1929                     61.   Solanki U, Mandal P (2022) Phase sensitive VO2-metal switch-
43. Khatami SA, Rezaei P, Zamzam P (2022) Quad band metal-                     able plasmonic metasurface for thermal controlling of broad
    dielectric-metal perfect absorber to selective sensing applica-            band near-infrared absorption. Opt Quant Electron 54:794
    tion. Opt Quant Electron 54:638                                      62.   Chau Y-FC, Lim CM, Chiang C-Y, Voo NY, Idris NSM, Chai
44. Wua P, Chena Z, Jileb H, Zhangc C, Xud D, Lve L (2020)                     SU (2016) Tunable silver-shell dielectric core nano-beads array
    An infrared perfect absorber based on metal-dielectric-metal               for thin-film solar cell application. J Nanopart Res 18:88
    multi-layer films with nanocircle holes arrays. Results in Phys-     63.   Li Q, Gao J, Yang H, Liu H, Wang X, Li Z, Guo X (2017)
    ics 16:1029                                                                Tunable Plasmonic Absorber Based on Propagating and Local-
45. Mandal P (2018) Visible frequency plasmonic perfect absorber               ized Surface Plasmons Using Metal-Dielectric-Metal Structure.
    made of a thin metal layer containing cylindrical grooves. Pho-            Plasmonics 12:1037–1043
    tonics and Nanostructures-Fundamentals and Applications              64.   Zhou W, Li K, Song C, Hao P, Chi M, Yu M, Wu Y (2015)
    31:66–70                                                                   Polarization-independent and omnidirectional nearly perfect
46. Cheng Y, Zhang H, Mao XS, Gong RZ (2018) Dual-band plas-                   absorber with ultra-thin 2D subwavelength metal grating in the
    monic perfect absorber based on all-metal nanostructure for                visible region. Opt Express 23:A413–A418
    refractive index sensing application. Mater Lett 219:123–126         65.   Chau Y-FC, Chao C-TC, Chiang H-P, Lim CM, Voo NY, Mahadi
47. Yu J, Lang T, Chen H (2021) All-Metal Terahertz Metamaterial               AH (2018) Plasmonic effects in composite metal nanostructures
    Absorber and Refractive Index Sensing Performance. Photonics 8:164         for sensing applications. J Nanopart Res 20:190
48. Cheng Y, Li Z, Cheng Z (2021) Terahertz perfect absorber based       66.   Mandal P, Nandi A, Ramakrishna SA (2012) Propagating sur-
    on InSb metasurface for both temperature and refractive index              face plasmon resonances in two-dimensional patterned gold-
    sensing. Opt Mater 117:111129                                              grating templates and surface enhanced Raman scattering. J
49. Wang S, Chen F, Ji R, Hou M, Yi F, Zheng W, Zhang T, Lu W                  Appl Phys 112:044314
    (2019) Large-Area Low-Cost Dielectric Perfect Absorber by            67.   Khanna A, Subramanian AZ, Häyrinen M, Selvaraja S,
    One-Step Sputtering. Adv Optical Mater 7:1801596                           Verheyen P, Thourhout DV, Honkanen S, Lipsanen H, Baets
50. Nishiyama N, Ishikawa R, Ohfuji H, Marquardt H, Kurnosov                   R (2014) Impact of ALD grown passivation layers on silicon
    A, Taniguchi T, Kim B-N, Yoshida H, Masuno A, Bednarcik                    nitride based integrated optic devices for very-near-infrared
    J, Kulik E, Ikuhara Y, Wakai F, Irifune T (2017) Transparent               wavelengths. Opt Exp 22:5684
    polycrystalline cubic silicon nitride. Sci Rep 7:44755
51. Cuyvers S, Hermans A, Kiewiet M, Goyvaerts J, Roelkens G,            Publisher's Note Springer Nature remains neutral with regard to
    Gasse KV, Thourhout DV, Kuyken B (2022) Heterogeneous                jurisdictional claims in published maps and institutional affiliations.
    integration of Si photodiodes on silicon nitride for near-visible
    light detection. Opt Lett 47:937–940                                 Springer Nature or its licensor (e.g. a society or other partner) holds
52. Hegedüs N, Balázsi K, Balázsi C (2021) Silicon Nitride and           exclusive rights to this article under a publishing agreement with the
    Hydrogenated Silicon Nitride Thin Films: A Review of Fabrica-        author(s) or other rightsholder(s); author self-archiving of the accepted
    tion Methods and Applications. Materials 14:5658                     manuscript version of this article is solely governed by the terms of
53. Hamouche H, Shabat MM (2020) Periodic silicon nitride-               such publishing agreement and applicable law.
    metamaterials structure for enhanced solar cell efficiency. Int