Ⅲ. Plasmon-enhanced Infrared Spectroscopy Based on Metamaterial Absorbers with Dielectric
4.3 Simulation and Calculation of Optical Responses
FDTD calculation and simulation were conducted using a commercial software simulator (Lumerical FDTD solutions, 2020a). The optical properties for each unit structure of the three plasmonic MA structures are calculated by applying boundary conditions with anti-symmetric along the x-direction, symmetric along the y-direction, and perfectly matched layer (PML) along the z-direction. The integrated nearfield intensities and enhanced electric nearfield profiles at only plasmonic resonance wavelength under the x-polarized plane wave were calculated. The integrated nearfield intensities are calculated by collected data from three-dimensional index and field monitors. All element values from index monitor only including conformal points by 3 nm from the gold and air boundary are processed as 1, and all others are converted as 0. The integrated nearfield intensities are calculated as the sum of product of the elements of processed indices and values of squared electric fields. The unit structure was simulated with local mesh x=y=z=1 nm, and up to 1×10-7 of auto shutoff min to optimize runtime, collected data, and precise calculations for considering 3 nm thickness of the adsorbed ODT monolayer.
The imaginary part of the dielectric constant of the ODT molecule is doubled for appearance of distinct molecular vibration peak. The unit structure is composed of the top metal and SiO2 as ‘Rectangular Polygon with Rounded Corners’ in embedded components group. Its radius of edges for top metal is 60 nm, and the radius of silicon dioxide is determined by ((60 nm / width of metal) × (width of SiO2)) under the change of the laterally undercut etch depth. The resolution of rounded corners is applied with 1000 of vertices to approximate roundness.
The baseline of measured spectra is applied by using embedded asymmetric least square smoothing in DataAnalysis group, data analysis and graphing software (commercial software, OriginPro 2020). The asymmetric factor is set to 1× 10−7 for positive peaks to specify the weight of the points above the baseline in each iteration. The smaller the threshold is, the more points above the baseline will be excluded to determine the baseline in next iteration. The threshold is set to 0.01 to determine ratio of a critical distance of point to baseline to that of positive peaks to baseline. The smoothing factor and number of iterations are set to 3.3 and 8, respectively.
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The optical system of MA as a single port resonator system is well explained by the analytic framework of the temporal coupled mode theory (TCMT) as schematically depicted in Figure 4.3.1 (a). From the TCMT analysis, absorption (A) of the optical cavity without the ODT monolayer coating (coupling rate, μ1 = μ2 = 0) is described as following equation (4.1), which show that absorption of the MA associated with the ratio of the radiation loss rate (γrad) to the absorption loss rate (γabs).3
𝐴 = 4𝛾𝑎𝑏𝑠𝛾𝑟𝑎𝑑
(𝜔 − 𝜔0)2+ (𝛾𝑎𝑏𝑠+ 𝛾𝑟𝑎𝑑)2
(4.1) Where ω0 is the plasmonic resonance frequency of the optical cavity. The coupling conditions are classified into three cases governed by the ratio of the two loss rates: critical-coupling (γrad = γabs) which accomplishes perfect (unity) absorption theoretically at the resonance frequency, under-coupling (γrad <
γabs), and over-coupling (γrad > γabs). The radiation loss rate, and absorption loss rate are primarily influenced by the geometries of the optical cavity, and constituents with its intrinsic loss tangent, respectively. In the SEIRA application based on the MAs, a strong mode amplitude and nearfield intensity are provided in the cavity, when the two loss rates are similar, enhancing the SEIRA sensing signal. As the thickness of dielectric spacer is further reduced below its optimal value which accomplishes near-perfect absorption (critical-coupling), the ratio of the loss rate (γrad / γabs) moves away from 1 (γrad / γabs < 1) due to the strong gap surface plasmon resonance induced in the structure, which places the MA in a deep under-coupling regime. In consequence, absorption of the MA is reduced, and nearfield intensity induced in the structure is also decreased, making it less efficient for SEIRA sensing applications. This limitation can be somewhat overcome when using a thick layer for the top Au nanoantenna. However, it can lead to high process costs and difficult fabrication challenges. The MA structure with vertical nanogap proposed in this research can successfully resolve this limitation and can be applied as a fascinating sensing platform that can considerably boost the molecule sensing signal.
Qualitatively, the vertical nanogap through the undercut etching of the ultrathin SiO2 spacer in the MAs leads to disturb the magnetic dipole generation inside dielectric spacer, resulting in an increase in radiation loss rate. Therefore, it can achieve high absorption and nearfield enhancement maintaining ultrathin dielectric spacer thickness, while simultaneously increasing the effective sensing area as shown in Figure 4.3.1 (b). Moreover, a strong nearfield enhancement is induced at the bottom region of edges of nanoantenna corners, as the thickness of the SiO2 spacer becomes thinner.
To verify our concept, numerical analysis through finite-difference time-domain (FDTD) simulation was conducted applying to the nanoantenna with rounded edge corners from the SEM image of the
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fabricated SEIRA devices. Figure 4.3.1 (c) shows the change in radiation loss rate (left y-axis) and the absorption loss rate (right y-axis) with change of undercut etch depth (U in Figure 4.3.1 (b)) of the MA with three different dielectric spacer thickness, which are extracted from their FDTD simulated reflection spectra. The “unetched” condition in the x-axis (undercut depth) means that the SiO2 spacer is not patterned at all as a dielectric film, and the undercut etch depth of 0 nm indicates that only the region of SiO2 layer is etched in vertical direction to the bottom metal backplane, excluding the region underneath the top cross nanoantenna. The two loss rates are extracted from TCMT analysis from the simulated reflection spectra by rising the undercut depth in the lateral direction from ‘unetched’ to 50 nm with 10 nm step. The starting points of the two loss rates are different owing to their different geometrical dimensions for three MAs. However, the FDTD simulation is shown as a general trend. As the undercut etch depth continues to be increased, the radiation loss rate also increases significantly, but in contrast, the absorption loss rate hardly changes. It can be explained by the formation of undercut in the dielectric spacer, which interferes with generation of magnetic dipole resonance inside a dielectric spacer, resulting in increasing radiation loss rate. This tendency can be more clearly identified by taking the ratio of the two loss rates (γrad / γabs) under the change in the undercut etch depth as shown in Figure 4.3.1 (d). As the undercut etch depth continues to be increased, the ratio of the two loss rates increases, and consequently, the absorption of the three MAs can be raised to 0.87 or more according to Equation (4.1). From the point of view of TMCT analysis, the three MA with similar absorption levels can be considered as optical systems similar to each other. However, in SEIRA spectroscopy, even if the three MAs have similar absorption levels, nearfield intensities interactions with fingerprint vibrations of analyte molecule are applied differently depending on their geometries. A key factor in determining the efficiency of SEIRA detection is the integrated nearfield intensities according to sensing volume occupied by the ODT monolayer. Taking the thickness of the ODT monolayer molecules into account, we calculate the integrated nearfield intensities from the exposed Au surface to the 3 nm-thick free space regions for three MAs with change of different undercut depths, as shown in Figure 4.3.1 (e). The three MA have similar absorption levels, but as the thickness of the spacer becomes thinner, a greater integrated nearfield intensities are induced and also increases linearly with raising the undercut etch depth.
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Figure 4.3.1. FDTD simulation and analysis on the physical parameters. (a) Schematic of the optical coupling system between MA cavity and vibrational modes for TCMT analysis model. (b) Schematic images of the edge portion of the MA structure with different nearfield enhancement for various vertical nanogap thicknesses and undercut depths. (c) The radiation loss rate γrad (left y-axis) and absorption loss rate γabs (right y-axis) extracted from FDTD reflection spectra of the three MAs for different undercut depths by using TCMT analysis. (d) Extracted two loss rate ratio γrad / γabs (left y-axis) and absorption (right y-axis) of the three MAs for different undercut etch depths. (e) Calculation results of the integrated nearfield intensities of the three MAs for different undercut etch depths.
The simulated reflection spectra for the undercut depth from ‘unetched’ to 50 nm with a 10 nm step for the three MAs are shown in Figure 4.3.2. As the undercut depth of dielectric spacer increases, the radiation loss rate increases to achieve high absorption.
Figure 4.3.2. Simulated reflection spectra for the MA with 10 nm (a), 15 nm (b), and 30 nm (c) vertical nanogap for different undercut etch depth from unetched to 50 nm with 10 nm step.
(d)
(c) (e)
10 nm
30 nm U=20 nm
30 nm U=50 nm
10 nm
(a)
U=20 nm
U=50 nm Near-field
enhancement ↑
(1) Nanogap=30nm, U=20nm (2) Nanogap=10nm, U=20nm
(3) Nanogap=30nm, U=50nm (4) Nanogap=10nm, U=50nm
Near-field enhancement ↑
(b)
• Sensing area ↑
• Loss rate ratio ( ) ↑
• Near-field enhancement ↑
rad/ abs
• Sensing area ↑
• Loss rate ratio ( ) ↑
• Near-field enhancement ↑
rad/ abs
MA
abs
rad
2 rad k=
S− S+
ODT
1
2
1 ODT
2
-10 0 10 20 30 40 50
0.3 0.4 0.5 0.6 0.7 0.8
0.71 0.82 0.89 0.94 0.97 0.99
Absorption
Loss Rate Ratio
Undercut Depth (nm) Nanogap 10 nm Nanogap 15 nm Nanogap 30 nm
Unetched
-10 0 10 20 30 40 50
0.5 1.0 1.5 2.0 2.5 3.0 3.5
Nanogap 10 nm Nanogap 15 nm Nanogap 30 nm
Undercut Depth (nm)
Radiation Loss Rate (THz)
Unetched
1.0
1.5 2.0 2.5 3.0 3.5 4.0
Absorption Loss Rate (THz)
-10 0 10 20 30 40 50
0 2 4 6 8 10
Integrated Nearfield Intensity (´108nm3)
Undercut Depth (nm) Nanogap 10 nm Nanogap 15 nm Nanogap 30 nm
Unetched Au
SiO2
Au
3.0 3.5 4.0 4.5 5.0
0.0 0.2 0.4 0.6 0.8 1.0
Reflection
Wavelength (m) No etch 0 nm 10 nm 20 nm 30 nm 40 nm 50 nm
(a)
3.0 3.5 4.0 4.5 5.0
0.0 0.2 0.4 0.6 0.8 1.0
Reflection
Wavelength (m) No etch 0 nm 10 nm 20 nm 30 nm 40 nm 50 nm
3.0 3.5 4.0 4.5 5.0
0.0 0.2 0.4 0.6 0.8 1.0
Reflection
Wavelength (m) No etch 0 nm 10 nm 20 nm 30 nm 40 nm 50 nm
(b) (c)
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The simulated nearfield enhancement (E / E0) for the three MA at an undercut depth of 50 nm was monitored in top view (top panel) and vertical cross-sectional view (bottom panel) at the interface between the top cross nanoantenna and the SiO2 dielectric spacer along the red dotted line of an edge of the long arm of the cross nanoantenna, as shown in Figure 4.3.3 (a-c). More than 80 strong nearfield enhancement are induced at the corner edges of the top nanoantenna in the three MAs. As the dielectric spacer thickness decreases, more uniform and higher nearfield enhancement are induced in the region of the undercut etched volume for the air gap between the top and bottom metal layers. Uniformly distributed nearfield enhancement in the vertical nanogap induces strong coupling with vibrational modes of an analyte monolayer. This implies that high sensitivity of the enhanced SEIRA signal can be obtained.
Figure 4.3.3. The FDTD simulation results for three metamaterial absorbers with an undercut depth of 50 nm. Top view (top panel) and cross-sectional view (bottom panel) of the simulated nearfield enhancement (E / E0) profiles for the MA with 10 nm (a), 15 nm (b), and 30 nm (c) vertical nanogap monitored at resonance wavelength for each structure.
To directly verify the SEIRA sensing capability, the reflection spectra was obtained through FDTD simulation for the MA structure with vertical nanogap coated with a 3 nm-thick monolayer of ODT molecules around the exposed Au surface, and the results are shown in Figure 4.3.4. Figure 4.3.4 (a-b) shows the simulated reflection spectra and reflection difference SEIRA sensing signals by an ODT monolayer, respectively. The SEIRA signals were calculated by subtracting simulated reflection spectra with the signature of molecular fingerprint vibrations from the baseline through the asymmetric least- squares smoothing (AsLSS) algorithm89 for the MA structure with 10 nm thick vertical nanogap for the
0 15 30 45 60 75 90
-300 -200 -100 0 100 200 300 X (nm) -300
Y (nm)
-200 -100 0 100 200 300
0 14 29 43 58 72 87
-600
X (nm)
-400 -200 0 200 400 600 -600
-400 -200 0 200 400 600
Y (nm)
0 100 200 300 400 -100
-200 -300 -400
X (nm) -400
-300 -200 -100 0 100 200 300 400
Y (nm)
0 13.8 27.5 41.3 55.1 68.8 82.6
-300 -200 -100 0 100 200 300 0
100 200 300 400
X (nm)
Z (nm)
0 14.2 28.4 42.5 56.7 70.9 85.1
0 13 26 39 52 64.9 77.9
-600 -400 -200 0 200 400 600 0
100 200 300 400
X (nm)
Z (nm)
0 12.8 25.6 38.4 51.2 64.1 76.9
0 100 200 300 400 -100
-200 -300 -400 100
0 200 300 400
X (nm)
Z (nm)
(a) (b) (c)
Nanogap=10nm, U=50nm Nanogap=15nm, U=50nm Nanogap=30nm, U=50nm
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different undercut etch depths of dielectric spacer. In the proposed SEIRA sensing platform based on vertical nanogap, the spectral blue-shift by lower effective refractive index and the increase in SEIRA sensing signals by the enhancement of the integrated nearfield intensities can be clearly confirmed as the undercut etch depth increases. Figure 4.3.4 (c-d) shows the simulated reflection spectra and SEIRA sensing signals (reflection difference) for three different thickness of a dielectric spacer at undercut etch depth of 50 nm, respectively. An enhanced SEIRA signals are obtained as the thickness of the dielectric spacer decreases, which is in good agreement with the tendency of the calculated values of the integrated nearfield intensities shown in Figure 4.3.1 (e).
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Figure 4.3.4. (a) FDTD simulated reflection spectra and (b) SEIRA sensing signals (reflection difference) of the ODT-coated MA with a 10 nm vertical nanogap for different undercut etch depths of dielectric spacer. The blue and orange vertical lines indicate the two vibrational absorption peaks of the ODT molecules. (c) FDTD simulated reflection spectra and (d) the SEIRA sensing signals (reflection difference) of the ODT-coated MA with 30 (top), 15 (middle), 10 nm (bottom) vertical nanogap with undercut etch depth of 50 nm.
(a) (b)
2.5 3.0 3.5 4.0 4.5 5.0 0
1 0 1 0 1 0 1 0 1
Wavelength (m) Unetched
Undercut 0 nm
Reflection
Undercut 20 nm Undercut 40 nm Undercut 50 nm
3.30 3.35 3.40 3.45 3.50 3.55 3.60 0.0
0.5 0.0 0.5 0.0 0.5 0.0 0.5 0.0 0.5
Wavelength (m) Unetched
Undercut 0 nm
Reflection Difference Undercut 20 nm
Undercut 40 nm Undercut 50 nm
(c) (d)
2.5 3.0 3.5 4.0 4.5 5.0 0.0
0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0
Wavelength (m) Nanogap 10 nm
Reflection
Nanogap 15 nm Nanogap 30 nm
3.30 3.35 3.40 3.45 3.50 3.55 3.60 0.0
0.5 0.0 0.5 0.0 0.5
Wavelength (m) Nanogap 10 nm
Reflection Difference Nanogap 15 nm
Nanogap 30 nm
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