1. Introduction

Near perfect absorbing components using metallic metamaterial has attracted wide attentions due to its potential applications in various applications in multi spectral imaging, photovoltaic and environment sensing [1–7]. Optical absorber utilizing continuous layer gap plasmon resonator (CL-GPR) has been reported to have perfect absorption in visible and infrared regime in recent years [8,16,17]. Such resonator structure consists of thin bottom metallic layer, continuous dielectric (optically thin) layer and metallic patches of different shapes to tailor absorption spectra of the structure. Also by using multiple metal strip supported by dielectric patchwork on continuous metal layer underlay is reported to efficiently route the incoming photons by their colors towards one of the two groups of antenna [2,9]. While the MIM sorting structures discussed in [2,9] efficiently route the photons by their color toward their respective antenna, it is sensitive to polarization of incident angle. Such MIM ribbon structure could only be used for TM polarization of incidence wave. Recently study has been made to design wideband infrared absorber independent to polarization of incidence radiation utilizing the square MIM patch arrays [3]. Such array has shown higher tolerance to incidence angle and polarization of incidence radiation.

Different techniques like photo-lithography, low power chemical vapor deposition (LPCVD), atomic layer deposition (ADL) are widely used for fabrication of nano and micro structures. Precision control techniques are required to realize the exact transfer of numerical design to fabricated device. However, depending on fabrication process and steps, dimensional and structural variation is generally expected in fabricated device. It is therefore important to know the critical parameter of designed device and effect of dimensional variation in device performance so as to control fabrication steps. Various study on metallic metamaterial have been reported, however these studies were focused on describing design methods for wideband and wide angle operations [1–8, 16,17]. Most of these studies describes CL-GPR resonator, on which the pattering is done only for top metallic patches. The shift in resonance wavelength between designed and fabricated device is attributed to the change in effective resonator length (top metal patchwork) [16-17]. This scenario is valid for CL-GPR as the resonance wavelength is determined by width of metallic patches. However, in MIM structures where the patterning is done for two layers (top metal patch and middle insulating core), the resonance wavelength could depend on different stack parameters (e.g. Slope and shape of edges). Previous studies has provided a way to understand the shift in resonance wavelength in metamaterial by considering effective resonator length. However, the study on shape of spectral response and how it is affected by MIM geometric variation has been lacking.

In this paper, we study the influence of dimensional variations of Metal-Insulator-Metal (MIM) stack in its spectral response. The effect of incidence angles to spectral response of metamaterial is not discussed in this paper as it has been presented in different studies [3–6,16,17]. In this study we use CMOS compatible materials, Tungsten (W) and amorphous silicon (a-Si), to tailor multi spectral absorption in $7\mu m-14\mu m$ infrared range and numerically study the influence of dimensional variation in its spectral response.

2. MIM antenna array design and fabrication errors

Dielectric-Metal interface is known to excite propagative surface plasmon polariton (P-SPP) when electromagnetic wave interacts with metallic surface under phase matching condition [10-11]. In presence of subwavelength conductive scattering center, localized surface plasmon polariton (L-SPP) could be excited, independent of angle of incidence [11]. In optical patch antenna, which consists of ground metal plate, dielectric spacer and top metal patch, as shown in Fig. 1(a) the surface plasmon polaritons (SPP) is excited in the metal-dielectric interface when incident electromagnetic wave interacts with antenna structure. The excited SPP in the interface couples to the insulator layer laterally. This induces oscillating fields inside the core creating Fabry-Perot like resonator. If the core thickness $h$ is much smaller than incident wavelength, such structure can support confined $T{M}_{100}$ mode with resonant wavelength ${\lambda }_r$ determined by width $W$ and mode effective index $n_g$ of patch antenna [12-13].

 

Fig. 1 (a) Geometry of differently sized square patch antenna array made of tungsten (W) top patch and bottom ground plate, and amorphous silicon (a-Si) insulator core of thickness defined as $h_{ins}$. (b) Top view of antenna array, where four different patch antenna with widths defined as W1, W2, W3 are arranged in square lattice. The centre-to centre distance between each patch is defined as Pl. SEM image of fabricated antenna array (c) perspective view, (d) cross section view of one of the antenna in the array

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Equation (1) can be used to determine approximate width of MIM patches for desired resonant wavelength, when the core material is specified. However it does not provide any information on influence of centre-to-centre distance between each patches and core thickness of MIM stack in an array, which are important parameters that determine the critical coupling of incidence wave to an antenna array. To tailor multi spectral absorption in mid-infrared $\left(7\mu m-14\mu m\right)$, we design periodic array of differently sized square patch antennas. The unit cell of such antenna array is shown in Fig. 1. Figure 1(a)-1(b) show the perspective and top view of unit cell respectively considered for the study. The top metal patch thickness $(h_{umet})$ of 50nm and ground plate thickness $(h_{gp})$ of 100nm were considered for study. Four different patches with individual widths $W2: 1220nm$, $W3: 1400nm$ and $W1: 1600nm$, are arranged in square lattice as shown in Fig. 1(b). The centre-to-centre distance (Pl) between the patches are considered to be 2000nm such that the resonance of individual patches are intrinsic. The a-Si spacer thickness ($h_{ins}$) of 350nm is considered for study. For simplicity this antenna array is named 3CS here on.

First we numerically study the absorption response of such antenna array using homemade Rigorous coupled wave analysis (RCWA) routine. The refractive index of tungsten is adopted from Palik’s handbook of optical constants [14], whereas constant refractive index of 3.6 is used for a-Si. The reflection (R) and transmission (T) from the antenna array are calculated using RCWA routine first and then absorption A is evaluated using A = 1-R-T. We then, fabricated in CMOS platform of LETI, Grenoble. The tilted and cross section SEM image of fabricated array are shown in Fig. 2(a) and Fig. 1(b) respectively. The fabricated antenna array is characterized using Fourier transform Infrared spectrometer (FTIR) from Bruker (IFS55). The global infrared source (silicon carbide) and mercury cadmium telluride (HgCdTe), or MCT, detector is used in the setup for infrared source and detector respectively. The source aperture of 2.4mm is used in setup, which is incident on sample through 6mm aperture. ${90}^o$ off axis parabolic mirror with 38mm parent focal length is used as the collection mirror to collect the reflected light from sample which is then detected by MCT. The reflection from the antenna array is normalized to the reflection of gold mirror. The absorption of an antenna array is then calculated using A = 1-R, where A is the absorption of an antenna array and R is the normalized reflection of antenna array.

 

Fig. 2 (a) SEM image of fabricated antenna arrays (a) perspective view, (b) cross section view of one of the antenna in the array, (c) simulated and measured absorption spectra (TE,TM) for antenna array 3CS

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Figure 2(c) shows the absorption spectra of fabricated antenna array measured for an incidence angle of ${20}^o$ along with simulated spectra without considering any dimensional variation in stack layer (ideal stack). The azimuthal angle of incidence for measurement and simulation is considered to be $0^o$. It can be seen that simulation of ideal stack cannot predict experimental behavior of antenna array with good agreement. We observed decrease in overall absorption and broadening of spectral width for fabricated device compared to simulation using ideal stack. It can be seen from Figs. 2(a)-2(b) that the fabricated patch antenna dimension varies from original design. Also the antenna face slopes are slanted and edges are rounded. The width of different stack layer varies significantly as can be seen in Fig. 2(b). This is expected in fabrication as different steps cannot be controlled with very high accuracy to produce ideal patch antenna stack with perfect corners and vertical face walls. Understanding the effect of dimensional variation on spectral response could therefore facilitate the process variation and achieve good agreement of spectral response between numerical and experimental results. In the following sections we will study different cases of dimensional variation and its influence on spectral response of MIM antenna arrays.

3. Dimensional variations of the MIM stack layer and its influence on spectral response

Exact transfer of numerical design to fabricated device can rarely be achieved. There are various parameters that can deviate from numerical design while realizing the fabricated device. Some of those parameters includes but not limited to, center-to-center distance (Pl) between the patches, core thickness ($h_{ins}$), patch size (W) roundness of patch edges and corners, Slanted face slopes, thickness of metallic layers ($h_{umet}$), and slanted top metallic layer. Center-to center distance (Pl) is one of the most important parameter for an array. It should be chosen such that patches in a unit cell array behave as an isolated antenna, the resonance of which is intrinsic one. The other parameter, core thickness (h) of MIM stack determines the critical coupling of an incidence wave to an antenna stack. For specific core thickness, the scattering cross section area and absorption cross section area of an antenna could obtain same value, at which maximum absorption of incidence wave could be achieved. Variation in these parameters during fabrication could change significantly the spectral response of an array. However, this study focuses on variation of MIM stack layers and its influence in spectral response. Therefore, we assume center-to-center distance (Pl) and core thickness ($h_{ins}$) does not vary from numerical design.

3.1 Variation in patch size (W)

For the periodic array of differently sized antennas, individual patch size (W) could be derived using relation (1). However, no information on spectral bandwidth and average absorption could be extracted from such relation. For given center-to-center distance (Pl) and core thickness ($h_{ins}$), variation in patch size could affect the mutual coupling between differently sized antennas in an array which could in turn change the spectral response of an array.

For antenna array 3CS described in previous section, we study the influence of variation in patch size in spectral response, given that other parameters remain constant. Figure 3(a) shows (again) the unit cell of antenna array 3CS with different patch sizes of $W1: 1600nm$, $W2: 1220nm$ $W3: 1400nm$ arranged in square lattice with local period $Pl:2000nm$. Figure 2(b) shows the conceptual diagram of patch size variation where where $\Delta$ is used to scale the patch size. With center-to-center distance $Pl$ fixed to $2000nm$ and core thickness $h_{ins}$ to 350nm, $\Delta$ is varied from $-10\%$ to $+10\%$. Figure 3(c) shows the absorption of antenna array $3CS$ as a function of $\Delta$ and wavelengths. It can be seen that the resonance wavelength of individual patch antenna in an array blue shifts when $\Delta <0$ and red shifts when $\Delta >0$ in accordance to relation (1).

 

Fig. 3 (a) Unit cell of periodic antenna array $3CS$, (b) Conceptual diagram showing the patch size variation of individual patch antenna in periodic array $3CS$, (c) Absorption as a function of $\Delta$ and wavelength for antenna array $3CS$, (d) Absorption as function of wavelength for different $\Delta$. The spectrum corresponds to the vertical cross cuts shown in (c).

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Broadening of absorption spectrum is observed with increase in $\Delta$, meanwhile average absorption of antenna array remains above 70%. Figure 3(d) shows the absorption spectrum as a function of wavelength for $\Delta : -5\%$, $0\%$ and $+5\%$ respectively which corresponds to the vertical cross cuts shown in Fig. 3(c). We see that even for the patch size variation as small as $\pm 5\%$ the individual resonance peak changes by $~500nm$. It is therefore, very important to reduce this variation to achieve the resonance at desired wavelengths.

3.2 Rounding of the stack edge

The fabrication techniques and process steps for square patch introduce the rounding effects, especially at the patch edges and corners. In this section we study the effect of edge rounding on spectral response of antenna arrays while keeping other parameters constant.

Rounded edge with radius R such that $2R\le W$ in the square patches could be introduced by creating composite structure consisting of five cuboids and four quarter cylinders as shown in Fig. 4(a). To study the antenna array with different edge roundness, we introduce the scaling factor $r$ which creates the cylinder whose radius is proportional to half width of the patch:

 

Fig. 4 (a) Individual structures which creates the rounded patch (b) Top view of rounded patch showing the center of cylindrical patch edge and its trajectory (c-e) top view of patch for different scaling factor $r$. (f) Absorption as a function of scaling factor $r$ and wavelengths for $3CS$, (g) absorption as a function of wavelength for various scaling factor $(r= 0, 0.5, and 1)$

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When $r=0$, we get ideal patch edge, while $r\ne 0$, we get the rounded edge with radius given by Eq. (2), whose center moves along the diagonal of the square patch as shown in Fig. 4 (b). In the extreme case when $r=1$, we get the circular patch with radius $R=\frac{W}{2}$ . Figures 4 (c)-(e) shows the top view of corner shapes for different values of $r$ . The patch edges in the antenna array $3CS$ were rounded whose radius is a fraction of its individual width as given by Eq. (2). This means, the individual patches in an array does not have same radius of roundness but have the common scaling factor $r$.

Figure 4(f) shows the absorption as a function of scaling factor $r$ and wavelength for antenna array $3CS$ for TM polarization of incidence wave. It can be seen that the wavelength of absorption peak (or resonance wavelength) of each antenna in array exhibits the common trend. As the antenna patch is gradually deformed from square into circle by increasing the radius of edge roundness, the wavelength at which antennas resonate blue shifts significantly. This blue shift of resonance wavelength on increasing the radius of roundness is attributed to the spread-out charge distribution on the edges and faces of metal interfaces [15]. It can be seen that the resonance wavelength blue shifts faster when scaling factor is higher $(r>0.5)$. Interestingly, in antenna array 3CS for specific scaling factors, overlap of resonance wavelength of two antennas in an array is observed as visible in Fig. 4(f) for $r\ge 0.7$. Therefore only two resonance absorption is observed for higher degree of edge roundness $(r\ge 0.7)$. Figure 4(g) shows the absorption as a function of wavelength for various values of scaling factor $(r= 0, 0.5, and 1)$ corresponds to absorption maps shown in Fig. 4(f). It can be seen that the edge roundness significantly affects the resonance and spectral width of patch antenna along with magnitude of absorption at resonance. To better predict the spectral response of differently sized antenna array it is therefore important to incorporate the edge roundness in numerical calculations.

3.3 Variation in the antenna stack slope

Other non-idealities that could occur during fabrication process of patch antenna are non-vertical side faces of antenna stack. Due to the etching process of metal and a-Si, the side faces are generally slanted. The slope angle relative to surface normal of ground plate depends on the etching method, etching rate and chemical used. In this section we study the effect of slope angle in spectral response of an antenna array.

For a patch antenna array we learned in previous sections that the antenna width determines the resonance wavelength. The ideal situation would be to be able to fabricate an antenna stack with same width of core material in both top metal patch interface and bottom ground plate interface. For simplicity, we would call the width of core material in the top metal patch interface, top width $\left(W_{top}\right)$ and that in ground plate interface, bottom width $\left(W_{bottom}\right)$. However, due to the non-idealities introduced by etching process, it is convenient to target either top width or bottom width of antenna stack to acquire the designed value. Many variations have to be considered to exactly model the effect of stack slope, for example the rounded edges and corners, different slope of top metal patch, index variation of core material has also to be included within the model to accurately match the experimental results. However, the effect could be studied step by step starting with simple case and then introduce more non-idealities. We study the different cases to understand the effect of slope variations.

3.3.1 Target bottom width $\left(W_{bottom}\right)$

First we consider the simple case where the bottom width is targeted to acquire designed width as shown in Fig. 5(a). Figure 5(a) shows the cross section of square patch in which shaded region is the materials that are etched during the process. The slope angle $(\theta )$ is considered relative to surface normal of ground plate at the edge of the patch as shown.

 

Fig. 5 (a) Schematic for bottom width target (b) absorption as a function of wavelength of periodic antenna width patch width W: 1400nm and period P: 2000nm (c) absorption as a function of wavelength of antenna array 3CS for different slope angles

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When the slope angle is introduced, the top width $\left(W_{top}\right)$ and top metal width $\left(W_{t-metal}\right)$ at superstrate-metal interface are smaller than bottom width $\left(W_{bottom}\right)$. These widths can be calculated as:

Figure 5(b) shows the absorption of antenna array with patch width $W: 1400nm$ arranged periodically in square lattice with array period $P: 2000nm$ for different slope angles $\left(\theta =0^o,{10}^o, {20}^o\right)$. The a-Si core height $\left( h_{ins}\right)$ and tungsten top metal thickness $\left(h_{umet}\right)$ of $350nm$ and $50nm$ were considered respectively. It can be seen that the resonance wavelength blue shifts significantly along with in decrease in absorption when the slope angle is varied from $0^o-{20}^o$. Similar trend can be seen for the antenna array $3CS$ as shown in Fig. 5 (c) as the slope angle is varied. We assume this blue shift of resonance is due to decrease in top width $( W_{top})$ of antenna array as slope angle increases.

Using relation (1) which relates the resonance wavelength with width of antenna patch, we can calculate the resonance wavelength for various slope angles. When slope angle $\left(\theta =0^o\right)$, the top width and bottom width are same, therefore

We see that the resonance of wavelength for antenna with slanted side face depends on two factors: the slope angle $(\theta )$ and the effective index ratio $\frac{n_{eff}^{\text{'}}}{n_{eff}}$.

Figure (6) shows the term inside bracket in right hand side of Eq. (9) and the ratio $\frac{n_{eff}^{\text{'}}}{n_{eff}}$ calculated for different antenna array with patch widths $W_{bottom}: 1400nm, 1500nm and 1600nm$ arranged periodically in square lattice with array period $P: 2000nm$ for various slope angles $(\theta )$. The term $\left(1-\frac{2h_{ins}\tan (\theta )}{W_{bottom}}\right)$ in Eq. (9) decreases with increase in slope angle for given bottom width of antenna stack as can be seen in Fig. 6(a). If there were no blue shift of absorption spectra then the ratio $\frac{n_{eff}^{\text{'}}}{n_{eff}}$ should increase accordingly. However, it remains almost constant (at numerical noise imprecision) when slope angle of slanted side face is increased as shown in Fig. 6(b). The black dotted line in Fig. 6 (b) shows the reference with $\frac{n_{eff}^{\text{'}}}{n_{eff}}=1$.

 

Fig. 6 (a) $\left(1-\frac{2h_{ins}\tan (\theta )}{W_{bottom}}\right)$ and (b) $\frac{n_{eff}^{\text{'}}}{n_{eff}}$ as a function of slope angle $(\theta )$ for various patch widths $(W:1400nm,1500nmand1600nm)$

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It can therefore be said that the blue shift in absorption spectra as shown in Fig. 5(b) and Fig. 5(c) is due to the decrease in top width of antenna stack when slope angle is increased. To achieve better agreement in resonance condition between the numerical design and fabricated antenna array, one should therefore target the top width $( W_{top})$ of antenna stack to acquire design value.

3.3.2 Target top width $\left(W_{top}\right)$

We now study how the spectral response of patch antenna gets affected when the top width of antenna stack is targeted to acquire designed value. Figure 7(a) shows the cross section of antenna stack in which the region shaded in green is the excess core material relative to the vertical side face. The region shade in red is the top metal which is etched during the process. We vary the stack slope angle $\left(\theta \right)$ relative to vertical side face as shown in Fig. 7(a). The slope of excess core material and etched top metal patch is considered to have same value for the analysis.

 

Fig. 7 (a) Schematic for top width target (b) absorption as a function of wavelength of periodic antenna width patch width W: 1400nm and period P: 2000nm (c) absorption as a function of wavelength of antenna array $3CS$ for different slope angles.

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For the given slope angle $\left(\theta \right)$, the bottom width $\left(W_{bottom}\right)$ is larger and the top metal width $\left(W_{t-metal}\right)$ in superstrate-metal interface is smaller than the top width $\left(W_{top}\right)$ which are given by:

Figure 7(b) shows the absorption as a function of wavelength for an antenna array with patch width $W: 1400nm$ arranged periodically in square lattice with array period $P: 2000nm$ for different slope angles $\left(\theta =0^o,{10}^o, {20}^o\right)$. The a-Si core height $\left( h_{ins}\right)$ and tungsten top metal thickness $\left(h_{umet}\right)$ were kept constant to the values considered in previous section. It can be seen that the absorption spectra red shifts when slope angle is increased. Similar trend can be seen in absorption spectra of antenna array $3CS$ as shown in Fig. 7(c), when slope angle of slanted side face is increased.

However, the absorption spectra red shifts slowly compared to blue shift due to decrease in top metal width discussed in previous section. From previous section we know that the top width of antenna stack determines the resonance wavelength. The red shift in absorption spectra as seen in Fig. 7(b) and Fig. 7(c) with fixed top width therefore should arise due to increase in effective index of the antenna array. To validate this assumption, we follow the similar approach as in previous section to find the ratio of resonance wavelengths with slanted side face $(\theta \ne 0^o)$ to that with vertical side face $\left(\theta =0^o\right)$:

Figure (8) shows the term inside bracket in right hand side of Eq. (14) and the ratio $\frac{n_{eff}^{\text{'}}}{n_{eff}}$ calculated for different antenna array with patch widths $W_{top}: 1200nm, 1300nm, 1400nm$ arranged periodically in square lattice with array period $P: 2000nm$ for various slope angles $(\theta )$. For fixed top width $\left(W_{top}\right)$ it can be seen that the term in bracket in right hind side of Eq. (14) decreases with increase in slope angle $(\theta )$ as shown in Fig. 8(a). The ratio $\frac{n_{eff}^{\text{'}}}{n_{eff}}$ calculated for antenna array with different patch widths are shown in Fig. 8(b). It can be seen that the ratio increases significantly with increase in slope angles. The simultaneous increase of ratio $\frac{n_{eff}^{\text{'}}}{n_{eff}}$ and decrease of term $1-\frac{2h_{ins}\tan (\theta )}{W_{top}+2h_{ins}\tan (\theta )}$ in Eq. (14) counteract each other and tries to keep the resonance wavelength at same position. However due to higher rate of change of ratio $\frac{n_{eff}^{\text{'}}}{n_{eff}}$ compare to term $1-\frac{2h_{ins}\tan (\theta )}{W_{top}+2h_{ins}\tan (\theta )}$ induce slight red shift of absorption spectra which is visible in Fig. 7 (b) and Fig. 7 (c).

 

Fig. 8 (a) $\left(1-\frac{2h_{ins}\tan (\theta )}{W_{top}+2h_{ins}\tan (\theta )}\right)$ and (b)$\frac{n_{eff}^{\text{'}}}{n_{eff}}$ as a function of slope angle $(\theta )$ for various patch widths $(W:1200nm,1300nm,1400nm)$

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We can therefore allow the top width to be smaller than the designed value allowing slanted side faces of antenna stack to achieve better agreement between numerically calculated absorption spectra and that of fabricated antenna array. The new top width can be calculated using Eq. (14) knowing all other parameters. However, finding new value of top width is non-trivial as the etching of material and thus the slope angles induced are purely dependent on process parameters.

3.3.3 Target top width $\left(W_{top}\right)$, different angles for etched top metal and excess core material

In the previous two cases we targeted the top width $\left(W_{top}\right)$ and bottom width $\left(W_{bottom}\right)$ to acquire the designed value and introduce the slope for side faces of the antenna stack. In both cases the slope of top metal patch were considered to have same values as the slope of core material. However, the metal patch could have different slope angle compared to the slope of core material. In this section we consider different slope angles for core material and top metal patch of antenna stack while targeting the top width to acquire designed patch width.

Figure 9(a) shows the cross section of antenna patch, in which the region shaded in green is the excess core material relative to the vertical side face. The region shaded in red is the top metal which is etched during the process. We vary the core slope angle $\left({\theta }_h\right)$ and metal slope angle $\left({\theta }_m\right)$ relative to vertical side face as shown in Fig. 9(a). Figure 9(b) shows the absorption spectra as a function of wavelength for fixed core slope $\left({\theta }_h: {20}^o\right)$ and various metal slopes $\left({\theta }_m: {40}^o,{60}^o,{80}^o\right)$ for the antenna array $3CS$ with patch widths, $W1: 1600nm$, $W2: 1220nm W3: 1400nm$ arranged periodically. The absorption spectrum of ideal antenna stack with vertical side faces $\left({\theta }_h={\theta }_m=0^o\right)$ is shown as a reference in black dotted line. The red shift of absorption spectra for non-ideal antenna stack with slopes is attributed to increase in effective index of antenna array as discussed in previous section.

 

Fig. 9 Schematic for top width target with different slope angle for core material and top metal patch (b) absorption as a function of wavelength of antenna array $3CS$ for various metal slopes $\left({\theta }_m: {40}^o,{60}^o,{80}^o\right)$ with fixed core slope $\left({\theta }_h: {20}^o\right)$ (c) metal thickness at the edge of antenna patch normalized to designed metal thickness $\left(h_{umet}\right)$ for various metal slopes $\left({\theta }_m: {20}^o,{40}^o,{60}^o,{80}^o\right)$

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It can be seen that for fixed core slope of ${20}^o$ the wavelength of peak absorption does not changes significantly, when metal slope is increased to the value as large as ${60}^o$. However for higher slope angle blue shift of absorption spectra is observed along with decrease in average absorption of the antenna array. This could be attributed to decrease in metal thickness at the edge of antenna patch as the metal slope increases. Figure 9 (c) shows the metal thickness at the edge of antenna patch normalized to design metal thickness $\left(h_{umet}\right)$ for various metal slope angles $\left({\theta }_m\right)$ as a function of spatial position $(x)$. The inset in Fig. 9(c) illustrate the parameters considered for calculating the ratio $\frac{h_{umet}^{\text{'}}}{h_{umet}}$. $h_{umet}^{\text{'}}$ is the metal thickness along the spatial position $(x)$ for which the metal is etched away and has slanted face.

We can see that for higher slope angles, the metal thickness at the edges of antenna could be significantly less than the designed value. This could decrease the effective width of the patch which in turns results in blue shift of resonance wavelength of an antenna. Moreover, the lower thickness of the top metal edge for considerable width of top metal patch could induce the transparency for longer wavelength, broadening the spectral response, as is visible in Fig. 9(b) for $\left({\theta }_m: {80}^o\right)$ .

Figure 10 shows the absorption spectra of antenna array $3CS$ for various slopes of core material $\left({\theta }_h: {10}^o,{20}^o,{40}^o\right)$ with fixed metal slope angle $\left({\theta }_m: {70}^o\right)$. The absorption spectrum of ideal antenna stack is shown as a reference in black dotted line. With increase in core angles the absorption spectrum of antenna array red shifts as visible in Fig. 10. The red shift is attributed to increase in effective index of antenna array. It can be seen that the average absorption is lower than that of ideal antenna array for all the core angles considered. Moreover, the spectral broadening can be observed for longer wavelengths. This spectral broadening can be attributed to lower thickness of top metal patch at the edges for given metal slope of ${70}^o$. Interestingly, the absorption peaks do not vary significantly for the antenna array with core slope angle of ${10}^o$ compared to ideal antenna array. This indicates that even with larger portion of metal etched at the edges of top metal patch, slope of core material could be controlled to achieve accurate agreement between the designed and experimental resonance wavelengths.

 

Fig. 10 Absorption as a function of wavelength of antenna array $3CS$ for various core slopes $\left({\theta }_h: {10}^o,{20}^o,{40}^o\right)$ with fixed metal slope $\left({\theta }_m: {70}^o\right)$

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4. Comparison of realistic antenna modeling with experimental results

In the previous section we discussed the effect of different types of dimensional variation in spectral response of antenna arrays. We also see in section 2 that the fabricated device has variation in dimensions compared to simulated values. From analysis of SEM images, we found a 1.25% increase in top patch width, while a-Si core thickness of 368nm, top metal thickness of 58nm and ground plate thickness of 105nm were determined. The stack slope of fabricated device was found to be ${\theta }_h~{15}^o$ and ${\theta }_m~{76}^o$ for core and top metal patch respectively. With experimentally extracted dimensions and using edge rounding factor $=0.5$, we simulated more realistic antenna structure.

Figure 11 shows the absorption spectra of antenna array incorporating dimensional variation along with measured spectra for TM polarization. The absorption spectrum of original design is also shown for comparison. It can be seen that the realistic optical simulation incorporating dimensional variation is in good agreement with experimental absorption spectra. Realistic simulation model does predict spectral broadening and lower absorption values compared to ideal model. We therefore stress in importance of incorporating dimensional variation in simulation model so as to better predict experimental results.

 

Fig. 11 Simulated absorption spectra incorporating dimensional variation compared to experimental data and ideal stack for antenna array 3CS.

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5. Summary

We numerically and experimentally investigated periodic array of differently sized patch antenna with CMOS compatible materials; tungsten and amorphous silicon for multi spectral absorption. We have shown that using these materials multi spectral absorption in mid infrared $7\mu m-14\mu m$ regime with efficiency as high as 80% could be achieved. We studied the influence of dimensional variation of stack layer in MIM structure and showed that the slope of MIM stack plays a vital role in determining the resonance peak. We found that the effective width of top metallic layer in stack determines the resonance condition given the stack slope angle is not large. Etching of top metallic layer around the edges during stack development process increases the stack slope therefore decreasing effective width of top metal and hence resonant wavelength of stack. We also showed that the edge roundness of stack layer affect severely the peak resonance and spectral width of absorption spectra of periodically arranged differently sized patch antenna. Overall we showed that the etching parameters for these kinds of structures have to be carefully chosen such that the better agreement between numerical and experimental spectral response could be achieved.