# A Distributed Terahertz Metasurface with Cold-Electron Bolometers for Cosmology Missions

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## Abstract

**:**

^{9}V/W for the current-biased series array. Simulation of the noise performance shows realization of background noise-limited performance with NEP

_{tot}< NEP

_{phot}for the optical power load P

_{0}> 15 pW. Results of numerical simulation made for the unit cell of the array are presented together with the equivalent diagram based on lumped network elements. The unit cell also was developed numerically to operate in two radiation modes.

## 1. Introduction

## 2. Numerical Model

_{FSS}(Ohm per square) of the periodic array of CEBs should be matched to the electrodynamic environment. Unlike conventional frequency selective surfaces, which do not contain active elements, a layout of the unit cell of the bolometric array must contain DC-lines for biasing and readout. It turns out that the way how DC-biasing issue is resolved determines the polarization of the incoming signal the array is sensitive to. The equivalent diagram of the array sitting on the back of a silicon lens without a back-reflector can be represented (see Figure 1) by the two impedances, vacuum impedance (Z

_{VAC}) and silicon impedance (Z

_{SI}) connected in parallel to Z

_{FSS}. They are frequency independent and correspond to the characteristic impedances of the vacuum and the silicon half-spaces. If Z

_{FSS}= 90 Ω then Pabs, the fraction of the RF-power coupled from Z

_{SI}to Z

_{FSS}, will be about 80% [14].

_{FSS}close to the optimal value 90 Ω in a wide frequency range. Gaps between the neighboring rings result in capacitive Z

_{FSS}and therefore poor matching with Z

_{SI}. The orthogonal mode #2 is sensitive to the gaps between the neighboring rings and has poor matching because of capacitive Z

_{FSS}. The unit cell has periodic boundaries in X and Y directions, while the two Floquet ports are defined at the boundaries corresponding to the maximum and the minimum of z-coordinates. These parts are touching vacuum and silicon spaces correspondingly. The reference planes of both ports are touching the array of model by a lumped element with a series connection of resistance R and capacitance C. For a real CEB, R is determined by the DC resistance of the normal absorber, while C is the capacitance of the two SIN-junctions connected in series to the absorber. The optimal capacitance C = 20 fF and the resistance R = 100 Ω for each CEB.

_{FSS}. Biasing wires between the rings can be represented by small resistance r connected in series with inductance Lw. Vertical wires seen by mode #1 have ohmic contacts to the rings, while horizontal wires seen by mode #2 with horizontal polarization have a thin SiO

_{2}layer between the wire pad and the ring in the overlapping area that creates series capacitance Cw, such that Cw >> Cr. Impedance of wire inductance Lw is shunting large impedance of Cr and reduces its reactance to the value comparable to the reactance of the ring with the four CEBs. Both equivalent networks shown in Figure 4b and representing Z

_{FSS}are equivalent to a series resonant network, which impedance around the resonant frequency is real and equal to the resistance R = 100 Ω of the CEB.

_{FSS}for both modes. As is shown, both modes can see the DC-biasing wires (the horizontal and vertical wires) and capacitive coupling between two adjacent unit cells can be tuned out at around 350 GHz for mode#1 and 750 GHz for mode#2. Series capacitance Cw shifts the absorption frequency for mode#2 and increases the absorption bandwidth (see Figure 6). Figure 6a shows absorption of the waves coming from the silicon half-space for both orthogonal modes, Absorption of arbitrary polarization Pabs can be calculated as total absorption of different waves with amplitude a and random uniform distribution of polarization angle θ. The inset in Figure 6b shows vectors P1 and P2 corresponding to polarizations of mode #1 and mode #2. Pabs can be found by taking a simple integral:

^{(1)}is absorbed power of mode#1 and Pabs

^{(2)}is absorbed power of mode#2.

## 3. Noise Analysis

_{e}and T

_{ph}are, respectively, the electron and phonon temperatures of the absorber, ${P}_{cool}(V,{T}_{e},{T}_{ph})$ is the cooling power of the SIN tunnel junction, R

_{j}is the sub-gap resistance of the tunnel junction, R

_{a}is the resistance of the absorber, $\delta P(t)$ is the incoming RF power changes and P

_{0}is absorbed signal power. We can separate Equation (2) into the time independent term,

_{SIN}, compensates for the change of signal power in the bolometer. The second term in Equation (4), ${G}_{e-ph}=5\Sigma \Lambda {T}_{e}^{4}$, is the electron-phonon thermal conductance of the absorber. From Equation (4), we can define an effective complex thermal conductance that controls the temperature response of the CEB to the incident signal power:

_{V}, is described by the voltage response to the incoming power:

_{e-ph}is the noise associated with electron–phonon interaction:

_{SIN}is the noise of the SIN tunnel junctions. The SIN noise has three components: the shot noise, 2eI/ S2I, the fluctuation of the heat flow through the tunnel junctions, and the correlation between these two processes:

^{−1/2}and pA Hz

^{−1/2}:

_{tot}= 7 × 10

^{−17}W/Hz

^{1/2}less than photon noise of the signal NEP

_{phot}= 1.1 × 10

^{−16}W/Hz

^{1/2}for the array with a series and parallel combination of CEBs at the optical power load of 20 pW. Improvement of the NEP in 2D array is achieved due to distribution of the optical power load between 400 CEBs and the decrease in the amplifier noise, as determined by the product of the amplifier current noise and the Rd (11). Dynamic resistance of the array is matched to the noise impedance of the amplifier by proper combination of two CEBs in parallel (W = 2) and 64 CEBs in series (N = 64).

_{tot}< NEP

_{phot}for R = 1 kΩ.

_{0}, are shown in Figure 7b. As we can see from Figure 7b, the noise performance for the optical power load P

_{0}> 15 pW fits the requirements of background noise limited performance with NEP

_{tot}< NEP

_{phot}. Relatively large crossover power load is related with a large number of bolometers for wideband realization and consumption of large power load typical for the balloon experiments type of LSPE.

## 4. Experimental Check

^{9}V/W [14].

## 5. Conclusions

^{9}V/W and absorbing 80% of the incident power in the frequency range 100–800 GHz. Simulation of the noise performance shows realization of background noise limited performance with NEP

_{tot}< NEP

_{phot}for the optical power load P

_{0}> 15 pW. We also optimized the structure for performance in two modes, so that we have a high level of the absorption powers for two modes.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Unit cell of the CEB array: (

**a**) 3D model with lumped elements representing CEBs [14], (

**b**) SEM-image.

**Figure 4.**(

**a**) Unit cell layout for dual mode sensing. (

**b**) Equivalent circuits for Z

_{FSS}for two orthogonal modes of the Floquet port.

**Figure 6.**(

**a**) Pabs of mode#1 and mode#2, (

**b**) Pabs

^{arb}of the unit cell for arbitrary polarization.

**Figure 7.**(

**a**) NEP components for the 2D periodic array of cold-electron bolometers with 10 × 10 unit cells, each containing four bolometers incorporated into a ring. Electron temperature, Te, is shown for both cases referring to the right axis. Parameters: f = 350 GHz, Po = 20 pW Iamp = 5 fA/Hz

^{1/2}, Vamp = 5 nV/Hz

^{1/2}(JFET), R = 1 kΩ, Λ = 0.02 µm

^{−3}, T = 300 mK, (

**b**) dependence of the noise component and electron temperature on optical power of absorbed signal.

**Figure 9.**Experimental frequency response of the CEB-array [14].

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**MDPI and ACS Style**

Beiranvand, B.; Sobolev, A.S.; Larionov, M.Y.; Kuzmin, L.S. A Distributed Terahertz Metasurface with Cold-Electron Bolometers for Cosmology Missions. *Appl. Sci.* **2021**, *11*, 4459.
https://doi.org/10.3390/app11104459

**AMA Style**

Beiranvand B, Sobolev AS, Larionov MY, Kuzmin LS. A Distributed Terahertz Metasurface with Cold-Electron Bolometers for Cosmology Missions. *Applied Sciences*. 2021; 11(10):4459.
https://doi.org/10.3390/app11104459

**Chicago/Turabian Style**

Beiranvand, Behrokh, Alexander S. Sobolev, Michael Yu. Larionov, and Leonid S. Kuzmin. 2021. "A Distributed Terahertz Metasurface with Cold-Electron Bolometers for Cosmology Missions" *Applied Sciences* 11, no. 10: 4459.
https://doi.org/10.3390/app11104459