Procedia Chemistry Procedia Chemistry 1 (2009) 1135–1138 www.elsevier.com/locate/procedia Proceedings of the Eurosensors XXIII conference Theoretical and experimental studies of metallic grids absorption: Application to the design of a bolometer S.Ben Mbareka *, T.Barona, S.Euphrasiea, B.Cretina, P.Vairaca, R.Adamb, L.Chusseaub, J.P.Guilletb, A. Penarierb a FEMTOST, université de Franche Comté,CNRS, ENSMM, UTBM, 25044 Besançon, France b IES de Montpellier, UMR 5507, CNRSMEN, CC67, université de Montpellier II, 34095, France Abstract We present a theoretical model of metallic absorbers for electromagnetic waves. This model allows the design of any kind of structured absorber metallic films and dielectrics. The absorption theory of metallic structures was studied with aim of a room temperature bolometer design. To validate the theoretical concept, grids of size much larger than the wavelength were built and measured. Transmission, reflection and absorption results obtained at 0.3 THz are in good agreement with the model. Grids of size smaller than the wavelength were built and measured at RF frequencies. Results show the tremendous influence of grid size over wavelength in term of equivalent resistivity and absorption. Keywords: Absorption; bolometer; absorber; resistivity 1. Introduction A bolometer is a thermal detector that measures the electromagnetic radiation power by converting it into heat. The absorber with its thermal bridges is one of the key parts of the bolometer. It absorbs the incident electromagnetic radiation and transforms it into a temperature variation through ohmic effect. Metal films can be used as absorbers. However, they must be thin enough to have the best absorption [1], typically a few nanometres or even less. Such a thickness requirement is too drastic to be fulfilled and well controlled with microfabrication techniques. Like Bock et al [2], we used instead structured metallic layers for which the equivalent resistivity can be tailored at any desired value. 2. Theoretical model 2.1. Structured metal layers * Corresponding author. Tel.: +33381853978; fax: +33381853998 Email address: sofiane.benmbarek@femtost.fr 18766196/09 © 2009 Published by Elsevier B.V. Open access under CC BYNCND license. doi:10.1016/j.proche.2009.07.283 1136 S. Ben Mbarek et al. / Procedia Chemistry 1 (2009) 1135–1138 Based on the work of Hadley [3] and Hilsum [1], we developed a numerical tool to compute the absorption, reflection and transmission of a plane wave on several layers of dielectric and metal. In the model, grids are implemented as homogenous metal layers whose resistivities depend on the geometry. g 2a tg’ t σ σ eq = g σ 2a Fig.1. Representation and notation used for specifying the p Fig.2. Metallic grid dimensions and its equivalent media and incident, reflected, and transmitted waves. conductivity Like Hadley, we suppose the continuity of tangential electrical and magnetic fields. In the case of the system represented in Fig.1, the boundary conditions at the interface x=xq lead to the twin equations: e − jk q t q n q +1 n E iq = 1 + E i ( q +1) + 1 − q +1 E r ( q +1) (1) 2 nq nq e jk q t q nq +1 n E rq = 1 − E i ( q + 1) + 1 − q +1 E r ( q + 1) 2 nq nq (2) With n the refraction index, tq =xqxq1 and E the electric field. By taking Eip equals to 1, the series defined by equations (1) and (2) allow us to calculate all the electrical fields, then the transmission, reflection and absorption coefficients. 2.2. Absorption of structured metal layers The inductive grids are presented in Fig. 2. According to Ulrich [4], the electrical field is continuous across the grids and the profile of the current, localized in the skin depth δ in both side of the metal, is symmetric. Unlike Ulrich, we used a current profile which is not symmetric and follow an exponential decrease across the grid. This exponential decrease is governed by the equivalent skin depth parameter δeq. It depends of the conductivity of the metal σ and the geometry of the grid. When no diffraction effects are taken into account, and the thickness of the grid is far smaller than δeq , absorption is given by [5]: −2 t grid 4η Γ 2 1 − e δ eq δ eq σZ 0 (3) A= − 2 t grid − t grid t grid δ eq δ eq cos 1+ e − 2e δ eq With Γ: the electrical field reflective coefficient, η=g/2a, δeq= δ* η1/2 and Z0 the vacuum impedance. To validate this model, 2D numerical simulations were done with COMSOL MULTIPHYSIC’s RF module (Fig. 3). Boundary conditions were used to have a plane wave. This figure shows the concordance between our model and the simulation results. S. Ben Mbarek et al. / Procedia Chemistry 1 (2009) 1135–1138 1137 Fig. 3. Comparison for unsupported metal between (a): model results and (b): COMSOL MULTIPHYSIC’s . Numerical values: λ/g=100, η=10 2.3. Electrical model Our model allows the conception of the grid with ratios g/λ less than 0.01 with small errors. However, technology limits this ratio. Therefore diffraction effects must be taken into account. Furthermore, the grids are usually supported by a dielectric which also must be included. We used Ulrich’s electrical line equivalent model [4]: electrical lines before and after a lumped impedance representing the grid. This impedance is constituted of an inductance in parallel with a capacity, and a resistor R in series. The dielectric is modeled as a line of characteristic impedance Zn=Z0/n and a length d. R represents the absorption and is obtained from equation (4) and the relation A = 2 R Γ in the case of 2 metallic grid alone: −2 t grid 2η δ 1 − e eq δ eq σZ 0 R= − 2 t grid − t grid (4) δ eq δ eq t grid 1+ e − 2e cos δ eq 3. Terahertz grids characterization: To validate our theoretical concept, grids of size much larger than the wavelength were built and measured. Measurements were performed at 0.3 THz on various grid geometries. The test bench is composed of an electronic source and liquidHe bolometer for detection. Grids sample 2a (µm) g (µm) 1 1 20 2 1 100 3 2.5 50 4 4 200 5 10 200 6 2 200 7 2 200 8 4 200 9 20 400 Table 1: Grids parameters Fig.3: Absorption, reflection and transmission measured and predicted at 0.3 THz for different grid dimensions 1138 S. Ben Mbarek et al. / Procedia Chemistry 1 (2009) 1135–1138 All grids were built on glass substrate using clean room techniques. The metal used is titanium with a thickness of 160nm. Grid parameters are summarized in table1. Overall grid dimensions far larger than the wavelength were used here (1.5x1.5 cm2). Results are in good agreement with the expected model data (Fig.3). Discrepancies are attributed to bad knowledge of the substrate’s thickness. RF grids characterization: Grids smaller than the wavelength are useful to improve spatial resolution. They were investigated at RF frequencies using a specially designed TEM guide involving two parallel conductors whose gap and lateral dimensions are chosen to have 50Ohm impedance. Experiments were conducted with 1cm and 2cm grid sizes measured at 900 MHz (Fig.4), 1.5 GHz, 1.8 GHz and 10 GHz. They show an important variation of the equivalent resistivity as a function of the ratio between the grid size (Gs) and the wavelength (λ) (Fig.5). Fig.4: Measures at 900 MHz of 1cm grids size (dots) Fig.5: Variation of equivalent resistivity with the ratio between grid size Extraction of an equivalent resistivity (lines) and wavelength at RF frequencies: ρ0 : measured resistivity of chrome film (100nm thickness) Conclusion The conception of structured absorbers is usually based on previous experimentations. In this paper, we proposed a theoretical study and experimentally validated that allows design all configurations of structured and unstructured metallic absorbers. Metallic grids were made using techniques of clean room and were characterized at RF and terahertz frequencies. THz characterizations show a good agreement with our model. New grids on better controlled substrate should soon give better results. First experiments with grids smaller than the wavelength were conducted at RF frequencies. They give a first insight of how the equivalent resistivity evolves with the ratio between grid size and the wavelength. Acknowledgement: The authors thank the French ANR program and region of FrancheComté for supporting this project References: 1. C. Hilsum,”Infrared Absorption of Thin Metal Films”, J. Opt. Soc. Am. Vol.44, p. 188191, 1954. 2. J. J. Bock, D. Chen, P. D. Mauskopf and A. E. Lange,“A Novel Bolometer for Infrared And MillimeterWave Astrophysics“ Space Science Reviews, vol. 74, p. 229235, 1995 3. L. N. Hadley and D. M. Dennison,”Reflection and Transmission Interference filters”, J. Opt. Soc. Am., Vol. 37, p. 451465, 1947 4. R. Ulrich,”FarInfrared Propreties of Metallic Mesh and its Complementary Structure”, Infrared Physics, Vol. 7, p. 3755, 1967 5. T. Baron, S. Euphrasie, S. Ben Mbarek, P. Vairac and B. Cretin,”Design of metallic mesch absorbers for high bandwidth electromagnetic waves”, Progress In Electromagnetic Research C, Vol. 8, 135147, 2009
Enter the password to open this PDF file:











