Supporting Information: Thermo-responsive mechano-optical plasmonic nano-antenna Yunbo Liu 1,, Younggeun Park 3, and Somin Eunice Lee 1,,4,5 1 Department of Electrical & Computer Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA Biointerfaces Institute, University of Michigan, Ann Arbor, Michigan 48109, USA 3 Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA 4 Department of Biomedical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA 5 Applied Physics Program, University of Michigan, Ann Arbor, Michigan 48109, USA In this paper, the temperature-dependent mechanical displacement of the nano-antenna is represented by the parameter Rc. and predicted by classical bending theory and thus calculated using the Timoshenko formula 1 3 (Equation (1)). The equation relates the mechanical displacement with material properties and calculates the Rc of the nano-antenna under temperature elevation ΔT. In the equation, E1 and E are the Young s Moduli, α1 and α are the coefficients of thermal expansion, w1 and w are the layer width, t1 and t are the layer thicknesses for materials of the first and the second layer. 1
1 6w1w E1E t1t (t1 t)( 1 ) T Rc (w E t ) (w E t ) w w E E t t ( t 3t t 1 1 1 1 1 1 1 1 t Equation (1) Based on the calculated Rc, the corresponding structural models were established and simulated for corresponding Δλ of all nano-antenna configurations in the structural design and material design study. In the material design study, the material properties of the five different nano-antenna configurations used in figure c, including coefficient of thermal expansion and Young s Modulus, are listed in figure s1. The first layer is Au for all five configurations and the second layer are materials with distinct coefficients of thermal expansion. The materials for the second layer were selected with α spanning a range above and below the value of α1 so that the optical response of the nano-antenna associated with different mechanical displacements can be investigated. Following the conceptual verification and structural design study, forty different material configurations were simulated as part of the study aiming for material design guidelines. The corresponding coefficients of thermal expansion, Young s Moduli and the resulting Δλ for each configuration are listed in figure sb - sf. The material composition of the first layer was chosen to be metallic materials surface plasmon resonances in the visible to near-infrared wavelength range. In addition to the four representative configurations shown in figure 3a, figure sa shows the positions of all forty configurations on the interpolation map of Young s Modulus and wavelength shift. The mechano-optical plasmonic nano-antenna could be freely suspended in solution or anchored on a thin film skin using a Si support beam. To ensure that )
there was no effect of the Si support beam on the optical response, the antenna optical response was simulated with and without the Si support beam. Such a Si support beam could be fabricated by top down etching and undercutting processes. In the simulation, the Si support beam (dimensions 5 nm x 30 nm x 4 nm) is located at the center position of the nano-antenna (dimensions 160 nm x 30 nm x 7 nm). The absorption spectrum is shown in figure s3. The result suggested that the presence of the Si support beam did not affect the optical response of the nano-antenna, and therefore all calculations and simulations regarding the proposed nano-antenna were carried out without support structures. It is possible that the orientation of the nano-antenna will affect the plasmonic response depending on the polarization direction of the incident light. The nano-antenna will have the largest extinction cross-section when the electric field is fully aligned with the longitudinal axis of the device. In practice, this orientation effect can be overcome by using polarized light to obtain the temperature measurement. 1 O. Schumacher, S. Mendach, H. Welsch, A. Schramm, C. Heyn, and W. Hansen, Appl. Phys. Lett. 86, 143109 (005). V.Y. Prinz, V.A. Seleznev, A.K. Gutakovsky, A. V. Chehovskiy, V. V. Preobrazhenskii, M.A. Putyato, and T.A. Gavrilova, Phys. E Low-Dimensional Syst. Nanostructures 6, 88 (000). 3 C. Deneke, C. Müller, N.Y. Jin-Phillipp, and O.G. Schmidt, Semicond. Sci. Technol. 17, 178 (00). 3
Material α 1 E 1 α E Au/Ni 14. 79 13.4 00 Au/Pt 14. 79 9.0 168 Au/Si 14. 79.6 170 Au/Sn 14. 79 3.0 50 Au/polymer 14. 79 1000.0 Fig. s1
E 0 400 800 a λ (nm) 40 5 10 100 00 300 400 E 1 Fig. s
b Material 1 Mg α 1 E 1 Material Polymer α E λ (nm) 5.0 45 1000.0 10 10 5.0 45 1000.0 0 5.0 45 1000.0 50 10 5.0 45 1000.0 100 5 5.0 45 1000.0 00.5 5.0 45 1000.0 600 5.0 45 1000.0 800 1. 5.0 45 1000.0 1000 1 Fig. s
c Material 1 Al α 1 E 1 Material Polymer α E λ (nm). 69 997. 10 30. 69 997. 0 35. 69 997. 50 36. 69 997. 100 3. 69 997. 00 4. 69 997. 600 11. 69 997. 800 9. 69 997. 1000 6 Fig. s
d Material 1 Au α 1 E 1 Material Polymer α E λ (nm) 14. 79 989. 10 7 14. 79 989. 0 39 14. 79 989. 50 40 14. 79 989. 100 37 14. 79 989. 00 5 14. 79 989. 600 13 14. 79 989. 800 1 14. 79 989. 1000 11 Fig. s
e Material 1 Ni α 1 E 1 Material Polymer α E λ (nm) 10.0 170 988.0 10 18 10.0 170 988.0 0 3 10.0 170 988.0 50 37 10.0 170 988.0 100 38 10.0 170 988.0 00 36 10.0 170 988.0 600 4 10.0 170 988.0 800 19 10.0 170 988.0 1000 17 Fig. s
f Material 1 W α 1 E 1 Material Polymer α E λ (nm) 4.3 411 979.3 10 11 4.3 411 979.3 0 18 4.3 411 979.3 50 8 4.3 411 979.3 100 34 4.3 411 979.3 00 36 4.3 411 979.3 600 3 4.3 411 979.3 800 8 4.3 411 979.3 1000 6 Fig. s
Absorption (x 10 4 nm ) Absorption (x 10 4 nm ) 6 a 6 b 4 4 With support No support 0 0 1000 100 1400 Wavelength (nm) 1000 100 1400 Wavelength (nm) Fig. s3
Supplementary figure captions Figure s1. Complete table of material properties for nano-antenna configurations. Table listing material types, coefficients of thermal expansion, and Young s Moduli used in the simulation for figure b and figure c. Figure s. Complete interpolation map of Young s Moduli and wavelength shift. a) Forty configurations used to complete the interpolation map in figure 3b. b) - f) Tables listing the coefficients of thermal expansion and Young s Moduli of Mg, Al, Au, Ni, W and polymer used in all forty configurations. Each table represents configurations of one particular metal paired with eight different polymer materials (shown as one column of eight data points on the interpolation map in figure sa). Figure s3. Calculated absorption cross-section of the nano-antenna with and without a Si support beam. a) The calculated absorption cross-section (nm ) of the nano-antenna with a Si support beam for substrate anchoring. b) The calculated absorption cross-section (nm ) of the nano-antenna without the Si support beam. 4