6.2 Simulation results
6.2.1 Simulation results of SRR
-1 1 2 2
cos (2t'[1-(r -t' )]) 2πm
Re(n)= Re ( )+
kd kd
± , m= integer (6.6)
6.2 Simulation results
6.2.1 Simulation results of SRR
The simulation results of SRR with different azimuths of light are presented in Figure 6-3. The definition of “Symmetry” means E field parallel to patterns of SRR and also parallel to symmetrical axis of SRR (shown as Figure 6-2), while “Asymmetry” means E field parallel to patterns of SRR and is orthogonal to symmetrical axis of SRR (shown as Figure 6-1). For simulations of SRR, H field was set normal to SRR, while E field and K were parallel to SRR.
Port-1 was the excitation port to link the light source and port-2 was detection port. All E.M waves set as plane waves and boundary condition were maximum and minimum of x-plane
=open, maximum and minimum of y-plane = Et=0, maximum and minimum of z-plane = Ht=0. 4 SRR’s cells were plotted for calculus. Thickness of copper was 50nm and silicon substrate was 200nm thick for setting up the simulation parameters.
E
H K
Figure 6-1 Diagram of E, H and K of asymmetrical incidence of SRR
E
H K
Figure 6-2 Diagram of E, H and K of symmetrical incidence of SRR
600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 -80
-60 -40 -20 0 20
S2,1 (dB)
cm-1
symmetry asymmetry
Figure 6-3 Simulation results of symmetrical and asymmetrical incidence of SRR
The derived permeability for different azimuths of SRR (i.e. symmetric or asymmetrical experimental geometries of SRR) are shown in Figures 6-4.and 6-5.
THz
Figure 6-4 Permeability of symmetrical incidence of SRR
THz
Figure 6-5 Permeability of asymmetrical incidence of SRR
From above results of simulation, transmission dips at S2,1 at k=768cm-1 (f=23.04 THz) and k=838cm-1(f=25.14THz) were observed for asymmetrical E field of SRR (i.e.
corresponding to the type I arrangement of SRR), and at k=842cm-1(f=25.26THz) for symmetrical E field of SRR (i.e. the type II arrangement of SRR).
In fact, Figures 6-4 and 6-5 are the conversion of transmission and reflection to permeability of two type arrangement of SRR. From the figures, both two types of SRR are shown to have the effect of negative permeability at a frequency range of approximately 23~26THz, i.e., k = 766.7 – 866.7 cm-1that was in consistency with the experimental results.
Therefore, although the model structure for simulations was simpler, it still proved a quick and efficient mean for estimate. Simulations also explored that there were deeper and wider dips in the case of symmetrical E field of SRR, compared the results obtained for asymmetrical E field of SRR. This phenomenon was opposite to the report in ref [42], but it is a clear evidence that there is negative permeability in this Cu SRR patterns array in the mid-IR range.
Chapter 7
Conclusion
Meta-materials were studied in this thesis work, because their interesting “negative”
optical properties. Three types of patterns, i.e., SRR, WIRE, and CMM were designed at the scale of ~200 nm, and were fabricated using a newly developed techniques, in which Cu patterns were made through Cu replacement reaction of Si backbone structures that were made by damascenes together with CMP. Optical measurements were then performed using FTIR for all three types of structure Below is a summary for all observations relating to those novel optical properties of Cu meta-materials：
1. SRR
The spectra of normalized reflectance of two arrangements of SRR showed somer interesting results for optical measurement in Figure 5-17. In type I arrangement, there are two reflection peaks at k=767.6cm-1(f=23.028THz) and k=864cm-1 (f=25.92THz), respectively. In type II arrangement, two peaks were observed at k=825.51cm-1 (f=24.77THz) and k=941.24cm-1 (f=28.24THz). At K=1250cm-1 (f=37.50THz) there exists a strong reflection feature in all spectra, which has been assigned due to interference of residual silicon dioxide layer. In chapter 6 for simulations, we have obtained simulation results：For Figure 6-1 (asymmetry, similar to type I arrangement), there were two S2,1 dips at k=838cm-1 (f=25.14THz) and k=768cm-1 (f=23.04THz). For Figure 6-2 (symmetry, similar to type II arrangement), there was only one dip at k=842.20cm-1 (f=25.27THz) (but it has wide range for
S2,1 dip.)
Therefore, the observed features could be assigned due to the effect of negative permeability in the SRR sample made of Cu metallization and silicon substrate.
2. WIRE
For WIRE patterns, only one feature at k=1018.39cm-1 (f=30.55THz) was observed in the reflection spectrum for the measurement arrangement of type I. No obvious features could be assigned to the enhanced reflectance because there exists no resonance the the spectrum for the experiment with a type II arrangement,
So, one can conclude that the effect of negative permittivity of discrete WIRE was successfully observed.
3. CMM
For the type I arrangement, there were three interesting reflectance features at k=736.79cm-1 (f=22.10THz)、k=852.51cm-1 (f=25.58THz), and k=929.66cm-1 (f=27.89THz), respectively. Noted that two of these three (i.e. k=736.79cm-1 (f=22.10THz) 、k=852.51cm-1 (f=25.58THz)) were similar to those observed from the sample with only patterns of SRR, while both have little peak shift to lower wavenumber.
For the type II arrangement, there was only one distinct feature at k=945.09cm-1 (f=28.35THz). Compared to the experiments with the type II arrangement of SRR and WIRE, only SRR showed a reflectance peak at k=941.24cm-1 (f=28.24THz), which is close to the feature of type II arrangement CMM (k=945.09cm-1 (f=28.35THz) in term of the wavenumber position). But the first peak of SRR was absent in type II CMM. Therefore, no conclusion could be made whether there was any feature due to negative refraction index in the mid-IR range.
Reference
[1] V. G. Veselago, “The electrodynamics of substance with simultaneously negative values of ε and μ”, Sov. Phys. Usp., vol. 10, pp. 509, 1968.
[2] J. B. Pendry, A. J. Holden, W. J. Stewart and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures”, Phys. Rev. Lett., vol. 76, pp. 4773, 1996.
[3] J. B. Pendry, A. J. Holden, D. J. Robbins and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena”, IEEE Trans. Microwave Theory and Tech., vol. 47, pp. 2075, 1999.
[4] D. R. Smith , W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser and S. Schultz,
“Composite medium with simultaneously negative permeability and permittivity“, Phys. Rev. Lett., vol. 84, pp. 4184, 2000.
[5] R. A. Shelby, D. R. Smithand S. Schultz, “Experimental Verification of a Negative Index of Refraction”, Science, vol. 292, pp. 77, 2001.
[6] J. B. Pendry, “Negative refraction”, Contemp. Phys., vol. 45, pp. 191, 2004.
[7] J. T. Shen and P. M. Platzmann, “Near field imaging with negative dielectric constant lenses”, Appl. Phys. Lett., vol. 80, pp. 3286, 2002.
[8] S. A. Ramamkrishna, ”Physics of negative refractive index materials”, Rep. Prog.
Phys., vol. 68, pp. 449-521, 2005.
[9] J. B. Pendry, A. J. Holden, D. J. Robbins and W. J. Steward, ”Low frequency
plasmons in thin-wire structures”, J. Phys.: Condens. Matter, vol. 10, pp. 4785, 1998.
[10] D. F. Sievenpiper, M. E. Sickmiller and E. Yablonovitch, ”3D Wire mesh photonic crystals”, Phys. Rev. Lett., vol. 76, pp. 2480, 1996.
[11] C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Kontenbah and M. H. Tanielian,
“Experimental verification and simulation of negative index of refraction using snell’s law”, Phys. Rev. Lett., vol. 90, pp. 107401,2003.
[12] K. Li, S. J. McLean, R. B. Greegor, C. G. Parazzoli and M. H. Tanielian, ” Free-space focused-beam characterization of left-handed materials”, Appl. Phys.
Lett., vol. 82, pp. 2535, 2003.
[13] T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov and X. Zhang, “Terahertz magnetic response from artificial materials”, Science, vol.
303, pp. 1494, 2004.
[14] P. Gay-Balmaz and O. J. F. Martin, “Electromagnetic resonances in individual and coupled split-ring resonators”, J. Appl. Phys., vol. 92, pp. 2929, 2002.
[15] P. Gay-Balmaz and O. J. F. Martin, ”Efficient isotropic magnetic resonators”, Appl.
Phys. Lett., vol. 81, pp. 939, 2002.
[16] M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale and J.
V. Hajnal, “Microstructured magnetic materials for RF flux guides in magnetic resonance imaging”, Science, vol. 291, pp. 849, 2001.
[17] M. C. K. Wiltshire, J. V. Hajnal, J. B. Pendry and D. J. Edwards, “RF field transmission through swiss rolls – an anisotropic magnetic metamaterial”, Opt.
Express, vol. 11, pp. 709, 2003.
[18] L. V. Panina, A. N. Grigorenko and D. P. Makhnovskiy, “Optomagnetic composite medium with conducting nanoelements”, Phys. Rev. B, vol. 66, pp. 155411, 2002.
[19] S. Hrabar , J. Bartolic, Z. Eres, “Capacitively Loaded Loop as Basic Element of Negative Permeability Meta-material”, 32nd European Microwave Conference Proceedings, pp. 327-330, Milan, Italy, 24-26 September 2002.
[20] E. Shamonina, V. A. Kalinin, K. H. Ringhofer and L. Solymar, “Magnetoinductive waves in one, two, and three dimensions”, J. Appl. Phys., vol. 92, pp. 6252, 2002.
[21] M. Shamonin, E. Shamonina, V. Kalinin and L. Solymar, “Properties of a
metamaterial element: Analytical solutions and numerical simulations for a singly split double ring”, J. Appl. Phys., vol. 95, pp. 3778, 2004.
[22] M. M. I. Saadoun and N. Engheta, “A reciprocal phase shifter using novel pseudochiral or ω medium”, Microwave Opt. Tech. Lett., vol. 5, pp. 184, 1992.
[23] C. R. Simovsky and S. He, “Frequency range and explicit expressions for negative permittivity and permeability for an isotropic medium formed by a lattice of perfectly conducting Ω particles”, Phys. Lett. A, vol. 311, pp. 254, 2003.
[24] R. Marques, F. Medina and R. Rafii-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed metamaterials”, Phys. Rev. B, vol. 65, pp. 144440, 2002.
[25] P. Gay-Balmaz and O. J. F. Martin, “Electromagnetic resonances in individual and coupled split-ring resonators”, J. Appl. Phys., vol. 92, pp. 2929, 2002.
[26] Koray Aydin, Irfan Bulu, Kaan Guven, Maria Kafesaki, Costas M Soukoulis, and Ekmel Ozbay, “Investigation of magnetic resonances for different split-ring resonator parameters and designs”, New Journal of Physics, vol. 7, pp. 168, 2005.
[27] T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov and X. Zhang, “Terahertz magnetic response from artificial materials”, Science, vol.
303, pp.1494, 2004.
[28] S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny and C. M. Soukoulis,
“Magnetic Response of Metamaterials at 100 Terahertz”, Science, vol. 306, pp. 1351, 2004.
[29] N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou and C. M. Soukoulis,
“Electric coupling to the magnetic resonance of split ring resonators”, Appl. Phys.
Lett., vol. 84, pp. 2943, 2004.
[30] R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser and S. Schultz, “Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial
”, Appl. Phys. Lett., vol. 78, pp. 489, 2001.
[31] Ekmel Ozbay, Koray Aydin, Ertugrul Cubukcu, and Mehmet Bayindir,
“Transmission and reflection properties of composite double negative metamaterials in free space“, IEEE transactions on antennas and propagation, vol. 51, no. 10, pp.
2592-2595, OCTOBER 2003.
[32] D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys.
Rev. Lett., vol. 85, no. 14, pp. 2933–2936, Oct. 2000.
[33] M. Bayindir, K. Aydin, E. Ozbay, P. Markos, and C. M. Soukoulis, “Transmission properties of composite metamaterials in free space,” Appl. Phys. Lett., vol. 81, no. 1, pp. 120–122, July 2002.
[34] R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave
transmission through a two-dimensional, isotropic, left-handed metamaterial,” Appl.
Phys. Lett., vol. 78, no. 4, pp. 489–491, Jan. 2001.
[35] R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E, vol. 64, no.056 625, pp. 1–15, Oct.
2001.
[36] D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of
permittivity and permeability of metamaterials from scattering data,” Phys. Rev. B, vol. 65, no. 195 104, May 2002.
[37] P. Markos, I. Rousochatzakis, and C. M. Soukoulis, “Transmission losses in left-handed materials,” Phys. Rev. E, vol. 66, no. 045 601, Oct. 2002.
[38] H. O. Moser,B. D. F. Casse, O. Wilhelmi, and B. T. Saw, “Terahertz response of a microfabricated rod–split-ring-resonator electromagnetic metamaterial”, phys. Rev.
let., vol. 94, pp. 063901, 2005.
[39] S. Roberts, “Optical properties of copper”, phys. rev., vol. 118, no. 6, june 15,1960.
[40] N. Katsarakis, T. Koschny, and M. Kafesaki, E. N. Economou, C. M. Soukoulis,
“Electric coupling to the magnetic resonance of split ring resonators”, App. Phys.
Let., vol. 84, pp. 2943, 2004.
[41] T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Effective medium theory of left-handed materials”, Phys. Rev. Lett., vol. 93, pp. 107402, 2004.
[42] N. Katsarakis, T. Koschny, and M. Kafesaki, E. N. Economou, C. M. Soukoulis,
“Electric coupling to the magnetic resonance of split ring resonators”, App. Phys.
Let., vol. 84, pp. 2943, 2004.
[43] S. I. Maslovsky, S. A. Tretyakov and P. A. Belov, ” Wire media with negative
effective permittivity: A quasi-static model”, Microwave Opt. Tech. Lett., vol. 35, pp.
47, 2002.
[44] H. Raether, “Excitation of plasmons and interband transitions by electrons”, Applied Optics IP, vol. 20, no. 20, pp. 3588 , 1980.
[45] Yin-Ping Lee, Ming-Shih Tsai, Ting-Chen Hu, Bau-Tong Dai, and Ming-Shiann Fenga, “Selective copper metallization by electrochemical contact displacement with amorphous silicon film”, Electrochemical and Solid-State Letters, vol. 4, no. 7, pp. C47-C49, 2001.
[46]. G. Li, E. A. Kneer, B. Vermeire, H. G. Parks, and S. Raghavan, “A comparative electrochemical study of copper deposition onto silicon from dilute and buffered hydrofluoric acids”, J. Electrochem. Soc., vol. 145, pp. 241, 1998.
[47]. B. Zhao, P. K. Vasudev, and C. H. Ting, “Selective and blanket electroless Copper deposition for ultralarge scale integration”, J. Electrochem. Soc., vol.144, pp.898,
1997.
[48]. Y. Shacham-Diamand and S. Lopatin, “Integrated electroless metallization for ULSI”, Electrochim. Acta,vol. 44, pp.3639, 1999.
[49]. G. J. Norga, M. Platero, K. A. Black, A. J. Reddy, J. Michel, and L. C. Kimerling,
“Mechanism of copper deposition on silicon from dilute hydrofluoric acid solution”, J. Electrochem. Soc., vol. 144, pp.2801,1997.
[50]. M. K. Lee, J. J. Wang, and H. D. Wang, “Deposition of copper films on silicon from cupric sulfate and hydrofluoric acid”, J. Electrochem. Soc., vol. 144, pp.1777, 1997.
[51] M. K. afesaki, T. Koschny, R. S. Penciu, T. F.Gundogdu, E. N. Economou and C M Soukoulis, “Left-handed metamaterials: detailed numerical studies of the
transmission properties”, J. Opt. A: Pure Appl. Opt., vol. 7, pp. S12–S22, 2005.
[52] D. R. Smith and S. Schultz, P. Markos and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients”, phys. rev. B, vol. 65, pp. 195104, 2002.
Curriculum Vita
Pei-Hsuan Han was born in Taipei, Taiwan, on October 10, 1983. He received the B.S. degree in Physics from National Central University (NCU) in June 2005.
He entered the Institute of Electronics, National Chiao Tung University (NCTU), in September 2005. His major study was meta-materials. He received the M.S. degree from NCTU in August 2007.