Ab-initio determination of porous silicon refractive index confirmed by infrared transmittance measurements of an omnidirectional multilayer reflector
Article
First Online:
Received:
Accepted:
- 43 Downloads
Abstract
We report a multiscale design of omnidirectional Bragg mirrors based on dielectric multilayers by combining quantum mechanical and electromagnetic theories. This design begins with the calculation of electric permittivity for each layer using the density functional theory, followed by a transfer matrix study of light propagation along the multilayer reflector. The theoretical results were further validated by fabricating free-standing porous silicon multilayer films obtained through electrochemical etching of p+-type [100]-oriented crystalline Si wafers, alternating two anodic current densities. The measured infrared transmittance spectra confirm the position and width of the photonic bandgap predicted by the multiscale design.
Notes
Acknowledgements
We would like to thank Omar Novelo and Yolanda Flores for their technical assistance. This work has been partially supported by UNAM-IN106317 and CONACyT-252943. Computations were performed at Miztli of DGTIC, UNAM.
References
- 1.M. Anderson (ed.), The Book of the Mirror. An Interdisciplinary Collection Exploring the Cultural Story of the Mirror (Cambridge Scholars Publishing, Newcastle upon Tyne, 2007)Google Scholar
- 2.Y. Fink, J.N. Winn, S. Fan, C. Chen, J. Michel, J.D. Joannopoulos, E.L. Thomas, A dielectric omnidirectional reflector. Science 282, 1679 (1998)ADSCrossRefGoogle Scholar
- 3.J. Lekner, Light in periodically stratified media. J. Opt. Soc. Am. A 11, 2892 (1994)ADSCrossRefGoogle Scholar
- 4.R. Szipocs, K. Ferencz, C. Spielmann, F. Krausz, Chirped multilayer coatings for broadband dispersion control in femtosecond lasers. Opt. Lett. 19, 201 (1994)ADSCrossRefGoogle Scholar
- 5.E. Xifré-Pérez, L.F. Marsal, J. Pallarès, J. Ferré-Borrull, Porous silicon mirrors with enlarged omnidirectional band gap. J. Appl. Phys. 97, 064503 (2005)ADSCrossRefGoogle Scholar
- 6.M. Ibanescu, S.G. Johnson, M. Soljacic, J.D. Joannopoulos, Y. Fink, O. Weisberg, T.D. Engeness, S.A. Jacobs, M. Skorobogatiy, Analysis of mode structure in hollow dielectric waveguide fibers. Phys. Rev. E 67, 046608 (2003)ADSCrossRefGoogle Scholar
- 7.Y. Yao, K.-T. Lee, X. Sheng, N.A. Batara, N. Hong, J. He, L. Xu, M.M. Hussain, H.A. Atwater, N.S. Lewis, R.G. Nuzzo, J.A. Rogers, Porous nanomaterials for ultrabroadband omnidirectional anti-reflection surfaces with applications in high concentration photovoltaics. Adv. Energy Mater. 7, 1601992 (2017)CrossRefGoogle Scholar
- 8.L. Canham (ed.), Handbook of Porous Silicon (Springer, Zug, 2014)Google Scholar
- 9.J.E. Lugo, H.A. Lopez, S. Chan, P.M. Fauchet, Porous silicon multilayer structures. A photonic band gap analysis. J. Appl. Phys. 91, 4966 (2002)ADSCrossRefGoogle Scholar
- 10.E. Xifré-Pérez, L.F. Marsal, J. Ferré-Borrull, J. Pallarès, Porous silicon omnidirectional mirrors and distributed Bragg reflectors for planar waveguide applications. J. Appl. Phys. 102, 063111 (2007)ADSCrossRefGoogle Scholar
- 11.D. Ariza-Flores, L.M. Gaggero-Sager, V. Agarwal, Study of the omnidirectional photonic bandgap for dielectric mirrors based on porous silicon: effect of optical and physical thickness. Nanoscale Res. Lett. 7, 391 (2012)ADSCrossRefGoogle Scholar
- 12.D. Estrada-Wiese, J.A. del Río, R. Nava, J. Gómez-Ocampo, J. Tagüeña-Martínez, Z. Montiel-González, Staggered Padé wavelength distribution for multi-Bragg photonic mirrors. Solar Energy Mater. Solar Cells 141, 315 (2015)CrossRefGoogle Scholar
- 13.M.D. Segall, P.J.D. Lindan, M.J. Probert, C.J. Pickcard, P.J. Hasnip, S.J. Clark, M.C. Payne, First-principles simulation: ideas, illustrations and the CASTEP code. J. Phys. Condens. Matter. 14, 2717 (2002)ADSCrossRefGoogle Scholar
- 14.Y. Bonder, C. Wang, A first-principles model of birefringent porous silicon. J. Appl. Phys. 100, 044319 (2006)ADSCrossRefGoogle Scholar
- 15.T.C. Choy, Effective Medium Theory. Principles and Applications. (Oxford University Press, New York, 1999)Google Scholar
- 16.P. Yeh, Optical Waves in Layered Media (Wiley, New Jersey, 2005), p. 102Google Scholar
- 17.J.J. Saarinen, S.M. Weiss, P.M. Fauchet, J.E. Sipe, Reflectance analysis of a multilayer one-dimensional porous silicon structure: theory and experiment. J. Appl. Phys. 104, 013103 (2008)ADSCrossRefGoogle Scholar
- 18.S. Chandrasekhar, Radiative Transfer (Dover Pub. Inc., New York, 1960), p. 30Google Scholar
- 19.R. Cisneros, C. Ramírez, C. Wang, Ellipsometry and ab initio approaches to the refractive index of porous silicon. J. Phys. Condens. Matter. 19, 395010 (2007)CrossRefGoogle Scholar
- 20.P. Alfaro, A. Palavicini, C. Wang, Hydrogen: oxygen and hydroxyl on porous silicon surface: a joint density-functional perturbation theory and infrared spectroscopy approach. Thin Solid Films 571, 206 (2014)ADSCrossRefGoogle Scholar
- 21.Y.H. Ogata in Handbook of Porous Silicon, ed. by L. Canham (Springer, Zug, 2014), p. 473Google Scholar
- 22.B.C. Smith, Fundamentals of Fourier Transform Infrared Spectroscopy, 2nd edn. (CRC Press, Florida, 2011), p. 12CrossRefGoogle Scholar
- 23.E. Xifré-Pérez, L.F. Marsal, J. Ferré-Borrull, J. Pallarès, Low refractive index contrast porous silicon omnidirectional reflectors. Appl. Phys. B 95, 169 (2009)ADSCrossRefGoogle Scholar
- 24.M. Song, P. Belov, P. Kapitanova, Wireless power transfer inspired by the modern trends in electromagnetics. Appl. Phys. Rev. 4, 021102 (2017)ADSCrossRefGoogle Scholar
- 25.M.A. Kats, F. Capasso, Optical absorbers based on strong interference in ultra-thin films. Laser Photon. Rev. 10, 735 (2016)CrossRefGoogle Scholar
Copyright information
© Springer-Verlag GmbH Germany, part of Springer Nature 2018