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.
Similar content being viewed by others
References
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)
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)
J. Lekner, Light in periodically stratified media. J. Opt. Soc. Am. A 11, 2892 (1994)
R. Szipocs, K. Ferencz, C. Spielmann, F. Krausz, Chirped multilayer coatings for broadband dispersion control in femtosecond lasers. Opt. Lett. 19, 201 (1994)
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)
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)
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)
L. Canham (ed.), Handbook of Porous Silicon (Springer, Zug, 2014)
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)
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)
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)
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)
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)
Y. Bonder, C. Wang, A first-principles model of birefringent porous silicon. J. Appl. Phys. 100, 044319 (2006)
T.C. Choy, Effective Medium Theory. Principles and Applications. (Oxford University Press, New York, 1999)
P. Yeh, Optical Waves in Layered Media (Wiley, New Jersey, 2005), p. 102
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)
S. Chandrasekhar, Radiative Transfer (Dover Pub. Inc., New York, 1960), p. 30
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)
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)
Y.H. Ogata in Handbook of Porous Silicon, ed. by L. Canham (Springer, Zug, 2014), p. 473
B.C. Smith, Fundamentals of Fourier Transform Infrared Spectroscopy, 2nd edn. (CRC Press, Florida, 2011), p. 12
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)
M. Song, P. Belov, P. Kapitanova, Wireless power transfer inspired by the modern trends in electromagnetics. Appl. Phys. Rev. 4, 021102 (2017)
M.A. Kats, F. Capasso, Optical absorbers based on strong interference in ultra-thin films. Laser Photon. Rev. 10, 735 (2016)
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Palavicini, A., Wang, C. Ab-initio determination of porous silicon refractive index confirmed by infrared transmittance measurements of an omnidirectional multilayer reflector. Appl. Phys. B 124, 65 (2018). https://doi.org/10.1007/s00340-018-6938-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00340-018-6938-5