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Refractive Index of Porous Silicon

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Handbook of Porous Silicon

Abstract

The optical properties of porous silicon layer described as a mixture of air, silicon, and silicon dioxide are determined by the thickness, porosity, refractive index, and the shape and size of pores. Refractive index of porous silicon is reviewed in this chapter. Full theoretical solutions can be provided by different effective medium approximation methods such as Maxwell-Garnett’s, Looyenga’s, or Bruggeman’s. In the case of semiempirical approaches, the refractive indices are measured using spectroscopic ellipsometry, and then, the model parameters, such as the layer thickness and calculated effective dielectric function, are adjusted to fit the spectra. Various methods based on optical transmission and reflection measurements are used to calculate the refractive index data for both fresh and oxidized porous silicon using the envelope, Maxwell-Garnett, and Goodman method. The coherent transfer matrix technique and Heavens theory were used to determine the complex refractive index of porous silicon for the reflectance of an absorbing layer on an absorbing substrate. An ab initio quantum mechanical study of the effects of oxidation process in porous silicon using an interconnected supercell structure and its complex refractive index was compared with experimental data obtained from spectroscopic ellipsometry. The spectroscopic ellipsometry evaluation of a porous silicon multilayer was reported for the preparation of porous silicon multilayer stacks. The effects of oxidation on the Bragg reflector parameters and the variations in the refractive index and thickness after oxidation were reported.

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References

  • Arenas MC, Hu H, Nava R, Del Río JA (2010) Determination of the complex refractive index of porous silicon layers on crystalline silicon substrates. Int J Mod Phys B 24:4835–4850

    Article  CAS  Google Scholar 

  • Arrand HF (1997) Optical waveguides and components based on porous silicon. University of Nottingham, Nottingham, pp 63–66

    Google Scholar 

  • Aspnes DE, Studna AA (1983) Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV. Phys Rev B 27:985–1009

    Article  CAS  Google Scholar 

  • Astrova EV, Tolmachev VA (2000) Effective refractive index and composition of oxidized porous silicon films. Mater Sci Eng B 69-70:142–148

    Article  Google Scholar 

  • Astrova EV, Voronkov VB, Remenyuk AD, Shuman VB, Tolmachev VA (1999) Variation of the parameters and composition of thin films of porous silicon as a result of oxidation: ellipsometric studies. Semiconductors 33:1149–1155

    Article  CAS  Google Scholar 

  • Bazaru T, Vlad VI, Petris A, Miu M (2010) Optical linear and third-order nonlinear properties of nano-porous Si. J Optoelectron Adv M 12:43–47

    CAS  Google Scholar 

  • Berger MG, Arens-Fisher R, Thönissen M, Krüger M, Billat S, Lüth H, Hilbrich S, Theiss W, Grosse P (1997) Dielectric filters made of PS: advanced performance by oxidation and new layer structures. Thin Solid Films 297:237–240

    Article  CAS  Google Scholar 

  • Bisi O, Ossicini S, Pavesi L (2000) Porous silicon: a quantum sponge structure for silicon based optoelectronics. Surf Sci Rep 38:1–126

    Article  CAS  Google Scholar 

  • Bruggeman DAG (1935) Dielectric constant and conductivity of mixtures of isotropic materials. Ann Phys 24:636–679

    Article  CAS  Google Scholar 

  • Charrier J, Pirasteh P, Boucher YG, Gadonna M (2012) Bragg reflector formed on oxidised porous silicon. Micro Nano Lett 7:105–108

    Article  CAS  Google Scholar 

  • Cisneros R, Ramírez C, Wang C (2007) Ellipsometry and ab initio approaches to the refractive index of porous silicon. J Phys Condens Matter 19:395010

    Article  CAS  Google Scholar 

  • Garnett JCM (1904) Colours in metal glasses and in metallic films. Philos Trans R Soc Lond Ser A 203:385–420

    Article  CAS  Google Scholar 

  • He J, Cada M (1992) Combined distributed feedback and Fabry-Perot structures with a phase-matching layer for optical bistable devices. Appl Phys Lett 61:2150–2152

    Article  Google Scholar 

  • Jackson JD (1975) Classical electrodynamics. Wiley, New York

    Google Scholar 

  • Jellison GE Jr, Modine FA (1994) Optical functions of silicon at elevated temperatures. J Appl Phys 76:3758–3761

    Article  CAS  Google Scholar 

  • Khardani M, Bouaïcha M, Bessaïs B (2007) Bruggeman effective medium approach for modelling optical properties of porous silicon: comparison with experiment. Phys Status Solidi C 4:1986–1990

    Article  CAS  Google Scholar 

  • Krzyżanowska H, Kulik M, Żuk J (1999) Ellipsometric study of refractive index anisotropy in porous silicon. J Lumin 80:183–186

    Article  Google Scholar 

  • Laghla Y, Sched E (1997) Optical study of undoped, B or P-doped polysilicon. Thin Solid Films 306:67–73

    Article  CAS  Google Scholar 

  • Looyenga H (1965) Dielectric constants of heterogeneous mixtures. Physica 31:401–406

    Article  CAS  Google Scholar 

  • Makara VA, Odarych VA, Vakulenko OV, Dacenko OI (1999) Ellipsometric studies of porous silicon. Thin Solid Films 342:230–237

    Article  CAS  Google Scholar 

  • Manifacier JC, Gasiot J, Fillard JP (1976) A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film. J Phys E 9:1002–1004

    Article  CAS  Google Scholar 

  • Nava R, de la Mora MB, Tagüeña-Martínez J, del Río JA (2009) Refractive index contrast in porous silicon multilayers. Phys Status Solidi C 6:1721–1724

    Article  CAS  Google Scholar 

  • Pan LK, Sun CQ, Li CM (2005) Estimating the extent of surface oxidation by measuring the porosity dependent dielectrics of oxygenated porous silicon. Appl Surf Sci 240:19–23

    Article  CAS  Google Scholar 

  • Pap AE, Kordás K, Vähäkangas J, Uusimäki A, Leppävuori S, Pilon L, Szatmári S (2006) Optical properties of porous silicon. Part III: comparison of experimental and theoretical results. Opt Mater 28:506–513

    Article  CAS  Google Scholar 

  • Shokrollahi A, Zare M, Mortezaali A, Ramezani Sani S (2012) Analysis of optical properties of porous silicon nanostructure single and gradient-porosity layers for optical applications. J Appl Phys 112:053506

    Article  CAS  Google Scholar 

  • Snow PA, Squire EK, Russell PSJ, Canham LT (1999) Vapor sensing using the optical properties of porous silicon Bragg mirrors. J Appl Phys 86:1781–1784

    Article  CAS  Google Scholar 

  • Strashnikova MI (2002) On measurements of the refractive index dispersion in porous silicon. Opt Spectrosc 93:132–135

    Article  CAS  Google Scholar 

  • Theiss W (1997) Optical properties of porous silicon. Surf Sci Rep 29:91–192

    Article  CAS  Google Scholar 

  • Theiss W, Hilbrich S (1997) Refractive index of porous silicon. In: Canham L (ed) Properties of porous silicon. Institution of Engineering and Technology, London, pp 223–228

    Google Scholar 

  • Theiss W, Henkel S, Arntzen M (1995) Connecting microscopic and macroscopic properties of porous media: choosing appropriate effective medium concepts. Thin Solid Films 255:177–180

    Article  CAS  Google Scholar 

  • Torres-Costa V, Martín-Palma RJ, Martínez-Duart JM (2004) Optical constants of porous silicon films and multilayers determined by genetic algorithms. J Appl Phys 96:4197–4203

    Article  CAS  Google Scholar 

  • Volk J, Fried M, Polgár O, Bársony I (2003) Optimisation of porous silicon based passive optical elements by means of spectroscopic ellipsometry. Phys Status Solidi A 197:208–211

    Article  CAS  Google Scholar 

  • Wolf A, Terheiden B, Brendel R (2008) Light scattering and diffuse light propagation in sintered porous silicon. J Appl Phys 104:033106

    Article  CAS  Google Scholar 

  • Zettner J, Thönissen M, Hierl T, Brendel R, Schulz M (1998) Novel porous silicon backside light reflector for thin silicon solar cells. Prog Photovolt 6:423–432

    Article  CAS  Google Scholar 

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Correspondence to Honglae Sohn .

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Sohn, H. (2018). Refractive Index of Porous Silicon. In: Canham, L. (eds) Handbook of Porous Silicon. Springer, Cham. https://doi.org/10.1007/978-3-319-71381-6_25

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