Abstract

Porous materials with nanometer-scale structure are important in a wide variety of applications including electronics, photonics, biomedicine, and chemistry. Recent interest focuses on understanding and controlling the properties of these materials. Here we demonstrate porous silicon interference filters, deposited in vacuum with a technique that enables continuous variation of the refractive index between that of bulk silicon and that of the ambient (n ∼ 3.5 to 1). Nanometer-scale oscillations in porosity were introduced with glancing angle deposition, a technique that combines oblique deposition onto a flat substrate of glass or silicon in a high vacuum with computer control of substrate tilt and rotation. Complex refractive index profiles were achieved including apodized filters, with Gaussian amplitude modulations of a sinusoidal index variation, as well as filters with index matching antireflection regions. A novel quintic antireflection coating is demonstrated where the refractive index is smoothly decreased to that of the ambient, reducing reflection over a broad range of the infrared spectrum. Optical transmission characteristics of the filters were accurately predicted with effective medium modeling coupled with a calibration performed with spectroscopic ellipsometry.

© 2003 Optical Society of America

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2002 (2)

F. Cunin, T. A. Schmedake, J. R. Link, Y. Y. Li, J. Koh, S. N. Bhatia, M. J. Sailor, “Biomolecular screening with encoded porous-silicon photonic crystals,” Nature Materials 1, 39–41 (2002).
[CrossRef]

O. Toader, S. John, “Square spiral photonic crystals: Robust architecture for microfabrication of materials with large three-dimensional photonic band gaps,” Phys. Rev. E 66, 1–18 (2002).
[CrossRef]

2001 (3)

O. Toader, S. John, “Proposed square spiral microfabrication architecture for large three-dimensional photonic band gap crystals,” Science 292, 1133–1135 (2001).
[CrossRef] [PubMed]

S. Zangooie, M. Schubert, C. Trimble, D. W. Thompson, J. A. Woollam, “Infrared ellipsometry characterization of porous silicon Bragg reflectors,” Appl. Opt. 40, 906–912 (2001).
[CrossRef]

D. A. Linkens, M. F. Abbod, J. Metcalfe, B. Nichols, “Modeling and fabrication of optical interference rugate filters,” ISA Transactions 40, 2–16 (2001).
[CrossRef]

2000 (3)

S. Cianci, J. Bland-Hawthorn, J. O’Byrne, “Rugate filters: quasars beyond z ∼ 7?,” Astron. Soc. Pac. Conf. Ser. 195, 391–397 (2000).

L. Martinu, D. Poitras, “Plasma deposition of optical films and coatings: A review,” J. Vac. Sci. Technol. A 18, 2619–2645 (2000).
[CrossRef]

R. Messier, V. C. Venugopal, P. D. Sunal, “Origin and evolution of sculptured thin films,” J. Vac. Sci. Technol. A 18, 1538–1545 (2000).
[CrossRef]

1999 (2)

K. Robbie, C. Shafail, M. J. Brett, “Thin films with nanometer-scale pillar microstructure,” J. Mater. Res. 14, 3158–3163 (1999).
[CrossRef]

P. A. Snow, E. K. Squire, P. St. J. Russell, L. T. Canham, “Vapor sensing using the optical properties of porous silicon Bragg mirrors,” J. Appl. Phys. 86, 1781–1784 (1999).
[CrossRef]

1998 (2)

1997 (4)

L. Abelmann, C. Lodder, “Oblique evaporation and surface diffusion,” Thin Solid Films 305, 1–21 (1997).
[CrossRef]

M. G. Berger, M. Arens-Fischer, M. Tonissen, M. Kruger, S. Billat, H. Luth, S. Hilbrich, W. Thieb, P. Grosse, “Dielectric filters made of PS: advanced performance by oxidation and new layer structures,” Thin Solid Films 297, 237–240 (1997).
[CrossRef]

K. Robbie, A. J. P. Hnatiw, M. J. Brett, R. I. MacDonald, N. J. McMullin, “Inhomogeneous thin film optical filters fabricated using glancing angle deposition,” Electron. Lett. 33, 1213–1214 (1997).
[CrossRef]

K. Robbie, M. J. Brett, “Sculptured thin films and glancing angle deposition: Growth mechanics and applications,” J. Vac. Sci. Technol. A 15, 1460–1465 (1997).
[CrossRef]

1996 (2)

S. Lim, S. Shih, J. G. Wager, “Design and fabrication of a double bandstop rugate filter grown by plasma-enhanced chemical vapor deposition,” Thin Solid Films 277, 144–146 (1996).
[CrossRef]

K. Robbie, M. J. Brett, A. Lakhtakia, “Chiral sculpted thin films,” Nature 384, 616–616 (1996).
[CrossRef]

1994 (1)

S. Lim, J. H. Ryu, J. F. Wager, T. K. Plant, “Rugate filters grown by plasma-enhanced chemical vapor deposition,” Thin Solid Films 245, (1994).

1993 (2)

1992 (2)

H. Fabricius, “Gradient-index filters: designing filters with steep skirts, high reflection, and quintic matching layers,” Appl. Opt. 31, 5191–5196 (1992).
[CrossRef] [PubMed]

R. Overend, D. R. Gibson, R. Marshall, “Rugate filter fabrication using neutral cluster beam deposition,” Vacuum 43, 51–54 (1992).
[CrossRef]

1989 (3)

1988 (1)

1985 (1)

Abbod, M. F.

D. A. Linkens, M. F. Abbod, J. Metcalfe, B. Nichols, “Modeling and fabrication of optical interference rugate filters,” ISA Transactions 40, 2–16 (2001).
[CrossRef]

Abelmann, L.

L. Abelmann, C. Lodder, “Oblique evaporation and surface diffusion,” Thin Solid Films 305, 1–21 (1997).
[CrossRef]

Abu-Safia, H. A.

Aljarayesh, I. O.

Al-Sharif, A. I.

Arens-Fischer, M.

M. G. Berger, M. Arens-Fischer, M. Tonissen, M. Kruger, S. Billat, H. Luth, S. Hilbrich, W. Thieb, P. Grosse, “Dielectric filters made of PS: advanced performance by oxidation and new layer structures,” Thin Solid Films 297, 237–240 (1997).
[CrossRef]

Barabasi, A. L.

A. L. Barabasi, H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge University, Cambridge, UK, 1995).
[CrossRef]

Berger, M. G.

M. G. Berger, M. Arens-Fischer, M. Tonissen, M. Kruger, S. Billat, H. Luth, S. Hilbrich, W. Thieb, P. Grosse, “Dielectric filters made of PS: advanced performance by oxidation and new layer structures,” Thin Solid Films 297, 237–240 (1997).
[CrossRef]

Bhatia, S. N.

F. Cunin, T. A. Schmedake, J. R. Link, Y. Y. Li, J. Koh, S. N. Bhatia, M. J. Sailor, “Biomolecular screening with encoded porous-silicon photonic crystals,” Nature Materials 1, 39–41 (2002).
[CrossRef]

Billat, S.

M. G. Berger, M. Arens-Fischer, M. Tonissen, M. Kruger, S. Billat, H. Luth, S. Hilbrich, W. Thieb, P. Grosse, “Dielectric filters made of PS: advanced performance by oxidation and new layer structures,” Thin Solid Films 297, 237–240 (1997).
[CrossRef]

Bland-Hawthorn, J.

S. Cianci, J. Bland-Hawthorn, J. O’Byrne, “Rugate filters: quasars beyond z ∼ 7?,” Astron. Soc. Pac. Conf. Ser. 195, 391–397 (2000).

Bovard, B. G.

Brett, M. J.

K. Robbie, C. Shafail, M. J. Brett, “Thin films with nanometer-scale pillar microstructure,” J. Mater. Res. 14, 3158–3163 (1999).
[CrossRef]

K. Robbie, A. J. P. Hnatiw, M. J. Brett, R. I. MacDonald, N. J. McMullin, “Inhomogeneous thin film optical filters fabricated using glancing angle deposition,” Electron. Lett. 33, 1213–1214 (1997).
[CrossRef]

K. Robbie, M. J. Brett, “Sculptured thin films and glancing angle deposition: Growth mechanics and applications,” J. Vac. Sci. Technol. A 15, 1460–1465 (1997).
[CrossRef]

K. Robbie, M. J. Brett, A. Lakhtakia, “Chiral sculpted thin films,” Nature 384, 616–616 (1996).
[CrossRef]

Canham, L. T.

P. A. Snow, E. K. Squire, P. St. J. Russell, L. T. Canham, “Vapor sensing using the optical properties of porous silicon Bragg mirrors,” J. Appl. Phys. 86, 1781–1784 (1999).
[CrossRef]

Cianci, S.

S. Cianci, J. Bland-Hawthorn, J. O’Byrne, “Rugate filters: quasars beyond z ∼ 7?,” Astron. Soc. Pac. Conf. Ser. 195, 391–397 (2000).

Cunin, F.

F. Cunin, T. A. Schmedake, J. R. Link, Y. Y. Li, J. Koh, S. N. Bhatia, M. J. Sailor, “Biomolecular screening with encoded porous-silicon photonic crystals,” Nature Materials 1, 39–41 (2002).
[CrossRef]

Fabricius, H.

Fan, S.

Fink, Y.

Gibson, D. R.

R. Overend, D. R. Gibson, R. Marshall, “Rugate filter fabrication using neutral cluster beam deposition,” Vacuum 43, 51–54 (1992).
[CrossRef]

Gou, Z.

G. Placido, J. Russell, Z. Gou, “Graded-index films using aluminium oxynitrides,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 159–168 (1996).
[CrossRef]

Grosse, P.

M. G. Berger, M. Arens-Fischer, M. Tonissen, M. Kruger, S. Billat, H. Luth, S. Hilbrich, W. Thieb, P. Grosse, “Dielectric filters made of PS: advanced performance by oxidation and new layer structures,” Thin Solid Films 297, 237–240 (1997).
[CrossRef]

Hall, R. L.

Hilbrich, S.

M. G. Berger, M. Arens-Fischer, M. Tonissen, M. Kruger, S. Billat, H. Luth, S. Hilbrich, W. Thieb, P. Grosse, “Dielectric filters made of PS: advanced performance by oxidation and new layer structures,” Thin Solid Films 297, 237–240 (1997).
[CrossRef]

Hnatiw, A. J. P.

K. Robbie, A. J. P. Hnatiw, M. J. Brett, R. I. MacDonald, N. J. McMullin, “Inhomogeneous thin film optical filters fabricated using glancing angle deposition,” Electron. Lett. 33, 1213–1214 (1997).
[CrossRef]

Hodgkinson, I. J.

A. J. McPhun, Q. H. Wu, I. J. Hodgkinson, “Birefringent rugate filters,” Electron. Lett. 34, 360–361 (1998).
[CrossRef]

I. J. Hodgkinson, F. Horowitz, H. A. Macleod, M. Sikkens, J. J. Wharton, “Measurement of the principal refractive indices of thin films deposited at oblique incidence,” J. Opt. Soc. Am. A 2, 1693–1697 (1985).
[CrossRef]

I. J. Hodgkinson, Q. Hong Wu, Birefringent Thin Films and Polarizing Elements (World Scientific, Singapore, 1997).
[CrossRef]

Hong Wu, Q.

I. J. Hodgkinson, Q. Hong Wu, Birefringent Thin Films and Polarizing Elements (World Scientific, Singapore, 1997).
[CrossRef]

Horowitz, F.

Joannopoulos, J. D.

John, S.

O. Toader, S. John, “Square spiral photonic crystals: Robust architecture for microfabrication of materials with large three-dimensional photonic band gaps,” Phys. Rev. E 66, 1–18 (2002).
[CrossRef]

O. Toader, S. John, “Proposed square spiral microfabrication architecture for large three-dimensional photonic band gap crystals,” Science 292, 1133–1135 (2001).
[CrossRef] [PubMed]

Koh, J.

F. Cunin, T. A. Schmedake, J. R. Link, Y. Y. Li, J. Koh, S. N. Bhatia, M. J. Sailor, “Biomolecular screening with encoded porous-silicon photonic crystals,” Nature Materials 1, 39–41 (2002).
[CrossRef]

Kruger, M.

M. G. Berger, M. Arens-Fischer, M. Tonissen, M. Kruger, S. Billat, H. Luth, S. Hilbrich, W. Thieb, P. Grosse, “Dielectric filters made of PS: advanced performance by oxidation and new layer structures,” Thin Solid Films 297, 237–240 (1997).
[CrossRef]

Lakhtakia, A.

K. Robbie, M. J. Brett, A. Lakhtakia, “Chiral sculpted thin films,” Nature 384, 616–616 (1996).
[CrossRef]

Li, Y. Y.

F. Cunin, T. A. Schmedake, J. R. Link, Y. Y. Li, J. Koh, S. N. Bhatia, M. J. Sailor, “Biomolecular screening with encoded porous-silicon photonic crystals,” Nature Materials 1, 39–41 (2002).
[CrossRef]

Lim, S.

S. Lim, S. Shih, J. G. Wager, “Design and fabrication of a double bandstop rugate filter grown by plasma-enhanced chemical vapor deposition,” Thin Solid Films 277, 144–146 (1996).
[CrossRef]

S. Lim, J. H. Ryu, J. F. Wager, T. K. Plant, “Rugate filters grown by plasma-enhanced chemical vapor deposition,” Thin Solid Films 245, (1994).

Link, J. R.

F. Cunin, T. A. Schmedake, J. R. Link, Y. Y. Li, J. Koh, S. N. Bhatia, M. J. Sailor, “Biomolecular screening with encoded porous-silicon photonic crystals,” Nature Materials 1, 39–41 (2002).
[CrossRef]

Linkens, D. A.

D. A. Linkens, M. F. Abbod, J. Metcalfe, B. Nichols, “Modeling and fabrication of optical interference rugate filters,” ISA Transactions 40, 2–16 (2001).
[CrossRef]

Lodder, C.

L. Abelmann, C. Lodder, “Oblique evaporation and surface diffusion,” Thin Solid Films 305, 1–21 (1997).
[CrossRef]

Luth, H.

M. G. Berger, M. Arens-Fischer, M. Tonissen, M. Kruger, S. Billat, H. Luth, S. Hilbrich, W. Thieb, P. Grosse, “Dielectric filters made of PS: advanced performance by oxidation and new layer structures,” Thin Solid Films 297, 237–240 (1997).
[CrossRef]

MacDonald, R. I.

K. Robbie, A. J. P. Hnatiw, M. J. Brett, R. I. MacDonald, N. J. McMullin, “Inhomogeneous thin film optical filters fabricated using glancing angle deposition,” Electron. Lett. 33, 1213–1214 (1997).
[CrossRef]

Macleod, A.

A. Macleod, “Challenges in the design and production of narrow band filters for optical fiber telecommunications,” in Optical and Infrared Thin Films, M. L. Fulton, ed., Proc. SPIE4094, 46–57 (2000).
[CrossRef]

Macleod, H. A.

Marshall, R.

R. Overend, D. R. Gibson, R. Marshall, “Rugate filter fabrication using neutral cluster beam deposition,” Vacuum 43, 51–54 (1992).
[CrossRef]

Martinu, L.

L. Martinu, D. Poitras, “Plasma deposition of optical films and coatings: A review,” J. Vac. Sci. Technol. A 18, 2619–2645 (2000).
[CrossRef]

McGahan, W. A.

H. G. Tompkins, W. A. McGahan, Spectroscopic Ellipsometry and Reflectometry (Wiley, New York, 1999).

McMullin, N. J.

K. Robbie, A. J. P. Hnatiw, M. J. Brett, R. I. MacDonald, N. J. McMullin, “Inhomogeneous thin film optical filters fabricated using glancing angle deposition,” Electron. Lett. 33, 1213–1214 (1997).
[CrossRef]

McPhun, A. J.

A. J. McPhun, Q. H. Wu, I. J. Hodgkinson, “Birefringent rugate filters,” Electron. Lett. 34, 360–361 (1998).
[CrossRef]

Messier, R.

R. Messier, V. C. Venugopal, P. D. Sunal, “Origin and evolution of sculptured thin films,” J. Vac. Sci. Technol. A 18, 1538–1545 (2000).
[CrossRef]

Metcalfe, J.

D. A. Linkens, M. F. Abbod, J. Metcalfe, B. Nichols, “Modeling and fabrication of optical interference rugate filters,” ISA Transactions 40, 2–16 (2001).
[CrossRef]

Motohiro, T.

Nichols, B.

D. A. Linkens, M. F. Abbod, J. Metcalfe, B. Nichols, “Modeling and fabrication of optical interference rugate filters,” ISA Transactions 40, 2–16 (2001).
[CrossRef]

O’Byrne, J.

S. Cianci, J. Bland-Hawthorn, J. O’Byrne, “Rugate filters: quasars beyond z ∼ 7?,” Astron. Soc. Pac. Conf. Ser. 195, 391–397 (2000).

Overend, R.

R. Overend, D. R. Gibson, R. Marshall, “Rugate filter fabrication using neutral cluster beam deposition,” Vacuum 43, 51–54 (1992).
[CrossRef]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, San Diego, Calif., 1985).

Placido, G.

G. Placido, J. Russell, Z. Gou, “Graded-index films using aluminium oxynitrides,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 159–168 (1996).
[CrossRef]

Plant, T. K.

S. Lim, J. H. Ryu, J. F. Wager, T. K. Plant, “Rugate filters grown by plasma-enhanced chemical vapor deposition,” Thin Solid Films 245, (1994).

Poitras, D.

L. Martinu, D. Poitras, “Plasma deposition of optical films and coatings: A review,” J. Vac. Sci. Technol. A 18, 2619–2645 (2000).
[CrossRef]

Robbie, K.

K. Robbie, C. Shafail, M. J. Brett, “Thin films with nanometer-scale pillar microstructure,” J. Mater. Res. 14, 3158–3163 (1999).
[CrossRef]

K. Robbie, M. J. Brett, “Sculptured thin films and glancing angle deposition: Growth mechanics and applications,” J. Vac. Sci. Technol. A 15, 1460–1465 (1997).
[CrossRef]

K. Robbie, A. J. P. Hnatiw, M. J. Brett, R. I. MacDonald, N. J. McMullin, “Inhomogeneous thin film optical filters fabricated using glancing angle deposition,” Electron. Lett. 33, 1213–1214 (1997).
[CrossRef]

K. Robbie, M. J. Brett, A. Lakhtakia, “Chiral sculpted thin films,” Nature 384, 616–616 (1996).
[CrossRef]

Russell, J.

G. Placido, J. Russell, Z. Gou, “Graded-index films using aluminium oxynitrides,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 159–168 (1996).
[CrossRef]

Russell, P. St. J.

P. A. Snow, E. K. Squire, P. St. J. Russell, L. T. Canham, “Vapor sensing using the optical properties of porous silicon Bragg mirrors,” J. Appl. Phys. 86, 1781–1784 (1999).
[CrossRef]

Ryu, J. H.

S. Lim, J. H. Ryu, J. F. Wager, T. K. Plant, “Rugate filters grown by plasma-enhanced chemical vapor deposition,” Thin Solid Films 245, (1994).

Sailor, M. J.

F. Cunin, T. A. Schmedake, J. R. Link, Y. Y. Li, J. Koh, S. N. Bhatia, M. J. Sailor, “Biomolecular screening with encoded porous-silicon photonic crystals,” Nature Materials 1, 39–41 (2002).
[CrossRef]

Schmedake, T. A.

F. Cunin, T. A. Schmedake, J. R. Link, Y. Y. Li, J. Koh, S. N. Bhatia, M. J. Sailor, “Biomolecular screening with encoded porous-silicon photonic crystals,” Nature Materials 1, 39–41 (2002).
[CrossRef]

Schubert, M.

Shafail, C.

K. Robbie, C. Shafail, M. J. Brett, “Thin films with nanometer-scale pillar microstructure,” J. Mater. Res. 14, 3158–3163 (1999).
[CrossRef]

Shih, S.

S. Lim, S. Shih, J. G. Wager, “Design and fabrication of a double bandstop rugate filter grown by plasma-enhanced chemical vapor deposition,” Thin Solid Films 277, 144–146 (1996).
[CrossRef]

Sikkens, M.

Snow, P. A.

P. A. Snow, E. K. Squire, P. St. J. Russell, L. T. Canham, “Vapor sensing using the optical properties of porous silicon Bragg mirrors,” J. Appl. Phys. 86, 1781–1784 (1999).
[CrossRef]

Southwell, W. H.

Squire, E. K.

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[CrossRef]

S. Lim, S. Shih, J. G. Wager, “Design and fabrication of a double bandstop rugate filter grown by plasma-enhanced chemical vapor deposition,” Thin Solid Films 277, 144–146 (1996).
[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Schematic of the GLAD system.

Fig. 2
Fig. 2

Results of spectroscopic ellipsometry calibration. The set of films used for the study consisted of eight porous, amorphous silicon films made at constant substrate tilt angles. A Bruggemann uniaxial effective medium approximation model was used to extract index and thickness information. (a) Variation of refractive index with wavelength (for eight substrate tilt angles). The refractive index of the films decreases with the increasing substrate tilt as the films become more porous. (b) Variation of film thickness with substrate tilt angle. Increased atomic shadowing at higher deposition angles produces porosity that increases the thickness of the films above the cosine trend at all tilt angles.

Fig. 3
Fig. 3

Refractive index profiles for the rugate filter designs. (a) Simple rugate filter design with λ o = 850 nm, n average = 1.72, and n peak = 0.95. (b) Fully-apodized rugate filter design. A Gaussian apodization function was imposed to the top and the bottom of the simple rugate index profile. (c) Half-apodized rugate filter design. A Gaussian apodization function was imposed to only the top of the simple rugate index profile.

Fig. 4
Fig. 4

Transmission spectra for the refractive index profiles shown in Fig. 3. (a) Theoretical transmission calculated using the characteristic matrix method. An absorption model was included in the calculation. (b) Measured transmission for the rugate filters grown with GLAD. The sidelobes are significantly reduced with apodization.

Fig. 5
Fig. 5

Nanostructure of the rugate filters studied with SEM. (a) Simple rugate filter. (b) Half-apodized rugate filter. (c) High resolution SEM image of the simple rugate filter showing perturbed ballistic aggregation. Branching structure is resolved to the resolution limit of the microscope (approximately 10 nm).

Fig. 6
Fig. 6

Effect of matching layers on the transmission spectrum of the simple rugate filter. (a) Refractive index profile for the simple rugate filter with a quarter-wave matching layer to air. (b) Refractive index profile for the simple rugate filter with a quintic matching layer to air. This design provides smooth index matching down to the refractive index of air, which is a novel result.

Fig. 7
Fig. 7

Transmission spectra for the refractive index profiles shown in Fig. 6. The quarter-wave design reduces the sidelobes near the central wavelength, whereas quintic matching produces a wideband suppression.

Equations (3)

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tanΨejΔ=RPRS,
nx=naverage+12 npeak sin4πnaveragexλo,
nx=nair+naverage-nair10xt3-15xt4+6xt5,

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