Infrared Physics & Technology 53 (2010) 292–294

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Infrared Physics & Technology

journal homepage: www.elsevier .com/locate / infrared

Porous silicon based extended-bandwidth rugate filters for mid-infrared application

Nobuyuki Ishikura a, Minoru Fujii a,*, Kohei Nishida a, Shinji Hayashi a, Joachim Diener b

a Department of Electrical and Electronic Engineering, Graduate School of Engineering, Kobe University, Rokkodai, Nada, Kobe 657-8501, Japanb Physik-Department E16, Technische Universität München, D-85747 Garching, Germany

a r t i c l e i n f o a b s t r a c t

Article history:Received 19 October 2009Available online 5 May 2010

Keywords:Porous siliconRugate filterInfrared

1350-4495/$ - see front matter � 2010 Elsevier B.V. Adoi:10.1016/j.infrared.2010.04.005

* Corresponding author. Tel./fax: +81 78 8036081.E-mail address: fujii@eedept.kobe-u.ac.jp (M. Fujii

Porous silicon-based rugate filters operating in the mid-infrared spectral range are fabricated by electro-chemical etching of bulk silicon wafers. The rugate filter has a high reflectivity stop-band at 5 lm with nohigher-order harmonics and very small sidelobes. Furthermore, broadband high pass filter having thecutoff wavelength in a mid-infrared range is demonstrated by combining five rugate structures.

� 2010 Elsevier B.V. All rights reserved.

1. Introduction

Porous silicon produced by electrochemical etching of a siliconwafer is a material of great interest for the fabrication of opticalmultilayer structures. The refractive index of porous silicon canbe controlled by the porosity, which is determined by the currentdensity during the electrochemical etching process [1]. The elec-trochemical etching proceeds at the etching front and thus alreadyetched layers are unaffected by subsequent etching. This propertymakes porous silicon an almost ideal system to realize one-dimen-sional refractive index profiles. In fact, various types of one-dimen-sional multilayer structures, such as Bragg reflectors [2],omnidirectional mirrors [3] and Fabry–Perot optical microcavities[4,5] have been fabricated by controlling the current densityperiodically.

When the etching current is changed continuously, a rugate fil-ter is fabricated. A rugate filter is a kind of an interference filtercharacterized by a continuous sinusoidal index variation in thedirection perpendicular to the film plane [6]. As in the case of Braggreflectors, it shows a high reflectivity ‘‘stop-band” in a specificwavelength range. Advantages of rugate filters compared withBragg reflectors are a smaller sensitivity to angle variation of inci-dence light [7] and a suppression of higher-order harmonics. Ber-ger et al. [8] first reported the fabrication of a porous silicon-based rugate filter, and after that several types of porous silicon-based rugate filters including birefringent rugate filters have beendemonstrated [9].

The porous silicon-based rugate filters so far fabricated are de-signed for visible and near infrared wavelength ranges, and thosefor mid-infrared applications are not successfully produced. To

ll rights reserved.

).

realize mid-infrared stop-band very thick films (P30 lm) are re-quired. The thick rugate filters are hard to achieve in typical fabri-cation techniques such as vacuum evaporation, chemical vapordeposition and sputtering [10–12] because of the low formationrate and difficulty in controlling refractive index sinusoidally. Thepurpose of this work is to realize porous silicon-based rugate filtersfor mid-infrared applications (e.g., gas sensors and pyroelectricdetectors). We demonstrate that a rugate-type refractive indexprofile with the thickness of up to 200 lm can be achieved by por-ous silicon and the structure results in a rugate filter having a stop-band in a mid-infrared range without higher-order harmonics andsidelobes.

2. Experimental details

Porous silicon structures were produced by electrochemicaletching of (100) oriented p+ Si wafers (0.02 X cm). The etchingsolution was a 2:3 by volume mixture of HF (46 wt.% in water)and ethanol. The current density was changed from 5 mA/cm2 to109 mA/cm2 with the minimum step of 0.5 mA/cm2 by com-puter-controlled current source (Agilent 6612C). In this currentdensity range, the refractive index of porous silicon was changedfrom 2.38 to 1.30 (at the wavelength of 2 lm). The refractive indi-ces of porous silicon were obtained either from interference pat-terns of uniform layers with known thicknesses or Bruggemaneffective medium approximation [13]. The total etching time wasin the range of 1 to 4 hours depending on the structure. Duringetching, the etching rate decreases slowly [1], i.e., about 1.5% dur-ing the etching of 10 lm. This effect was compensated by control-ling the etching time. All porous silicon structures were detachedfrom Si substrates by a high current pulse (400 mA/cm2, 1.6 s) afterfinishing the etching procedure. Transmittance spectra of fabri-cated structures were measured by Fourier transform infrared

Ref

ract

ive

inde

xTr

ansm

ittan

ce (%

)

2.2

2.0

1.4

1.6

1.8

100

0

20

40

60

80

050 402010 30Depth (µm)

Wavelength (µm)61 532 014 97 8

Calculated Measured

a

b

Fig. 2. (a) Refractive index profile vs. depth from the film surface and (b) calculatedand measured transmittance spectra of a single rugate structure.

N. Ishikura et al. / Infrared Physics & Technology 53 (2010) 292–294 293

spectrometer (PerkinElmer Spectrum GX) over the spectral rangeof 1–10 lm.

3. Theory

The rugate refractive index profile used in this work is the sameas that in Ref. [14]. It is expressed as

nðxÞ ¼ expln nH þ ln nL

2þ ln nH � ln nL

2sin

4pxk0þ /

� �� �; ð1Þ

where x is the optical path length, nH and nL are maximum and min-imum refractive indices used in the layer, k0 is the wavelength ofthe stop-band position, and / is the phase angle [6,15]. To reducesidelobes arising from sudden truncation of the refractive indexoscillation at the surface, apodization function is applied to the in-dex profile. We choose a quintic apodization function [16], which isknown to have significant sidelobes suppression properties. We alsouse a half-apodization technique, in which the maxima of therefractive index oscillation are modulated, while the minima arefixed [17,15]. In porous Si rugate filters, this technique reducesthe total etching time. Furthermore, to remove sidelobes causedby large refractive index mismatch between the rugate structureand the surrounding media, the quintic index-matching layers areadded to the front and back of the filter. The refractive index profileof the quintic index-matching layer [18] that matches indices formn1 to n2 is expressed as

nðtÞ ¼ n1 þ ðn2 � n1Þð10t3 � 15t4 þ 6t5Þ; ð2Þ

where t is the normalized layer thickness that varies from 0 to 1.

4. Results and discussion

Fig. 1 shows a cross-sectional scanning electron microscope(SEM) image of a rugate structure designed for the stop-band at5 lm. The rugate structure consists of 30 periods with quintic apo-dization and index-matching layers. We can see a periodic contrastdue to the repetition of high and low porosity layers. The interfaceis rather smooth and the periodic patterns are maintained over thewhole layer in spite of very long etching time (about 1 h) and verylarge thickness. The refractive index profile of this structure isshown in Fig. 2a and the measured and simulated transmittancespectra are shown in Fig. 2b. Details of the simulation can be foundin Ref. [19]. A stop-band is centered at 5 lm and no higher-orderharmonics can be seen because of the rugate profile. Thanks tothe quintic apodization and index-matching layers, the sidelobesare rather small. The almost perfect agreement between the exper-iment and calculation implies that the etching process is well con-trolled. The broad absorption band around 9260 nm is due to the

20µm

Fig. 1. Cross-sectional SEM image of a single rugate structure designed for the stop-band at 5 lm.

Si–O stretching vibration arising from native oxides on the surfaceof porous silicon. This absorption limits the usable range of poroussilicon filters if samples are not properly protected from oxidationatmosphere.

In some applications of rugate filters, e.g., edge filters, a verywide stop-band is required. To extend the width of the rugatestop-band, five rugate profiles are combined as shown in Fig. 3a.To reduce the total film thickness, neighboring rugate profiles arepartly overlapped [20]. Each rugate profile consists of 30 periodswith quintic apodization and the stop-bands are centered at4700, 5405, 6216, 7148 and 8220 nm. The distances betweenneighboring stop-bands are determined to be as large as possibleto extend the stop-band while keeping the high reflection. Combi-nation of rugate profiles results in two optical density minima(dips) in the stop-band. Depths of these dips are usually uneven,but they can be made equal by adjusting the phase (/) of the ru-gate profiles [20]. To equalize these dips, the phase is shifted byp/6 with respect to the neighboring rugate profile. Details of thiscombination method are found in our previous paper [14]. Thetransmittance spectra of the filter described in Fig. 3a are shownin Fig. 3b. We can see a very broad stop-band in the mid-infraredregion extending from 4 to 9 lm, while keeping high transmittancebelow 2 lm. The sharp absorption peaks in the 2–4 lm range arehigher-order harmonics. Although the agreement between theexperiment and the simulation is not perfect, it is in an acceptablelevel by considering the very complicated etching profiles. We be-lieve that further optimization of the etching process will improvethe accuracy of the filter characteristics.

In Figs. 2b and 3b, sidelobes of measured spectra are sometimessmaller than those of calculations. Furthermore, in Fig. 3b, thestop-band is flatter in measured spectra than calculation. The rea-son for better performances of the actual samples than calculations

Tran

smitt

ance

(%)

2.2

2.0

1.4

1.6

1.8

100

0

20

40

60

80

1600 8040 120Depth (µm)

Wavelength (µm)61 532 104 97 8

Calculated Measured

Ref

ract

ive

inde

xa

b

Fig. 3. (a) Refractive index profile vs. depth from the film surface and (b) calculatedand measured transmittance spectra of a rugate structure consisting of five rugateprofiles.

294 N. Ishikura et al. / Infrared Physics & Technology 53 (2010) 292–294

is not very clear. A plausible explanation is that there exists spatialinhomogeneities in actual samples and they smoothen the opticalresponses of the samples.

5. Conclusion

In conclusion, we have succeeded in producing mid-infrared ru-gate filters consisting of a sinusoidally varying apodized refractiveindex profile and index-matching layers by electrochemical etch-ing of porous silicon. The filter has a stop-band at 5 lm withouthigher-order harmonics and sidelobes. We also successfully fabri-cate very broad stop-band rugate filters with the stop-band widthof 5 lm by the combination of five mid-infrared rugate refractiveindex profiles. The present results demonstrate that deep etchingof porous silicon up to 200 lm does not degrade the property asoptical filters and its operation range covers from visible range toabout 9 lm.

References

[1] A.G. Cullis, L.T. Canham, P.D.J. Calcott, J. Appl. Phys. 82 (1997) 909.[2] G. Vincent, Appl. Phys. Lett. 64 (1994) 2367.[3] A. Bruyant, G. Lérondel, P.J. Reece, M. Gal, Appl. Phys. Lett. 82 (2003) 3227.[4] P.J. Reece, G. Lérondel, W.H. Zheng, M. Gal, Appl. Phys. Lett. 81 (2002) 4895.[5] V. Pellegrini, A. Tredicucci, C. Mazzoleni, L. Pavesi, Phys. Rev. B 52 (1995)

14328.[6] B.G. Bovard, Appl. Opt. 32 (1993) 5427.[7] W.H. Southwell, J. Opt. Soc. Am. A 5 (1988) 1558.[8] M.G. Berger, R. Arens-Fischer, M. Thönissen, M. Krüger, S. Billat, H. Lüth, S.

Hilbrich, W. Theiß, P. Grosse, Thin Solid Films 297 (1997) 237.[9] N. Ishikura, M. Fujii, K. Nishida, S. Hayashi, J. Diener, Opt. Express 16 (2008)

15531.[10] K. Kaminska, T. Brown, G. Beydaghyan, K. Robbie, Appl. Opt. 42 (2003) 4212.[11] S. Lim, S. Shih, J.F. Wager, Thin Solid Films 277 (1996) 144.[12] W.J. Gunning, R.L. Hall, F.J. Woodberry, W.H. Southwell, N.S. Gluck, Appl. Opt.

28 (1989) 2945.[13] P.A. Snow, E.K. Squire, P.St.J. Russell, L.T. Canham, J. Appl. Phys. 86 (1999) 1781.[14] N. Ishikura, M. Fujii, K. Nishida, S. Hayashi, J. Diener, M. Mizuhata, S. Deki, Opt.

Mater. 31 (2008) 102.[15] E. Lorenzo, C.J. Oton, N.E. Capuj, M. Ghulinyan, D. Navarro-Urrios, Z. Gaburro, L.

Pavesi, Appl. Opt. 44 (2005) 5415.[16] W.H. Southwell, Appl. Opt. 28 (1989) 5091.[17] H.A. Abu-Safia, A.I. Al-Sharif, I.O. Abu Alijarayesh, Appl. Opt. 32 (1993) 4831.[18] W.H. Southwell, Opt. Lett. 8 (1983) 584.[19] M. Born, E. Wolf, Principles of Optics, Cambridge University Press, 1999.[20] W.H. Southwell, Appl. Opt. 36 (1997) 314.