J. MATER. CHEM., 1994,4(8), 1263-1265 Porosity of Pyrolysed Sol-Gel Waveguides Jeremy J. Ramsden Department of Biophysical Chemistry, Basel University, Klingelbergstrasse 70, 4056 Basel, Switzerland The pyrolysis of a sol-gel film dip-coated on a substrate is a convenient and inexpensive way of preparing optical waveguides with a wide range of refractive indices. Such waveguides are, however, microporous. For many uses, in particular sensing applications such as the chemical analysis of solutions, the porosity is one of the key parameters determining the response of the waveguide to its environment. In this paper, the porosity of a planar waveguide is accurately determined by measuring the mode indices for two modes with the pores filled alternately with liquid H20 and D,O.Planar dielectric waveguides can be fabricated by a simple, inexpensive process by first preparing a sol of the precursor of the dielectric material, typically a metal oxide, in an organic solvent,? e.g. isopropyl alcohol. A planar substrate is vertically lowered into and withdrawn from the sol. This procedure results in a thin layer of the sol remaining on the substrate. The solvent is then allowed to evaporate, whereupon a semirigid gel is formed. Finally the waveguiding layer is pyrolysed in an oxidizing atmosphere usually in a first stage at 300°C and in a second at 500°C; water and CO, are expelled and a pure metal oxide is formed.' The optimal temperature of the second stage depends on the substrate. During the second stage the layer becomes more compact, i.e.it becomes thinner and its refractive index increases. Films produced in this way are isotropic, homogeneous and show low losses, provided the thermal expansion coefficients of film and substrate are well matched. The process is applicable to many different materials, yielding waveguiding films over a wide range of refractive indices. During drying but before pyrolysis, i.e. in the gel-like state, microstructuring of the waveguide surface can readily be carried out, e.g. gratings can be embossed into When the waveguides are placed in water or other liquids, it has been empirically established that the thickness (by ca. 1-2%) and refractive index of the films increase, over a period of several hours. The process is reversible, and appears to be qualitatively consistent with the waveguide being com- posed of fine channels embedded in a dense matrix, initially filled with air, which is gradually replaced by the liquid in which the waveguide is immersed.A recent and potentially important application of these waveguides is as sensing elements. Optical switches and gas sensors based on grating couplers fabricated out of such coatings have been rep~rted.~ The waveguides also respond to changes in the concentration of ions in the solution bathing the waveguide,' and can thus function as sensors for small soluble ions. In this type of application, it is important to know the porosity of the waveguide, which is a key parameter determin- ing the response of the waveguide to a given ambient.In this report, an accurate method of determining the porosity in situ is described, and results from a commercially available planar waveguide are presented. Experimental Planar optical waveguides fabricated by dip-coating and pyrolysing a sol-gel film were obtained from AS1 AG, Zurich, Switzerland (type 2400). The given specifications of the wave- t Aqueous sols tend to be rather unstable and aggregate. guides were: material, Si, -xTi,02, x x0.4, refractive index of the waveguiding film nF, 1.8; thickness dF, 160-200nm; substrate, AF45 glass (Schott DESAG) with refractive index ns =1.525 781. The waveguides incorporated a grating coupler of period A =4165 nm. A waveguide was first equilibrated in H20,$ purified using a Barnstead (Dubuque, Iowa) Nanopure installation (conductivityx 18 MQ cm), for at least 48 h.It was then mounted on a goniometer scanning instrument (10s-1,AS1 AG, Zurich, Switzerland) which allows the angle of incidence of a linearly polarized external beam (He-Ne laser, A= 632.8 nm) to be varied while measuring the incoupled power by means of photodiodes positioned at the ends of the waveguide. The angular resolution of the instrument is 1.25x rad. Incoupling occurs when the angle a fulfills the following ~ondition:~ N =nai,sin a +LA/A (1) where N is the effective refractive index of the waveguide and L the diffraction order. a was determined for the zeroth-order transverse electric (TE) and transverse magnetic (TM ) modes.During the measurement, a small water-filled cuvette was sealed over the grating region with an '0'-ring, the waveguide thus forming one wall of the cuvette. The temperature was monitored by a Pt-100 resistance thermometer embedded in the goniometer head. Typically 20-30 readings were taken and averaged. The standard error in N did not exceed 4 x The mode equations for zeroth-order modes in a three-layer waveguide 2n: -A d, J(ni -N2)= with p equal to 0 and 1, respectively, for TE and TM modes. n, is the refractive index of the solution covering the wave- guide. Since the pyrolysed sol-gel material can be considered to be isotropic,' both TE and TM modes have the same nF. Hence eqn. (2) can be solved simultaneously for the two unknowns nF and dF using the measured N.n, for water was taken from the work of Tilton and Taylor." $, The porosity in the presence of water was investigated because of the author's interest in the response of waveguides to aqueous ions. The metal oxides which are often used for fabricating high-refractive- index waveguiding layers become hydrated in contact with aqueous The hydrated oxides often form complexes with other metal iom8 J. MATER. CHEM., 1994, VOL. 4 H20 and D20 are chemically and structurally very similar molecules, and it can be assumed that the waveguide structure is not changed when one is substituted for the other. Their refractive indices differ appreciably from each other, however.Hence, the waveguide was then soaked in D,O, 99.9% pure (Isotec, Miamisburg, Ohio) for a further 48 h, and NT, and N,, again determined. The sequence of soaking in H,O, measuring N, soaking in D,O and measuring N again was repeated several times. The refractive index of D20 was measured in a Rayleigh interferometer (L13, Carl Zeiss Jena, Germany), calibrated with an He-Ne laser. Results and Discussion Table 1 shows the measured values of N, together with nF calculated using eqn. (2). The refractive index of the micropo- rous waveguiding film measured in the presence of a liquid 1 can be written as: (3) where 8 is the porosity, defined as the fraction of film volume occupied by pores. The pores are assumed to be uniformly distributed within the film, and to be connected with one another and the external medium.The close similarity of H20 and D,O allows it to be assumed that 8 is unchanged by the substitution of one for the other. Eqn. (3) solved simultaneously with successively I =H20 and D20 (data from Table 1) gave 8=0.1418 &0.0015 and nSi(Ti)O, = 1.8896-t 0.0016. Measurement of the porosity of several wave- guides of the same type gave values of I3 in the range 0.14-0.17. Sources of Uncertainty In eqn. (l),the main sources of uncertainty are in a, A and A. Owing to slight mechanical instabilities, a is measured to an accuracy of ca. 0.3". The variation in the refractive index of air12 can be neglected. Hence the uncertainty in the first term is ca.2 parts in lo6. Fluctuations in the wavelength of the He-Ne laser are of the order of 1 part in lo6. From the average thermal expansion coefficients of quartz13 and rutile,I4 5.5 x and 9.5 x 'C-', respectively, we calculate a weighted mean of 4.7 x "C-'; the thermal expansion coefficient of the AF45 glass used as the waveguide support is almost identical to 4.5 x "C-' (data from DESAG). Hence the uncertainty in A due to temperature variations is ca. 0.2 parts in lo6, and the overall uncertainty in the second term 1.2 parts in lo6. Combining the uncertainties from the first two terms gives an uncertainty in the measured N of ca. 2 parts in lo6. Measurements (the standard deviation of a long series of points recorded under unchanging conditions) corroborated this figure.The uncertainties given for I3 and nSi(Ti)O, may be slightly overestimated since some of the given uncertainties are due to small fluctuations in the temperature, the consequences of which are correlated in the quantities combined to calculate 6' and nSi(Ti)O,. Table 1 Measured waveguide parameters in H,O and D20 1 n, =nl NTE NTM nF ~ ~ H2O 1.331 556 1.618 582 1.572 960 1.810470 (uncertainty) (0.000005) (0.000004) (0.000004) (0.000015) D20 1.325 641 1.617 630 1.571 898 1.809 535 (uncertainty) (0.000005) (0.000004) (0.000004) (0.000015) ~~~~~ i=632.8 nm. The waveguide thickness dF did not change according to the ambient liquid and had a value of 178.342k0.072 nm. Measurements were carried out at 22.05 0.05 "C.Rapid Determination of Waveguide Porosity If the chemical composition of the waveguide is known, then a single determination of nF suffices to determine the porosity, as can be seen by rearranging eqn. (3): %(Ti)O, -nF (4)%i(Ti)O, -Validity of the Model Since the waveguides are too thin to allow more than one mode to be excited for each of the two polarizations, TE and TM, it is not possible to verify that the waveguides remain isotropic when water diffuses into the microchannels. The most likely source of anisotropy would be a structure approaching that of a system of rods, filled with the ambient medium, perpendicular to the plane of the waveguide, embed- ded in the Ti(Si)O,. Wiener" has shown that such a system will exhibit positive birefringence, the magnitude of which depends on the difference between the two media, i.e.-ncl. Since this difference will diminish when water replaces air in the channels, the birefringence must necessarily decrease, and hence since the waveguides were found to be isotropic in air,' they must remain so in water. On the other hand, the exact nature of the change, in particular the increase in apparent thickness when previously unimmersed wave-guides are immersed in water, is not clear. It is assumed that after the lengthy period (ca. 48 h) of equilibration required the F layer is uniformly hydrated, but this has not been indepen- dently verified. Interpretation of B (Microstructure of the Waveguide) The packing density D, of randomly packed spheres in three dimensions lies between 0.61 and 0.64,16 i.e.8 is predicted to be ca. 0.37, but the measured value is significantly less. Two possible reasons for the discrepancy are: (i ) the particles constituting the waveguide are not spheres, but irregularly shaped objects. They are hard and no significant deformation is expected to take place during drying or pyrolysis. The density of randomly packed irregular objects has not been systematically investigated but for certain shapes could be higher than for spheres; (ii) since D, (for spheres) exceeds the percolation threshold not all voids may be accessible to the surface. The volume fraction of inaccessible voids is 13inacc.pore --1-D3-Orneas.=0.21. In this case the computed refractive index of 1.8896 must apply to Si(Ti)02 plus the inaccessible pores, which are presumably filled with vapour with a refrac- tive index of ca. 1. Reapplying eqn. (3) gives the result that the refractive index of Si(Ti)O, is practically equal to that of pure TiO,, an inference ruled out by the composition of the starting materials. It is doubtless incorrect to think of the waveguide as a percolating cluster of hard spherules. During drying pyrolysis solvent vapour and CO, escaping through the gel may render most of the voids accessible from the surface. The porosity strongly depends on the pyrolysis temperature. Films fired at higher temperatures are more compact. For example, waveguides fired at 800 "C (compared with 500 "C used for the type 2400 waveguides) have a porosity I3 of only a few per cent.17,18 Interpretation of nsivi)o, The measured value of 1.8896 reflects the chemical composi- tion of the waveguiding film.The sol-gel system used to coat J. MATER. CHEM., 1994, VOL. 4 the glass substrate was a Liquicoat (Merck) solution composed of premixed SiO, and TiO, precur~ors.~~ The ratio of the Si and Ti is not specified precisely by the manufacturer and may, moreover, change during dip-coating and drying, both because of the differing volatilities of the organometallic precursors, and because Ti may be preferentially leached from the film.,' Therefore film composition was analysed with X-ray photo- electron spectroscopy (XPS) at the Institute for Experimental Physics of Condensed Matter of the University of Basel.,' Samples were analysed using a Leybold EA11/100 spec- trometer using Mg-Ka radiation (1253.6 eV).The residual gas pressure in the spectrometer was <lo-'' mbar. Fortunately the material was conductive enough to prevent the samples charging up sufficiently to vitiate the determination of the mole fractions of titanium, silicon and oxygen. Apart from the surface region, 1-2 nm in depth, the material was slightly substoichiometric with respect to oxygen [i.e. Si(Ti)01.87]. the ratio of Ti to Si was 38 :62, i.e. x =0.38. We can write %i(Ti)O, =xnTiO, +( -x)nSiO, (5) Taking the value of nSiOz (fused quartz) as 1.458,,, we obtain nTiO,=2.56.This value corresponds to the refractive index of TiO, films produced by reactive ion plating,23 which is known to produce films with a density between 95 and 100% of bulk material. Conclusion A convenient way of measuring the porosity and refractive index of optical waveguides has been devised, based on measuring their refractive indices in the presence of two liquids, chemically similar but with differing refractivities. Results for pyrolysed sol-gel dip-coated waveguide show that the porosity is much lower (about half) than that expected from sintered spheres. The fabrication process appears to result in a denser, more compact structure with all remaining pores accessible to the external medium. The method is useful for determining the porosity of thin film materials in situ.Other available methods for porosity characterization require the material to be present in powder form (e.g. ref. 24.). The present method can be used with any pore-filling liquid, provided that a pair of chemically similar molecules can be found. Deuteriated solvents are especially convenient for this purpose. The author thanks the Kommission zur Forderung der wissen- schaftlichen Forschung, Bern for support, Dr P. P. Herrmann for a fruitful discussion and a critical reading of an earlier version of the manuscript, and Mr. R. Gampp of the Institute for Experimental Physics of Condensed Matter of the University of Basel for the X-ray photoelectron spectrometry. References 1 P. P. Herrmann and D.Wildmann, IEEE J. Quantum Electron., 1983,19,1735. 2 W. Lukosz and K. Tiefenthaler, Opt. Lett., 1983,8, 53'. 3 K. Heuberger and W. Lukosz, Appl. Opt. Lett., 1986,25.1499. 4 K. Tiefenthaler and W. Lukosz, Opt. Lett., 1984, 10, 1.17. 5 J. J. Ramsden, D. U. Roemer and J. E. Prenosil, PrIc ECIO 6, 1993,12-38. 6 T. W. Healy and L. R. White, Adc. Colloid Interfact Sci., 1978, 9, 303. 7 D. N. Furlong, D. E. Yates and T. W. Healy, Fundamental Properties of the OxidelAqueous Solution Interface, in Electrodes of Conductive Metal Oxides, ed. S. Trasatti, Part 13, Elsevier, Amsterdam, 1981, p. 367. 8 R. J. Hunter, Zeta Potential in Colloid Science, Acadcmic Press, London, 1981. 9 K. Tiefenthaler and W. Lukosz, J. Opt. Soc. Am. B, 19h9,6,209.10 A. Ghatak and K. Thagarajan, Optical Electronics, Cambridge University Press, Cambridge, 1989. 11 L. W. Tilton and J. K. Taylor, J. Res. Natl Bur. StIind., 1938, 20,419. 12 H. Barrel1 and J. E. Sears, Philos. Trans. R. Soc. Lonam, Ser. A, 1939,238, 1. 13 Handbook of Chemistry and Physics, ed. R. C. Weast, RC Press, Boca Raton, 56th edn., 1975-6, p. F-78. 14 F. A. Grant, Rev. Mod. Phys., 1959,31,646. 15 0. Wiener, Abh. Math.-Phjls. K1. Kgl. Sachs. Ges. Mb., 1912. 32, 503. 16 K. Gotoh and J. L. Finney, Nature (London), 1974,252,202. 17 Ch. Stamm and W. Lukosz, Sensors Actuators B, 1993, 11, 177. 18 Ph. M. Nellen and W. Lukosz, Biosensors Bioelectro~iics, 1993, 8, 129. 19 K. Tiefenthaler, V. Briguet, E. Buser, M. Horisbt-rger and W. Lukosz, Proc. SPIE, 1983,401, 165. 20 K. Shingyouchi, A. Makishima, M. Tutumi, S. Takenlwchi and S. Konishi, J. Nun-Cryst. Solids, 1988, 100, 383. 21 P. Oelhafen, D. Ugolini, S. Schelz and J. Eitle, in Diamond and Diamond-like Films and Coatings, ed. R. E. Clawing, L. I . Horton, J. C. Angus and P. Koidl, Plenum Press, New York, 1991,p. 377. 22 Handbook of Chemistry and Physics, ed. R. C. Weast, CMC Press, Boca Raton, 56th edn., 1975, p. E-224. 23 K. Bange, C. R. Ottermann, 0. Anderson, U. Jerchowski, M. Laube and R. Feile, Thin Solid Films, 1991, 197, 279. 24 J. H. Strange, M. Rahman and E. G. Smith, Phys. Rev. LTtt., 1993, 71, 3589. Paper 4/02688H; Received 6th May, 1994