Photodarkening of amorphous As2Se3 thin films was generated by a 633-nm HeNe laser. The refractive index and absorption coefficient of the chalcogenide glass was determined, both before and after exposure, by analyzing the material’s transmission spectrum. In order to accurately determine the optical constants, the thin film’s non-uniform thickness was accounted for. The increase in the refractive index and the coefficient of absorption was investigated and was found to demonstrate saturation with increased exposure time. Index changes as high as 0.05, or 2%, were obtained in As2Se3, a promising glass for all-optical switching.
©2002 Optical Society of America
Chalcogenide glasses exhibit many attractive optical properties, including a high refractive index, large nonlinearities, and excellent transmission at infrared wavelengths [1,2]. Consequently, chalcogenides are very promising glasses for ultrafast all-optical switching [3,4]. In particular, As2Se3 has a Kerr index approximately 1000× that of silica glass .
Chalcogenide glasses also exhibit many photoinduced and electron beam induced phenomena [5,6], including photoexpansion [7,8] and reversible photodarkening . Illuminating amorphous chalcogenide with near band-gap light will cause a red shift of the optical absorption edge and a corresponding increase in the refractive index. The initial state can be recovered by annealing near the glass transition temperature. The exact mechanisms involved are not fully understood and further study is required.
The optical properties of amorphous thin films can be measured by analyzing the material’s transmission spectrum. This analysis was pioneered by J. C. Manificer, et al.  and extended by R. Swanepoel , and since then has been successfully applied to several chalcogenide glasses, including As2Se3 . Swanepoel’s original work  assumed a film of uniform thickness. However, it is common for thin films to exhibit a wedge-shaped profile, which may lead to errors in the analysis if left unaccounted for. Fortunately, Swanepoel has also published methods describing how to determine the optical properties of such non-ideal films , and these too have been applied to chalcogenide glass [14–16]. Swanepoel’s methods are advantageous because they are non-destructive and yield the dispersion relation over a large range of wavelengths without any prior knowledge of the film’s thickness.
In order to use chalcogenide glasses in integrated optics, including wavelength selective devices for WDM networks , it is important to know the optical constants and how they can be changed with band-gap illumination. We report on the exposure-dependent change in optical constants of As2Se3 across a broad spectral range.
Fig. 1 is a model of a thin film deposited on a transparent substrate. The film and substrate are surrounded by air of index no=1, and the incident light from the spectrophotometer (used to measure transmittance) is normal to the substrate. The film has a refractive index n=n-ik and a coefficient of absorption α = 4πk/λ. The substrate has a refractive index s, and must be thick enough to eliminate any resonant modes apart from those within the film. The film is assumed to have a wedge-shaped profile so that the area under illumination varies linearly in thickness according to:
The transmission spectrum will contain interference fringes that obey the basic formula:
where: m = 1, 2, 3, … at maximum points in the transmission spectrum.
m = ½, , , … at minimum points in the transmission spectrum.
Swanepoel’s method [11, 13] requires envelopes to be constructed through the peaks and troughs of the transmission spectrum. Let TM (λ) describe an envelope containing all the maxima in the transmission spectrum and let Tm (λ) describe an envelope containing all the minima; both are considered to be continuous functions of λ. Restricting the analysis to the highly transparent region (n2 ≫ k2) and setting α = 0, two transcendental equations result:
where a = A /(B+D) and b = C/(B+D). Furthermore, A = 16 n2s, B = (n+1)3 (n+s2), C = 2(n2-1)(n2-s2), and D = (n-1)3 (n-s2).
Eq. (3) and (4) will yield a unique solution for both n and Δd in the region 0 <Δd< λ/4n. By solving Eq. (2) for a pair of adjacent maxima or minima described by (n1, λ1) and (n2, λ2) the average thickness of the film can be found:
2.1 Fringe order correction and calculation of the absorption coefficient
Having calculated the film thickness and refractive index, the accuracy of the results can be greatly improved by using Eq. (2) to evaluate the fringe order. By rounding off m to its exact integer or half integer value, the film thickness can be recalculated, averaged, and used to recalculate n, via Eq. (2). A Cauchy dispersion relation can be used to fit n (λ):
3. Experimental Procedure
As2Se3 films were prepared by vacuum thermal deposition at an evaporation rate of 4 nm/s on air cleaned glass substrates at a base pressure of 1×10-4 Pa. Depositions were performed at room temperature and the homogeneity and correct composition of each As2Se3 thin film was confirmed by x-ray microprobe analysis.
A schematic of the experimental setup used to produce photodarkening in As2Se3 films is given in Fig. 2. A 10 mW, 633-nm HeNe laser was used to expose the films, the duration of each exposure was controlled by a timed shutter, and the power of the laser was measured at the sample stage before and after each exposure. The laser power was sufficiently stable during exposures to avoid significant uncertainty in the total supplied energy dose. The laser beam was expanded from an initial beam waist of 1.0 mm (FWHM) using a plano-concave lens and collimated with a second plano-concave lens. At the sample stage an aperture was used to admit only the central maximum of the laser beam, irradiating the As2Se3 film with a fairly uniform intensity as is necessary to produce a uniform index change. The final intensity was approximately 25 mW/cm2.
A Perkin Elmer Lambda 900 UV/VIS/NIR Spectrometer was used to measure the transmission spectrum of the substrate with and without the As2Se3 thin film. Transmission measurements were made one week after the film was exposed and samples were kept in the dark between experiments. Finally, a Tencor Alphastep-200 Profilometer was used to verify the thickness of the thin film.
4. Results and Discussion
As2Se3 films were exposed to a 10 mW, 633-nm HeNe laser for various periods of time ranging from 1 minute to over 4 hours. The transmission spectrum of each film was measured both before and after exposure, and Swanepoel’s method was used to determine the refractive index change caused by photodarkening. The absorption coefficient for As2Se3 at 633 nm is approximately 1.5×104 cm-1 [9,14]. This implies that the refractive index change may not have been uniform throughout the depth of the film. However, assuming the variation in n is very small, Swanepoel’s method remains a very good approximation for determining the optical constants.
The spectrophotometer measured the transmission spectrum of the As2Se3 film from 500 nm to 2500 nm. The slit width was set to 1 nm and the spacing of neighboring interference fringes was great enough to ignore the correction factor required to account for the finite bandwidth of the spectrophotometer . The spectrophotometer beam spot was approximately 18 mm2 and was not intense enough to produce photodarkening.
Figure 3 illustrates a typical transmission spectrum prior to exposure. The results of a before- exposure transmission spectrum and subsequent analysis are summarized in Table 1. The transmissivity values that were determined by the envelopes, TM (λ) and Tm (λ), were generated by a parabolic interpolation of three neighboring extremes and appear in Table 1 in bold. The transmission spectrum of the substrate alone was used to determine s , and both n1 and Δd were found by substituting Eq. (3) and (4) into an iterative computer algorithm. Finally, the average film thickness d1, was calculated using Eq. (5) for each pair of adjacent maxima and minima. The mean value for Δd was 15 nm and the mean value for d1 was 777 ± 19 nm. At this point the fringe orders were calculated and rounded to their exact integer and half integer values, as described in Section 2.1. The final average thickness was 770 ± 4 nm, which was used to recalculate the refractive index n2. Notice the large reduction in the uncertainty of the film thickness that resulted from the fringe order correction. The dispersion relation fit to the final index values is shown in Fig. 4 and agrees well with published results .
Swanepoel’s method was applied to each film after exposure to laser radiation. In each case, only the transmission extremes that occurred at wavelengths greater than 828 nm were used in determining the final dispersion relation (although transmittance values at shorter wavelengths were used in the construction of the envelopes). Beyond 828 nm, which corresponds to a photon energy of 1.5 eV, As2Se3 can be considered transparent , satisfying the assumptions outlined in Section 2.
The change in the refractive index was defined as the refractive index measured after exposure minus the initial refractive index at a given wavelength. The initial refractive index is found by averaging together all of the refractive index values, at a given wavelength, measured from the before-exposure transmission spectra. The final results are shown in Fig. 5 for Δn at 1550 nm. The average unexposed index value was 2.72 and the change in refractive index tends to follow a Δn∝log(t) behavior as apparent in Fig. 5. Figure 6 shows the change in refractive index as a function of wavelength for several different exposure times. The magnitude of the change in the real part of the refractive index increases as the band-edge is approached as would be predicted by the Kramers-Kronig relationship.
Fig. 7 and Fig. 8 display similar results for the change in the absorption coefficient, which is calculated using Eq. 7. Fig. 7 shows the change in the absorption coefficient as a function of exposure time, at 560 nm, and is consistent with a recent study on the transient and metastable behavior of photodarkening (Δα) produced by an argon ion laser (2.41 eV) . Fig. 8 is a plot of the absorption coefficient versus photon energy for an exposed and unexposed As2Se3 film. According to the Tauc Law, the value of the x-intercept of Fig. 8 is the value of the energy-gap . The energy gap of the unexposed film was 1.76 eV, in agreement with .
5. Summary and Conclusions
Band-gap illumination of a chalcogenide glass is known to cause photodarkening, which produces an increase in the refractive index of the glass. Swanepoel’s method was used to determine the refractive index and the absorption coefficient of amorphous As2Se3 thin films, before and after exposure to near band-gap radiation. It was necessary to account for the non-uniform thickness of the thin films in order to accurately determine the optical properties. We found that the photoinduced change in the refractive index demonstrated signs of saturation with respect to exposure time. After the longest exposures we observed a change of 0.05, or 2%, in the refractive index of As2Se3 at 1550 nm; this is consistent with a recent study involving photoinduced Bragg gratings in amorphous As2Se3 . Similar behavior was observed with regards to the absorption coefficient, where changes were as high as 1×104 cm-1 at 560 nm. Future research will investigate the behavior of Δn as a function of the laser wavelength used to generate photodarkening in amorphous chalcogenides.
This project was made possible by financial support from NSERC (Canada). The authors would like to thanks TRLabs for providing the research facilities and financial support necessary to complete this work.
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