April 1999 Materials Letters 39 Ž1999. 122–128 Optical properties of amorphous As–Se and Ge–As–Se thin films L. Tichy´ a a,) , H. Ticha´ b, P. Nagels c , R. Callaerts c , R. Mertens c , M. Vlcek ˇ a Joint Laboratory of Solid State Chemistry of the Academy of Sciences of Czech Republic and UniÕersity of Pardubice, 530 09 Pardubice, Czech Republic b UniÕersity of Pardubice, 532 10 Pardubice, Czech Republic c RUCA-UniÕersity of Antwerp, B-2020 Antwerp, Belgium Received 29 June 1998; received in revised form 26 October 1998; accepted 9 November 1998 Abstract Amorphous As–Se and Ge–As–Se thin films were prepared by thermal evaporation. From parameters of the Wemple– DiDomenico model, the values of the third-order non-linear susceptibility were estimated using the generalized Miller’s rule. Measurements of photodarkening at 78 K showed that the optical gap and the slope of the optical absorption edge are intercorrelated. The kinetics of the photoinduced shift of the gap are described using a stretched exponential law. A possible role of the concentration of Se atoms on the rate of photodarkening on one hand and of the network rigidity Žmeasured by the mean coordination number. on the other are briefly discussed. q 1999 Elsevier Science B.V. All rights reserved. PACS: 78.66.Jg Keywords: Amorphous selenides; Index of refraction; Photodarkening 1. Introduction Amorphous chalcogenide thin films possess interesting optical properties including high refractive indices Ž n., good transparency in the infrared spectral region Že.g., selenide bulk glasses are transparent up to 11 mm if the content of oxygen impurities is of the order of ppm., and photoinduced changes of the optical properties. In the last 20 years, considerable attention has been given to the study of photostructural properties Žincluding photodarkening, i.e., a photoinduced red shift of the optical gap. of amor- ) Corresponding author. Tel.: q42-40-6036504; E-mail: ladislav.tichy@upce.cz phous chalcogenides, see, e.g., Refs. w1–6x and references cited there. In most cases, the photodarkening was reported mainly for room temperature conditions, and a study of the kinetics of photodarkening at low temperatures is rather scarce. In connection with the high refractive index Ž2 F n F 3.7. of the chalcogenide glasses and thin films, the non-linear optical properties of these materials are also of interest. There are some indications Žsee, for example, Refs. w7–9x. that amorphous chalcogenides have a rather high non-linear optical susceptibility, and consequently, these materials could be promising candidates for application as non-linear optical elements. Based on UV–VIS spectroscopy of some As–Se and Ge–As–Se thin amorphous films, we report in this communication our experimental data addressed 00167-577Xr99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 7 7 X Ž 9 8 . 0 0 2 2 7 - 4 L. Tichy´ et al.r Materials Letters 39 (1999) 122–128 to: Ži. linear refractive index dispersion and its relation to non-linear optical susceptibility, and Žii. kinetics of photodarkening at around liquid nitrogen temperature. 2. Experimental Amorphous thin films were prepared by thermal evaporation ŽBalzers system BAE 250 T, p ; 10y4 Pa, rate of evaporation 5–10 nmrs. of a bulk material Žat normal incidence. onto standard microscope glass substrates. The thickness of the films Ž d . was between 0.8–1.2 mm. The chemical composition of the films Žsee Tables 1 and 2. was determined by electron microprobe X-ray analysis ŽKevex D5 system, quantum detector.. The estimated average precision was around "1.6% in atomic fraction of an element. Before illumination, the samples Žexcept of a-As 3 Se 97 and As 22 Se 78 . were annealed for 3 h in dry nitrogen atmosphere at a temperature T s TS y 80, where TS Žsee Table 2. is the softening temperature estimated using penetration probe measurements Ža load of 50 g.. Films ‘relaxed’ in this way ŽAs 3 Se 97 and As 22 Se 78 films were relaxed for 4 months in a dark desiccator. are described as ‘ virgin’ films. The optical properties were measured in a similar way as described in Ref. w10x. All the measurements of photodarkening were made in an optical cryostat Cryoson XL 500 with a halogen lamp Žequipped with an infrared-cut filter. in the sample compartment of a Beckman DU-640 UV–VIS spectrometer. 123 Hence, during illumination, the sample was never removed from the system and its position in the sample compartment was always the same. The measurements were carried out at T ; 78 K with helium gas in the inner part of cryostat in order to improve the heat transfer between the sample and cooling system of the cryostat. There are some indications that photodarkening is a spectral sensitive property Žsee, for example, Refs. w11x.. Hence, for a correct comparison of photodarkening of the films with different band gap, one has to take this into consideration. In our experiments, we were limited, for technical reasons, by using a halogen lamp equipped with an infrared-cut filter as a source of the excitation light. ŽThe estimated incident power density was ; 50 mWrcm2 .. In order to make any comparison of photodarkening in the various films, we selected those with a similar bandgaps but with a Se content as different as possible Žsee Table 2.. The values of the optical gap Ž Eg . were taken as the intercept of plots Ž a " v .1r2 against " v for a s 0 w12x: Ž a"v. 1r2 s B 1r2 Ž " v y Eg . , Ž 1. where B 1r2 is the slope of the edge, a is the absorption coefficient w13x and " v is the photon energy. The transmission range below 20% was used to determine the a values. The values of the reflectance R s 23% ŽAs 3 Se 97 ., R s 24% ŽAs 22 Se 78 ., R s 28% ŽAs 39 Se 61 , Ge 5 As 35 Se 60 ., R s 30% ŽGe 2 As 40 Se 58 ., and R s 22% ŽGe18.5 As 6 Se 75.5 . were used in the calculation of a values. The optical Table 1 The sample number, the chemical composition, the optical gap Ž Eg ., the single oscillator energy Ž E0 ., the dispersion energy-experimental Ž Ed,ex . and calculated ŽEq. Ž3.. Ž Ed,cal ., the refractive index Ž n 0 , " v ™ 0., and the third-order non-linear susceptibility Ž X Ž3. . Sample no. Chemical composition Eg ŽeV. E0 ŽeV. Ed,ex ŽeV. Ed,cal ŽeV. nŽ0. X Ž3. )10y12 Žesu. 1 2 3 4 5 6 7 As 3 Se 97 As 22 Se 78 As 41 Se 59 As 39 Se 61 Ge 9 As 25 Se 66 Ge 5 As 35 Se 60 Ge 2 As 40 Se 58 1.935 1.872 1.79 1.79 1.92 2 1.82 8 1.78 3 3.66 3.63 3.59 3.60 3.62 3.69 3.63 18.9 20.1 23.0 23.4 20.9 22.9 23.8 19.6 21.5 22.4 22.4 20 22.6 23.1 2.479 2.557 2.72 3 2.735 2.60 3 2.68 2.74 8 2.87 3.85 6.94 7.24 4.56 6.09 7.52 T ; 300 K. L. Tichy´ et al.r Materials Letters 39 (1999) 122–128 124 Table 2 The sample number, the chemical composition, the optical gap of ‘ virgin’ film Ž Eg Žv.., the calculated–saturated photodarkened gap Ž Eg Ž`.., the overall relaxation time Žt ., and exponent Ž b . Žsee Eq. Ž8.., at T ; 78 K Sample no. Chemical composition Eg Žv. ŽeV. Eg Ž`. ŽeV. t Žmin. b TS ŽK. 1 2 4 6 7 8 As 3 Se 97 As 22 Se 78 As 39 Se 61 Ge 5 As 35 Se 60 Ge 2 As 40 Se 58 Ge18.5 As 6 Se 75.5 2.094 2.03 4 1.92 8 1.98 5 1.92 6 2.153 1.96 5 1.86 8 1.79 8 1.85 1.79 2.02 6 18.1 43 121.5 142 211 19.5 0.60 0.57 0.63 0.85 0.68 0.92 318 369 446 458 453 413 Last column—the softening temperature ŽTS .. transmission spectra for calculation of the refractive index dispersion were measured at room temperature using a standard solid sample holder. w16,17x. the X Ž3. value is approximately equal to the fourth power of X Ž1. and consequently: 4 X Ž3. s w X Ž1. x = 10y10 Ž esu . s Ed E0r4p Ž E02 3. Results and discussion yŽ " v . From the spectral dependences of transmission, we calculated the dispersion of the refractive index n of some films Žusing Swanepoel’s method w14x.. The results are summarized in Fig. 1 in the form Ž n2 y 1.y1 against " v according to the single oscillator formula of Wemple and DiDomenico w15x: 2 n2 Ž v . y 1 s E0 Edr Ž E02 y Ž " v . . . 2 . 4 = 10y10 Ž esu . . Ž 4. In the limit " v ™ 0, we obtain from Eq. Ž4.: 4 X Ž3. s 4.02 = 10y15 Ž EdrE0 . Ž esu . . Ž 5. Ž3. In Table 1, the X values for the wavelength l s 5 mm calculated according to Eq. Ž4., are summarized. Our X Ž3. values are large, and are comparable with Ž 2. In Table 1, the values of E0 , Ed , nŽ0. are summarized. In Eq. Ž2., E0 is the single oscillator energy, and Ed is the dispersion energy which obeys a simple empirical relation w15x: Ed s b Nc Za Ne Ž 3. where Nc is the coordination number of the nearestneighbour cation to the anion, Za is the formal chemical valency of the anion, Ne is total number of valence electrons per anion, and b s 0.37 " 0.04 eV for covalent materials. Taking for simplicity b s 0.4 eV and Nc ŽGe. s 4, Nc ŽAs. s 3, Nc ŽSe. s 2, Za s 2, and corresponding numbers of valence electrons, i.e., 4, 5, 6, for Ge, As, Se atoms, respectively, the calculated Ed values agree reasonably with the ‘experimental’ Ed values Žsee Table 1.. The parameters of the Wemple and DiDomenico ŽWD. model can be used for a rough estimation of the X Ž3. value—the third-order non-linear optical susceptibility. According to the generalized Miller’s rule Že.g., Refs. Fig. 1. The dispersion of the refractive index n in the form Ž n 2 y1.y1 against E 2 Ž s Ž " v . 2 .. The lines correspond to Eq. Ž2.. The numbers in parentheses indicate the chemical compositions of the films Žsee Table 1.. L. Tichy´ et al.r Materials Letters 39 (1999) 122–128 X Ž3. values of some other chalcogenide glasses Žsee for example, Refs. w7,8x.. Figs. 2 and 3 are typical plots of Ž a " v .1r2 against " v for some As–Se and Ge–As–Se thin films for the two extremes in illumination time, i.e., for the ‘ virgin’, and for the final illuminated state of the films. The full lines Ž‘ virgin’ state. and dashed lines Žfinal illuminated state. represent the best fit of our experimental data to Eq. Ž1.. Similarly, as in our recent communication w10x, we observe a focal point in Ž a " v .1r2 vs. " v dependences indicating a possible correlation between the photoinduced change of the slope of the Tauc edge Ž B 1r2 . and the photoinduced change of the Tauc gap Ž Eg .. The decrease of the slope of the Tauc edge induced by illumination indicates that a decrease of the gap is accompanied by an increase of disorder. If we follow the suggestion of Fortunato et al. w19x that the optical gap could be diminished by a broadening of the conduction and valence bands due to a redistribution of the states within some range of energies, i.e., within a certain gap E1 , then the following equation relates the Eg and B values w19x: 3 B s Constr Ž E1 y Eg . . Ž 6. 125 Fig. 3. The spectral dependences of Ž a " v .1r 2 . The full curves for some Ge–As–Se thin films. The lines correspond to Eq. Ž1.. Full lines are for virgin states and dotted lines are for final darkened states. The points indicate relevant chemical compositions, upper points indicate the focal point. of the illumination time Ž t ., the following relation results from Eq. Ž6. w10x: Eg Ž t . s E1 y ConstXrB 1r3 Ž t . . Ž 7. Assuming that the E1 gap is practically independent In Fig. 4, our experimental Eg Ž t . and B Ž t . values Žpoints. are plotted according to Eq. Ž7.. The agree- Fig. 2. The spectral dependences of Ž a " v .1r 2 . The full curves are for some As–Se thin films. The lines correspond to Eq. Ž1.. Full lines are for virgin states and dotted lines are for final darkened states. The points indicate relevant chemical compositions and upper points indicate the focal point. Fig. 4. Plots of Eg against 1r B 1r 3 according to Eq. Ž7.. The full symbols are experimental values, the lines correspond to Eq. Ž7.. The numbers in parentheses indicate chemical compositions of the films Žsee Table 2.. E1Ž . . . . are the values of a ‘certain gap’ Žsee Eq. Ž6... L. Tichy´ et al.r Materials Letters 39 (1999) 122–128 126 ment seems satisfactory. Hence, it is reasonable to assume that photodarkening could proceed due to a broadening of the conduction and valence bands into the gap. In Fig. 5, the results of the measurements of the kinetics of photodarkening are summarized. The points indicate the experimental values, the curves indicate fits to the equation: Eg Ž t . s Eg Ž v . q Ž Eg Ž ` . ž yEg Ž v . . 1 y exp y Ž trt . b /. Ž 8. Here, Eg Ž t . is the gap value after time t Žin min. of illumination, Eg Žv. stands for the virgin film gap, Eg Ž`. stands for saturated–photodarkened gap and t is an overall relaxation time. In Refs. w20–22x, the room temperature kinetics of photodarkening of various amorphous chalcogenide films have been described by a first-order reaction model. For a formal description of the kinetics of photodarkening, we have used the stretched-exponential law, SEL, Eq. Ž8.. The SEL always gave better agreement with our experimental data than either a single exponential Žln. or a numerical fit Žnon-linear regression.. Moreover, there are at least two important physical reasons for using Eq. Ž8. for an overall description of Fig. 5. The dependence Eg Ž t . induced by illumination at T ; 78 K. The points are experimental values, the curves correspond to Eq. Ž8.. The numbers in parentheses indicate the chemical compositions of the films Žsee Table 2., where also the parameters of the fit Ž Eg Ž`., t , b , see Eq. Ž8.., are summarized. the kinetics of photodarkening. The first is based on Tanaka’s w11x configuration–coordination model of photodarkening. In this model, illumination induces a structural transformation from a stable Žground. configuration to a quasistable Ždarkened. configuration. It was shown, e.g., in Refs. w23,24x, that in such a system Žtwo-level configuration coordinate diagram., if all defects in the amorphous solids are distributed exponentially in energy, the population of the defects Ž NB . in the quasistable state ŽB. with respect to the ground state ŽA. is given by the equation: NB Ž t . s NB Ž 0 . q Ž NB Ž ` . ž yNB Ž 0 . . 1 y exp y Ž trt . b / Ž 9. where NB Ž0., NB Ž`. are the initial, and saturated populations of defects in state B, respectively, and NB Ž t . is the population of defects in state B after illumination for a time t. Consequently, if the original distribution of the states A and B characterized by Eg Žv. is changed by illumination according to Eq. Ž9., the overall change in Eg Ž t . can be described by Eq. Ž8.. Hence, Eg Ž t . reflects the kinetics of the changes in population of the quasistable defects B. The second reason for applying the SEL to our kinetic data is that it also provides a good description of the overall kinetics of a process resulting from competition between excitation and de-excitation. It applies, for example, in the case of promotion ŽP. from a ground state to an excited-quasistable state and backward ŽB. Že.g., by thermal processes. from a quasistable state to the ground state, if the excitation and de-excitation rates are written as k P s At by1 and K B s Bt by1, respectively Žsee for example, Refs. w6x.. Unfortunately, our data cannot be discussed quantitatively within either of the above mentioned physical origins of the SEL. The main reason is the absence of a knowledge of the temperature dependence of the kinetics of photodarkening. Another is a problem of the excitation light used. Despite the fact that we select thin films with a rather relatively similar energy gap Ž1.93 eV - Eg Žv, 78 K. - 2.11 eV. one cannot exclude the possibility that during illumination, the efficiency of photodarkening changes with decreasing energy gap. Finally, the experimental inaccessibility of the saturated Eg Ž`. L. Tichy´ et al.r Materials Letters 39 (1999) 122–128 values makes the parameters of the fits of our experimental data to Eq. Ž8. insufficiently accurate for a quantitative analysis. If, however, the calculated values of t and Eg Ž`. correspond to reality, the major difference between thin films is in the ‘rate’ of photodarkening rather than in the magnitude of photodarkening measured as D Eg Ž`. s Ž Eg Žv. y Eg Ž`.. Žsee Table 2.. For a rough estimation of the ‘rate’ of photodarkening, the illumination time t s t necessary to reach the conversion point cŽ t s t . s Ž Eg Ž t . y Eg Ž`..rŽ Eg Žv. y Eg Ž`.. s 0.367, is taken. As evident from Table 2, a rather high rate of photodarkening is observed for Se-rich samples Ž1, 2, 8. while for nearly stoichiometric samples Ž4, 6. or for the Se-deficient sample Ž7., the times Ž t s t . which are approximately 5 times longer are necessary to reach the same degree of conversion. The present results indicate that the concentration of Se-atoms is responsible for the ‘rate’ of photodarkening since the rate of photodarkening increases as the content of Se increases. Hence, as is generally accepted, the chalcogen atoms seem to have a crucial role in photodarkening. This is consistent with our discussion of the interrelation between B 1r2 and Eg . The difference between E1 and Eg values is small: 0.62 eV F Ž E1 y Eg Žv.. F 0.71 eV; 0.775 eV F Ž E1 y Eg Ž`.. F 1.08 eV Žsee Fig. 4 and Table 2. which indicates that photoinduced changes in the density of states occur in a rather narrow range at the bottom of the conduction band and the top of the valence band. The later one is formed from p-LP states of Se-atoms. Finally, we speculate that it is not only the concentration of the chalcogen atom, but also the matrix rigidity as measured by the mean coordination number Ž²CN:., for example, which is of considerable importance in the photodarkening process. We suppose that for a matrix with low ²CN:, e.g., ²CN: 2.4 1 , the flexibility of the matrix allows rather rapid relaxation from the quasistable Žilluminated. state back to a ground state. Such a relaxation could be depressed by illumination at low temperatures. A rigid matrix would make it more difficult to create a 1 Note that ²CN: s 2.4 corresponds to the Phillips–Thorpe threshold w25,26x, where the system is mechanically stable. When ²CN: - 2.4, the system is soft or floppy, and when ²CN: ) 2.4, it is rigid. 127 quasistable illuminated state but once attained it could be relatively stable since rigidity would suppress relaxation back to a ground state. This seems to be consistent with our visual observation of a ‘stability’ of the darkened spot after an illuminated sample was annealed at room temperature and removed from the cryostat. In the case of Sample 1 Ž²CN: s 2.03., we did not observe any darkened spot, while for Sample 2 Ž²CN: s 2.22., a weak spot was seen but it was stable for a only short time Žh.. Dark spots in Samples 4 and 6–8 Ž2.39 F ²CN: F 2.45. were stable for weeks. Note that Samples no. 2 and 8 have comparable content of Se atoms but more stable Sample no. 8 has the mean coordination number 2.43 while Sample no. 2 has ²CN: s 2.22. Hence, the matrix rigidity of Sample no. 8 is less flexible, a relaxation back to a ground state is more difficult and the dark spot of this sample is more stable. An open question remains—the values D E s Eg Žv. y Eg Ž`., which except for Sample no. 2 Ž D E ( 0.17 eV., are practically constant: D E ( 0.13 eV, see Table 2. Within our speculation concerning a possible role of a matrix rigidity in overall photodarkening process, we suppose that the illumination temperature ŽT ; 78 K. is rather high temperature with respect to the matrix flexibility of Sample no. 1 with ²CN: s 2.03. Consequently, in such floppy matrix, the relaxation back to a ground state is significant, and overall red shift of the gap Ž D E . is limited by this backward relaxation. This seems to be in agreement with our recent observation of the role of a temperature in photodarkening in Se-rich Ge x Se1yx films w18x. Nearly constant matrix rigidity of Samples no. 4, 6–8 could then be responsible for rather constant final values of a red shift of the gap, while more flexible matrix of Sample no. 2 allows to reach higher values of D E at the temperature T s 78 K. Further experimental work is necessary in order to elucidate a possible role of a matrix rigidity in the overall photodarkening process. One can suppose that the stability of the photodarkened state is related to the glass transition temperature ŽTg , which is close to TS ., see Table 2, thus the lower Tg , the less stable is the photodarkening stability. However, according to Tanaka w27x, Tg can be related Žat least in the region 2²CN: - 2.7. to ²CN: by equation: ln Ž Tg . s 1.6²CN: q 2.3 Ž 10 . 128 L. Tichy´ et al.r Materials Letters 39 (1999) 122–128 and hence, in first approximation, Tg Žor TS . can be taken as a rough measure of the network rigidity. 4. Conclusion Ži. Using parameters of the Wemple–DiDomenico single oscillator model for the linear refractive index dispersion and Miller’s rule, we estimated the values of the third-order non-linear optical susceptibility for several amorphous chalcogenide thin films. Estimated values are large Žup to X Ž3. s 7.52)10y12 Žesu. for Ge 2 As 40 Se 58 thin films. and are comparable with X Ž3. values observed for other chalcogenide systems w8x. Žii. We found a correlation between the photoinduced shift of the optical gap and the slope of the optical absorption edge. Within Tauc’s model, this correlation indicates that the observed photodarkening is due to an increase in disorder at the expense of delocalized states close to the band edges. Žiii. We found that the kinetics of photodarkening at liquid nitrogen temperature can be described using a stretched-exponential law. Comparing the time of illumination necessary to reach the isoconversion state in photodarkening of all studied films Žnote that the conversion is always equal to 36.7% for t s t , where t is the time of illumination and t is the overall relaxation time., we suppose that the concentration of Se atoms is responsible for the ‘rate’ of photodarkening. We also speculated that the stability of photodarkened films can be influenced by the mean coordination number which is taken as a rough measure of the network rigidity. 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