relaxation process of holographic gratings in amorphous as_2s_3 films

2498 J. Opt. Soc. Am. B/Vol. 14, No. 10 /October 1997 J. Teteris and O. Nordman

Relaxation process of holographic gratings inamorphous As2S3 films

Janis Teteris* and Olli Nordman

Department of Physics, University of Joensuu, P.O. Box 111, FIN-80101 Joensuu, Finland

Received October 28, 1996; revised manuscript received March 4, 1997

A detailed study of the relaxation self-enhancement (RSE) of the holographic gratings in amorphous As2S3films is presented. The changes of the diffraction efficiency have been measured as functions of the aging timeand the recording light intensity. The role of the internal mechanical stress of the films in the self-enhancement phenomenon has been discussed. It is shown that the RSE has a vectorial character owing tothe uniaxial periodically distributed stress relaxation. A model based on the photoinduced stress relaxationand viscous flow of amorphous film is proposed to explain the experiments qualitatively. It is further shownthat the stress-induced optical anisotropy of the films is responsible for the RSE. © 1997 Optical Society ofAmerica [S0740-3224(97)01909-7]

1. INTRODUCTIONIt is known that a number of physical and chemical prop-erties of amorphous chalcogenide semiconductors (ChS)can be changed by light illumination.1–3 Among these,the phenomena of the photodarkening and photoinducedrefractive-index changes are the most frequently studiedowing to their applicability for the practical purposes.Depending on the preparation conditions, the photoin-duced changes in ChS can be either reversible or irrevers-ible. Irreversible changes are usually observed in amor-phous thin films prepared by the vacuum thermaldeposition or the sputtering process.

The photodarkening in As2S3 films is an increase of theabsorption coefficient near the optical absorption edge.The bandgap energy of the unexposed films is 2.38 eV,and its photoinduced decrease is ;75 meV (Ref. 4). Thevalue of the photoinduced refractive-index increase de-pends on the wavelength of the light. At 632.8 nm, theas-evaporated As2S3 films have the initial refractive indexof 2.45 and the maximum photoinduced change Dn' 0.13 (Ref. 5).

Amorphous films of ChS obtained by thermal deposi-tion in vacuum can be characterized by a variety of fea-tures. This includes structural and compositional disor-der and the presence of pores, voids, and other deviationsfrom the regular structure.6,7 Therefore excess energy isstored into films after their evaporation. This energytends to diminish over time, causing the relaxation of theoptical, the mechanical, and the chemical properties.AsxS12x films with arsenic content 0.3 , x , 0.4 have themaximum changes, and their relaxation is saturated in;100 days at room temperature.8,9

During the study of the holographic properties of theamorphous As–S films doped with bromide, an increase ofthe diffraction efficiency (DE) after the recording was ob-served by Brandes et al.10 This phenomenon, called re-laxation (or dark) self-enhancement (RSE) of holograms(an increase of diffraction efficiency over time without anyspecial treatment) in amorphous As2S3 films, was studied

0740-3224/97/102498-07$10.00 ©

in detail by Ozols et al.11 and Salminen et al.12 The phe-nomenological periodically distributed stress relaxationmodel was used to explain the RSE. According to themodel, the RSE results from a periodical spatial mechani-cal stress modulation induced by the holographic grating(HG). The stress causes the translational motion of va-cancies, pores, and voids from HG maxima to minima.

The purpose of this paper is to investigate the pecu-liarities of the holographic recording and the self-enhancement phenomenon in amorphous As2S3 films.This is done by use of different structural ordering ob-tained through thermal treatments of the films. The sig-nificant role of the internal mechanical stress of the filmsin the self-enhancement phenomenon has been verifiedexperimentally. A mechanism of the RSE based on thephotoinduced stress relaxation and on the viscous flow ofamorphous semiconductor has been discussed.

2. EXPERIMENTS AND RESULTSAmorphous As2S3 films (thickness d 5 10 mm) were pre-pared by thermal evaporation in vacuum at the pressureof 5 3 1024 Pa, and the deposition rate was 80 Å/s.Some of the samples were annealed. Two different tem-peratures were used, namely, 373 K and the glass transi-tion temperature Tg 5 463 K. The annealing time was20 min. Fused quartz, optical K-8 glass, and LiF wereused as As2S3 film substrates. The thermal expansioncoefficients of the materials are 7 3 1026 K21 (K8), 303 1026 K21 [a-As2S3 (Ref. 13)], 5 3 1027 K21 (fusedquartz), and 41 3 1026 K21 (LiF). Experiments werestarted 2 weeks after the deposition.

Transmission holographic gratings with period ofL 5 0.9 mm were recorded by two symmetrically incidentAr1 laser beams of equal intensity. The recording wave-length l1 was 514.5 nm, thus the photon energyhn 5 2.41 eV is close to optical bandgap Eg 5 2.38 eV ofthe a-As2S3 films.4 The probing of the gratings (duringthe recording) and the RSE was done with a He–Ne laser(l2 5 632.8 nm). The probing beam was set to the

1997 Optical Society of America

J. Teteris and O. Nordman Vol. 14, No. 10 /October 1997 /J. Opt. Soc. Am. B 2499

Bragg angle. The average intensity of the beam I05 1 mW/cm2. To minimize the He–Ne laser light influ-ence on the recording process, we probed periodically, us-ing a mechanical shutter. Figure 1 shows the measuringsetup. The recording laser and the probing laser had lin-early, vertically polarized beams. The beams were s (orTE) polarized because the plane of the polarization wasperpendicular to the plane of incidence.

The diffraction efficiency h (t) was defined as

h ~t ! 5Id

I0, (1)

where Id is the intensity of the first-order diffractedbeam. In our experiments we stopped the recording pro-cess when h (t) 5 h0 5 0.5%. Different intensities wereused for the recording. After the recording process, theRSE measurements were started immediately. The de-gree of RSE was determined by the RSE factor

j~t ! 5h ~t !

h0, (2)

where h(t) is the DE at time t elapsed from the recording.To study the changes of the optical anisotropy of the RSE,we also probed the gratings with a p- (or TM-) polarizedHe–Ne laser beam (light polarized perpendicular to thegrating lines). The DEs are denoted by h' ( p polariza-tion) and h i (s polarization).

The recording of the HG up to the initial diffraction ef-ficiency of h0 5 0.5% (using different intensities) and thefollowing increase of the DE (caused by the RSE) during 1h are shown in Fig. 2. (The end of the recording and thebeginning of the RSE is defined as ‘‘0’’ on the time axis.)These experiments were done with fused-quartz, glass,and LiF substrates. However, practically no differencewas observed in the recording and the RSE processes be-tween different substrates. According to the figure, theHG recording kinetics can be described with a growing ex-ponential function depending on the light intensity andthe amorphous state of the films. Also, the RSE is foundto be dependent on these same parameters. The inten-sity dependence is particularly strong for the as-evaporated films [Fig. 2(a)]. The decrease of the RSE isobserved in the films annealed at 373 K [Fig. 2(b)]. The

Fig. 1. Experimental setup for the holographic recording andmeasurement of the RSE: M, mirror; S, shutter; BS, beam split-ter; and PD, photodiode.

films annealed at a temperature close to the glass transi-tion temperature (Tg 5 463 K) practically do not exhibitthe RSE at all [Fig. 2(c)].

The saturation value of the RSE for the curves of Fig.2(a) was measured 6 months after the recording. The re-sults are displayed in Fig. 3. According to the measure-ments, the saturation value decreases linearly with de-creasing light intensity. When the linear behavior wasextrapolated, the smallest intensity (threshold) Ith for the

Fig. 2. Changes of the diffraction efficiency during the recording(R) and the RSE processes in a-As2S3 films. (A) As-evaporatedfilm with the following recording light intensities: a,0.71 mW/cm2; b, 2.2 mW/cm2; c, 17 mW/cm2; d, 80 mW/cm2; ande, 160 mW/cm2. (B) After thermal annealing at 373 K. (C) Af-ter thermal annealing at 463 K.


recording is of the order of 1025 W/cm2. This valueagrees quite well with our previous results.12

Figure 4 shows the RSE for the probing light with dif-ferent polarization (h' and h i). Note that immediatelyafter the HG recording, the values of the initial DEs weredifferent and h' . h i . After prolonged monitoring ofthe RSE, the DEs started to behave differently for thereadout light with different polarizations. The increasein the s-polarized probing was more intense, and the signof the HG optical anisotropy, defined as (h i 2 h')/(h i 1 h'), changes after ; 20 h, as curve c in Fig. 4shows. Similar behavior was observed for all recordinglight intensities, and it was not affected by the substratematerial.

3. DISCUSSIONA. Grating-Induced Stress and Relaxational StructuralChanges Including RSE and Optical AnisotropyAmorphous ChS film obtained with thermal deposition invacuum has excess energy owing to structural disorder(distortions in bond angles and bond lengths4), composi-tional disorder (presence of 30% homopolar As—As and

Fig. 3. RSE saturation factor hs /h0 as a function of the record-ing light intensity.

Fig. 4. Increase of diffraction efficiency in the RSE of the as-evaporated As2S3 films. The readout laser beam had s (curve a)and p polarizations (curve b). Curve c shows the change of theHG optical anisotropy. The intensity of the recording light was2.2 mW/cm2 and the initial diffraction efficiencies were h0 5 h i

5 0.5%. K8 glass substrates were used.

S—S bonds14), and the presence of pores, voids, and otherdeviations from the regular structure. The appearanceof the internal mechanical stresses and strains in amor-phous As2S3 films during their formation was shown byTrunov and Anchugin.15 The compressive stress of sc' 23 3 107 Pa in As2S3 layers deposited at temperatureintervals of 100–293 K was observed. The annealing ofthe films to the temperature of 373 K was accompanied bythe disappearance of the compressive stress. Whensamples were cooled, tensile stress appeared. Similarly,for the as-evaporated films during the light illumination,the initial compressive stress decreased to zero, but afterswitching the light off, tensile stress arose. These resultsare in a good agreement with the photoinduced contrac-tion observed in as-evaporated As2S3 films (the initialstate of the films has compressive stress16). Agreementis also good with the photoinduced expansion observed infilms annealed at Tg (the initial state of the films has ten-sile stress17). The annealing of the as-evaporated filmsat temperatures close to or exceeding the glass transitiontemperature (Tg 5 463 K) of As2S3 significantly changesthe situation. In this case, the residual mechanicalstress in the films at room temperature is determined bythe equation18

s 5 const DT~a f 2 as!, (3)

where a f and as are the thermal expansion coefficients ofthe As2S3 film and the substrate material and DT 5 Tg2 293 K. The reason for this different behavior is thatnear the glass transition temperature the structure of theAs2S3 films changes. This will be discussed in the nextsection where we speak about the viscosity.

The illumination of the As2S3 films causes the photoin-duced relaxation of the internal mechanical stress. Thismeans that when HG are recorded, the internal mechani-cal stress has a spatially periodic distribution in the film,depending on the period. The distribution of the stressin a film before and after the HG recording is presented inFig. 5 by curves (a) and (b). During the recording, thephotoinduced decrease of the compressive stress takesplace in grating maxima. As a result, a difference of themechanical stress (Ds) between maximum and minimumarises with the mechanical stress gradient.

ds

dx5 2

Ds

L, (4)

where L is the HG period.The significant role of the internal mechanical stress in

the RSE of the amorphous As2S3 films is confirmed by themeasurements presented in Figs. 6 and 7. AmorphousAs2S3 films deposited on LiF and fused-quartz substrateswere used for the measurements. After recording theHG up to its initial diffraction efficiency h0 5 0.5%, westored the films at room temperature in the dark for 2weeks. Because of the relatively long storage time, theRSE was nearly saturated. After storage, the films wereheated to 355 K with the rate of ;1 K/min, and then theywere allowed to cool. The changes of the DE were mea-sured simultaneously. From the experimental results(Figs. 6 and 7) one can conclude that the behavior of theDE of the samples depends on the substrate material. Inthe films on LiF substrates, the increase of the DE with


heating to 345 K is followed by the rapid decrease at thetemperatures above 345 K (Fig. 6). In the films on thefused-quartz substrates, heating causes the decrease ofthe DE (Fig. 7). The different behavior can be explainedwith the aid of the different internal mechanical stressfields induced by the substrate materials. According toEq. (3), the sign of the stress fields of the films is opposite.In the case of the LiF substrates, as . a f , and the rise ofthe temperature causes an increase of the compressivestress. In films deposited on the fused-quartz substrate,as , a f , and the decrease of the compressive stress takesplace. Note that the change of the DE is reversible up to345 K, but heating above 345 K is accompanied by the ir-reversible decrease of the DE. These thermally inducedmodifications of the compressive stress between HGmaxima and minima cause the changes in the refractiveindex (Dn), and corresponding changes in the DE are ob-served. The reversibility of the changes up to 345 K in-dicates the elasto-optical character of the RSE. The irre-versible decrease of the DE at the temperatures above345 K is connected with the disappearance of the internalmechanical stress,9,15 which is connected to the change inthe film structure (Subsection 3.B).

The changes in the optical anisotropy during one of thethermal treatments discussed above are displayed in Fig.6 (curve c). The optical anisotropy of the As2S3 films has

Fig. 5. Model of the mechanical stress distribution in amor-phous As2S3 film (a) before and (b) after the HG recording.

Fig. 6. Changes of the diffraction efficiency during the heatingwith the rate of 1 K/min and cooling following it for the s (curvea) and p polarizations (curve b) of the readout light. The opticalanisotropy is presented by curve c. As2S3 films on LiF sub-strates were used.

been annealed at temperatures above 345 K. Conse-quently, the RSE is a vectorial phenomenon that is an-nealed at ;100 K below the glass transition temperatureTg . The result is in accordance with the results of Ref.19.

As already mentioned, immediately after the deposi-tion of the amorphous As2S3 samples, the relaxation of anumber of physical and chemical properties takesplace.8,9 The temperature dependence of the relaxationobeys the Arrhenius law with the activation energy of1.14 eV (Ref. 9). However, the RSE takes place even inthe samples that were either ; 3 years at roomtemperature12 or annealed at 373 K [Fig. 2(b)]. It can beexplained with the aid of the stress relaxation theory indisordered materials. Stress relaxation in glasses can beexpressed as a sum of two constituents20:

s~t ! 5 s0 expF2S ttr

D nG 1 s` , (5)

where s0 is a constituent of stress that can be relaxed,and s` is stress of equilibrium state in material. Evi-dently, the recording process of the HG in aged As2S3films or in films annealed at 373 K causes the changes instress equilibrium state s` , and the RSE can take place.

A remarkable aspect of the structural relaxation inamorphous and glassy systems, both electronic andatomic, is that the more homogeneous the system, i.e., thesmaller the extent of the onset of the spinodal phase sepa-ration or microcrystallization, the more accurately its re-laxation can be described by the stretched exponentialfunction often called the Kohlraush–Williams–Wattsfunction9,21:

K~t ! 5 K0 expF2S ttr

D nG , (6)

where K is a quantity belonging to the relaxation process,tr is the relaxation time of the process, and n is a param-eter characterizing the relaxation process. This expres-sion is also often used to represent mechanical stress re-laxation functions. Parameter n in these cases has acharacteristic value between 0 and 1 describing a broad

Fig. 7. Changes of the diffraction efficiency (s polarization) in a-As2S3 films on fused-quartz substrates during heating at the rateof 1 K/min and subsequent cooling.


distribution of the relaxation times. For the RSE of theas-evaporated films and the films annealed at 373 K, weget [Figs. 2(a) and 2(b)]

h~t ! 5 h0 1 ~hs 2 h0!$1 2 exp@2~kt !n#%, (7)

where k is the rate constant of the relaxation process(k 5 1/tr). After taking the logarithm twice, we get theprevious expression in the form

lnF2lnS hs 2 h~t !

hs 2 h0D G 5 n ln k 1 n ln t. (8)

It is seen from Fig. 8 that the RSE results obtained ex-perimentally for as-evaporated films satisfactorily lie inthe straight lines constructed in coordinates ln(2ln$@hs2 h (t)#/ (hs 2 h0)%) and ln(t). This confirms that the RSEreally is due to the structural relaxation as we alreadyhave supposed. From the steepness of the straight linesone can obtain n values, which vary from 0.2 to 0.4 de-pending on the recording light intensity.

B. Stress Connected with Microhardness and ViscousFlowThe structure of the amorphous as-evaporated As2S3 filmsis, in a metastable state, due to the distortions in both thebond angles and lengths, the presence of ;30% homopo-lar As—As and S—S bonds, and the presence of pores,voids, and other deviations from the regular structure.These influences on the viscosity of the film lead to its sig-nificant reduction. This conclusion is supported by themicrohardness (H) measurements of the amorphousAs2S3 films.3 The microhardness of the as-evaporatedfilms and the films annealed at temperature Tg differssignificantly. The values of the microhardness are 500MPa (as-evaporated) and 1300 MPa (annealed). Thereare also two different temperature regions with differentH characteristics for as-evaporated films. H decreasesslowly with increasing temperature up to 395 K. Furthertemperature elevation to 465 K (Tg temperature) is con-nected with drastic H increase. In other words, micro-hardness H has an anomalous temperature dependence.The increase of H in the annealing process for tempera-tures above 395 K can be explained by the rearrangementof the structural units leading to a more rigid structure.Consequently, the viscosity of As2S3 films annealed atT . 395 K increases significantly. According to Eq. (3),

Fig. 8. RSE for as-evaporated As2S3 film in the coordinatesln(2ln$@hs 2 h (t)#/(hs 2 h0)%) and ln t.

the sign of the mechanical stress (tensile or compressive)in the films annealed at Tg depends on the difference be-tween the thermal expansion coefficients of the As2S3 film(a 5 30 3 1026 K21) and the substrate material. There-fore the compressive stress in As2S3 films on LiF (a5 41 3 1026 K21) substrates and the tensile stress onfused-quartz (a 5 5 3 1027 K21) and glass (a5 7 3 1026 K21) substrates can be obtained. Our calcu-lations show that the values of the compressive or tensilestresses in the films after annealing at Tg must be higherthan the stresses in as-evaporated films. This is con-firmed experimentally by Trunov and Anchugin15 withthe As2S3 films on the mica substrates(a 5 20 3 1026 K21). However, as it is shown in our ex-periments [Fig. 2(c)], the films annealed at Tg practicallylack the RSE effect. It can be explained by the high vis-cosity of As2S3 films after their annealing at the glasstransition temperature. In such films, the structure isfrozen owing to the high viscosity, and the relaxation pro-cesses are practically unavailable in real time (as men-tioned previously).

It is further suggested21,22 that the viscous flow, whichoccurs in strained glass, is responsible for the stress re-laxation. Strained glass flows to accommodate either thevolume change caused by the expansion or the contractioncaused by tensile or compressive stresses. Such viscousflow of the material is mainly determined by the viscosity.Since the molecular structure of the amorphous ChSlacks the long-range order, molecules can move relative toeach other in the manner of the fluid. But because inter-molecular forces in amorphous material are strong, theviscosity g (T) is high and also has a strong dependenceon the temperature according to the exponential equation

g ~T ! 5 g0 expS DEkBT D , (9)

where DE is the activation energy for the flow, kB is theBoltzmann constant, and g0 is a constant that representsthe high-temperature limit of g (T). The characteristictime for the structural relaxation tr at glass transitiontemperature Tg is of the order of 100 s. [The character-istic viscosity of glass material at this temperature is1012.5 Pa(s)] (Ref. 21). Accordingly, the effects of struc-tural reorganization can be easily detected in real time.The measured activation energy of the relaxation processin as-evaporated As2S3 films at the temperatures up to345 K is 1.14 eV, and the relaxation time is estimated tobe of the order of 100 s at the temperature of 343 K (Ref.9). Consequently, using Eq. (9) and the relationship22

tr 5 const. g ~T !, (10)

the relaxation time and the viscosity of the as-evaporatedamorphous As2S3 films at room temperature can be calcu-lated to be of the order of 2 days and 1015.5 Pa(s).

C. Stress-Induced Optical Anisotropy and Change ofthe Refractive IndexOptical anisotropy is believed to be an inherent propertyof the ChS because of their random structures. However,it is known that besides the photodarkening and thephotoinduced refractive-index changes, ChS have photo-induced anisotropy (Ref. 19). The appearance of the lin-


ear photoinduced dichroism and the linear photoinducedbirefringence have been verified.23 In amorphous As2S3films, a photoinduced birefringence value (n' 2 ni) of1.2 3 1023 has been observed (n' and ni are the refrac-tive indices for the 632.8-nm probing light with p and spolarizations).

According to our measurements in the beginning ofthe RSE, h' . hi (Fig. 4). Hence it follows that inthe holographic recording, the value of the refractive-index modulation (Dn) between HG maxima and minimadepends on the orientation of polarization planes ofthe recording and the probing laser beams. The relation-ship between the DE and the refractive-index modulationfor thick, phase-transmission gratings can be expressedas24

hi 5 sin2S pdDni

l cos u D (11)

for the s-polarized light and

h' 5 ~ ı • !2 sin2S pdDn'

l cos u D (12)

for the p-polarized light. In these formulas, d is thethickness of the grating, l is the wavelength of the read-out light, and u is the Bragg angle of the readout light.Unit vectors ı and show the propagation directions ofthe signal and the readout beams. In our case, the dotproduct has a value of 0.75. From the previous equationsit follows that we have to multiply h' values by the factorof 1.76 if we want to compare n' to ni . Anyway, theRSE in amorphous As2S3 films is connected with the op-tical anisotropy.

Arsenic sulfide as well as other ChS are high-molecularinorganic compounds with a network structure, and theirphysical properties are greatly determined by the van derWaals forces between polymeric networks. The struc-tural building units of the amorphous ChS are aniso-tropic, but because of their random distribution, amor-phous films macroscopically have isotropic properties.When ChS are subjected to a uniaxial tensile or compres-sive stress field, the structural building units are par-tially oriented and optical birefringence appears.25 FromEq. (4) and Fig. 5 it follows that the mechanical stressgradient is directed perpendicularly to the HG lines.This uniaxial stress in amorphous As2S3 films causeselastoplastic deformations accompanied by the appear-ance of the optical anisotropy. In ChS the sign of theelasto-optical constant C0 , defined as

C0 5ne 2 no

s, (14)

depends on the dimensionality of the structure.26 In thedefinition above, s is the axial stress and ne and no arethe refractive indices of the extraordinary ray (parallel tothe strain axis) and the ordinary ray (perpendicular to thestrain axis). Accordingly, ne 5 n' and no 5 ni . Fortwo-dimensional ChS such as As—S and As—Se, theelasto-optical constant C0 is negative. From the resultspresented in Ref. 11 we know that the refractive-indexchanges are positive. When the recording is started, themodulus of the periodic negative stress begins to grow.

It means that Dn' has to grow faster than Dni . This isreally seen in Fig. 4. When the recording is stopped, themodulus of the negative stress starts to decrease owing tothe relaxation forcing Dni to increase faster than Dn'.This is also seen in Fig. 4.

4. CONCLUSIONSThe holographic recording and the HG-induced RSE inamorphous As2S3 films have been studied. The signifi-cant role of the internal mechanical stress of the films onthe RSE process is confirmed experimentally. It isshown that during the RSE, an essential change in theoptical anisotropy of the HG occurs. A model of the RSEbased on the photoinduced mechanical stress relaxationand viscous flow of amorphous chalcogenide semiconduc-tors (ChS) is discussed.

It is known that amorphous As2S3 films obtained bythermal deposition in vacuum contain internal compres-sive stresses. Illumination with light causes a signifi-cant decrease in the viscosity of As2S3 (Ref. 27). Thispromotes the relaxation of the internal mechanical stressin the exposed film area. Therefore after the recording ofthe holographic diffraction grating, the internal mechani-cal stress has a spatially periodic distribution dependingon the HG, the recording light intensity, the diffraction ef-ficiency, and the thickness of the films. We think thatthis mechanical stress gradient is the main reason for theappearance of the RSE phenomenon. The gradient is di-rected perpendicularly to the HG lines, and it induceselastoplastic deformations in the film accompanied by theincrease of the refractive-index modulation of the HG.Simultaneous changes in the HG optical anisotropy canbe expected (Figs. 4 and 6).

Based on the thermal annealing measurements (Figs. 6and 7), one can conclude that the RSE in As2S3 films in-volves both elastic and plastic deformations. A partial ir-reversible decrease of the DE observed during the sampleheating can be explained by the elasto-optical effect,which disappears together with compressive stress attemperatures above 345 K. The component of the DEconnected with plastic deformations can be annealed atthe temperatures close to glass transition Tg .

The strong influence of the recording light intensity onthe RSE kinetics [Fig. 2(a)] and the saturation factorhs /h0 (Fig. 2) show that the threshold value for the re-cording light intensity Ith < 1025 W/cm2 can be expected.This result coincides with the conclusion presented in Ref.12.

ACKNOWLEDGMENTSJ. Teteris thanks T. Jaaskelainen for his invitation tocarry out research work at the Department of Physics,University of Joensuu, Finland. These studies are sup-ported by Centre for International Mobility (CIMO), Fin-land.

*Permanent address, Institute of Solid State Physics,University of Latvia, LV-1063, Riga, Latvia.


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relaxation process of holographic gratings in amorphous as_2s_3 films

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