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On the photodissolution kinetics of silver in glassy As2S3
Journal of Non-Crystalline Solids 356 (2010) 147–152
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On the photodissolution kinetics of silver in glassy As2S3 D. Tsiulyanu *, I. Stratan Department of Physics, Technical University, bd. Dacia 41, Chisinau MD-2060, Republic of Moldova
a r t i c l e
i n f o
Article history: Received 17 February 2009 Received in revised form 24 September 2009
Keyword: Chalcogenides
a b s t r a c t The kinetics of the photodissolution of Ag into glassy As2S3 films and its dependence on temperature have been studied by monitoring the changes that occur both in their transmission spectra and transmission of weakly absorbed broadband light. It was shown that besides of a low induction period, the photodissolution kinetics consists of two linear steps with different activation energies, followed by a parabolic tail. The transitions between photodissolution steps was found to be not monotonous and explained in terms of Elliott’s model, which asserts a simultaneous ionic and electronic charge transport controlled by chalcogenide properties, illumination and temperature. The evidence is given that the islanding of Ag layer in the course of photoreaction, results in an inversion of maxima and minima of transmission spectra. It is suggested that the islanding of Ag layer is not a consequence of a non-uniform dissolution but arises itself at critical thickness, at which Ag forms a continuous film. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction The phenomenon of photodissolution (synonymously called photodoping or photodiffusion) of certain metals (e.g. Ag) in chalcogenide glasses (ChG) discovered by Kostyshin et al. [1] is of great scientific interests (see an extensive review in Ref. [2]). This is due to its application in light, electrons or ions lithography and programmable metallization cell (PMC) technologies (reviews Refs. [3] and [4] respectively). Arsenic trisulphide (As2S3) was the first ChG in which the photodissolution (PD) of metals was observed and, being a typical glassy compound, so far remains the most attractive for investigation of this unique phenomenon. The experimental investigations of photodissolution [5–7] and migration [8] of silver in glassy As2S3, as well as ionic conductivity of Ag photodoped As2S3 [9] and electrostatic potential at the Ag– As2S3 interface [10] led to development of a unified mechanism for metal PD in chalcogenide materials [11,12]. The mechanism suggested for the PD of silver in ChG comprises at least three processes: 1) A solid state chemical reaction between Ag and the chalcogenide, which results in formation of a superionic conductor, that is a ternary Ag-containing ChG with high (105–103 X1 cm1) ionic conductivity.
* Corresponding author. Tel.: +373 22 564269. E-mail address: [email protected] (D. Tsiulyanu). 0022-3093/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2009.10.003
2) Photo-creation of free holes at the superionc/electronic (doped/undoped) chalcogenide interface, followed by their drift through superionic chalcogenide to Ag layer and production of ions by reaction
Ag0 þ h ! Agþ : 3) Motion of Ag+ ions in opposite direction i.e. towards the boundary doped/undoped chalcogenide through the doped (superionic region). Recently, Jain and coworkers [13] have pointed out an additional (the fourth) process, which originates from the presence in freshly deposited As2S3 thin films of a significant number (10– 15%) of homopolar (S–S or As–As) bonds. The silver dissolution starts at the interface by chemical reaction between S–S segments and neutral Ag as:
4Ag þ ½S—S ! 2Ag2 S: Then the recently formed Ag2S reacts with ‘‘wrong” As–As segments converting both the ‘‘wrong” bonds into stable As–S bonds and metallic silver into Ag+ ions, which are able to diffuse deeper in the chalcogenide film. All listed processes occur simultaneously and it is not easy to distinguish between them. At the same time they together control the kinetics of PD (plot of Ag layer thickness change versus time), which usually consists of four stages: (I) induction period; (II) linear dependence; (III) square-root dependence and (IV) cessation of PD when Ag layer is exhausted or when the photodoped front has
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penetrated the entire thickness of the ChG layer. That is why knowledge of the kinetics of photodissolution is essential to distinguish between stages of the PD process and to understand the mechanism of this phenomenon for its applications, particularly in PMC devices [14,15]. In the present paper, we report some new results concerning the kinetics of PD of silver in glassy As2S3 and its dependence on temperature, measured by monitoring the spectra of optical transmittance along with transmittance of a broadband light weakly absorbed in As2S3.
2. Experimental procedures The samples were prepared by subsequent evaporation of As2S3 and silver in a vacuum of 105 Torr (broken between evaporations) onto Pyrex glass substrates with a thickness of 1 mm. The film thicknesses were kept constant from sample to sample at 103 nm and 60 nm for the As2S3 and Ag layers respectively. The photodissolution of silver onto As2S3 was performed by illumination the Ag film, lying on the top of the multilayer structure, through substrate and chalcogenide glass, using the light of a halogen 100 W lamp focused by a quartz lens. The integral intensity of applied illumination was 250 mW/cm2. The PD rate was measured by monitoring the changes that occur in the transmittance of the sample of weakly absorbed in As2S3 broadband light (k > 0.65 lm) as photodissolution proceeds. For this purpose a cut filter (KC-15) with transparence range 650– 3000 nm was placed behind the sample, i.e. in front of photomultiplier, which served as light detector. A PC with a data acquisition board manufactured by National Instruments Inc. was used for processing. The effect of temperature on PD kinetics was studied by placing the multilayer structure on a resistive electrical heater but a platinum resistance detector Pt-100 close to sample has been used for assisting the temperature control. The transmission spectra were carried out using a computercontrolled MDR-23U monochromator. These experiments were accomplished as follows: a) The As2S3 film was deposited onto glass substrate and its transmission spectrum has been registered in the wavelength range k = 0.4 1.0 lm. The power of each monochromatic light did not exceed 0.15 lW/cm2. b) The Ag layer was deposited on the top of the structure through a rigid mask to obtain the patterns of both pure silver and two-layer structure As2S3/Ag areas. c) The transmission spectrum of Ag film has been registered in the same range of wavelengths. d) A portion of two-layer structure As2S3/Ag has been illuminated with monochromatic light k = 0.506 lm for different exposure times and after each exposure process the transmission spectra have been registered. The power of monochromatic light used for exposure (i.e. for PD process) was normalized at 45 lW/cm2, that is 300 times higher than the power of the light used for spectra registration. Thus, the PD process was supposed not to be affected by light during the registration of transmission spectra. Fig. 1(a) shows schematically the multilayer structure of the sample. There are three well-defined boundaries: (1) substrate/undoped As2S3; (2) undoped As2S3/photodoped material (solid electrolyte); (3) photodoped material/Ag. During the photodissolution the boundary between photodoped material and undoped As2S3 propagates towards the substrate, but the boundary between photodoped material and Ag propagates in opposite direction i.e.
Fig. 1. Schematic cross section through a sample during the photodissolution process (a). Transmission of a broadband light k > 0.65 lm of two-layer structure versus: exposure time (b) and amount of photodissolved silver (c). The dot line indicates the transmittance of the pure As2S3 film.
towards surface, so that the thickness of both Ag layer and undoped As2S3 glass decrease with time. The movement of the boundary between photodoped and undoped As2S3 was used to measure the photodissolution rate by technique based on monitoring the changes that occur in reflectivity of the sample [7] but the movement of the boundary between photodoped material and Ag was used for the same purpose by technique based on continuous measurement of silver layer resistance [9,11]. In the present work we tracked the movement of boundary between photodoped material and Ag layer measuring the transmission of weakly absorbed in ChG light with PD of silver in progress. This method allows tracking the evolution of transmission spectra of the two-layer structure as PD proceeds, which can give information about the last stage of PD when the Ag layer exhausts.
3. Results 3.1. Kinetics of photodissolution Fig. 1(b) shows the optical transmission of the two-layer structure As2S3/Ag (broadband light k > 0.650 lm) versus exposure time as PD proceeds, at several temperatures. The dot line indicates the transmittance of pure As2S3 film, i.e. without Ag layer. It is seen that independently of temperature the transmission in the region of weakly absorbed light recovers to that of As2S3 before Ag evaporation with increase of the exposure time. Obviously this is due to a decrease of Ag layer effective thickness: the absorption coefficient of Ag film in this region of spectrum, being of about 105 cm1 [16], is much higher than the absorption coefficient of doped/undoped As2S3 double layer, which is less than 102 cm1 [17]. Hence, the PD rate of Ag can be estimated by measuring the recovery rate of optical transmission of two-layer structure As2S3/Ag in IR region of spectrum if the thickness dependence of Ag film transmittance is a priory known. The instantaneous transmission of unreacted Ag layer (TAg) and that of the whole two-layered As2S3/Ag structure (T) are interdependent as TAg = T/T0, where T0 is the transmission of pure As2S3 layer on glassy substrate. We have calculated and plotted the thickness of unreacted Ag film versus exposure time (PD kinetics) applying our experimental
D. Tsiulyanu, I. Stratan / Journal of Non-Crystalline Solids 356 (2010) 147–152
data (TAg) to the thickness dependence of transmission spectra of silver films measured by Sun et al. [18]. Fig. 2 shows the unreacted Ag layer thickness versus exposure time for different temperatures. Several steps of PD kinetics can clearly been distinguished: (I) the relatively slow step observed only at curve measured at 30 °C; (II) the second one, where the thickness of Ag layer linearly decreases with exposure time, but the slope (the PD rate) is strongly influenced by temperature; (III) the third step that is also linear but with a slope only slowly dependent on temperature; and a final step (IV), which exhibits a sublinear dependence of thickness change of Ag layer on time, particularly observed at low (less than 60 °C) temperatures. In order to check whether the observed change in the slope of PD kinetics is due not to formation of different chemical products (in the doped layer) on the different stages of the dissolution, an additional set of samples was applied. These samples were prepared by multiple evaporation of silver each time followed by its total PD into As2S3. The transmission of a broadband light (k = 0.65 1.2 lm) has been measured for different amount of photodissolved silver. The results are illustrated in Fig. 1(c). One can see that the transmission of Ag: As2S3 mixture insignificantly varies with amount of adopted silver, that is the thickness – exposure time dependences (Fig. 2) are really due to PD process. Note that the transmission of Ag:As2S3 mixture versus amount of adopted silver (Fig. 1(c)) allows to provide an error analysis of the applied experimental method. In fact, the error of such a method is mainly due to progressive light absorption in doped layer during PD. The relative error of transmission, being minimal at the beginning of PD process, becomes maximal of about 5% closely to its finish. However, the transmission of Ag layer below 20 nm increases very rapidly with decrease of its thickness [18]. Therefore the error in Ag thickness determination below 20 nm, by 5% error in transmission of unreacted Ag film, is assessed to be of about 1 nm. The error bars are displayed on the data in Fig. 2. 3.2. Transmission spectra Fig. 3 shows the changes in the transmission spectrum of twolayer structure Ag/As2S3 after illumination for different exposure times at room (25 °C) temperature. The dot and dash lines show the transmission spectra of As2S3 layer without Ag film on top of it and of the silver film, growth directly on the glass substrate respectively. One can see that, in spite of interference phenomenon, the As2S3 film is almost transparent for wavelengths longer
Ag thickness [nm]
50
149
Fig. 3. Transmission spectra of two-layer structure Ag/As2S3 after different exposure times at incident light 45 lW/cm2, k = 0.506 lm.
than 530 nm. Consequently, one can assert that the transparence of the Ag/As2S3 system in IR region is mainly conditioned by absorption/reflection of Ag layer. When PD proceeds the effective thickness of Ag layer decreases, resulting in an increase both of its proper transmittance and transmittance of the whole layered structure. Along with increase of transmittance the shift of interference picture towards longer wavelengths occurs. Obviously it is due both to a shift of transmission edge towards a longer wavelength [5] and increasing of refractive index of doped material [19] with increasing the silver content photodissolved into As2S3. The shift of minima and maxima of interference is most pronounced at the beginning of the PD process. They appear in the transmission spectra because of interference of two light beams: one of them passes through the whole layered structure without any reflection and the other passes through the structure being twice reflected, firstly from Ag layer and secondly from the glass substrate. It is supposed that after each step of exposure the silver rapidly achieves a homogeneous distribution in certain depth of As2S3 [20] but the doped/undoped interface is not sufficiently abrupt to influence the spectra. In this context an interesting peculiar feature can be seen in the Fig. 5: at certain critical exposure
o
30 C o 45 C o 60 C o 75 C o 90 C
40 30 20 10 0
20
40
60
80
100
120
Exposure time [sec] Fig. 2. Decrease of Ag film thickness versus exposure time at various temperatures. The straight dash–dot lines on the curve for 30 °C (j) are drawn as guides to the eyes. In order not to overload the picture, the error bars (being identical) are displayed only for several data points.
Fig. 4. Arrhenius plot for the second (a) and third (b) stages of PD kinetics; (c) temperature dependence of thickness of Ag layer photodissolved before transition between two linear steps of PD occurs. The lines are drawn as guides to the eyes.
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Fig. 5. Decrease of silver thickness versus exposure time at fourth (quasi-parabolic) step of PD. The number by each curve shows the photodiffusion coefficient KT multiplied by 1013 cm2/s. The lines are drawn as guides to the eyes.
time (200 min) the inversion of maxima and minima of transmission spectra occurs.
4. Discussion The segmentation of PD kinetics curve into several distinct sections is of course not new and has been done by everybody studying PD process [2,9,12]. None the less, here we observed some new peculiarities of PD kinetics, which can play an important role in further understanding of the PD mechanism. First it should be mentioned that the kinetics can be divided into four distinct sections instead of three or even two sections usually observed. Secondly, with exception of transition between the first and second steps, the transitions between other steps are not monotonic but rather sharp. We suppose that the reason for these peculiarities of PD kinetics is due to the special conditions of our experiment, which imply the high intensity of illumination applied (250 mW/ cm2) and the thick films of silver (60 nm) combined with a direct measurement of optical transmission of the sample as the photodissolution proceeds. Our results are consistent with the unified model for metal PD in amorphous chalcogenide materials proposed by Elliott [12] and, what is more, they bring to light the experimental confirmation of some theoretical predictions underlined in this model. The first step of PD kinetics, were the PD is very slow (in our experiments observed only at 30 °C), is ascribed to so called ‘‘induction period” generally observed in solid state photoinduced reactions between metals and chalcogenide glasses [2]. The origin of the induction period was suggested [12] to be the lateral diffusion of metal in ChG between dendritic nuclei of reaction product. It depends on intensity and wavelength of illumination [21] and strongly decreases with temperature increase [9]. Namely the last explains why the induction period observed on the kinetic profile (Fig. 2) measured at 30 °C disappears on the curves measured at higher temperatures. The second step is a period during which the reaction proceeds at an approximately constant rate for each temperature, but this rate strongly increases with temperature increase. Fig. 4(a) shows the temperature dependence of PD rate at this stage plotted in Arrhenius coordinates. The slope of the obtained line exhibits a rather high value of 0.34 eV that indicates a high effect of temperature on PD process. The constant rate of photodissolution is generally agreed to be determined by reaction between metal and
ChG, which occurs simultaneously in two different spatial regions of the sample: (I) absorption of photons by breaking As–S bonds that results in a simultaneous producing of non-bridged chalcogen atoms with a single unpaired electron (dangling bond) and generation of free holes at or near the doped/undoped interface, and (II) creation of Ag+ ions at the Ag/doped As2S3 interface were photogenerated holes, after the drift through doped layer react with neutral Ag atoms. In turn, Ag+ ions after the drift towards the doped/ undoped interface accept the unpaired electron from chalcogen dangling bond and a photodoped ternary Ag–As–S compound is created. Thus, the reaction limited step of PD depends either on electronic (hole) photoconductivity of doped layer rph or its ionic conductivity rAgþ . Investigation of the effect of temperature on the PD kinetics allows in principle to distinguish between effects of photoconductivity rph and ions conductivity rAgþ of doped layer on reaction rate. To date was found that PD process of Ag into As2S3, being thermally activated, exhibits activation energy of 0.1–0.2 eV [9,11,22]. Such a relatively weak temperature dependence of PD kinetics is usually ascribed to photoconductivity and the solid state reaction is assert to be limited by the holes flux under condition rph << rAgþ . The opposite situation, that is rph >> rAgþ , means the reaction rate limitation by Ag+-ion conductivity. It has not been observed experimentally so far, but was predicted by Elliott [12] to exhibit the activation energy in the range of 0.3 0.5 eV. We suppose that our experiment confirms this prediction. The high temperature dependence observed on the second step of PD process, which exhibits activation energy EAg = 0.34 eV indicates that Ag+-ion conductivity becomes rate-limiting. It is interesting to note that the activation energy of ‘‘superionic conductor” Ag2.6As2S3 synthesized by Polcharski and coworkers [9] was found to be the same, i.e. 0.34 eV that confirms our assert. The third step of PD kinetics shows also a linear dependence of the change of Ag thickness on time, but its slope only slowly increases with temperature increase. Fig. 4(b) illustrates the photoreaction rate estimated from third step of PD kinetics versus temperature in Arrhenius coordinates. The slope of this line exhibits a relatively low value of 0.1 eV, which as mentioned above, should be attributed to activation energy of photoconductivity, i.e. Eph 0.1 eV. In fact, the photoconductivity of photodoped As2S3 thin layer exponentially increases with temperature increase, but the activation energy depends both on light intensity and temperature regime. At high intensities and temperatures 300–370 K (applied in present work) the activation energy of photoconductivity was found [23] to be of 0.9–0.14 eV, which comprises estimated from the third step of PD value Eph 0.1 eV. Thus, the PD kinetics on the third step is a reaction limited process, but it is controlled by photoconductivity rph under condition that rph << rAgþ . The transition from the ion conductivity limiting to photoconductivity limiting is probably due to increasing in time both of the concentration C Agþ and mobility lAgþ of Ag+ ions in doped region, but the first reason seems to be the main. The transition point corresponds to situation when
rAgþ rph exp
Eph ; kT
ð1Þ
where k is the Boltzman’s constant and T – is the thermodynamic temperature. On the other hand, assuming the homogeneity of silver ion concentration in the doped layer,
rAgþ C Agþ Ddtr ;
ð2Þ
where Ddtr is the thickness of the photodissolved Ag layer until the transition to photoconductivity limiting occurs (transition point). Consequently, the proportionality as:
D. Tsiulyanu, I. Stratan / Journal of Non-Crystalline Solids 356 (2010) 147–152
Eph Ddtr exp ; kT
ð3Þ
should be expected. The lnðDdtr Þ versus reciprocal temperature is plotted in Fig. 4(c). The slope of the presented line is approximately 0.1 eV which coincides with activation energy Eph calculated from temperature dependence of photoreaction rate, related to third step of PD process. Obviously, this coincidence confirms our suggestion concerning the nature of a sharp transition between the second and the third steps of PD kinetics. The final (fourth) step of PD kinetics is a deceleratory stage of the process, particularly visible at low temperatures. It appears to be a quasi-parabolic step, i.e. with a square-root dependence of Ag thickness on time. Fig. 5 shows the thickness change of Ag layer as a function of square-root of exposure time for different temperatures related to the last step of PD kinetics. One can see that each of curves is a straight line that characterizes a diffusion controlled process. Such a PD process is consistent with model [12] wherein both ionic and electronic charge transport occur simultaneously by the condition that the flux of ions jAgþ balances that of holes jh in reverse direction:
jAgþ ¼ jh :
ð4Þ
Each of curves from Fig. 5 can be described by relation: 1
DdT ¼ AT t2 :
ð5Þ
The coefficient of proportionality AT seems not much to depend on temperature and was assessed [12] as: 1 2
AT ¼ ð2K T Þ ¼
2rph DlAg C Agþ F 2
151
!12 ;
ð6Þ
where rph is the electronic (hole) conductivity of doped ChG, DlAg is the difference between the chemical potentials of Ag at Ag/doped As2S3 and doped/undoped As2S3 interfaces (Fig. 1(a)), F is the Faraday constant. The values of coefficient KT can be estimated from the slope of these curves. One can see that the slope of the lines in Fig. 5 does not vary essentially no monotonically with temperature. Perhaps this is due to micrononhomogeneity of the superionic conductor obtained by PD process. Such micrononhomogeneity was observed at the surface of the sample by Kovalskiy et al. [24], using high resolution X-photoelectron spectroscopy. The values of the coefficient KT (shown in Fig. 5 by each curve) are in the range of (2.9–3.8) 1013 cm2/s. These values are with three orders of magnitude higher than either the thermodiffusion coefficient of Ag in As2S3 determined experimentally [9] or its value estimated by indirect calculations [12]. An essential increasing of parabolic constant KT in a PD process comparative with its dark value in a thermodiffusion process was predicted by Elliott [12] and obviously is due to a high photoconductivity of Ag doped ChG. Namely the photoconductivity rph is involved as electronic conductivity in Eq. (6), but as shown in [23], the photoconductivity of doped As2S3 layer (As2S3Ag0.15) is much higher than its dark conductivity, particularly at low temperatures and high light intensities. As far as the inversion of maxima and minima of transmission spectra is concerned (Section 3.2) such a inversion can be due either by disappearance (exhaustion) of Ag layer or, at least, its islanding. In fact, before critical exposure time one of the interfering light beam passing from doped As2S3 with a refractive index nch 2.8 (k = 0.75 lm) [17] is reflected from highly absorbing Ag layer with losing a half of wavelength [25], but after critical exposure time this beam becomes reflected from air na = 1 without a phase shift
Fig. 6. Decrease of silver thickness versus exposure time tracked through maxima of interference, taking into consideration the phase shift. The arrow shows the critical exposure time and critical thickness at which the phase shift occurs.
as na < nch. In order to clarify whether does the Ag layer exhaust at critical exposure time or simply becomes discontinuous, we have applied the thickness dependence of transmittance of Ag films, carried out in [18] to our experimental data. Fig. 6 shows the decrease of Ag layer thickness with time obtained by tracking the increasing of transmission through maxima of interference, taking into consideration the phase shift (dot–dash line in Fig. 3). One can see that the critical exposure time corresponds to a thickness (shown by an arrow in Fig. 6) of approximately 17 nm. Namely this value was found in [18] to be the critical thickness below which the pure Ag film becomes discontinuous. Thus, we assert that the inversion of transmission spectra at critical exposure time is due to occurrence of an islanding of Ag film. Note that this phenomenon has been observed early at PD of Ag into amorphous GeSe2 films [26] and was explained by a non-uniform dissolution process. Actually it appears that the islanding of Ag films occurs itself at its critical thickness. The increasing of transmittance after the critical exposure time is due to continuation of PD, as well as to decreasing and narrowing of islands of the Ag film with illumination. The last explains the lack of wavelength shift of transmission extremes after their inversion at critical exposure time.
5. Conclusions The kinetics profile of Ag photodissolution (PD) in glassy As2S3 comprises two linear steps with activation energies of about 0.34 eV and 0.1 eV followed by a parabolic tail. The linear steps are ascribed to ion conductivity limiting and photoconductivity limiting solid state reaction respectively, but the parabolic tail appears to be derived from a diffusion controlled process. The diffusion coefficient varies not essentially no monotonically with temperature, being of about (2.9–3.8) 1013 cm2/s. At the last stage of PD process the islanding of Ag film occurs, which is revealed by inversion of transmission spectra of the whole layered structure. The islanding of Ag film originates not from its non-uniform photodissolution but occurs itself at some critical thickness. References [1] M.T. Kostyshin, E.U. Mikhailovskya, P.F. Romanenko, Sov. Phys. (Solid State) 8 (1966) 451. [2] A.V. Kolobov, S.R. Elliott, Adv. Phys. 40 (1991) 625.
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[3] D. Tsiulyanu, in: G. Lucovsky, M. Popescu (Eds.), Non-Crystalline Materials for Optoelectronics, INOE, Bucharest, 2004, p. 297. [4] M. Mitkova, M.N. Kozicki, in: G. Lucovsky, M. Popescu (Eds.), Non-Crystalline Materials for Optoelectronics, INOE Bucharest, 2004, p. 297. [5] H. Mizuno, K. Tanaka, M. Kikuchi, Solid State Commun. 12 (1973) 999. [6] A.V. Kolobov, V.M. Lyubin, J. Troltzsch, Phys. Status Solidi (a) 115 (1989) K139. [7] P.J.S. Ewen, A. Zakery, A.P. Firth, A.E. Owen, J. Non-Cryst. Solids 97&98 (1987) 1127. [8] A. Buroff, E. Nebauer, P. Süptitz, I. Willert, Phys. Status Solidi (a) 40 (1977) K195. [9] J. Polcharski, J. Przyluski, M. Teodoreczyk, J. Non-Cryst. Solids 93 (1987) 303. [10] H. Kokado, I. Shimizu, T. Tatsuno, E. Inoue, J. Non-Cryst. Solids 21 (1976) 225. [11] A.V. Kolobov, S.R. Elliott, M.A. Taguirdzhanov, Philos. Mag. B 61 (1990) 859. [12] S.R. Elliott, J. Non-Cryst. Solids 130 (1991) 85. [13] H. Jain, A. Kovalskiy, A. Miller, J. Non-Cryst. Solids 352 (2006) 562. [14] I. Stratan, D. Tsiulyanu, I. Eisele, J. Optoelectr. Adv. Mater. 8 (2006) 2117.
[15] M.N. Kozicki et al., US Patent No. 6998312 B2, 2006. [16] I. An, H. Oh, J. Korean Phys. Soc. 29 (1996) 370. [17] M.T. Kostyshin, O.P. Kosyarum, A.A. Kudryavtsev, Ucranian J. Phys. 32 (1987) 1061 (in Russian). [18] X. Sun, R. Hong, H. Hou, Z. Fan, J. Shao, Thin Solid Films 515 (2007) 6962. [19] T. Wagner, J. Optoelectr. Adv. Mater. 4 (2002) 717. [20] G. Kluge, Phys. Status Solidi (a) 101 (1987) 105. [21] J.H.S. Rennie, S.R. Elliott, J. Non-Cryst. Solids 77&78 (1985) 1161. [22] M.T. Kostyshin, V.I. Miniko, Ucranian J. Phys. 22 (1977) 1560 (in Russian). [23] V.M. Ganin, B.T. Kolomiets, V.M. Lyubin, Sov. Technol. Phys. Lett. 5 (1979) 158. [24] A. Kovalskiy et al., J. Non-Cryst. Solids (2009), doi:10.1016/ j.jnoncrysol. 2008.12.021. [25] O.S. Heavens, in: G. Hass, R.D. Thun (Eds.), Physics of Thin Films, vol. 2, Academic Press, New York and London, 1964, p. 396. [26] J.H.S. Rennie, S.R. Elliott, J. Non-Cryst. Solids 97&98 (1987) 1239.
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On the photodissolution kinetics of silver in glassy As2S3 D. Tsiulyanu *, I. Stratan Department of Physics, Technical University, bd. Dacia 41, Chisinau MD-2060, Republic of Moldova
a r t i c l e
i n f o
Article history: Received 17 February 2009 Received in revised form 24 September 2009
Keyword: Chalcogenides
a b s t r a c t The kinetics of the photodissolution of Ag into glassy As2S3 films and its dependence on temperature have been studied by monitoring the changes that occur both in their transmission spectra and transmission of weakly absorbed broadband light. It was shown that besides of a low induction period, the photodissolution kinetics consists of two linear steps with different activation energies, followed by a parabolic tail. The transitions between photodissolution steps was found to be not monotonous and explained in terms of Elliott’s model, which asserts a simultaneous ionic and electronic charge transport controlled by chalcogenide properties, illumination and temperature. The evidence is given that the islanding of Ag layer in the course of photoreaction, results in an inversion of maxima and minima of transmission spectra. It is suggested that the islanding of Ag layer is not a consequence of a non-uniform dissolution but arises itself at critical thickness, at which Ag forms a continuous film. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction The phenomenon of photodissolution (synonymously called photodoping or photodiffusion) of certain metals (e.g. Ag) in chalcogenide glasses (ChG) discovered by Kostyshin et al. [1] is of great scientific interests (see an extensive review in Ref. [2]). This is due to its application in light, electrons or ions lithography and programmable metallization cell (PMC) technologies (reviews Refs. [3] and [4] respectively). Arsenic trisulphide (As2S3) was the first ChG in which the photodissolution (PD) of metals was observed and, being a typical glassy compound, so far remains the most attractive for investigation of this unique phenomenon. The experimental investigations of photodissolution [5–7] and migration [8] of silver in glassy As2S3, as well as ionic conductivity of Ag photodoped As2S3 [9] and electrostatic potential at the Ag– As2S3 interface [10] led to development of a unified mechanism for metal PD in chalcogenide materials [11,12]. The mechanism suggested for the PD of silver in ChG comprises at least three processes: 1) A solid state chemical reaction between Ag and the chalcogenide, which results in formation of a superionic conductor, that is a ternary Ag-containing ChG with high (105–103 X1 cm1) ionic conductivity.
* Corresponding author. Tel.: +373 22 564269. E-mail address: [email protected] (D. Tsiulyanu). 0022-3093/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2009.10.003
2) Photo-creation of free holes at the superionc/electronic (doped/undoped) chalcogenide interface, followed by their drift through superionic chalcogenide to Ag layer and production of ions by reaction
Ag0 þ h ! Agþ : 3) Motion of Ag+ ions in opposite direction i.e. towards the boundary doped/undoped chalcogenide through the doped (superionic region). Recently, Jain and coworkers [13] have pointed out an additional (the fourth) process, which originates from the presence in freshly deposited As2S3 thin films of a significant number (10– 15%) of homopolar (S–S or As–As) bonds. The silver dissolution starts at the interface by chemical reaction between S–S segments and neutral Ag as:
4Ag þ ½S—S ! 2Ag2 S: Then the recently formed Ag2S reacts with ‘‘wrong” As–As segments converting both the ‘‘wrong” bonds into stable As–S bonds and metallic silver into Ag+ ions, which are able to diffuse deeper in the chalcogenide film. All listed processes occur simultaneously and it is not easy to distinguish between them. At the same time they together control the kinetics of PD (plot of Ag layer thickness change versus time), which usually consists of four stages: (I) induction period; (II) linear dependence; (III) square-root dependence and (IV) cessation of PD when Ag layer is exhausted or when the photodoped front has
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penetrated the entire thickness of the ChG layer. That is why knowledge of the kinetics of photodissolution is essential to distinguish between stages of the PD process and to understand the mechanism of this phenomenon for its applications, particularly in PMC devices [14,15]. In the present paper, we report some new results concerning the kinetics of PD of silver in glassy As2S3 and its dependence on temperature, measured by monitoring the spectra of optical transmittance along with transmittance of a broadband light weakly absorbed in As2S3.
2. Experimental procedures The samples were prepared by subsequent evaporation of As2S3 and silver in a vacuum of 105 Torr (broken between evaporations) onto Pyrex glass substrates with a thickness of 1 mm. The film thicknesses were kept constant from sample to sample at 103 nm and 60 nm for the As2S3 and Ag layers respectively. The photodissolution of silver onto As2S3 was performed by illumination the Ag film, lying on the top of the multilayer structure, through substrate and chalcogenide glass, using the light of a halogen 100 W lamp focused by a quartz lens. The integral intensity of applied illumination was 250 mW/cm2. The PD rate was measured by monitoring the changes that occur in the transmittance of the sample of weakly absorbed in As2S3 broadband light (k > 0.65 lm) as photodissolution proceeds. For this purpose a cut filter (KC-15) with transparence range 650– 3000 nm was placed behind the sample, i.e. in front of photomultiplier, which served as light detector. A PC with a data acquisition board manufactured by National Instruments Inc. was used for processing. The effect of temperature on PD kinetics was studied by placing the multilayer structure on a resistive electrical heater but a platinum resistance detector Pt-100 close to sample has been used for assisting the temperature control. The transmission spectra were carried out using a computercontrolled MDR-23U monochromator. These experiments were accomplished as follows: a) The As2S3 film was deposited onto glass substrate and its transmission spectrum has been registered in the wavelength range k = 0.4 1.0 lm. The power of each monochromatic light did not exceed 0.15 lW/cm2. b) The Ag layer was deposited on the top of the structure through a rigid mask to obtain the patterns of both pure silver and two-layer structure As2S3/Ag areas. c) The transmission spectrum of Ag film has been registered in the same range of wavelengths. d) A portion of two-layer structure As2S3/Ag has been illuminated with monochromatic light k = 0.506 lm for different exposure times and after each exposure process the transmission spectra have been registered. The power of monochromatic light used for exposure (i.e. for PD process) was normalized at 45 lW/cm2, that is 300 times higher than the power of the light used for spectra registration. Thus, the PD process was supposed not to be affected by light during the registration of transmission spectra. Fig. 1(a) shows schematically the multilayer structure of the sample. There are three well-defined boundaries: (1) substrate/undoped As2S3; (2) undoped As2S3/photodoped material (solid electrolyte); (3) photodoped material/Ag. During the photodissolution the boundary between photodoped material and undoped As2S3 propagates towards the substrate, but the boundary between photodoped material and Ag propagates in opposite direction i.e.
Fig. 1. Schematic cross section through a sample during the photodissolution process (a). Transmission of a broadband light k > 0.65 lm of two-layer structure versus: exposure time (b) and amount of photodissolved silver (c). The dot line indicates the transmittance of the pure As2S3 film.
towards surface, so that the thickness of both Ag layer and undoped As2S3 glass decrease with time. The movement of the boundary between photodoped and undoped As2S3 was used to measure the photodissolution rate by technique based on monitoring the changes that occur in reflectivity of the sample [7] but the movement of the boundary between photodoped material and Ag was used for the same purpose by technique based on continuous measurement of silver layer resistance [9,11]. In the present work we tracked the movement of boundary between photodoped material and Ag layer measuring the transmission of weakly absorbed in ChG light with PD of silver in progress. This method allows tracking the evolution of transmission spectra of the two-layer structure as PD proceeds, which can give information about the last stage of PD when the Ag layer exhausts.
3. Results 3.1. Kinetics of photodissolution Fig. 1(b) shows the optical transmission of the two-layer structure As2S3/Ag (broadband light k > 0.650 lm) versus exposure time as PD proceeds, at several temperatures. The dot line indicates the transmittance of pure As2S3 film, i.e. without Ag layer. It is seen that independently of temperature the transmission in the region of weakly absorbed light recovers to that of As2S3 before Ag evaporation with increase of the exposure time. Obviously this is due to a decrease of Ag layer effective thickness: the absorption coefficient of Ag film in this region of spectrum, being of about 105 cm1 [16], is much higher than the absorption coefficient of doped/undoped As2S3 double layer, which is less than 102 cm1 [17]. Hence, the PD rate of Ag can be estimated by measuring the recovery rate of optical transmission of two-layer structure As2S3/Ag in IR region of spectrum if the thickness dependence of Ag film transmittance is a priory known. The instantaneous transmission of unreacted Ag layer (TAg) and that of the whole two-layered As2S3/Ag structure (T) are interdependent as TAg = T/T0, where T0 is the transmission of pure As2S3 layer on glassy substrate. We have calculated and plotted the thickness of unreacted Ag film versus exposure time (PD kinetics) applying our experimental
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data (TAg) to the thickness dependence of transmission spectra of silver films measured by Sun et al. [18]. Fig. 2 shows the unreacted Ag layer thickness versus exposure time for different temperatures. Several steps of PD kinetics can clearly been distinguished: (I) the relatively slow step observed only at curve measured at 30 °C; (II) the second one, where the thickness of Ag layer linearly decreases with exposure time, but the slope (the PD rate) is strongly influenced by temperature; (III) the third step that is also linear but with a slope only slowly dependent on temperature; and a final step (IV), which exhibits a sublinear dependence of thickness change of Ag layer on time, particularly observed at low (less than 60 °C) temperatures. In order to check whether the observed change in the slope of PD kinetics is due not to formation of different chemical products (in the doped layer) on the different stages of the dissolution, an additional set of samples was applied. These samples were prepared by multiple evaporation of silver each time followed by its total PD into As2S3. The transmission of a broadband light (k = 0.65 1.2 lm) has been measured for different amount of photodissolved silver. The results are illustrated in Fig. 1(c). One can see that the transmission of Ag: As2S3 mixture insignificantly varies with amount of adopted silver, that is the thickness – exposure time dependences (Fig. 2) are really due to PD process. Note that the transmission of Ag:As2S3 mixture versus amount of adopted silver (Fig. 1(c)) allows to provide an error analysis of the applied experimental method. In fact, the error of such a method is mainly due to progressive light absorption in doped layer during PD. The relative error of transmission, being minimal at the beginning of PD process, becomes maximal of about 5% closely to its finish. However, the transmission of Ag layer below 20 nm increases very rapidly with decrease of its thickness [18]. Therefore the error in Ag thickness determination below 20 nm, by 5% error in transmission of unreacted Ag film, is assessed to be of about 1 nm. The error bars are displayed on the data in Fig. 2. 3.2. Transmission spectra Fig. 3 shows the changes in the transmission spectrum of twolayer structure Ag/As2S3 after illumination for different exposure times at room (25 °C) temperature. The dot and dash lines show the transmission spectra of As2S3 layer without Ag film on top of it and of the silver film, growth directly on the glass substrate respectively. One can see that, in spite of interference phenomenon, the As2S3 film is almost transparent for wavelengths longer
Ag thickness [nm]
50
149
Fig. 3. Transmission spectra of two-layer structure Ag/As2S3 after different exposure times at incident light 45 lW/cm2, k = 0.506 lm.
than 530 nm. Consequently, one can assert that the transparence of the Ag/As2S3 system in IR region is mainly conditioned by absorption/reflection of Ag layer. When PD proceeds the effective thickness of Ag layer decreases, resulting in an increase both of its proper transmittance and transmittance of the whole layered structure. Along with increase of transmittance the shift of interference picture towards longer wavelengths occurs. Obviously it is due both to a shift of transmission edge towards a longer wavelength [5] and increasing of refractive index of doped material [19] with increasing the silver content photodissolved into As2S3. The shift of minima and maxima of interference is most pronounced at the beginning of the PD process. They appear in the transmission spectra because of interference of two light beams: one of them passes through the whole layered structure without any reflection and the other passes through the structure being twice reflected, firstly from Ag layer and secondly from the glass substrate. It is supposed that after each step of exposure the silver rapidly achieves a homogeneous distribution in certain depth of As2S3 [20] but the doped/undoped interface is not sufficiently abrupt to influence the spectra. In this context an interesting peculiar feature can be seen in the Fig. 5: at certain critical exposure
o
30 C o 45 C o 60 C o 75 C o 90 C
40 30 20 10 0
20
40
60
80
100
120
Exposure time [sec] Fig. 2. Decrease of Ag film thickness versus exposure time at various temperatures. The straight dash–dot lines on the curve for 30 °C (j) are drawn as guides to the eyes. In order not to overload the picture, the error bars (being identical) are displayed only for several data points.
Fig. 4. Arrhenius plot for the second (a) and third (b) stages of PD kinetics; (c) temperature dependence of thickness of Ag layer photodissolved before transition between two linear steps of PD occurs. The lines are drawn as guides to the eyes.
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Fig. 5. Decrease of silver thickness versus exposure time at fourth (quasi-parabolic) step of PD. The number by each curve shows the photodiffusion coefficient KT multiplied by 1013 cm2/s. The lines are drawn as guides to the eyes.
time (200 min) the inversion of maxima and minima of transmission spectra occurs.
4. Discussion The segmentation of PD kinetics curve into several distinct sections is of course not new and has been done by everybody studying PD process [2,9,12]. None the less, here we observed some new peculiarities of PD kinetics, which can play an important role in further understanding of the PD mechanism. First it should be mentioned that the kinetics can be divided into four distinct sections instead of three or even two sections usually observed. Secondly, with exception of transition between the first and second steps, the transitions between other steps are not monotonic but rather sharp. We suppose that the reason for these peculiarities of PD kinetics is due to the special conditions of our experiment, which imply the high intensity of illumination applied (250 mW/ cm2) and the thick films of silver (60 nm) combined with a direct measurement of optical transmission of the sample as the photodissolution proceeds. Our results are consistent with the unified model for metal PD in amorphous chalcogenide materials proposed by Elliott [12] and, what is more, they bring to light the experimental confirmation of some theoretical predictions underlined in this model. The first step of PD kinetics, were the PD is very slow (in our experiments observed only at 30 °C), is ascribed to so called ‘‘induction period” generally observed in solid state photoinduced reactions between metals and chalcogenide glasses [2]. The origin of the induction period was suggested [12] to be the lateral diffusion of metal in ChG between dendritic nuclei of reaction product. It depends on intensity and wavelength of illumination [21] and strongly decreases with temperature increase [9]. Namely the last explains why the induction period observed on the kinetic profile (Fig. 2) measured at 30 °C disappears on the curves measured at higher temperatures. The second step is a period during which the reaction proceeds at an approximately constant rate for each temperature, but this rate strongly increases with temperature increase. Fig. 4(a) shows the temperature dependence of PD rate at this stage plotted in Arrhenius coordinates. The slope of the obtained line exhibits a rather high value of 0.34 eV that indicates a high effect of temperature on PD process. The constant rate of photodissolution is generally agreed to be determined by reaction between metal and
ChG, which occurs simultaneously in two different spatial regions of the sample: (I) absorption of photons by breaking As–S bonds that results in a simultaneous producing of non-bridged chalcogen atoms with a single unpaired electron (dangling bond) and generation of free holes at or near the doped/undoped interface, and (II) creation of Ag+ ions at the Ag/doped As2S3 interface were photogenerated holes, after the drift through doped layer react with neutral Ag atoms. In turn, Ag+ ions after the drift towards the doped/ undoped interface accept the unpaired electron from chalcogen dangling bond and a photodoped ternary Ag–As–S compound is created. Thus, the reaction limited step of PD depends either on electronic (hole) photoconductivity of doped layer rph or its ionic conductivity rAgþ . Investigation of the effect of temperature on the PD kinetics allows in principle to distinguish between effects of photoconductivity rph and ions conductivity rAgþ of doped layer on reaction rate. To date was found that PD process of Ag into As2S3, being thermally activated, exhibits activation energy of 0.1–0.2 eV [9,11,22]. Such a relatively weak temperature dependence of PD kinetics is usually ascribed to photoconductivity and the solid state reaction is assert to be limited by the holes flux under condition rph << rAgþ . The opposite situation, that is rph >> rAgþ , means the reaction rate limitation by Ag+-ion conductivity. It has not been observed experimentally so far, but was predicted by Elliott [12] to exhibit the activation energy in the range of 0.3 0.5 eV. We suppose that our experiment confirms this prediction. The high temperature dependence observed on the second step of PD process, which exhibits activation energy EAg = 0.34 eV indicates that Ag+-ion conductivity becomes rate-limiting. It is interesting to note that the activation energy of ‘‘superionic conductor” Ag2.6As2S3 synthesized by Polcharski and coworkers [9] was found to be the same, i.e. 0.34 eV that confirms our assert. The third step of PD kinetics shows also a linear dependence of the change of Ag thickness on time, but its slope only slowly increases with temperature increase. Fig. 4(b) illustrates the photoreaction rate estimated from third step of PD kinetics versus temperature in Arrhenius coordinates. The slope of this line exhibits a relatively low value of 0.1 eV, which as mentioned above, should be attributed to activation energy of photoconductivity, i.e. Eph 0.1 eV. In fact, the photoconductivity of photodoped As2S3 thin layer exponentially increases with temperature increase, but the activation energy depends both on light intensity and temperature regime. At high intensities and temperatures 300–370 K (applied in present work) the activation energy of photoconductivity was found [23] to be of 0.9–0.14 eV, which comprises estimated from the third step of PD value Eph 0.1 eV. Thus, the PD kinetics on the third step is a reaction limited process, but it is controlled by photoconductivity rph under condition that rph << rAgþ . The transition from the ion conductivity limiting to photoconductivity limiting is probably due to increasing in time both of the concentration C Agþ and mobility lAgþ of Ag+ ions in doped region, but the first reason seems to be the main. The transition point corresponds to situation when
rAgþ rph exp
Eph ; kT
ð1Þ
where k is the Boltzman’s constant and T – is the thermodynamic temperature. On the other hand, assuming the homogeneity of silver ion concentration in the doped layer,
rAgþ C Agþ Ddtr ;
ð2Þ
where Ddtr is the thickness of the photodissolved Ag layer until the transition to photoconductivity limiting occurs (transition point). Consequently, the proportionality as:
D. Tsiulyanu, I. Stratan / Journal of Non-Crystalline Solids 356 (2010) 147–152
Eph Ddtr exp ; kT
ð3Þ
should be expected. The lnðDdtr Þ versus reciprocal temperature is plotted in Fig. 4(c). The slope of the presented line is approximately 0.1 eV which coincides with activation energy Eph calculated from temperature dependence of photoreaction rate, related to third step of PD process. Obviously, this coincidence confirms our suggestion concerning the nature of a sharp transition between the second and the third steps of PD kinetics. The final (fourth) step of PD kinetics is a deceleratory stage of the process, particularly visible at low temperatures. It appears to be a quasi-parabolic step, i.e. with a square-root dependence of Ag thickness on time. Fig. 5 shows the thickness change of Ag layer as a function of square-root of exposure time for different temperatures related to the last step of PD kinetics. One can see that each of curves is a straight line that characterizes a diffusion controlled process. Such a PD process is consistent with model [12] wherein both ionic and electronic charge transport occur simultaneously by the condition that the flux of ions jAgþ balances that of holes jh in reverse direction:
jAgþ ¼ jh :
ð4Þ
Each of curves from Fig. 5 can be described by relation: 1
DdT ¼ AT t2 :
ð5Þ
The coefficient of proportionality AT seems not much to depend on temperature and was assessed [12] as: 1 2
AT ¼ ð2K T Þ ¼
2rph DlAg C Agþ F 2
151
!12 ;
ð6Þ
where rph is the electronic (hole) conductivity of doped ChG, DlAg is the difference between the chemical potentials of Ag at Ag/doped As2S3 and doped/undoped As2S3 interfaces (Fig. 1(a)), F is the Faraday constant. The values of coefficient KT can be estimated from the slope of these curves. One can see that the slope of the lines in Fig. 5 does not vary essentially no monotonically with temperature. Perhaps this is due to micrononhomogeneity of the superionic conductor obtained by PD process. Such micrononhomogeneity was observed at the surface of the sample by Kovalskiy et al. [24], using high resolution X-photoelectron spectroscopy. The values of the coefficient KT (shown in Fig. 5 by each curve) are in the range of (2.9–3.8) 1013 cm2/s. These values are with three orders of magnitude higher than either the thermodiffusion coefficient of Ag in As2S3 determined experimentally [9] or its value estimated by indirect calculations [12]. An essential increasing of parabolic constant KT in a PD process comparative with its dark value in a thermodiffusion process was predicted by Elliott [12] and obviously is due to a high photoconductivity of Ag doped ChG. Namely the photoconductivity rph is involved as electronic conductivity in Eq. (6), but as shown in [23], the photoconductivity of doped As2S3 layer (As2S3Ag0.15) is much higher than its dark conductivity, particularly at low temperatures and high light intensities. As far as the inversion of maxima and minima of transmission spectra is concerned (Section 3.2) such a inversion can be due either by disappearance (exhaustion) of Ag layer or, at least, its islanding. In fact, before critical exposure time one of the interfering light beam passing from doped As2S3 with a refractive index nch 2.8 (k = 0.75 lm) [17] is reflected from highly absorbing Ag layer with losing a half of wavelength [25], but after critical exposure time this beam becomes reflected from air na = 1 without a phase shift
Fig. 6. Decrease of silver thickness versus exposure time tracked through maxima of interference, taking into consideration the phase shift. The arrow shows the critical exposure time and critical thickness at which the phase shift occurs.
as na < nch. In order to clarify whether does the Ag layer exhaust at critical exposure time or simply becomes discontinuous, we have applied the thickness dependence of transmittance of Ag films, carried out in [18] to our experimental data. Fig. 6 shows the decrease of Ag layer thickness with time obtained by tracking the increasing of transmission through maxima of interference, taking into consideration the phase shift (dot–dash line in Fig. 3). One can see that the critical exposure time corresponds to a thickness (shown by an arrow in Fig. 6) of approximately 17 nm. Namely this value was found in [18] to be the critical thickness below which the pure Ag film becomes discontinuous. Thus, we assert that the inversion of transmission spectra at critical exposure time is due to occurrence of an islanding of Ag film. Note that this phenomenon has been observed early at PD of Ag into amorphous GeSe2 films [26] and was explained by a non-uniform dissolution process. Actually it appears that the islanding of Ag films occurs itself at its critical thickness. The increasing of transmittance after the critical exposure time is due to continuation of PD, as well as to decreasing and narrowing of islands of the Ag film with illumination. The last explains the lack of wavelength shift of transmission extremes after their inversion at critical exposure time.
5. Conclusions The kinetics profile of Ag photodissolution (PD) in glassy As2S3 comprises two linear steps with activation energies of about 0.34 eV and 0.1 eV followed by a parabolic tail. The linear steps are ascribed to ion conductivity limiting and photoconductivity limiting solid state reaction respectively, but the parabolic tail appears to be derived from a diffusion controlled process. The diffusion coefficient varies not essentially no monotonically with temperature, being of about (2.9–3.8) 1013 cm2/s. At the last stage of PD process the islanding of Ag film occurs, which is revealed by inversion of transmission spectra of the whole layered structure. The islanding of Ag film originates not from its non-uniform photodissolution but occurs itself at some critical thickness. References [1] M.T. Kostyshin, E.U. Mikhailovskya, P.F. Romanenko, Sov. Phys. (Solid State) 8 (1966) 451. [2] A.V. Kolobov, S.R. Elliott, Adv. Phys. 40 (1991) 625.
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