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Self-organization in simulated arsenic chalcogenide networks
Journal of Non-Crystalline Solids 326&327 (2003) 385–388 www.elsevier.com/locate/jnoncrysol
Self-organization in simulated arsenic chalcogenide networks M. Popescu
*
National Institute of R&D for Materials Physics, P.O. Box MG.7, 76900 Bucharest-Magurele, Romania
Abstract Polymerization–depolymerization processes induced by bandgap light irradiation with alternating high and low intensity light control the nano-scale extension of disordered layer-like clusters in arsenic rich chalcogenides. These processes resulting in a fractal morphology of the clusters were simulated in the frame of a Monte-Carlo-Metropolis method. The fractal model for photo-darkening and photo-bleaching phenomena in arsenic chalcogenides is discussed. 2003 Elsevier B.V. All rights reserved. PACS: 61.43.Bn; 61.43.Fs; 61.43.Hv; 61.46.+w
1. Introduction Extended research is now dedicated for creating highly structured materials. One key issue is the formation of discrete aggregates of organized nanoparticles when subjected to light. These discrete aggregates allow for the fabrication of threedimensional structures with various optical, electrical and magnetic properties. Another alternative is to trigger the formation of specific aggregates of atomic configurations in rather homogeneous matrices using the energy-controlled self-assembling process [1]. The structure of layered chalcogenides in the amorphous state, as e.g. arsenic chalcogenides is not completely explained. The photo-darkening (PD) and photo-bleaching (PB) effects are subjects of high interest both from fundamental and prac-
*
Tel.: +40-21 493 0047/195; fax: +40-21 493 0267. E-mail address: [email protected]fim.ro (M. Popescu).
tical points of view. Nevertheless, the structural basis of PD and PB is poorly understood in spite of the numerous papers published till the present [2,3]. The discovery of reversible changes in the optical absorption of amorphous As2 S3 was reported in the early 1970s [4] and a consensus is now reached that the origin of the effect is the modification of the structure as shown by the reversible change in X-ray diffraction patterns [5]. Various models for reversible photo-structural transformations were proposed. Lyubin [6] takes into account the polymerization processes into chalcogenide networks. The PD and PB effects are explained by destruction and polymerization of layered-like structural units, respectively. Elliott [7] suggested a bond-breaking and/or bond-alternation change as a result of PD (PB). Grigorovici and Vancu [8] proposed a model for As4 Sex (x < 4) a model based on photon- and phonon-assisted transitions between a molecular ground state and a polymeric metastable, excited
0022-3093/$ - see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0022-3093(03)00443-5
386
M. Popescu / Journal of Non-Crystalline Solids 326&327 (2003) 385–388
state, the energy barrier being higher the stiffer the polymeric structure is, therefore as more trivalent arsenic atoms are contained in the system. Li and Drabold [9] found that homopolar bonds (As–As or Se–Se) are strongly implicated in photo-structural modifications of As2 Se3 . Shimakawa et al. [10] assume that the illumination of amorphous chalcogenides charges the disordered layers negatively, resulting in a Coulomb repulsion between them. This repulsion results in an expansion of the material and a slip motion of the layers. In As2 S3 and other, similar glasses some structural fragments were supposed to be present very similar to those in crystalline homologues. These fragments should be very small and can be generated by illumination [11]. Their modification, extension, shrinkage and rotation are supposed to explain PB, PD and anisotropy phenomena in the chalcogenide glasses. In this paper we simulated the processes of formation–destruction of large polymeric units, supposed to form the basis of the structure in arsenic chalcogenides, with the aim to show that a non-equilibrium rapid process of polymerization– depolymerization under the influence of light at variable intensity can lead to a more or less extended structural fragmentation with fractal morphology.
2. Theory and simulation method In the systems far from equilibrium new cooperative structures can be produced due to the amplification of the large fluctuations. The giant fluctuations are stabilized by the exchange of energy with the surrounding medium, as shown by Prigogine in his well-known theory of irreversible thermodynamics. Dissipative patterns are important and are related to the two-subsystems model of glass [12]: the solid-like ÔphaseÕ consisting of covalent clusters and the liquid-like ÔphaseÕ formed by inter-cluster boundaries [13]. One may consider oscillations of transmission [14] and a non-exponential relaxation of wave type [15], as large-scale processes that take place in glass and connected with dissipative patterns created there.
The simulation of the polymerization–depolymerization processes in arsenic chalcogenides was carried out in the frame of the Monte-CarloMetropolis method, using a 100 · 100 rectangular array of points. The simulation was essentially two-dimensional. Basically two opposite processes were supposed and simulated. In the first step the formation of a new structural unit (a monomer, as e.g. As2 Ch3 pyramidal unit, where Ch is the chalcogen, S or Se) attached to a randomly selected point on the array was simulated. The next step was to choose randomly an other point in the nearest vicinity of the first one that simulates the attachment of a new monomer from the liquid-like subsystem. The following simulation steps continued in the sequence: (1) a new unit was added with the rules: (a) random selection of the attachment position on the boundary of the cluster, and (b) relaxation in the first neighborhood permitted (the added unit is transferred to a new place only if the number of neighboring units in the new position increases); (2) a random position on the boundary of the cluster was again selected and the monomer unit from that place was destroyed by converting this monomer into a molecular As–Se unit embedded in the liquidlike phase that surrounds the cluster, thus simulating the depolymerization process. Thereafter, the whole process was repeated with three added units and two eliminated units, alternately. Thus, the number of aggregated units increases slowly. This type of modeling simulates the formation and growth of the disordered polymeric layers within the matrix of the chalcogenide material. The calculations were programmed in FORTRAN and run under LINUX on a PC Pentium.
3. Results After every stage of simulation the full image of the array was recorded and plotted. The total number of simulation events reached 100 000. Fig. 1 shows several snapshots of the array covered by structural units at different steps of modeling. As a consequence of alternation of two opposite processes (creation–destruction or polymerization– depolymerization) the structural configuration
M. Popescu / Journal of Non-Crystalline Solids 326&327 (2003) 385–388
387
Fig. 1. Snapshots of the evolution of the coverage of the 100 · 100 array during formation of the fractal morphology of the clusters: (a) 93 units; (b) 244 units; (c) 520 units; (d) 921 units.
obtained is surprisingly inhomogeneous but fragmented into fractal pieces that are distributed quasi-uniformly over the whole 100 · 100 array. Although we have simulated only the case of one layer the results can be easily extended to the clusters with 3–4 layers, that form the main structural entities in chalcogenide glasses.
4. Discussion In the frame of a non-equilibrium process the successive alternation of high/low intensity during light irradiation of amorphous chalcogenides determines a characteristic distribution of polymerized amorphous layers with small size extension. The control of the disordered layer-like clusters is important because many properties of these materials depend on the medium-range scale structure. Thus, as Meherun-Nessa et al. [16] have shown, that the optical absorption in amorphous chalcogenides can be interpreted by introducing the density-of-states on fractals. The presence of disorder strongly influences the nature of DOS. In our simulation the development of the polymeric layer-like configurations approaches the typical fractal morphology with the fractal dimension n ¼ 1:74 (determined from the morphology of the simulated clusters). The general configuration of structural units, thus obtained, gives a strong support of the explanation of the optical results by mean of the fractal concept, presented in [16]. The compactness of the disordered layers as simulated
in this work strongly depends on the relaxation of the added monolayers on the boundary. If relaxation at second neighboring sites is allowed, then less-branched clusters are formed while the fractal dimension of the clusters does not change significantly, the correlation length becomes smaller. On the other hand, the chalcogenide films show strong non-linear optical effects when illuminated by powerful bandgap light [17], which were confirmed by means of the Z-scan technique for virgin As2 S3 and As2 Se3 films [18]. The non-linear effects for the high fluency of light and short time action can be explained by microresonators built in the amorphous structure. The small size layer fragments simulated in this paper can play the role of the microresonators. The mechanism of PD and its dependence on the light intensity can be explained as being related to the modification of the order and morphology including the size-change of the layered fragments. In the model with a large distribution of small size amorphous layers, the PD is due to the increase of disorder and appearance of new homopolar bonds, while the layer extension increases. At the same time the volume of the material increases, i.e. an expansion occurs, as experimentally observed. This kind of interpretation is supported by Kolobov et al. [19]. As opposite, the PB is determined by the elimination of the wrong bonds and, possibly, the separation of molecular configurations in the case of non-stoichiometric compositions. Thus, the reciprocal slip of the small-area layers is facilitated, as in the model of Shimakawa, and the
388
M. Popescu / Journal of Non-Crystalline Solids 326&327 (2003) 385–388
volume of the amorphous material decreases, as observed in experiments. 5. Conclusions The results of the simulation of the complex polymerization–destruction processes show that a new structural state can be obtained in the amorphous chalcogenides based on disordered layers (arsenic chalcogenides). If this is really the case, an experiment with alternate sequence of high/low intensity illumination applied to the sample, could give the possibility to modify the amorphous chalcogenide thin films at atomic scale, and to reach a new state of structural organization by self-assembling of the basical structural units in the amorphous chalcogenides.
References [1] V.M. Rotello, Mater. Today (Nov/Dec) (2001) 24. [2] K. Shimakawa, A.V. Kolobov, S.R. Elliott, Adv. Phys. 44 (1995) 475.
[3] A.V. Kolobov, Ka. Tanaka, J. Optoelectron. Adv. Mater. 1 (4) (1999) 3. [4] J.S. Berkes, S.W. Ing, W.J. Hillegas, J. Appl. Phys. 42 (1971) 4908. [5] Ke. Tanaka, Appl. Phys. Lett. 26 (1975) 243. [6] V.M. Lyubin, in: Proc. 6th Int. Conf. Amorph. Liquid Semicond., Leningrad, SSSR, 1975, vol. Structure and Properties of Non-Cystalline Semiconductors, p. 415. [7] S.R. Elliott, J. Non-Cyst. Solids 81 (1986) 71. [8] R. Grigorovici, A. Vancu, J. Phys. 42 (10) (1981) C4-391. [9] Jun Li, D.A. Drabold, Phys. Rev. Lett. 85 (2000) 2785. [10] K. Shimakawa, N. Yoshida, A. Ganjoo, Y. Kuzukawa, J. Singh, Philos. Mag. Lett. 77 (1998) 153. [11] Ke. Tanaka, M. Notani, H. Hisakuni, Solid State Commun. 95 (1995) 461. [12] Ke. Tanaka, Rev. Solid State Sci. 4 (2&3) (1990) 641. [13] S.A. Dembovski, P.A. KozÕmin, Solid State Commun. 86 (1993) 623. [14] J. Hajto, I. Janossy, Philos. Mag. B 47 (1983) 347. [15] E.N. Voronkov, S.A. Kozyukin, V.N. Hirin, Solid State Commun. 89 (1994) 341. [16] Meherun-Nessa, K. Shimakawa, A. Ganjoo, J. Singh, J. Optoelectron. Adv. Mater. 2 (2) (2000) 133. [17] V. Chumash, I. Cojocaru, E. Fazio, F. Michelotti, M. Bertolotti, Prog. Opt. 36 (1996) 1. [18] F. Michelotti, E. Fazio, F. Senesi, M. Bertolotti, V. Chumash, A. Andriesh, Opt. Commun. 101 (1993) 74. [19] A.V. Kolobov, H. Oyanagi, A. Roy, Ka. Tanaka, J. NonCryst. Solids 232–234 (1998) 80.
Self-organization in simulated arsenic chalcogenide networks M. Popescu
*
National Institute of R&D for Materials Physics, P.O. Box MG.7, 76900 Bucharest-Magurele, Romania
Abstract Polymerization–depolymerization processes induced by bandgap light irradiation with alternating high and low intensity light control the nano-scale extension of disordered layer-like clusters in arsenic rich chalcogenides. These processes resulting in a fractal morphology of the clusters were simulated in the frame of a Monte-Carlo-Metropolis method. The fractal model for photo-darkening and photo-bleaching phenomena in arsenic chalcogenides is discussed. 2003 Elsevier B.V. All rights reserved. PACS: 61.43.Bn; 61.43.Fs; 61.43.Hv; 61.46.+w
1. Introduction Extended research is now dedicated for creating highly structured materials. One key issue is the formation of discrete aggregates of organized nanoparticles when subjected to light. These discrete aggregates allow for the fabrication of threedimensional structures with various optical, electrical and magnetic properties. Another alternative is to trigger the formation of specific aggregates of atomic configurations in rather homogeneous matrices using the energy-controlled self-assembling process [1]. The structure of layered chalcogenides in the amorphous state, as e.g. arsenic chalcogenides is not completely explained. The photo-darkening (PD) and photo-bleaching (PB) effects are subjects of high interest both from fundamental and prac-
*
Tel.: +40-21 493 0047/195; fax: +40-21 493 0267. E-mail address: [email protected]fim.ro (M. Popescu).
tical points of view. Nevertheless, the structural basis of PD and PB is poorly understood in spite of the numerous papers published till the present [2,3]. The discovery of reversible changes in the optical absorption of amorphous As2 S3 was reported in the early 1970s [4] and a consensus is now reached that the origin of the effect is the modification of the structure as shown by the reversible change in X-ray diffraction patterns [5]. Various models for reversible photo-structural transformations were proposed. Lyubin [6] takes into account the polymerization processes into chalcogenide networks. The PD and PB effects are explained by destruction and polymerization of layered-like structural units, respectively. Elliott [7] suggested a bond-breaking and/or bond-alternation change as a result of PD (PB). Grigorovici and Vancu [8] proposed a model for As4 Sex (x < 4) a model based on photon- and phonon-assisted transitions between a molecular ground state and a polymeric metastable, excited
0022-3093/$ - see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0022-3093(03)00443-5
386
M. Popescu / Journal of Non-Crystalline Solids 326&327 (2003) 385–388
state, the energy barrier being higher the stiffer the polymeric structure is, therefore as more trivalent arsenic atoms are contained in the system. Li and Drabold [9] found that homopolar bonds (As–As or Se–Se) are strongly implicated in photo-structural modifications of As2 Se3 . Shimakawa et al. [10] assume that the illumination of amorphous chalcogenides charges the disordered layers negatively, resulting in a Coulomb repulsion between them. This repulsion results in an expansion of the material and a slip motion of the layers. In As2 S3 and other, similar glasses some structural fragments were supposed to be present very similar to those in crystalline homologues. These fragments should be very small and can be generated by illumination [11]. Their modification, extension, shrinkage and rotation are supposed to explain PB, PD and anisotropy phenomena in the chalcogenide glasses. In this paper we simulated the processes of formation–destruction of large polymeric units, supposed to form the basis of the structure in arsenic chalcogenides, with the aim to show that a non-equilibrium rapid process of polymerization– depolymerization under the influence of light at variable intensity can lead to a more or less extended structural fragmentation with fractal morphology.
2. Theory and simulation method In the systems far from equilibrium new cooperative structures can be produced due to the amplification of the large fluctuations. The giant fluctuations are stabilized by the exchange of energy with the surrounding medium, as shown by Prigogine in his well-known theory of irreversible thermodynamics. Dissipative patterns are important and are related to the two-subsystems model of glass [12]: the solid-like ÔphaseÕ consisting of covalent clusters and the liquid-like ÔphaseÕ formed by inter-cluster boundaries [13]. One may consider oscillations of transmission [14] and a non-exponential relaxation of wave type [15], as large-scale processes that take place in glass and connected with dissipative patterns created there.
The simulation of the polymerization–depolymerization processes in arsenic chalcogenides was carried out in the frame of the Monte-CarloMetropolis method, using a 100 · 100 rectangular array of points. The simulation was essentially two-dimensional. Basically two opposite processes were supposed and simulated. In the first step the formation of a new structural unit (a monomer, as e.g. As2 Ch3 pyramidal unit, where Ch is the chalcogen, S or Se) attached to a randomly selected point on the array was simulated. The next step was to choose randomly an other point in the nearest vicinity of the first one that simulates the attachment of a new monomer from the liquid-like subsystem. The following simulation steps continued in the sequence: (1) a new unit was added with the rules: (a) random selection of the attachment position on the boundary of the cluster, and (b) relaxation in the first neighborhood permitted (the added unit is transferred to a new place only if the number of neighboring units in the new position increases); (2) a random position on the boundary of the cluster was again selected and the monomer unit from that place was destroyed by converting this monomer into a molecular As–Se unit embedded in the liquidlike phase that surrounds the cluster, thus simulating the depolymerization process. Thereafter, the whole process was repeated with three added units and two eliminated units, alternately. Thus, the number of aggregated units increases slowly. This type of modeling simulates the formation and growth of the disordered polymeric layers within the matrix of the chalcogenide material. The calculations were programmed in FORTRAN and run under LINUX on a PC Pentium.
3. Results After every stage of simulation the full image of the array was recorded and plotted. The total number of simulation events reached 100 000. Fig. 1 shows several snapshots of the array covered by structural units at different steps of modeling. As a consequence of alternation of two opposite processes (creation–destruction or polymerization– depolymerization) the structural configuration
M. Popescu / Journal of Non-Crystalline Solids 326&327 (2003) 385–388
387
Fig. 1. Snapshots of the evolution of the coverage of the 100 · 100 array during formation of the fractal morphology of the clusters: (a) 93 units; (b) 244 units; (c) 520 units; (d) 921 units.
obtained is surprisingly inhomogeneous but fragmented into fractal pieces that are distributed quasi-uniformly over the whole 100 · 100 array. Although we have simulated only the case of one layer the results can be easily extended to the clusters with 3–4 layers, that form the main structural entities in chalcogenide glasses.
4. Discussion In the frame of a non-equilibrium process the successive alternation of high/low intensity during light irradiation of amorphous chalcogenides determines a characteristic distribution of polymerized amorphous layers with small size extension. The control of the disordered layer-like clusters is important because many properties of these materials depend on the medium-range scale structure. Thus, as Meherun-Nessa et al. [16] have shown, that the optical absorption in amorphous chalcogenides can be interpreted by introducing the density-of-states on fractals. The presence of disorder strongly influences the nature of DOS. In our simulation the development of the polymeric layer-like configurations approaches the typical fractal morphology with the fractal dimension n ¼ 1:74 (determined from the morphology of the simulated clusters). The general configuration of structural units, thus obtained, gives a strong support of the explanation of the optical results by mean of the fractal concept, presented in [16]. The compactness of the disordered layers as simulated
in this work strongly depends on the relaxation of the added monolayers on the boundary. If relaxation at second neighboring sites is allowed, then less-branched clusters are formed while the fractal dimension of the clusters does not change significantly, the correlation length becomes smaller. On the other hand, the chalcogenide films show strong non-linear optical effects when illuminated by powerful bandgap light [17], which were confirmed by means of the Z-scan technique for virgin As2 S3 and As2 Se3 films [18]. The non-linear effects for the high fluency of light and short time action can be explained by microresonators built in the amorphous structure. The small size layer fragments simulated in this paper can play the role of the microresonators. The mechanism of PD and its dependence on the light intensity can be explained as being related to the modification of the order and morphology including the size-change of the layered fragments. In the model with a large distribution of small size amorphous layers, the PD is due to the increase of disorder and appearance of new homopolar bonds, while the layer extension increases. At the same time the volume of the material increases, i.e. an expansion occurs, as experimentally observed. This kind of interpretation is supported by Kolobov et al. [19]. As opposite, the PB is determined by the elimination of the wrong bonds and, possibly, the separation of molecular configurations in the case of non-stoichiometric compositions. Thus, the reciprocal slip of the small-area layers is facilitated, as in the model of Shimakawa, and the
388
M. Popescu / Journal of Non-Crystalline Solids 326&327 (2003) 385–388
volume of the amorphous material decreases, as observed in experiments. 5. Conclusions The results of the simulation of the complex polymerization–destruction processes show that a new structural state can be obtained in the amorphous chalcogenides based on disordered layers (arsenic chalcogenides). If this is really the case, an experiment with alternate sequence of high/low intensity illumination applied to the sample, could give the possibility to modify the amorphous chalcogenide thin films at atomic scale, and to reach a new state of structural organization by self-assembling of the basical structural units in the amorphous chalcogenides.
References [1] V.M. Rotello, Mater. Today (Nov/Dec) (2001) 24. [2] K. Shimakawa, A.V. Kolobov, S.R. Elliott, Adv. Phys. 44 (1995) 475.
[3] A.V. Kolobov, Ka. Tanaka, J. Optoelectron. Adv. Mater. 1 (4) (1999) 3. [4] J.S. Berkes, S.W. Ing, W.J. Hillegas, J. Appl. Phys. 42 (1971) 4908. [5] Ke. Tanaka, Appl. Phys. Lett. 26 (1975) 243. [6] V.M. Lyubin, in: Proc. 6th Int. Conf. Amorph. Liquid Semicond., Leningrad, SSSR, 1975, vol. Structure and Properties of Non-Cystalline Semiconductors, p. 415. [7] S.R. Elliott, J. Non-Cyst. Solids 81 (1986) 71. [8] R. Grigorovici, A. Vancu, J. Phys. 42 (10) (1981) C4-391. [9] Jun Li, D.A. Drabold, Phys. Rev. Lett. 85 (2000) 2785. [10] K. Shimakawa, N. Yoshida, A. Ganjoo, Y. Kuzukawa, J. Singh, Philos. Mag. Lett. 77 (1998) 153. [11] Ke. Tanaka, M. Notani, H. Hisakuni, Solid State Commun. 95 (1995) 461. [12] Ke. Tanaka, Rev. Solid State Sci. 4 (2&3) (1990) 641. [13] S.A. Dembovski, P.A. KozÕmin, Solid State Commun. 86 (1993) 623. [14] J. Hajto, I. Janossy, Philos. Mag. B 47 (1983) 347. [15] E.N. Voronkov, S.A. Kozyukin, V.N. Hirin, Solid State Commun. 89 (1994) 341. [16] Meherun-Nessa, K. Shimakawa, A. Ganjoo, J. Singh, J. Optoelectron. Adv. Mater. 2 (2) (2000) 133. [17] V. Chumash, I. Cojocaru, E. Fazio, F. Michelotti, M. Bertolotti, Prog. Opt. 36 (1996) 1. [18] F. Michelotti, E. Fazio, F. Senesi, M. Bertolotti, V. Chumash, A. Andriesh, Opt. Commun. 101 (1993) 74. [19] A.V. Kolobov, H. Oyanagi, A. Roy, Ka. Tanaka, J. NonCryst. Solids 232–234 (1998) 80.