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Crystalline–amorphous and amorphous–amorphous transitions in phase-change materials
Journal of Non-Crystalline Solids 355 (2009) 1820–1823
Contents lists available at ScienceDirect
Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol
Crystalline–amorphous and amorphous–amorphous transitions in phase-change materials } rinczi * M. Popescu, F. Sava, A. Velea, A. Lo National Institute of Materials Physics, 105 Bis Atomistilor St., 077125 Magurele, Ilfov, Romania
a r t i c l e
i n f o
Article history: Received 18 April 2008 Received in revised form 14 January 2009 Available online 27 July 2009 PACS: 61.46.Bc 63.22.Kn 63.50.Lm 64.60.Cn 64.70.Nd 64.75.Yz
a b s t r a c t The transition from the crystalline state to amorphous state and back has been studied in the particular case of the GeSb2Te4 phase-change material by a computer simulation procedure. Modelling at the nanoscale indicates specific structural characteristics, especially the multiplicity of the amorphous phase as opposite to the uniqueness of the crystalline phase. In the particular case of the Si12Ge10As30Te48 switching glass two types of ordering have been pointed out and characterized. Ó 2009 Elsevier B.V. All rights reserved.
Keywords: Glass transition Chalcogenides Nano-clusters Medium-range order
1. Introduction The non-crystalline state of the condensed matter was the subject of deep investigations in the last decades. The reversible switching phenomenon in Si18Ge7As35Te40 complex chalcogenide was discovered in the late ‘60s by Ovshinsky [1]. This phenomenon was challenging and promising for future applications. A review of the state-of-the art in the field of the properties and applications of the non-crystalline materials, experimental results and proposed structural models, has been published by Bicerano and Adler in 1987 [2]. They have already mentioned besides the threshold switching alloy like Si18Ge7As35Te40, several other memory switching alloys like Ge15Te81Sb2S2 and Ge24Te72Sb2S2, having a special place among amorphous solids without crystalline analogues. Recently, various compositions of Ge–Sb–Te (GST) ternary alloys were found to be efficient for phase-change applications, including electrical and optical switching [3]. Pseudo-binary compositions in the (GeTe)m(Sb2Te3)n system like GeSb2Te4, Ge2Sb2Te5 and GeSb2Te7 are of special interest. The GST phase-change memory materials and the related technology is strongly competing the currently widespread floating* Corresponding author. }rinczi). E-mail address: lorinczi@infim.ro (A. Lo 0022-3093/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2009.04.053
gate flash memory and technology, because of quicker response, longer life time, better scaling ability and lower power consumption [4]. In spite of the significant technological advances, some intimate features of the phase-change transitions are still not well understood. GST phase-change materials can be cycled by exposure to laser beam, and as a function of the pulse intensity and duration, the laser beam triggers the switching from crystalline to amorphous phase and back. Phase-change recording with GST compositions is possible by electrical current pulses or nanosecond laser pulses of high intensity. These pulses determine the melting of small regions of submicrometer size in the crystalline material. By subsequent quenching the melted region solidifies into an amorphous state. This is the ‘‘off”-state (state with low electric conductivity, or bit 0). A new pulse of lower intensity but longer duration heats the material and produces temperature gradients and reasonable cooling rates that give rise to re-crystallization. Thus, the ‘‘on”state (state with high electric conductivity, or bit 1) is obtained. These two states, crystalline and amorphous, exhibit strong differences in optical and electrical properties and this feature allows for reading the bit by a third very low-intensity pulse, which does not produce structural changes in the material [5]. For other kind of materials, as e.g. Si–Ge–As–Te glasses an other type of transformation seems to govern the switching phenomena,
M. Popescu et al. / Journal of Non-Crystalline Solids 355 (2009) 1820–1823
1821
namely a transition from a less ordered amorphous state to an other more ordered one, and back. This transition is called amorphous–amorphous transition. In this paper we report the results obtained during simulation of the structural transition from one ordering state to another one in Ge–Sb–Te and Si–Ge–As–Te phase-change materials.
2. Modelling 2.1. Qualitative overview It is a generally occurring question in modelling of glasses, how to imagine the building units and how to manage the end atoms of the 1D and 2D building units, like chains ends or sheet edges of atoms or molecules. An elegant solution to this problem is to admit that these entities will fold, to optimize their space requirement, i.e. to pack themselves optimally under the given physico-chemical conditions (composition, valences, bonding energies, etc.). The packing ability is essential for achieving a more-or-less ordered structure. Grigorovici and Gartner have considered and modelled even the possibility of hybridization change of the atoms involved in phase-change processes [6]. It seems that the nature and the strength of the bonds between the building units act as main ordering factors of the atoms. Due to instability processes in very large assemblies of interacting atoms the big clusters split into smaller ones. Cluster formation in various chalcogenide glasses has been considered in several papers, as for example by De Neufville et al. [7], Micoulaut and Phillips [8], Vempati and Boolchand [9] and Banik [10]. The modelling of crystalline–amorphous transition was made in the frame of a Monte-Carlo Metropolis procedure, starting from hand-built models. The cluster models of two typical glasses Si–As–Te (202 atoms) and Ge–Sb–Te (27 atoms) have been built by hand from plastic units and linked by plastic tubes according to the valence requirements of every type of atoms. The coordinates of the simulated atoms have been roughly measured directly on the model. Finally, the coordination of every atom has been tabulated and the arrays of data were introduced in a computer. Special programs that manage the Monte-Carlo calculations have been used with the purpose to calculate the structure of minimum free energy of every model. All calculations were performed in the frame of the valence force field model. Two interaction potentials have been used: the bond stretching potential and the bond bending potential, as reported by Keating [11] with the force constants reported by Martin [12].
Fig. 1. The modeling of the amorphous–amorphous transition: (a) less structured amorphous state; (b) more structured amorphous state.
The hand modelling demonstrated that the distances and bonds between atoms are compatible with the full satisfaction of the valence requirements and maintaining of the correct density of the material. The final demonstration of the realistic character of the model has been made only after the calculation of the structure of minimum free energy (relaxed structure). The relaxed continuous network model is shown in Fig. 1a. The relaxed structure corresponds to a free energy of 1.358 meV per atom. In the following step we modelled the phase transformation induced in these materials. It is supposed that, by applying e.g. an electrical field to the material, the stressed bonds are excited and this may produce the breaking of the bonds and their reforming in a new configuration. Let us speculate the idea that the breaking of the bonds between the layers is due to stressed bonds of Si–Te and Ge–Te. Tellurium substitutes Ge or Si in the layers and forms strong As–Te bonds that build a more ordered As2Te3 network. The remaining Ge and Si are supposed to build dimers or small clusters between the As2Te3 layers. Thus, a new model is obtained after relaxation. This model exhibits a lower free energy, i.e. the distorted bonds are in a less amount than in the first model. The free energy after relaxation is 2.082 leV per atom. The model is shown in Fig. 1b. By successive melting and quenching at different rates the material changes from one state to another and back. The model points out to a new and special transition from amorphous to another amorphous state that approaches the crystalline state. In fact we are dealing with a transition from an amorphous state to a quasi-crystalline state, and this behaviour ensures the rapidity of switching. Regarding the stability of the on and off states, it seems that after many cycles a couple of equilibrium states are reached. The above model has been reported previously [13,14] but only partially relaxed. Here we gave a more advanced relaxation.
2.2. Modelling of the quaternary ovonic composition: Si–Ge–As–Te 2.3. Modelling results of the phase-change memory material GeSb2Te4 The structural transition in the composition Si1GeAsTe has been simulated with the help of a model with 202 atoms. The quaternary amorphous composition has been modelled as a continuous random network of atoms linked by covalent bonds. The valences of the atoms were those characteristic to the atoms in the crystalline compounds. In this model the As–Te bonds are favoured. The material composition corresponds mainly of As + Te (78%) and the As/Te ratio approaches the ratio 2:3 as in the composition of the stoichiometric material: As2Te3. Because As2Te3 is known as a layered chalcogenide, we considered that the layer configuration is a plausible ingredient in our model. Therefore we decided to introduce Si and Ge between the As2Te3 layers. The introduction of the silicon and germanium atoms into the disordered network has been demonstrated to be possible as regarding the valence requirements and crystallochemistry principles. Of course, there are other possibilities, e.g. the substitution of Ge and Si within As2Te3 disordered layers.
On the example of GeSb2Te4 composition we simulated the transition from the crystalline state to the amorphous state. The crystalline state is the starting structure during cycling of the memory material. This corresponds to on state (bit 1), while the amorphous structure corresponds to the off state (bit 0). Welnic et al. [15] have shown that strong difference exists between a covalent semiconductor and Ge2Sb2Te5, a prototype compound of the GST series of compositions. While the covalent semiconductors have, in general, similar local arrangements, not only in crystalline, but also in amorphous state, GST undergoes a profound change in local order on amorphization. The GST class is characterized by two competing structures, with similar energy but different local order and different properties. The main hypothesis in the modelling of the transition from crystalline to amorphous state is: while in crystalline GeSb2Te4 the structure is cubical and the atoms exhibit roughly the same
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M. Popescu et al. / Journal of Non-Crystalline Solids 355 (2009) 1820–1823
coordination (6), in the amorphous (disordered) state of the same compound, the atoms take the normal coordination found in their usual crystalline compounds: 2 for Te, 3 for Sb and 4 for Ge [16]. The recrystallization means the return to the cubical octahedral structure. The change of state back and forth is controlled by the laser pulse energy. This mechanism allows to build a realistic model. Firstly there was built a cubical configuration that simulates the atomic arrangement in GeSb2Te4 (27 atoms). Thereafter the energetic relaxation of the structure has been performed. In the next step a few atoms have been switched to the coordination numbers as follows: Ge to 4, Sb to 3 and Te to 2. The relaxation was repeated. In the next few steps more-and-more atoms were switched to the above shown coordination numbers. The initial cubical configuration was thus gradually transformed into an amorphous cluster. Several ways of transformation are possible, and consequently, several amorphous clusters of similar or nearly similar free energy are possible. The transition between the crystalline and amorphous structures simulates the transformation that takes place into the material during the change of state. Fig. 2 shows the results. The free energy of different amorphous clusters differs by less than 25%. A heap of amorphous clusters is represented after energy relaxation in Fig. 3(a). The radial distribution function (RDF) and the bond angle distribution in the big amorphous cluster (543 atoms) are shown in Fig. 3(b) and (c). Both histograms demonstrate the plausibility of the model, because the main peaks in RDF reproduce the experimental ones [17] fairly well, and the width of the bonding angle distribution is below 20 degrees estimated from width of the second peak of experimental RDF. 3. Discussion The type of structural transition during switching in phasechange memories depends on the composition. In classical ovonic composition (e.g. Si–Ge–As–Te) we have shown that it is possible to have phase-change transition from an amorphous to quasi-crystalline state.
In our views the switching in Ge–Sb–Te is produced in the following way. In the first cycle the crystallites of the phase-change material are transformed into amorphous clusters and then back. After a high number of cycles, the amorphization–crystallization process determines the breaking of the big clusters into smaller ones. Finally, for very large number of cycles the small clusters dominates and the structure with small clusters remains stable for a very long time, i.e. the clusters switch rapidly from the disordered state to the crystalline one and back. It is interesting to remark that the transition from the crystalline state to the amorphous state(s) implies intermediary structures whose free energies are higher that those of the amorphous structures. We must admit that the transformation forth and back must overcome a certain energy barrier. This barrier, evidenced by modelling, could explain the stability of both configurations against phase-change transformation. The energy necessary for the system to pass across the barrier is provided by the electrical or by the laser pulse acting on the thin film material. As shown recently by Frumar et al. [18] the crystalline state in these phase-change materials is highly imperfect, with high amount of defects integrated into the structure. This means that in our model the switching back to the crystalline state is in fact a transition to a highly defective crystalline state. The easy switching from amorphous to crystalline structure can be explained starting from the idea presented by Baker et al. [16]. They suppose that the conjugated charge, or valence alternation pairs of over-coordinated tellurium and under-coordinated Sb or Ge play a role in facilitating the reverse amorphous–crystalline transitions important in optical and electrical memory devices. The electronic multistage switching can be understood if we admit that the conduction steps are dictated by the level of excitation that controls the appearance of various concentration ratios of quasi-amorphous/quasi-ordered clusters. These clusters can be melted and integrated into the amorphous matrix or new clusters can nucleate as a function of the characteristic energy and duration (or number) of pulses repeatedly applied to the thin phase-change film.
GeSb2.16 Te4.08 model
50
Ge2Sb2Te5 experimental
2
N*ΣZ i (104)
100
10 5 0
a
b
0
2
4
6
r (Å)
8
10
No. of bonding angle
Fig. 2. (a) Initial crystalline structure (0 free energy); (b) intermediary structure with crystal reminiscence (free energy/per atom 3.950 10 (mean free energy/per atom 2.687 10 3 eV).
c
3
eV); (c) amorphous structure
30 20 10 0 60
80
100
θ (º)
120
140
Fig. 3. Packing of a heap of clusters in the GST material (a), its radial distribution function (b), and the bond angle distribution for the adopted model (c).
M. Popescu et al. / Journal of Non-Crystalline Solids 355 (2009) 1820–1823
4. Conclusions There was shown that the transformations which occur in the phase-change materials can be explained either by a crystalline– amorphous transition or by transition from an amorphous state to a quasi-crystalline state. The type of transformations depends essentially on the type of the material used in switching. Acknowledgement The work has been supported under contracts CEEX 103/2006 and PN2-11-073/2007 by the Romanian Ministry of Education and Research. References [1] S.R. Ovshinsky, Phys. Rev. Lett. 21 (1968) 1450. [2] J. Bicerano, D. Adler, Pure Appl. Chem. 59 (1) (1987) 101. [3] J. Hegedüs, S.R. Elliott, Nat. Mater. (2008) 23.
1823
[4] A.L. Lacaita, Solid State Electron. 50 (2006) 24. [5] C. Steimer, W. Welnic, J. Kalb, M. Wuttig, J. Optoelectron. Adv. Mater. 8 (6) (2006) 2044. [6] R. Grigorovici, P. Gartner, J. Non-Cryst. Solids 75 (1985) 177. [7] J.P. De Neufville, S.C. Moss, S.R. Ovshinsky, J. Non-Cryst. Solids 13 (1974) 191. [8] M. Micoulaut, J.C. Phillips, J. Non-Cryst. Solids 353 (2007) 1732. [9] U. Vempati, P. Boolchand, J. Phys.: Condens. Matter 16 (2004) S5121. [10] I. Banik, J. Non-Cryst. Solids 353 (2007) 1920. [11] P.N. Keating, Phys. Rev. 145 (1966) 637. [12] R.M. Martin, Solid State Commun. 8 (1970) 799. [13] M. Popescu, J. Optoelectron. Adv. Mater. 8 (2) (2006) 755. } rinczi, I. Kaban, W. Hoyer, J. Optoelectron. [14] M. Popescu, F. Sava, A. Anghel, A. Lo Adv. Mater. 7 (4) (2005) 1743. [15] W. Welnic, A. Pamungkas, R. Detemple, C. Steimer, S. Bluegel, M. Wuttig, Nat. Mater. (2005) 1. [16] A.D. Baker, M.A. Paesler, G. Lucovsky, J. Mater. Sci.: Mater. Electron. 18 (2007) S399. [17] K. Kim, M.-C. Jung, J. Park, H.-J. Shin, B. Kuh, Y. Ha, S.A. Song, in: Proceedings of first Conference ‘‘Innovative Mass Storage Technologies European Phase Change Ovonic Science- IMST E-PCOS 06”, May 29–31, 2006, p. 271. [18] M. Frumar, B. Frumarova, T. Wagner, M. Hrdlicka, J. Mater. Sci.: Mater. Electron. 18 (2007) S169.
Contents lists available at ScienceDirect
Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol
Crystalline–amorphous and amorphous–amorphous transitions in phase-change materials } rinczi * M. Popescu, F. Sava, A. Velea, A. Lo National Institute of Materials Physics, 105 Bis Atomistilor St., 077125 Magurele, Ilfov, Romania
a r t i c l e
i n f o
Article history: Received 18 April 2008 Received in revised form 14 January 2009 Available online 27 July 2009 PACS: 61.46.Bc 63.22.Kn 63.50.Lm 64.60.Cn 64.70.Nd 64.75.Yz
a b s t r a c t The transition from the crystalline state to amorphous state and back has been studied in the particular case of the GeSb2Te4 phase-change material by a computer simulation procedure. Modelling at the nanoscale indicates specific structural characteristics, especially the multiplicity of the amorphous phase as opposite to the uniqueness of the crystalline phase. In the particular case of the Si12Ge10As30Te48 switching glass two types of ordering have been pointed out and characterized. Ó 2009 Elsevier B.V. All rights reserved.
Keywords: Glass transition Chalcogenides Nano-clusters Medium-range order
1. Introduction The non-crystalline state of the condensed matter was the subject of deep investigations in the last decades. The reversible switching phenomenon in Si18Ge7As35Te40 complex chalcogenide was discovered in the late ‘60s by Ovshinsky [1]. This phenomenon was challenging and promising for future applications. A review of the state-of-the art in the field of the properties and applications of the non-crystalline materials, experimental results and proposed structural models, has been published by Bicerano and Adler in 1987 [2]. They have already mentioned besides the threshold switching alloy like Si18Ge7As35Te40, several other memory switching alloys like Ge15Te81Sb2S2 and Ge24Te72Sb2S2, having a special place among amorphous solids without crystalline analogues. Recently, various compositions of Ge–Sb–Te (GST) ternary alloys were found to be efficient for phase-change applications, including electrical and optical switching [3]. Pseudo-binary compositions in the (GeTe)m(Sb2Te3)n system like GeSb2Te4, Ge2Sb2Te5 and GeSb2Te7 are of special interest. The GST phase-change memory materials and the related technology is strongly competing the currently widespread floating* Corresponding author. }rinczi). E-mail address: lorinczi@infim.ro (A. Lo 0022-3093/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2009.04.053
gate flash memory and technology, because of quicker response, longer life time, better scaling ability and lower power consumption [4]. In spite of the significant technological advances, some intimate features of the phase-change transitions are still not well understood. GST phase-change materials can be cycled by exposure to laser beam, and as a function of the pulse intensity and duration, the laser beam triggers the switching from crystalline to amorphous phase and back. Phase-change recording with GST compositions is possible by electrical current pulses or nanosecond laser pulses of high intensity. These pulses determine the melting of small regions of submicrometer size in the crystalline material. By subsequent quenching the melted region solidifies into an amorphous state. This is the ‘‘off”-state (state with low electric conductivity, or bit 0). A new pulse of lower intensity but longer duration heats the material and produces temperature gradients and reasonable cooling rates that give rise to re-crystallization. Thus, the ‘‘on”state (state with high electric conductivity, or bit 1) is obtained. These two states, crystalline and amorphous, exhibit strong differences in optical and electrical properties and this feature allows for reading the bit by a third very low-intensity pulse, which does not produce structural changes in the material [5]. For other kind of materials, as e.g. Si–Ge–As–Te glasses an other type of transformation seems to govern the switching phenomena,
M. Popescu et al. / Journal of Non-Crystalline Solids 355 (2009) 1820–1823
1821
namely a transition from a less ordered amorphous state to an other more ordered one, and back. This transition is called amorphous–amorphous transition. In this paper we report the results obtained during simulation of the structural transition from one ordering state to another one in Ge–Sb–Te and Si–Ge–As–Te phase-change materials.
2. Modelling 2.1. Qualitative overview It is a generally occurring question in modelling of glasses, how to imagine the building units and how to manage the end atoms of the 1D and 2D building units, like chains ends or sheet edges of atoms or molecules. An elegant solution to this problem is to admit that these entities will fold, to optimize their space requirement, i.e. to pack themselves optimally under the given physico-chemical conditions (composition, valences, bonding energies, etc.). The packing ability is essential for achieving a more-or-less ordered structure. Grigorovici and Gartner have considered and modelled even the possibility of hybridization change of the atoms involved in phase-change processes [6]. It seems that the nature and the strength of the bonds between the building units act as main ordering factors of the atoms. Due to instability processes in very large assemblies of interacting atoms the big clusters split into smaller ones. Cluster formation in various chalcogenide glasses has been considered in several papers, as for example by De Neufville et al. [7], Micoulaut and Phillips [8], Vempati and Boolchand [9] and Banik [10]. The modelling of crystalline–amorphous transition was made in the frame of a Monte-Carlo Metropolis procedure, starting from hand-built models. The cluster models of two typical glasses Si–As–Te (202 atoms) and Ge–Sb–Te (27 atoms) have been built by hand from plastic units and linked by plastic tubes according to the valence requirements of every type of atoms. The coordinates of the simulated atoms have been roughly measured directly on the model. Finally, the coordination of every atom has been tabulated and the arrays of data were introduced in a computer. Special programs that manage the Monte-Carlo calculations have been used with the purpose to calculate the structure of minimum free energy of every model. All calculations were performed in the frame of the valence force field model. Two interaction potentials have been used: the bond stretching potential and the bond bending potential, as reported by Keating [11] with the force constants reported by Martin [12].
Fig. 1. The modeling of the amorphous–amorphous transition: (a) less structured amorphous state; (b) more structured amorphous state.
The hand modelling demonstrated that the distances and bonds between atoms are compatible with the full satisfaction of the valence requirements and maintaining of the correct density of the material. The final demonstration of the realistic character of the model has been made only after the calculation of the structure of minimum free energy (relaxed structure). The relaxed continuous network model is shown in Fig. 1a. The relaxed structure corresponds to a free energy of 1.358 meV per atom. In the following step we modelled the phase transformation induced in these materials. It is supposed that, by applying e.g. an electrical field to the material, the stressed bonds are excited and this may produce the breaking of the bonds and their reforming in a new configuration. Let us speculate the idea that the breaking of the bonds between the layers is due to stressed bonds of Si–Te and Ge–Te. Tellurium substitutes Ge or Si in the layers and forms strong As–Te bonds that build a more ordered As2Te3 network. The remaining Ge and Si are supposed to build dimers or small clusters between the As2Te3 layers. Thus, a new model is obtained after relaxation. This model exhibits a lower free energy, i.e. the distorted bonds are in a less amount than in the first model. The free energy after relaxation is 2.082 leV per atom. The model is shown in Fig. 1b. By successive melting and quenching at different rates the material changes from one state to another and back. The model points out to a new and special transition from amorphous to another amorphous state that approaches the crystalline state. In fact we are dealing with a transition from an amorphous state to a quasi-crystalline state, and this behaviour ensures the rapidity of switching. Regarding the stability of the on and off states, it seems that after many cycles a couple of equilibrium states are reached. The above model has been reported previously [13,14] but only partially relaxed. Here we gave a more advanced relaxation.
2.2. Modelling of the quaternary ovonic composition: Si–Ge–As–Te 2.3. Modelling results of the phase-change memory material GeSb2Te4 The structural transition in the composition Si1GeAsTe has been simulated with the help of a model with 202 atoms. The quaternary amorphous composition has been modelled as a continuous random network of atoms linked by covalent bonds. The valences of the atoms were those characteristic to the atoms in the crystalline compounds. In this model the As–Te bonds are favoured. The material composition corresponds mainly of As + Te (78%) and the As/Te ratio approaches the ratio 2:3 as in the composition of the stoichiometric material: As2Te3. Because As2Te3 is known as a layered chalcogenide, we considered that the layer configuration is a plausible ingredient in our model. Therefore we decided to introduce Si and Ge between the As2Te3 layers. The introduction of the silicon and germanium atoms into the disordered network has been demonstrated to be possible as regarding the valence requirements and crystallochemistry principles. Of course, there are other possibilities, e.g. the substitution of Ge and Si within As2Te3 disordered layers.
On the example of GeSb2Te4 composition we simulated the transition from the crystalline state to the amorphous state. The crystalline state is the starting structure during cycling of the memory material. This corresponds to on state (bit 1), while the amorphous structure corresponds to the off state (bit 0). Welnic et al. [15] have shown that strong difference exists between a covalent semiconductor and Ge2Sb2Te5, a prototype compound of the GST series of compositions. While the covalent semiconductors have, in general, similar local arrangements, not only in crystalline, but also in amorphous state, GST undergoes a profound change in local order on amorphization. The GST class is characterized by two competing structures, with similar energy but different local order and different properties. The main hypothesis in the modelling of the transition from crystalline to amorphous state is: while in crystalline GeSb2Te4 the structure is cubical and the atoms exhibit roughly the same
1822
M. Popescu et al. / Journal of Non-Crystalline Solids 355 (2009) 1820–1823
coordination (6), in the amorphous (disordered) state of the same compound, the atoms take the normal coordination found in their usual crystalline compounds: 2 for Te, 3 for Sb and 4 for Ge [16]. The recrystallization means the return to the cubical octahedral structure. The change of state back and forth is controlled by the laser pulse energy. This mechanism allows to build a realistic model. Firstly there was built a cubical configuration that simulates the atomic arrangement in GeSb2Te4 (27 atoms). Thereafter the energetic relaxation of the structure has been performed. In the next step a few atoms have been switched to the coordination numbers as follows: Ge to 4, Sb to 3 and Te to 2. The relaxation was repeated. In the next few steps more-and-more atoms were switched to the above shown coordination numbers. The initial cubical configuration was thus gradually transformed into an amorphous cluster. Several ways of transformation are possible, and consequently, several amorphous clusters of similar or nearly similar free energy are possible. The transition between the crystalline and amorphous structures simulates the transformation that takes place into the material during the change of state. Fig. 2 shows the results. The free energy of different amorphous clusters differs by less than 25%. A heap of amorphous clusters is represented after energy relaxation in Fig. 3(a). The radial distribution function (RDF) and the bond angle distribution in the big amorphous cluster (543 atoms) are shown in Fig. 3(b) and (c). Both histograms demonstrate the plausibility of the model, because the main peaks in RDF reproduce the experimental ones [17] fairly well, and the width of the bonding angle distribution is below 20 degrees estimated from width of the second peak of experimental RDF. 3. Discussion The type of structural transition during switching in phasechange memories depends on the composition. In classical ovonic composition (e.g. Si–Ge–As–Te) we have shown that it is possible to have phase-change transition from an amorphous to quasi-crystalline state.
In our views the switching in Ge–Sb–Te is produced in the following way. In the first cycle the crystallites of the phase-change material are transformed into amorphous clusters and then back. After a high number of cycles, the amorphization–crystallization process determines the breaking of the big clusters into smaller ones. Finally, for very large number of cycles the small clusters dominates and the structure with small clusters remains stable for a very long time, i.e. the clusters switch rapidly from the disordered state to the crystalline one and back. It is interesting to remark that the transition from the crystalline state to the amorphous state(s) implies intermediary structures whose free energies are higher that those of the amorphous structures. We must admit that the transformation forth and back must overcome a certain energy barrier. This barrier, evidenced by modelling, could explain the stability of both configurations against phase-change transformation. The energy necessary for the system to pass across the barrier is provided by the electrical or by the laser pulse acting on the thin film material. As shown recently by Frumar et al. [18] the crystalline state in these phase-change materials is highly imperfect, with high amount of defects integrated into the structure. This means that in our model the switching back to the crystalline state is in fact a transition to a highly defective crystalline state. The easy switching from amorphous to crystalline structure can be explained starting from the idea presented by Baker et al. [16]. They suppose that the conjugated charge, or valence alternation pairs of over-coordinated tellurium and under-coordinated Sb or Ge play a role in facilitating the reverse amorphous–crystalline transitions important in optical and electrical memory devices. The electronic multistage switching can be understood if we admit that the conduction steps are dictated by the level of excitation that controls the appearance of various concentration ratios of quasi-amorphous/quasi-ordered clusters. These clusters can be melted and integrated into the amorphous matrix or new clusters can nucleate as a function of the characteristic energy and duration (or number) of pulses repeatedly applied to the thin phase-change film.
GeSb2.16 Te4.08 model
50
Ge2Sb2Te5 experimental
2
N*ΣZ i (104)
100
10 5 0
a
b
0
2
4
6
r (Å)
8
10
No. of bonding angle
Fig. 2. (a) Initial crystalline structure (0 free energy); (b) intermediary structure with crystal reminiscence (free energy/per atom 3.950 10 (mean free energy/per atom 2.687 10 3 eV).
c
3
eV); (c) amorphous structure
30 20 10 0 60
80
100
θ (º)
120
140
Fig. 3. Packing of a heap of clusters in the GST material (a), its radial distribution function (b), and the bond angle distribution for the adopted model (c).
M. Popescu et al. / Journal of Non-Crystalline Solids 355 (2009) 1820–1823
4. Conclusions There was shown that the transformations which occur in the phase-change materials can be explained either by a crystalline– amorphous transition or by transition from an amorphous state to a quasi-crystalline state. The type of transformations depends essentially on the type of the material used in switching. Acknowledgement The work has been supported under contracts CEEX 103/2006 and PN2-11-073/2007 by the Romanian Ministry of Education and Research. References [1] S.R. Ovshinsky, Phys. Rev. Lett. 21 (1968) 1450. [2] J. Bicerano, D. Adler, Pure Appl. Chem. 59 (1) (1987) 101. [3] J. Hegedüs, S.R. Elliott, Nat. Mater. (2008) 23.
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