Local Bonding Arrangements in Ge 2 Sb 2 Te 5 : Importance Of Ge And Te Bonding In Optical Memory Materials

Transcription

1 Local Bonding Arrangements in : Importance Of And Bonding In Optical Memory Materials D.A. Baker Physics Department, North arolina State University, Raleigh, N , USA Abstract. Studies of amorphous (a-) semiconductors he been driven by technological advances as well as fundamental theories. Observation of electrical switching, for example, fueled early interest in a-chalcogenides. More recently a-chalcogenide switching has been applied quite successfully to DVD technology where the quest for the discovery of better-suited materials continues. Thus, switching grants researchers today with an active arena of technological as well as fundamental study. On the theoretical front, bond constraint theory and rigidity theory provide a powerful framework for understanding the structure and properties of a-materials. Applications of these theories to switching in a-chalcogenides holds the promise of finding the best composition suited for switching applications. EXAFS spectroscopy is an ideally suited technique to investigate the switching properties of these materials. Results of previous EXAFS experiments will be presented and viewed through the lens of bond constraint theory. Keywords: halcogenides, EXAFS, Bond onstraint Theory, Glasses. PAS: j; Bn; Fs; Dm INTRODUTION (GST) has proven itself to be a robust and reliable material for use in optical and electrical switching applications. While the compound s properties and performance are well documented [1,2,3], a fundamental explanation of the suitability of GST for these applications has not been identified. Bond constraint theory (BT) [4,5] allows one to characterize the structure of various -- compositions, -- or any amorphous network solid [6] -- across a spectrum from floppy to stressed-rigid. In the compositional range between these two regions, an intermediate phase exists where a balance is struck between entropy and enthalpy. Such a material, referred to as unstressed-rigid, may switch between a free energy minimum of an a-state to a second minimum of a c-state. yclability is assured as the material neither falls into an enthalpy driven trap state characteristic of a crystalline state, nor does it slide down an entropy driven slope into an irretrievable amorphous state. BT couches the balance between stressed and floppy materials in terms of erage number of constraints per atom in interatomic force field space and the number of degrees of freedom in real space (i.e. three.) Materials characterized by this condition are so-called good glass formers. Local bonding configurations play a key role in the application of BT. EXAFS spectroscopy [7], it seems, is ideally suited to compliment this requirement of BT. In this paper, these two approaches are combined in order to gain insight into the optical memory material GST. Phase hange Materials Through the years research into amorphous semiconductors has been driven in large part by interest in switching phenomena [8]. This research has recently borne technological fruit in the development of phase-change memory devices that exploit rapidly crystallizing chalcogenide alloy materials in programmable memory devices [9]. While many amorphous chalcogenide alloys are reported in the literature, amorphous GST has received particular attention [10,11]. This material s crystallization kinetics he been studied, and its switching characteristics are also well documented [12]. On the -- ternary phase diagram shown in Fig. 1 GST lies at the intersection of two lines of interest: a tie-line joining and 2 3 ; and a bisector of the angle at the vertex. Of more physical interest is the tie line joining two potentially good glass-forming compositions: 2 3 and 2 3. At the intersection of this tie-line with the -bisector is the material When viewed in this manner, GST is seen to be a mixture of two units of and one of 2 3, and its structure is a mixture

2 of 2 3 and 2 3 in a matrix of cross-linked 2- and 3-fold coordinated atoms. This description of the local bonding arrangements offers insights to the switching properties of other GST compositions. 2 3 X X X X XX 226 X FIGURE 1. rnary phase diagram for -- compounds is shown as an open square and labeled to the right of the point is shown as a closed circle and labeled to the left of the point. Data points from Ref. 1 are inserted as open circles and X s on the appropriate tie lines. Experimental GST films were RF sputtered onto aluminum foil substrates to a thickness of 2.7 µm. Stacked samples created an effective film thickness of ~22 µm. EXAFS measurements of the K edges of,, and were taken in transmission mode using a Si(111) doublecrystal monochromator at line ID-10 (MR AT) of the Advanced Photon Source at Argonne National Laboratory. Incident and transmitted photons were measured at room temperature. Re[χ(q)] k(å -1 ) FIGURE 2. Plots of k 3 -weighted spectra for GST. Solid lines are data, dashed lines are fits. Normalization and background removal of the data were performed using the Athena software package [13]. The k 3 -weighted Fourier transformed spectra were fit using the Artemis analysis package [13], which is based on the FEFF [14] and IFEFFIT [15] codes. A small molecular cluster molecular model with no periodicity was used as a way to oid any bias toward crystallinity in the analysis. All three possible backscattering species were considered for each scattering atom, and of the six possible atom pairs, only three showed acceptable fits. Figure 4 shows the fits in k space for all three edges. Table 1 summarizes the data. These results show internal consistency, within the error, for heteropolar bond lengths (R - = 2.83Å and R - = 2.62 Å). The bond lengths agree with accepted covalent radii for each species [16]. N determinations indicate fully coordinated and with N = 3.9±0.8 and N = 2.8±0.5 and slightly over-coordinated with N = 2.4±0.6. TABLE 1. oordination numbers and nearest neighbor bond distances for a-gst as determined by EXAFS. Note the second, shorter - distance labeled in italics as -(e) indicating an electrostatic bond. Atom Bond oordination (N) R(Å) - 3.9± ± ± ± ± ±0.01 -(e) 0.5± ± ± ± ± ±0.01 Similarities in photoelectron backscattering render it quite difficult, if not impossible, to differentiate between - bonds and - covalent bonds. hemical preference, however, yields a guide for identifying the nature of the bonding environment. Bond energies for - (40.6 kpm) and - (39.6 kpm) [17] suggest that the - bonds account for most, if not all, of the backscattering signal from the atoms. The second, shorter - distance can be attributed to an electrostatic, or dative [18] bond between and a positively charged three-fold coordinated atom. Homopolar bond data suggest that virtually all atoms are bonded to one atom and three atoms in a 2 Se 3 type local bonding arrangement [19], as shown in Fig. 3. atoms are then interspersed evenly throughout the structure with three neighbors in 2 3 arrangements. The molecular structure of GST then includes the following local bonding arrangement: i) 2 3, ii) 2 3, and iii) three fold coordinated atoms, the nearest neighbors of which are and. In addition, the material includes dative bonds between positively charged

3 three-fold coordinated, and pyramidal groups that acquire a negative charge. FIGURE. 3. Proposed 2 3 configuration. Bond onstraint and Rigidity Theory The requirement that the number of constraints in an amorphous material equals the number of degrees of freedom in the space that material occupies (or network dimensionality) defines a criterion for an ideal, strain-free thin film or bulk material [4]. For the materials addressed here, the latter bond constraint metric is three, so that the erage number of bonds/atom is given in Eq. (1), = 3 (1) This equation is the basis for discriminating between materials with different degrees of ideality in the context of the ease of "glass formation". When it is met, a material may be considered to be a good glass-former. The subtlety of BT comes in determining the number of bonding constraints/atom in a system. One aspect of this application not included in Refs. 6 or 7, but addressed below, relates to broken constraints that derive from local bonding arrangements For a system comprised of 2-, 3-, and 4-fold coordinated atoms with N atoms in its molecular formula, can be written in terms of the stretching and bending constraints, f s and f b, respectively. If n r is the number of atoms with r-fold coordination in one molecular unit, it follows that 1 4 = nr ( fs + f N r = 2 b ). (2) In terms of the erage coordination <r>, this is [6] 5 = r 2. (3) 3 The condition that a material be a good glass former expressed in Eq. (1) is then equivalent to the condition that the erage coordination be given by r = 2.4. (4) An alternate approach that arrives at the same conclusion (Eq. 4) is given by rigidity theory. Developed originally by LaGrange and lerk Maxwell, and later by Thorpe and co-workers [20,21,5], rigidity theory considers vibrational modes in systems with 2-, 3- and 4-fold coordinated atoms in a material with local molecular units of N atoms. Among the total number of modes of vibration of such a system are modes that involve energy (i.e. constraints) and those that do not. The latter are the so-called zero-frequency or floppy modes, given the symbol F. F can be expressed as the difference between the total possible number of vibrational modes of the system, 3N, and the modes determined by constraint counting. Thus, F is given by 4 r F = 3N nr + [2r 3]. (5) r= 2 2 The fraction of zero-frequency modes, f = F 3N may then be calculated using Eq. (4),.and is given by: f =. (5) With increasing erage network coordination, the fraction of zero frequency modes decreases, and is exactly equal to zero at the condition given by in Eq. (4). The relationship between f and <r> for <r> = 2.4 is given by the solid line of Fig. 4. The equivalence of the approach based on the assumption inherent in BT (Eq. (1)) and the approach of rigidity theory (Eq. (4)) is manifest in the fact that each identify a material with <r> = 2.4 as lying at a nexus dividing materials that are floppy form those that are stressed-rigid with respect to material properties. f f '' <r> r <r> Intermediate phase FIGURE 4. Plot of f as a function of <r>. Theory shown by solid line and model shown by dashed line. Inset shows second derivative of f as a function of <r>. Figure adapted from Ref. 5. The Thorpe group goes beyond this treatment [22] by including computer modeling of large atomic networks that provides numerical determination of the fraction of zero-frequency modes, f. Plots of f as a

4 function of <r> reveal three distinct composition regions. One such plot for a system of 2-, 3-, and 4- fold coordinated atoms is shown as the dashed line of Fig. 4. A transition region (see inset) is readily identified in a plot of the second derivative of f with respect to <r> which shows a narrow transition region, 2.37 < <r> <2.44, between floppy and stress-rigid regimes. The lower bound of this transition region represents the onset of the development of small and isolated pockets of rigid clusters, or local rigidity, the number of which increases with the erage coordination. The upper bound indicates the percolation, or interconnection of, these locally rigid clusters, i.e., global rigidity, to generate a stressed-rigid material. For alloys with multiply-coordinated atoms such as x y 1-x-y these modeling efforts identify three types of material with different values of : i) a floppy a material with low erage coordination; ii) a stressed-rigid material with high erage coordination; and iii) an intermediate-phase material near <r> = 2.4 that is an ideal locally stressed material without percolation of stress, or unstressed rigid. One is clearly led to ask where GST lies on the ternary phase diagram with respect to the locus of the unstressed rigid material regime. The EXAFS data viewed in light of BT furnishes the answer. BT and EXAFS onsider local bonding. Table 1 gives a total coordination for of approximately four. The result is clearly an indication of tetrahedral coordination for all of the atoms. To zeroth order, using Eq. 2, a tetrahedral configuration yields =7, with five bending and two stretching constraints/atom. However, the combination of homopolar (-) and heteropolar (-) bonding affects constraint counting; bond-bending constraints can be removed by considering the local configuration. In particular, bending constraints around each atom are a mixture of -- and -- motions. The force constant for the -- bending motion is reduced with respect to that of a -- bending motion due to the different -- and -- bond energies. This permits the removal of 2.67 bending constraints (1.67 from two doubly-degenerate E-mode vibrations and 1 for a non-degenerate A-mode vibration) for the 2 3 arrangement. Results show all of the atoms in this configuration, so the number of bond-bending constraints around the erage atom are reduced from 5 to This reduces the total number of constraints for atoms from 7 to In the bonding environment, a three-fold pyramidal structure, there are 1.5 stretching constraints and 3 bending constraints, resulting in 4.5 total constraints. None of these constraints are broken. Finally, consider bonding. Table 1 shows that is over-coordinated. A bond counting exercise supports this result. Our model gives GST as a combination of 2 3 and 2 3 structural units. This counting results in a deficiency for the GST composition, as stoichiometry requires that the addition of these two units equal This 1/6, or 17%, deficiency is reflected in our results, as the percent of overcoordinated is 0.4/2.4 17%. A deficiency, combined with full coordination of and require that some atoms overcoordinate, resulting in the presence of both two-fold and three-fold geometries. No constraints can be removed for the former configuration, and in the latter, the bond order is reduced from one electron/bond to 2/3 electrons/bond. onstraints are removed for this configuration, but proportionally so [23], resulting in 2 constraints for both three- and two- fold coordinated. Therefore the number of total constraints for all atoms is 2. The total number of constraints for the GST alloy follows: contribution: 4.33 x 2 = 8.66; contribution: 4.5 x 2 = 9; contribution: 2 x 5 = 10. Thus, = = (9) 9 This value of is close the ideal value of 3 suggested for a material in the stress-free state, and more importantly, for a good glass former. In applying BT to GST and to other alloys, (identified by Yamada et al. and shown in Fig. 2), it is necessary to include broken bond-bending constraints for the tetrahedrally-bonded atoms in 2 3 arrangements. GST and the alloys on the tie-line (open circles in Fig. 2.) he values of 3.07 ± 0.05, whilst for alloys on the tie line (X's in Fig. 2.) increases systematically from 3.05 to 3.33 with increasing content. The fraction of 3-fold coordinated increases from 7.1% to 25% along the tie line, and from 12.5% to 68% along the tie line. The transmissivity as a function of temperature is shown in Fig. 5. The magnitudes of the changes in transmissivity upon crystallization correlate with 3-fold -atom bonding in the a-state. The transmissivity transition along the tieline occurs over a relatively narrow temperature range, <10, and scales linearly with the fraction of 3-fold. Along the tie line, the width of the transition increases with increasing 3-fold to >20. N increases as well, but the transmissivity change remains nearly constant. [1]

5 Transmissivity (arb. unit) AKNOWLEDGMENTS This work was begun under the direction of our colleague Dale Sayers, whose many contributions to the development of EXAFS and the study of amorphous materials provide a legacy to our field and ongoing benefit to us all. Work supported by the Air Force Research laboratory under grant F and by the NSF under grant DMR Use of the Advanced Photon Source was supported by the U. S. DOE, Office of Science, Office of Basic energy Sciences, under ontract W ENG-38. MRAT operations are supported by the Department of Energy and MRAT member institutions mperature ( ) FIGURE 5. Plot of optical transmissivity as a function of temperature for a number of different -- alloys, adapted from Ref. 1. Summary and Discussion EXAFS studies of the bonding of, and in as-deposited films indicate both - and - bonds. Analysis of the EXAFS spectra yields self-consistent atomic coordination numbers and bond lengths. Results indicate the following molecular structure: = , with i) 17% of the -atoms 3-fold, rather than 2-fold coordinated, and ii) 20% of the - atoms participating in electrostatic bonding to a nearby atom. The overcoordinated -atoms are assumed to he a positive formal charge of 1, and a subsequently smaller atomic radius, thereby accounting for the reduced distance associated with the - electrostatic bond. The erage bond coordination, <r>, and erage number of bond-stretching and -bending constraints/atom,, he been determined using bond constraint theory. The inclusion of - bonding in 2 3 groups provides the microscopic basis for; i) the different systematic variations in along the two tie-lines identified by Yamada et al.; ii) the important role of 3- fold in the amorphous to crystalline transition exploited in optical memory applications; and iii) the good glass forming capability of GST and its propensity for repeatable phase change transitions. REFERENES 1. N. Yamada, E. Ohno, K. Nishiuchi, and N. Akahira, J. Appl. Phys. 69, 2849 (1991). 2. T. Nonaka, G. Ohbayashi, Y Toriumi, Y Mori, and H. Hashimoto, Thin Solid Films, 370, (2000). 3. B. Lee, J.R. Abelson, S.G. Bishop, D Kang, B. heong, and K. Kim, J. Appl. Phys. 97, (2005). 4. J.. Phillips, J. Non-ryst. Solids 34, 153 (1979). 5. M. F. Thorpe, J. Non-ryst. Solids 57, 355 (1983). 6. Phase Transformations and Self-Organization, Ed. by J.. Phillips and M.F. Thorpe (Kluwer Academic/Plenum Pulbishers, 2001) p D.E. Sayers, F.W. Lytle, and E.A. Stern, Phys. Rev. B., 11, 4836 (1975). 8. S.R. Ovshinsky, Phys. Rev. Lett., 20, 1450 (1968). 9.. Peng and M. Mansuripur, Appl. Optics, 43, 4367 (2004). 10. A.V. Kolobov, P. Fons, A.I. Frenkel, A.L. Ankudinov, J. Tominaga, T. Uruga, Nature Mater., 3, 703 (2004). 11. A.V. Kolobov, Private ommunication (2005). 12. S. Hudgens and B. Johnson, MRS Bulletin, 1, Nov. (2004). 13. B. Rel, J. Synchrotron Rad. 12, 537 (2005). 14. J.J. Rehr, J. Mustre de Leon, S.I. Zabinsky, and T.. Albers, J. Am. hem. Soc. 113, 5135 (1991). 15. M. Newville, J. Synchrotron Rad. 8, 322 (2001). 16. F.A. otton and G. Wilkinson, Advanced Inorganic hemistry, 3rd Edition (Interscience Publishers, New York, 1972), hap. 3, p. 117 (Table 3.4). 17. R.T. Sanderson, hemical Bonds and Bond Energy, 2nd Edition (Academic Press, New York, 1976), hap. 3, p L. Pauling, The Nature of the hemical Bond, 3rd Edition (ornell University Press, 1960), p A. Feltz, Amorphe und glasartige anorganische Festkörper, (Akademi-Verlag, Berlin, (1983), p J.L. LaGrange, Mécanique Analytique, Paris (1788). 21. J.. Maxwell, Philos. Mag. 27, (1864). 22. D.J. Jacobs and M.F. Thorpe, Phys. Rev. Lett., 75, 22 (1995). 23. R. Kerner and J.. Phillips, Solid State ommunications, 117, 47 (2001).