Structural investigation for a-AIST clarify the difference between the
two types of contrastive phase-change mechanisms
T. Matsunaga1,2, J. Akola3,4,5, S. Kohara2,6, T. Honma6, K. Kobayashi7, E. Ikenaga6,
R. O. Jones3,8 , N. Yamada1,2 * , M. Takata2,6,9,10 and R. Kojima1
1

Panasonic Corporation, 3-1-1 Yagumo-Nakamachi, Moriguchi, Osaka 570-8501, Japan / 2JST, CREST, 5 Sanbancho,
Chiyoda-ku, Tokyo 102-0075, Japan / 3Institut für Festkörperforschung, Forschungszentrum Jülich, D-52425 Jülich,
Germany / 4Nanoscience Center, Department of Physics, University of Jyväskylä, PO Box 35, FI-40014 Jyväskylä, Finland /5
Department of Physics, Tampere University of Technology, PO Box 692, FI-33101 Tampere, Finland / 6Japan Synchrotron
Radiation Research Institute (SPring-8), 1-1-1 Kouto, Sayo-cho, Sayo-gun, Hyogo 679-5198, Japan / 7Beamline Station at
SPring-8, National Institute for Materials Science, 1-1-1 Kouto, Sayo-gun, Hyogo 679-5198, Japan / German Research
School for Simulation Sciences, FZ Jülich and RWTH Aachen University, D-52425 Jülich, Germany / RIKEN SPring-8
Center, 1-1-1 Kouto, Sayo-cho, Sayo-gun, Hyogo 679-5148, Japan / Department of Advanced Materials, University ofTokyo, Chiba 277-8561, Japan.
ABSTRACT
Nowadays the most common phase-change materials are GeTe-Sb2Te3 pseudobinary compounds and Sb-Te binary
compounds with small amounts of In, Ag and/or Ge. These materials possess sufficiently fast recrystallization speed;
however, recrystallization in the two materials is strikingly different, although their crystal structures are very similar toeach other. We have already determined the structure of the former amorphous pseudobinary materials and also scrutinized
this time the latter amorphous structure by using a combination of advanced syhnchrotron radiation x-ray measurements andmassive reverse Monte Carlo / density functional - molecular dynamics simulation; which clarified relationship between
amorphous structure and phase-change behavior and difference in mechanism of the high-speed phase change between thetwo kinds of materials. It was found in the former pseudobinary materials that the recrystallization begins all at once from
uncountable crystalline fragments embedded in the amorphous mark; whereas in the latter materials it starts from the rim of
the mark and moves toward its center through bond interchanges in the atomic network. (Key words: Ge-Sb-Te,
Ag-In-Sb-Te, DFT, RMC, amorphous, crystal, phase change)
1. INTRODUCTION
Phase change (PC) recording is now extensively used for high-density non-volatile memories [1]. Since 1970s, various
materials have been proposed for the purpose, and nowadays we have obtained two superior materials of GeTe-Sb2Te3(GST) [2] and Sb-Te based alloys such as AIST (Ag-In-Sb-Te quadruple compounds) [3]. These compounds possess two
indispensable features for data storage; i.e., high endurance of the amorphous phase and high-speed PC from the amorphousto the crystalline phase. Their recrystallization speeds are sufficiently fast; however, their PC processes are strikingly
different; although their crystal structures are very similar to each other (they have octahedral coordination structures
formed by the p-p bonding [4], [5], [6]). It is well known that in the former group recrystallization proceeds mainly by wayof nucleation inside the marks, in the latter group by way of crystal growth from the rim [6]. There have been numerous
studies on amorphous GST (a-GST); on the other hand, little is known about the structures of amorphous AIST (a-AIST). In
order to clarify difference, we analyse the structure of the AIST amorphous phase using a combination of advanced
syhnchrotron radiation x-ray measurements and massive reverse Monte Carlo (RMC) / density functional (DF)-molecular
dynamics (MD) simulation. We believe that this investigation will give us an important clue to develop new PC materials
for the next generation.
2. EXPERIMENTS
The Ag 3.5In3.8Sb75.0Te17.7 powder specimens for the XRD experiments were made by laminating a 5-nm-thick
ZnS–SiO2 film on a glass disc (diameter 120 mm) and sputtering to form a recording film of thickness 200–500 nm. The
specimen was removed from the glass substrate using a spatula, and its composition was studied using inductively coupledplasma atomic emission spectrometry. We performed diffraction experiments using the BL02B2 bending-magnet beamlineof SPring-8, run by the Japan Synchrotron Radiation Research Institute [7]. The beam energy was about 29.5 keV. Intensity

data were collected using a Debye-Scherrer camera with a 287 mm radius. An imaging plate with a pixel area of 100 µm2
was used as the detector; by reading it for a pixel area of 50 mm2, intensity data in steps of 0.01° were obtained. The
experiments at low and high temperatures were conducted by blowing N2 gas at a specified temperature onto the capillary.
The specimens for the EXAFS experiments were made by laminating a Kapton film of 25 µm thickness overlaid on a
glass disc with a diameter of 120 mm, followed by sputtering to form the recording films of thickness 300 nm. XRD
measurements confirmed that the films were amorphous. The Kapton film sheets were peeled from the glass discs and cut
into 10 mm squares, which were then stacked to form the specimens. The EXAFS measurements were carried out at theBL14B2, another bending-magnet beamline of SPring-8. The incident X-ray beam was monochromatized by a Si
double-crystal monochromator with (111) net planes. Contamination with higher harmonics in the incident beam wasremoved by rhodium-coated mirrors located downstream of the monochromator. Vertical focusing of the incident beam at
the sample was performed by slightly bending the mirrors. EXAFS data of Ag, In, Sb and Te K edges were collected intransmission mode. The backscattering amplitudes and the mean free paths used for the EXAFS analyses were obtained
from FEFF [8] calculations. The coordination numbers N and bond lengths r were determined by least-squares fitting using
the Rigaku REX2000 software [9]. The analysis was simplified by assuming that each absorbing atom was surrounded by
Sb atoms alone.
The XRD experiments for the RMC analysis were carried out at room temperature at the SPring-8 high-energy XRD
beamline BL04B2 [10] using a two-axis diffractometer dedicated to glass, liquid and amorphous materials. The incident
X-ray energy was 61.5 keV. The diffraction patterns of the powder sample in a thin-walled (10 μm) tube of 0.5 mm diameter(supplier: GLAS Müller, 13503 Berlin, Germany) and an empty tube were measured in transmission geometry. The intensityof incident X-rays was monitored by an ionization chamber filled with Ar gas, and the scattered X-rays were detected by a
Ge detector. A vacuum chamber was used to suppress the air scattering around the sample, and the data collected werecorrected using a standard program [10].
3. RESULTS
XRD and EXAFS analyses

60000

sputtered AIST film
<dT/dt>=10º/min
5min for each measurement

50000

Intensity (arb. units)

X-ray diffraction patterns of the amorphous AgIn
3.5 3.8Sb75.0Te17.7 taken at from RT to 506 K are shown in Fig. 1,
which clearly demonstrates the amorphous phase is stable up to
about 397 K (125ºC). Above 415 K or more, Bragg peaks showing
the formation of the crystalline phase (an A7-type structure)
emerged in the halo pattern of the amorphous phase. However, thepatterns obtained below 397 K are almost the same irrespective of
temperature; this strongly suggests that the atomic configuration inthis amorphous material remains unchanged not depending on
temperature up to the transition temperature to the crystalline phase.
Our EXAFS measurements performed at various temperatures
revealed that the a-AIST preserves its atomic configuration against
rise in temperature. We analyzed the local structures in thisamorphous material at several temperatures from 10 K to 300 K by
EXAFS method under the assumption that the four kinds ofconstituent atoms are all surrounded only by Sb atoms, because Sb
is the main element of this material (and besides, atomic numbers ofthese four atoms are very close to each other, which makes it very
difficult to distinguish these atoms in the x-ray analyses). The
structural parameters, coordination number N, bond length r,
Debye-Waller factor B etc. were obtained by least squares curve
fitting [8]. The graphs in Fig. 2 show the temperature dependence of
these structural parameters derived by the EXAFS method; as seenin these graphs, coordination numbers and bond lengths remain
almost unchanged with the increase of temperature. The
temperature dependences of the Debye–Waller factors (in the figure,
those are shown by transformed into B.), which represent the

40000

30000

506K
487K
469K
451K
433K
415K
397K
379K
361K
343K
295K

20000

10000

0
10

20

2-Theta (deg.)

Fig. 1.
Synchrotron X-ray diffraction patterns for a
Ag 3.5In3.8Sb75.0Te17.7 powder specimen taken at from RT
to 693 K.

2

B (Å )r (Å)

N

Temperature (ºC)
Temperature (ºC)
Temperature (ºC)
dynamic and static shifts
-200
-100
0
100
-200
-100
0
100
-200
-100
0
100
3.0
5
1.0
(fluctuation) their equilibriumIn
positions, gradually increase
Ag
2.9
4
with
temperature
raise;
0.8
Sb
however, their slopes are fairy
SbIn
gentle, which is remarkable
2.8
3
0.6
In, TeAgTewhen compared with those forAgSb
the crystalline phase [5]. It is
2.7
2
0.4
Te
suggest from these results thatthe atomic configuration and
2.6
1
0.2
the bond lengths remain almost
unchanged without depending
2.5
0
0.0
0
100
200
300
400
0
100
200
300
400
0
100
200
300
400
on temperature. In addition, it
Temperature (K)Temperature (K)Temperature (K)has been revealed that thedependence of the atomic Fig. 2.
Temperature dependences of the coordination numbers N, bond lengths r, andfluctuation on temperature is temperature factors (the atomic displacement parameters) B for the amorphous Ag3.5 In3.8 Sb75.0
considerably small. These Te17.7.
thermal behaviors elucidatethat the structure of amorphous phase is stable enough probably even at the high temperatures below the transition
temperature; in other words, such a structural feature (stability), probably given by the strong covalent bondings of theatoms, is presumed to enable this amorphous material to retain its phase for a sufficiently long time, especially around room
temperature. As shown below, RMC/DF-MD analysis revealed in fact that Sb atoms have 3 (short) +3 (long) coordination
structures both in the crystalline and amorphous phases; however, in the latter phase, the bond length of the former isconsiderably shorter than that in the
Table 1
Local structure of a-AIST determined by EXAFS at 26 K and DF / MD
crystalline phase, which corresponds
calculations. N, coordination number; r, nearest-neighbour bond length; Nbond, chemical
well to typical Sb-Sb covalent bondcoordination number. Theoretical values from RMC-refined DF geometry (NDF-MD
length. We can therefore regard theand rDF-MD) and chemical bond-order analysis. The Nbond values of c-AIST are given incoordination number of Sb as
parentheses.
approximately three, which satisfies the
8-N rule [11]. This bonding nature has
Atom (i)Nr (Å)
NDF/MDrDF/MD(Å)
Nbond
also been observed in the amorphousAg
3.3 ± 0.5 2.768 ± 0.006
4.42.80±0.05
1.9 (2.0)
GST [12], [13]; which is thereforeIn
4.3 ± 0.6 2.826 ± 0.006
3.1
2.85±0.05
2.5 (2.9)
considered to be a major reason that theSb
3.7 ± 0.3 2.872 ± 0.006
3.3
2.85±0.05
3.1 (3.2)
amorphous phases of these phase-changematerials show a sufficient endurance atTe
2.4 ± 0.4 2.827 ± 0.006
2.5
2.85±0.05
2.5 (2.6)
room temperature.

RMC/DF-MD analysis
As it is well known, MD is a computer simulation of physical movements of atoms and molecules, and DF theory iscurrently a very useful, another computational analysis method for examining structural, electronic, and dynamical
properties in materials science. The combination of these two methods, MD simulation based on DF makes it possible for us
to study dynamical processes such as structural transformations of covalently bonded materials as well as chemical reactions
in condensed matters. On the other hand, RMC simulation is also very useful to experimentally examine amorphous
structures [10]. However, it is ordinary difficult for us to analyze the actual structure of an amorphous material from only
one dimensional diffraction data. Besides that, the presence of four elements in AIST and the dominance of two (Sb, Te)with similar atomic numbers make it further difficult to determine the local structure by XRD alone. We then this timescrutinized the amorphous structure by using the combination of (DF) -MD and RMC simulations to reproduce X-ray
diffraction (XRD), and furthermore, hard X-ray photoelectron spectroscopy (HXPS) data [6].
The determined structure is shown in Fig. 3 together with that of GST225 (Ge2Sb2Te5). These results agree with thosefound in the EXAFS analyses. Table 1 also gives values for the RMC/DF-MD geometry on the basis of the partial pair
distribution functions and bond-order analysis [6]. The coordination numbers obtained from EXAFS measurements for Sb
and Te (3.7±0.3 and 2.4±0.4, respectively) agree well with the calculated values. The EXAFS measurements indicate that
there are only small differences between the bond lengths, with Ag bonds being slightly shorter (2.77 Å). This is consistent
with the RMC/DF-MD results, where the bond lengths are near 2.85±0.05 Å for most pair distribution functions. As

mentioned above, the coordination number of Sb
approximately satisfies the 8-N rule [11]; however, it
connects with other three at longer distance. We stress that
Sb atoms in the amorphous phase have 3+3 coordination
structures as well as in the crystalline phase as seen in Fig.
3(b).
Figure 4 shows the structure factors S(Q) of AIST and
ABAB squares
GST obtained using XRD. The crystalline forms of bothhave sharp Bragg peaks (red lines), and the amorphous
forms (black lines) have typical halo patterns. However,
oscillations up to the maximum Q value in a-AIST indicate
Fragment ofa structure with well defined short-range order. Fourier
NaCl lattice(a) GST (Ge2Sb2Te5)(b) AIST (Ag3 5In3 8Sb75 0Te17 7)transformation of the S(Q) leads to the total correlation
functions T(r) for c-GST and c-AIST (Fig. 2b), which arevery similar beyond 4 Å. Small differences between the two Fig. 3(a) Section of 460-atom DF-MD model of a-GST (24crystalline forms are found at shorter distances, for example Å × 24 Å × 12 Å). Ge, red; Sb, blue; Te, yellow; large cavity, pink.
the double peak in c-AIST (2.93 Å and 3.30 Å) and a single (b) Section of 640-atom DF-MD model of -AIST (24 Å × 24 Å ×peak in c-GST (2.97 Å). The T(r) for the amorphous 12 Å). Ag, silver; In, magenta; Sb, blue; Te, yellow. A large cavity
materials, however, are significantly different: the first peak is present among the atomic arrangement in the a-GST structure.
in a-AIST (2.86 Å) is only slightly shorter than that found Enlarged configuration (left bottom figure) shows that a-GST has
many structural units (ABAB-squares) with alternating Te and Ge
in c-AIST (2.93 Å), whereas the first peak in a-GST (2.79 (or Sb) atoms. We can observe even a fragment of NaCl lattice.
Å) is much shorter than that in c-GST (2.97 Å). We note On the other hand, few cavities are observed in the a- AIST
also that the shoulder on the second peak in a-AIST (3.5 Å, structure on the right.
arrowed) is near that observed in the crystalline form (3.30
Å). The pronounced difference between the diffraction patterns of the two materials is strong evidence that they crystallize
differently. The atomic motion and/or diffusion accompanying the PC are larger in GST than in AIST, where the PC is
accompanied by small changes in bond lengths.
4. DISCUSSION
Phase change in GST materials
It is well known that the most commonly used recording material is GeTe-Sb2Te3 pseudobinary compound. A recording
film made of this material can be switched rapidly and reversibly between the crystalline phase and the amorphous phase bya brief laser irradiation (several tens of nanoseconds). This pseudobinary compound maintains the same NaCl-type structure(space group: Fm 3 m ) over a wide range ofcompositions from 100 % of GeTe to at least
AIST(GeTe)1(Sb2Te3)2 (namely, Ge1Sb4Te7) when subjected
to instantaneous heating by laser irradiation followed byequally rapid cooling (see Fig. 3(a)) [4]. In this structure,
the Cl:4a site is (almost) completely occupied by Te
atoms, whereas the Na:4b site is randomly occupied by
GST
Ge and Sb atoms and vacancies. When the chemical
formula of the pseudobinary compound is expressed as(GeTe)x-(Sb2Te3)1-x; (0 ≤ x ≤ 1), the ratio of the vacancy
continuously changes according to (1-x)/(3-2x). The
atoms in the crystals are orthogonally connected with
six adjacent atoms (or vacancies) by p-p bonding; the(a)(b)
atomic network of this structure consists of fourfold andFig. 4.
HXRD data for AIST and GST, and atomic
sixfold rings. The atomic arrangement of the amorphousconfigurations of a-AIST and a-GST. (a) Structure factors S(Q) andphase can be geometrically obtained by minute shifting(b) total correlation functions T(r) of AIST and GST. Red line,of the atoms in random directions almost without bondexperimental data of crystalline phase; black line, experimental datainterchanges found in the phase change of AIST (this isof amorphous phase; blue line, DF-RMC model of a-AIST. The
shown below), which means that, when an amorphous
DF-RMC and experimental results are practically indistinguishable.

GST is given energy by laser irradiation (or ohmic heating) and then instantaneously cooled, the atomic migration distanceis so short that the solid instantaneously crystallizes into this type of highly symmetric (spatially isotropic) structure similar
to that of the amorphous phase.
Many structural investigations have been dedicatedto the GST amorphous materials. Coordination numbers
for three constituent atoms approximately follow the 8-N
rule, largely different from those of the crystalline phase;
for instance, those of a-GST225 are ca 3.7, 3.0, and 2.6hν
around Ge, Sb, and Te atoms respectively. These
approximately satisfy the 8-N rule, showing thecharacteristics of covalent bonds often observed incalcogenide amorphous materials. The bond lengths arealso shorter than in the crystalline phase. The atomic
configuration is maintained almost unchanged up to thetransition temperature to the crystalline phase [12], [13].
It has been considered that such a strong covalentbonding nature gives these amorphous materials
sufficientendurance,
namely,long-term
datapreservation. These GST materials contain three kinds ofatoms, Ge, Sb, and Te; which means that, if these atoms
connect with each other with equal probability in their(a) amorphous(b) crystalline
amorphous structures, six kinds of atomic pairs should
be found at the ratio provided by a random covalent
network model. It has been revealed, however, that theseFig. 5.
The central atom with three short (red) and three long(dashed) bonds crosses the center of the distorted octahedron,amorphous materials comprise a large number of Ge-Teinterchanging a short and a long bond. Green: resultant vector ofand Sb-Te atomic pairs beyond the above estimation
short bonds. The bonding electrons are excited by laser light (hν)(Note that the crystalline phase is formed by these two
to cause an interchange of bonding electrons, for example,
pairs as well). In a-GST225, 40% of the rings are
between the two bonds pointed by the yellow arch, which moves
fourfold or sixfold and a considerable amount of thethe atoms in the amorphous phase to form locally crystalline
relict GeTe4 tetrahedra and SbTe3 pyramids whose bondatomic configurations; the local crystalline atomic networks
anglesare distributed around 90º as same as those of the
finally form resonant bonding between periodic short and long
crystalline
phase [14], [15]; we can find even NaCl-typebonds, which leads to the crystalline A7 network. The grey sticks
crystalline fragments in the amorphous atomic network(lower right) correspond to the red bonds (upper right). Atomcolors as in Fig. 3(b).
as seen in Fig. 3(a). Once sufficient heat energy is
supplied to the amorphous material; however, thosecrystalline fragments act as first nuclei to crystallize their surroundings all at once. We presume that this is the rapid
phase-change mechanism of the GST materials. However, in addition to these countless nuclei, a large number of huge
voids (see Fig. 3(a)) are present in the amorphous phase, which impedes smooth crystal growth. As a result, the texture of
the crystallization-completed amorphous mark shows a mosaic pattern inlaid by a large number of tiny crystallites with 10 20 nm diameters. In addition, amorphous and crystalline GST materials have considerably low thermal conductivities,
meaning that these materials can locally heat up at once by laser irradiation or ohmic heating [13]. This feature is very
favorable to cause rapid PC. Major element in the GST materials is Te; its coordination number in the amorphous phase isapproximately two. This means that the Te atoms have to also form other bonds in addition to these existing ones by thetransformation to the crystalline phase.
Phase change in AIST materials
Laser-annealed Ag3.5 In3.8 Sb75.0 Te17.7 crystallizes into an A7 structure, as do As, Sb and Bi [16]. The A7 structure isshown in Fig. 5(b); four constituent atoms randomly occupy the 6(c) site of space group R 3 m [5]. As seen in Fig. 3 there
are three shorter interatomic distances (shown by gray thick line) and three longers between the central atom and its sixneighbors. This crystal can be described as a Jahn-Teller deformed structure to stabilize the electronic structure showing asemi-metallic feature [17], which can be regarded almost as a semiconductor. However, as mentioned above, the atoms in
the crystal are quasi-orthogonally connected with adjacent six atoms (3+3 octahedron) by p-p bonding as well as a
NaCl-type GST crystal; the atomic network of this structure consists of fourfold and sixfold rings. The densities of states(DOS) of both crystals are very similar to each other. Green arrows in the Fig. 5 show resultant vectors of short bonds,

which are parallel to each other and arranged along the c-axis direction. The
structure(bondlengthsandangles) and chemical coordination numbers obtained by the RMC/DF-MD simulation lead to the local environment aroundSb atoms shown in Fig. 5. Both a-AIST (left panel) and c-AIST (right panel) resemble a (distorted) 3 + 3 octahedron.
In the amorphous state, interatomic distance between the central atom and three shorter coordination atoms is
considerably shorter than in the crystalline state; they are connected to each other by a stronger covalent force than those in
the crystal to form isolated molecule by themselves. These molecules formed by the short bonds are flexibly connected byvertices or edges; a spatially periodic arrangement is not necessarily required of them. For this reason, the green arrows are
randomly oriented as seen in the left bottom panel of Fig. 5. However, once sufficient heat energy is given to the amorphousmaterial, it causes interchange of one bond in a 3+3 coordination octahedron to rearrange, parallel neighboring two vectors.
This rearrangement swiftly propagates from neighbor to neighbor forming the crystalline preferred orientation to acquire aperiodic atomic arrangement, which finally shows needle-like crystallization texture from the rim toward the center of themark (The crystalline phase is more opaque to the visible light; it is presumed that the crystalline wall around the rim isfaster heated than the amorphous mark). Fortunately for the growth dominated recrystallization materials, few voids toretard smooth crystal growth were found in the amorphous AIST. We presume that small number of elements, Ag and In
play an important role to form simple and spatially isotropic crystalline phase, which is an A7-type structure; for it isconsidered that atomic arrangements of the amorphous phase can be transformed into that crystalline phase through minimal
atomic shifts [18].
5. SUMMARY
According to the bond-interchange model, crystallization of a-AIST can be recognized as a rapid succession ofdiffusionless events where the 3 + 3 octahedra are aligned along the crystalline c axis imposed by the surrounding crystal(see Fig. 5). Heating or photon excitation causes the octahedra to align near the matrix boundary, and blade- or needle-likecrystallites can grow along the laser- scanning direction, as often observed in Sb-based PC materials. The lack of cavities
and chemical alternation in a-AIST favor smooth crystal growth. On the other hand, in the latter material, GST, high-speed
phase change begins from uncountable crystalline fragments embedded in the amorphous network all at once. In the former
material, Sb atoms are generally surrounded by Sb atoms of the same kind (with the same coordinate bonding nature);
whereas in the latter material, neighboring atom of Sb is almost always Te. This is presumed to be one major reason that theformer materials can take place such a bond-interchange phase transition.
REFERENCES
M. Wuttig and N.Yamada: Nat. Mater. 6, 824 (2007).
N. Yamada, E. Ohno, K. Nishiuchi, and N. Akahira, J. Appl. Phys. 69, 5, 2849 (1991).
H. Iwasaki, Y. Ide, Y. Harigaya, Y. Kageyama, and I. Fujimura: Jpn. J. Appl. Phys. Series 6 Proc. Int. Symp. on Optical Memory 68(1991).
[4] T. Matsunaga, R. Kojima, N. Yamada, K. Kifune, Y. Kubota, Y. Tabata, and M. Takata: Inorg. Chem. 45, 2235 (2006).
[5] T. Matsunaga, Y. Umetani, and N. Yamada: Physical Review B 64, 184116 (2001).
[6] T. Matsunaga, J. Akola, S. Kohara, T. Honma, K.Kobayashi, E. Ikenaga, R. Jones, N. Yamada, M.Takata and R. Kojima: Nat.
Mater. 10, 129 (2011).
[7] E. Nishibori, M. Takata, K. Kato, M. Sakata, Y. Kubota, S. Aoyagi, Y. Kuroiwa, M. Yamakata, and N. Ikeda, Nucl. Instrum.
Methods A 467−468, 1045 (2001).
[8] A. L. Ankudinov, B. Ravel, J. J. Rehr, and S. D. Conradson: Phys. Rev. B 58, 7565 (1998).
[9] T. Taguchi, T. Ozawa, and H. Yashiro, H. REX2000: Phys. Scr. T115, 205 (2005).
[10] S. Kohara, M. Itou, K. Suzuya, Y. Inamura, Y. Sakurai, Y. Ohishi, and M. Takata: J. Phys. Condens. Matter 19, 506101 (2007).
[11] N. F. Mott: Philos. Mag. 19, 835 (1969).
[12] T. Matsunaga, R. Kojima, N. Yamada, and M. Takata: Europian¥Phase Change and Ovonics Symposium 2008,
http://www.epcos.org/library/library2008.htm[13] T. Matsunaga, N. Yamada, R. Kojima, S. Shamoto, M. Sato, H. Tanida, T. Uruga, S. Kohara, M. Takata, P. Zalden, G. Bruns, I.
Sergueev, H. C. Wille, R. P. Hermann, M. Wuttig: Adv. Funct. Mater. 21, 12, 2232 (2011).
[14] S. Kohara, K. Kato, S. Kimura, H. Tanaka, T. Usuki, K. Suzuya, H. Tanaka, Y. Moritomo, T. Matsunaga, N. Yamada, Y. Tanaka, H.
Suematsu, and M. Takata, Appl. Phys. Lett. 89, 201910 (2006).
[15] J. Akola, R. O. Jones, S. Kohara, S. Kimura, K. Kobayashi, M. Takata, T. Matsunaga, R. Kojima, and N. Yamada: Phys. Rev. B 80,
020201 (2009).
[16] G. L. Clark: Applied X-rays (McGraw-Hill, 1955)[17] R. Hoffmann: Solids and Surfaces: A Chemist’s View of Bonding in Extended Structures (Wiley-VCH, 1989).
[18] T. Matsunaga and N. Yamada: Jpn. J. Appl. Phys. 43, 7B, 4704 (2004).
[1][2][3]