| Краткое содержание: | Metal–semiconductor transitions in condensed matter often
occur concurrently with structural transformations. There
is a longstanding and much debated issue as to whether the
driving force in these transitions is fundamentally electronic or
structural in origin (1). This problem is particularly challenging
in cases where the semiconducting phase is a glassy one, as in the
class of the technologically important phase-change materials
(2–4). These are typically alloys of Ge, Sb, and Te, which in
certain composition ranges, such as a canonical compound
Ge2Sb2Te5 (225), can be converted between the conducting
crystalline phase and a semiconducting amorphous phase. The
considerable body of work on these materials (5) has made it
clear that conversion to the amorphous state involves a change
in local coordination number resembling an ‘‘umbrella flip’’ (4)
in some members of the class. But, the 2 key fundamental
questions, why the system would tu
semiconducting on executing
this local structural rearrangement and what is the driving
force behind this process, still remain unanswered.
The difficulty in following the causal linkage between electronic
and atomistic configurations during the phase transition
(6, 7) lies in part in the short time scales of the process (4, 8), in
part, in the nonequilibrium (nonergodic) nature of the glassy
amorphous states (9), and, in part, in the global nature of the
usual experimental techniques, such as charge transport or
optical reflectivity (3). Electronic driving mechanisms for the
phase-change considered early on (2, 10) were never satisfactorily
proved (11), whereas numerous ab initio molecular dynamics
(MD) studies (12–15) tended to emphasize local atomic rearrangements
(16) while sidelining the relationship to electronic
structure.
Here, we demonstrate the causal link between the atomic and
electronic structure during the phase change by choosing a very
simple binary compound GeSb, having 2 critically important
advantages. First, it is nearly vacancy free. Unlike the complex
te
ary Ge2Sb2Te5 (225) that has a large number of vacancies
(17) (the 225 lattice is a 2-site NaCl type, with Te on the Cl
sublattice and Ge Sb vacancy on the Na sublattice), GeSb
has only 1 (Sb) lattice with Ge substituting on the Sb sites. This
is critical because during the phase-change process, along with
the (orders of magnitude) jump in resistivity (3), there is a
volume (density) change. The GeSb amorphous state is 8%
less dense than the crystalline form (18), so, by Le Chatelier’s
principle, applying pressure (decreasing volume) should induce
a change from the amorphous to the crystalline form.
This will give us an isothermal path to induce the phase change.
We note that pressure-induced crystallization of GeSb has
no analog in the 225 material. Instead, under pressure, there
is the contrary phenomenon of amorphization (19). This
process is clearly controlled by the high vacancy concentration
intrinsic to the 225 crystal structure, where pressure then acts
to ‘‘squeeze out’’ these vacancies, irreversibly denaturing the
crystalline 225.
Second, the crystallization velocity in GeSb is very high (8).
This—in addition to the isothermal means of reaching the
amorphous state being simpler—significantly reduces the demand
on computational resources (12, 14) required to track the
process by using ab initioMD(AIMD) and to test theMDresults
against our experimental data.
Our principal finding is that the process of structural reorganization
is driven by opening of the electronic gap, so that the
end stage of the amorphization process is a fully gapped system,
i.e., a semiconductor. The existence of an electronic driving force
behind the phase change has a potential to alter future technological
embodiments of this material class.
Results and Discussion
We focus on the eutectic composition (15 atm % Ge), which has
a robust amorphous phase (20) and large amorphous/crystalline
resistance ratio (see Fig. 1A). It crystallizes exothermally at
Author contributions: L.K.-E., D.M.N., G.J.M., and M.H.M. designed research; D.S., R.A.N.,
L.K.-E., G.J.M., D.M.N., B.G.E., X.-h.L., Z.E.H., S.P., C.C., D.B.S., D.N.B., Y.S., and M.H.M.
performed research; S.R. and Y.S. contributed new reagents/analytic tools; L.K.-E., D.M.N.,
G.J.M., and M.H.M. analyzed data; and L.K.-E., D.M.N., G.J.M., and M.H.M. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
Freely available online through the PNAS open access option.
To whom correspondence should be addressed. E-mail: krusin@us.ibm.com.
This article contains supporting information online at www.pnas.org/cgi/content/full/
0812942106/DCSupplemental.
www.pnas.orgcgidoi10.1073pnas.0812942106 PNAS Early Edition 1 of 5
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240 °C and has been demonstrated to amorphize by thermal
quench in a fast-switching device configuration at the nanoscale
(18). The structure of crystalline GeSb is shown by X-ray
diffraction to be the same A7 structure as pure antimony
[supporting information (SI) Fig. S1]. This structure is a distorted
(16) simple cubic lattice with Ge randomly occupying Sb
lattice sites. The nature of the distortion is that alte
ate planes
of atoms transverse to the (111) (or equivalent) axis in the simple
cubic structure displace in opposite directions along (111),
resulting in a layered structure of closely spaced bilayers spaced
apart relatively widely (Fig. 1B). The 6 equal nearest-neighbor
bonds of the simple cubic structure are replaced by 3 short
intrabilayer and 3 long interbilayer bonds. The distortion in Sb
(also in Bi) is caused by an intimate coupling between the
electronic structure and the lattice, the Peierls effect (21).
Our experiments demonstrate that under compressive load
(decrease in volume) amorphous GeSb crystallizes, forming
crystalline phases analogous to Sb (22, 23), which is known to
crystallize explosively near room temperature (24). As shown
in the X-ray diffraction data and Raman spectra under pressure
(see Materials and Methods), crystallization (appearance
of A7 structure Bragg peaks in Figs. 1C and Raman peaks in
Fig. 1D) occurs at a threshold pressure of 2 GPa. The
convergence of the (110) and (104) Bragg peaks seen in Fig.
1C indicates facile compression of the weak interbilayer bonds,
relative to the stiffer intrabilayer bonds, resulting, at a pressure
13 GPa, in the disappearance of the Peierls distortion and
formation of a simple cubic structure. At 14 Gpa, a further
transition to a new intertwined tetragonal ‘‘host–guest’’ structure,
also found in pure Sb (22), is observed. On decompression,
the sequence of structures is reversed with some hysteresis,
except that there is no retu
to the amorphous state. The
amorphous sample has been irreversibly crystallized by cycling
to above 2 GPa pressure—the hysteretic pressure–crystallization
sequence being clearly confirmed in Raman spectroscopy
(23); see Fig. S2.
We know that pure Sb (25) is a semimetal. So is GeSb, as
witnessed by its relatively high resistivity in the metallic state, see
Fig. 1. Indeed, it can be viewed as a Ge-doped Sb. This
semimetallicity is the consequence of a Peierls distortion (1, 21,
26), driven by Fermi surface nesting in the nearly half-filled
p-band, which underlies the simple cubic to A7 structural
distortion. The distortion opens an incomplete energy gap—a
‘‘pseudogap’’—at the Fermi level, lowering the total energy of
the occupied electronic states and, hence, lowering the total
electronic energy of the system (which ‘‘pays for’’ the elastic
energy of the lattice distortion). Accordingly, in the crystalline
phase, the measured metallic (Drude) conductivity (21) at low
frequencies ( 3 0) is relatively high as clearly observed in the
infrared (IR) conductivity data shown in Fig. 2A. In the crystalline
phase, a partial gap in IR conductivity ()—expected in
the Peierls picture—at 0.5 eV is evident. In the amorphous
phase, () shows a full semiconducting gap of 1 eV.
Clearly, the (Peierls) band-gap mechanism with Fermi surface
nesting no longer applies in the amorphous state (21) where
long-range translational order is absent nor is there, at present,
an analytically tractable theoretical model that can describe the
phenomena. We handle this situation by means of AIMD, a
technique that implements MD on a potential energy surface
derived from solving the many-particle Schro¨dinger equation in
the density functional approximation (12). AIMD (27) is used to
closely examine the amorphous state reached in 2 ways. In one,
the ensemble will be melted, followed by a rapid reduction in
temperature (tens of picoseconds) (12). In the other, we will
apply Le Chatelier’s principle in reverse: Our new AIMD
protocol will be used to amorphize GeSb by increasing the
volume, equivalent to applying a tensile load.
Fig. 2B shows the AIMD-calculated optical conductivity ()
of crystalline GeSb and of GeSb in the amorphous state, reached
by both the thermal and volume methods. It is apparent that all
basic experimental features of () in both the amorphous and
crystalline phase are reproduced. Note that the technique has
the precision to correctly obtain both the frequency and conductivity
scales to be in close correspondence with experiment
[the density functional approach is known to underestimate
energy gaps (14)]. We also note that optical conductivities of the
amorphous state obtained under thermal- and under volumequench
conditions are essentially identical.
The correspondence of amorphous phases reached either by
thermal or by nonthermal means is clearly evident in structural
and bonding changes on the local level. Figs. 2 C–E compare the
Ge coordination number and bond angle, for crystalline GeSb
and for the 2 kinds of amorphized systems. In the crystalline
phase (Fig. 2C), Ge tends to be 3-coordinated with nearly
simple-cubic bond angles (i.e., it is substitutional in the A7
structure). In contrast, in both thermally (Fig. 2D) and volumequenched
(Fig. 2E) amorphous phases Ge is predominantly
4-coordinated with tetrahedral bond angles. We also find 4-coordinated
Sb in the amorphous phases, but, instead of tetrahedral,
they have incomplete trigonal-bipyramidal coordination.
Our finding highlights the generality of 4-coordination in the
amorphous state, the presence of which was previously found in
the 225 compound (4). Indeed, this is unambigously confirmed
in the bond transformation calculations (28) represented by
Wannier functions in Fig. 2F for a 4-coordinated Ge site in the
amorphous state. They show 4 equally strong, approximately
Fig. 1. Thermal and pressure crystallization of eutectic GeSb. (A) (Upper)
Heat flow during a 10 °C/min temperature sweep shows the crystallization of
a free-standing GeSb film obtained by liftoff. (Lower) Abrupt change in
electrical resistivity during the phase change. (B) A7 Peierls distorted structure
of GeSb formed from simple cubic structure by motion of atomic planes
normal to (111) axis in alte
ate positive and negative senses. (C) Crystallization
under pressure: X-ray diffraction spectra measured during compression/
decompression cycle of initially amorphous GeSb to a maximum pressure of 21
GPa. The abrupt transition from the amorphous to the Peierls-distorted
crystalline phase at 2 GPa is shown by the appearance of Bragg peaks. With
increasing pressure, this distortion is removed (collapse of Bragg peak splitting
at 14 GPa), followed immediately by a transition to the complex host–guest
structure. (D) The amorphous–crystalline transformation monitored by Raman
spectroscopy over a lower pressure range.
2 of 5 www.pnas.orgcgidoi10.1073pnas.0812942106 Shakhvorostov et al.
tetrahedral, chemical bonds, unlike the 3 strong and 3 weak
bonds characteristic of the A7 structure.
Now we ask what drives the development of 4-coordination
during the amorphization process (see Movie S1) and whether and
how it connects with global order. We use the number of 4-coordinated
sites as a metric of local order. We find that this local order
parameter correlates closely with a global parameter, the total
electronic energy Etot
el . This is shown in Fig. 3A for volume amorphization,
where a drop in Etot
el and the drop in the number of
3-coordinated Ge atoms (P3) coincide. In Fig. 3B, the opening of
a gap, as shown by the decreasing curvature d2N(E)/dE2 of the
electronic density of states N(E), and by the drop in (bulk) dc
conductivity ( 0), develops in time along with the decrease in
P3. From the observed correlation between these 4 quantities, we
conclude that amorphization is driven by a lowering of the electronic
energy accompanying the opening of an energy gap in the
electronic spectrum. Future simulations of the amorphization process,
on much longer time scales, should access further details of gap
opening by formation of interlayer bonds.
We arrive at the same conclusion by analyzing amorphization
by quench from the melt. Fig. 3C shows 2 such amorphization
runs at different cooling rates plotted as dc conductivity (0) vs.
total energy Etot Etot
el Es, where Es represents lattice and
electron–lattice interaction terms. In quenching from the melt,
the system is lowering its global energy as it drops into a
(metastable) locally accessible valley in the glassy energy landscape
(9). Points of decreasing Etot represent points further along
in the quench. What is remarkable, is that for both quench rates
(and also for a single volume quench point) there is a seemingly
‘‘universal’’ relationship between (0) and Etot. We take decreasing
(0) as a measure of increasing semiconducting energy
gap. Thus, Etot is lowered (becomes increasingly negative) as the
energy gap increases. This is indeed expected and is consistent
with the gap-driven picture, and it confirms our results for the
volume amorphization in Fig. 3 A and B.
The electronic states in the neighborhood of the gap—as
determined from their participation ratio (see Fig. S3)—are
found to be poorly localized like typical band states, i.e., they
cannot be associated with particular local-molecular rehybridization
states. This supports the concept that phase change
material amorphization follows a general scenario (exemplified
in ref. 26) for structurally periodic systems), wherein a typically
half-filled system can lower its electronic energy by any structural
change, induced by electron–lattice coupling, which opens a gap
between filled and empty states. The Peierls distortion mechanism,
involving Fermi surface nesting, is just one example of this effect.
Now that we have established that the end state of the
amorphization process is independent of the way it is reached, we
note one unique and unusual feature of the volume-quench/
volume expansion cycle: it is hysteretic. Fig. 4A summarizes the
results of compressive (experiment) and tensile (simulation)
stress applied to GeSb. Under compressive stress, at a threshold
pressure 2 GPa, GeSb undergoes the amorphous-to-crystalline
transformation (see Fig. 1C), whereas the reverse (crystallineto-
amorphous) transformation is found in AIMD to take place
at a different threshold, approximately 2.5 GPa tensile load.
The kinetics of this hysteretic process can be illustrated in a
simple activation-energy picture of a free-energy diagram
sketched in Fig. 4B. Upon applying positive pressure, the activation
energy for crystallization is pulled down, so that the
process can occur at room temperature. Conversely, the activation
energy for amorphization is pulled down by expanding
volume equivalent to applying negative pressure.
Our studies of amorphization demonstrate the presence of
local structural changes—appearance of tetrahedrally bonded
Ge and incomplete trigonal–bipyramidal bonded Sb (4)—
distinguishing amorphization from crystallization. The absence
of localization in near-gap states supports a gap-driven mechanism
associated with the nearly half-filled p-band, where a gap
separating filled and empty states forms by electron–lattice
interaction, thus lowering the total electronic energy. The gapdriven
mechanism suggests that similar amorphous states, characterized,
e.g., by conductivity, reached by different paths (thermal
or volume quench) should have similar energies, leading to
89.9%
9.7%
0.4%
0%
5.9%
21.0%
50.5%
49.5%
73.1%
A C
B D
E
F
Fig. 2. Comparison of thermally and volume amorphized GeSb. (A) Measured infrared conductivity () for GeSb crystal and amorphous films. (B) Optical
conductivity () computed by 192-atom AIMD for crystal, amorphous [thermally (T-) quenched in up to 25 ps], and amorphous [volume (V-) quenched in up to
50 ps]. (C–E) Probability distributions P(Ge) of Sb-Ge-Sb bond angle Ge for different numbers ‘‘N’’ of Sb neighbors of Ge: crystal (C), amorphous (thermally
quenched) (D), and amorphous (volume quenched) (E). (F) Wannier functions around a typical 4-coordinated Ge atom (magenta) in the volume-amorphized
structure, showing the formation of 4 equivalent chemical bonds to Sb (gray), see Results and Discussion.
Shakhvorostov et al. PNAS Early Edition 3 of 5
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plots such as Fig. 3C, potentially a previously undescribed way of
classifying the phase change material glassy state. Further details
of the scaling properties in Fig. 3C could be elucidated by means
of a larger database of simulation runs in future work. Finally,
we remark that the pressure-induced phase change and the
corresponding hysteretic behavior are a consequence of GeSb
being vacancy-free. Such behavior is expected in other phasechange
materials in the ‘‘vacancy-free’’ class and can be envisioned
as the operating principle of switching technology (29)
requiring very low input power.
Materials and Methods
Experimental. In this study, eutectic GeSb films (typically 100 nm thick) were
deposited at room temperature, by using dc magnetron sputtering from a
nominally Ge(15%):Sb(85%) target, onto either thermally oxidized (100) Si
wafers for transport and optical temperature scans, or onto resist coated
wafers, with subsequent lift-off to obtain free-standing films for calorimetry
(see ref. 20 for details) and pressure studies. Raman studies were performed
under isotropic compression, by using a symmetric piston-cylinder diamond
anvil cell (DAC) equipped with 400-mculet diamond anvils. The pressure was
determined from the well-known pressure shift of the R1 ruby fluorescence
line (694.2 nm under ambient conditions) with an accuracy of0.05 GPa from
ruby (Cr3-doped -Al2O3) chips placed inside the gasket sample chamber (see
SI Text). The Raman spectra were collected in the range of 100–400 cm1,
covering all of the significant Raman active modes of GeSb. X-ray diffraction
spectra (at 30.55 keV; 0.4066 nm) were collected from GeSb in the same
DAC at the high-energy, high-intensity superconducting-wiggler X-ray beam
line X17C of the National Synchrotron Light Source at Brookhaven National
Laboratory (see SI Text). Spectroscopic ellipsometry was used to obtain complex
optical constants of amorphous (as deposited) and crystalline GeSb films
on polished Si and (out-of-plane c-axis oriented) sapphire substrates.Weused
an ellipsometric setup attached to a Michelson interferometer (30) to collect
data in infrared range 25 meV–1 eV; in visible-UV ranges, we used a standard
rotating analyzer ellipsometer.
Ab Initio MD. The Car–Parrinello ab initio MD (12) studies presented herein
were performed by using Kohn–Sham Density Functional Theory in conjunction
with the B-LYP approximate density functional (31), and superscalable
software and methods (27) on IBM’s Blue Gene/L supercomputer. The computations
were validated via extensive comparisons to previously published
results (13, 14) and ourownexperimental datasets. TheAIMDstructure factors
S(Q) for the crystalline and amorphous phases agree closely with experiments
(see Figs. S4 and S5).
ACKNOWLEDGMENTS. We acknowledge discussions with C. Lam, J. Crain, L.
Kale, and their research groups, especially E. Bohm; computer time on Sharcnet
and IBM Watson’s Blue Gene/L supercomputer; the referees whose thoughtful
comments helped improve the article; and the National Synchrotron Light
Source (X17C), J.HuandZ.Dong,for technical supportanduseful discussions. This
work was supported by the Natural Sciences and Engineering Research Council
(M.H.M.) and National Science Foundation Grant 0229959 (to G.J.M.). |
