Structural, Dynamical and Electronic Properties of Transition MetalDoped Ge2Sb2Te5 Phase-Change Materials Simulated by Ab Initio
Molecular Dynamics
Electronic Supplementary Material
1. Repeats of Simulations
The following are versions of the figures in the main text, generated from the data from the repeat simulations.
Figure S1 Simulated structures of TM-doped Ge2Sb2Te5. The images above show the relaxed amorphous (top) and
crystalline (bottom) structures of the (a) undoped and (b) Mn/(c) Zn-doped GST models at the end of the quench and
annealing periods of the simulation. An expanded view of the local atomic geometry around the TM atoms is shown to
the right of the doped models. The color-coding of the atoms is: Ge - blue, Sb - red, Te - green, Mn - purple and Zn orange. These images were produced using the VMD software (Ref. 1).
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Bonds Per Atom
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0
30
60
90
θ/
120
150
180
Figure S2 Bond-angle distributions for the TM atoms in the amorphous (solid lines) and crystalline (dashed lines)
phases. The color-coding of the lines is: Mn - purple, Zn - orange.
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Intensity / AU
(a)
80
60
40
20
0
(b)
50
100
150
Annealing Time / ps
250
60
(1)
50
MSD / Å2
200
(2)
(3)
40
30
(1)
20
(3)
(2)
10
0
0
50
100
150
Annealing Time / ps
200
250
Figure S3 Atomic dynamics of TM-doped Ge2Sb2Te5 during the phase transition. (a) A time-dependent Fourier analysis
indicates that the undoped (black line) and Mn/Zn-doped (purple/orange lines) systems all crystallised within 150 ps of
annealing. (b) The Zn mean-square displacements (MSDs) during annealing show large fluctuations, even after
crystallisation (marked by an arrow on the time axis). The inset shows the geometry around the Zn atom at the three
points marked on the curves. The color-coding of the atoms is as in Figure S1.
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0.60
Average Charge
0.50
0.40
0.30
0.20
0.10
0.00
Mn
Zn
Figure S4 Calculated TM-dopant atomic charges in amorphous (left, blue) and crystalline (middle, red) Ge 2Sb2Te5,
compared to those in the corresponding TM telluride minerals (right, yellow).
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2. Transition-Metal Atom Site Preferences
In the cubic Ge2Sb2Te5 (GST-225) crystal structure, transition metal (TM) dopant atoms could occupy cation or anion
sites. To investigate whether there are preferences for particular sites, we carried out a series of simulations in which
atoms in a crystalline model of undoped GST-225, obtained from a melt-quench-anneal molecular-dynamics simulation,
were substituted with a TM atom, and the resulting model relaxed. Snapshots of the models are shown in Figure S5, and
the energies of the configurations are compared in Table S1.
In addition, it is possible that the TM dopant atoms could occupy interstitial sites. To test this, we took the
relaxed crystalline models of the two doped systems obtained from our molecular-dynamics simulations, moved the TM
atom to an interstitial site, and relaxed the resulting model. Snapshots of these models are shown in Figure S5, and the
relative energies are given in the caption.
Mn substitution lowers the energy of the undoped system in all cases. It is most energetically favourable for Mn to
substitute at Ge/Sb (cation) sites than to replace Te at an anion site. There is a small preference for Ge sites over Sb sites
in these simulations, which may be due to local distortions allowing shorter bond lengths at the former.
In contrast, substitution with Zn raises the energy of the system. There appears to be a slight preference for the
anion site, although there is less of a difference in energy between anion/cation substitutions than observed with Mn. It is
worth noting that the relaxed models show some degree of distortion around Zn, reinforcing the idea that this atom, with
its preference for tetrahedral geometry, is not well accommodated at the lattice sites in the cubic crystal structure.
According to our molecular-dynamics simulations, in which all the doped systems were lower in energy than the
undoped ones, Zn appears to prefer to be located near voids, where it can adopt a range of coordination geometries,
which helps to explain our observations here.
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Figure S5 Snapshots of models of crystalline Ge2Sb2Te5 in which a Ge atom (a), Sb atom (b) and Te atom (c) has been
replaced by a TM atom. The top row shows the starting models, with the substituted atoms colored silver. The second
row shows the relaxed Mn-substituted models, and the third row the corresponding Zn-substituted ones. The colorcoding of the atoms is: Ge - blue, Sb - red, Te - green, Mn - purple and Zn - orange. These images were produced using
the VMD software (Ref. 1).
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Figure S6 Snapshots of models of Mn (a) and Zn (b)-doped crystalline Ge2Sb2Te5 in which the TM atom has been
moved to an interstitial site. The left-hand images show the starting configurations, and the right-hand ones the relaxed
models. Moving the Mn atom to an interstitial site causes an energy increase of 5.69 meV per atom, while the
corresponding energy change for moving Zn is 9.63 meV per atom.
∆E / meV per atom
Site
Mn
Zn
Ge
-49.98
25.85
Sb
-45.70
26.17
Te
-36.68
21.55
Table SI Energy changes per atom on substituting Ge, Sb and Te atoms in a model of crystalline Ge2Sb2Te5 with Mn and
Zn. The energy changes are calculated relative to the energy of the undoped model.
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3. Additional Characterisation
The following are additional figures giving the results of further characterisation on the three undoped and doped
systems, to supplement the information given in the main text. Unless otherwise stated, this analysis has been carried out
for one of the two sets of simulations only.
% Atoms
(a)
100
75
50
25
0
% Atoms
(b)
0
50
100
150
200
250
300
350
0
50
100
150
200
250
300
350
0
50
100
250
300
350
100
75
50
25
0
% Atoms
(c)
100
75
50
25
0
150
200
Simulation Time / ps
Figure S7 Dynamics of TM-doped Ge2Sb2Te5. These plots show the evolution of the percentage of atoms involved in
fourfold rings (a), planes (b) and cubes (c) with time during the simulated phase-change cycle. The color coding of the
lines is as follows: undoped - black, Mn-doped - purple, Zn-doped - orange. The mixing, liquid, quench and annealing
periods are delineated by vertical lines. A distance cutoff of 3.5 Å, corresponding to the radius of the first coordination
sphere, and an angle deviation tolerance of 20° was used to constrain these analyses; a detailed description can be found
in Hegedus and Elliott (Ref. 2) (a) and Lee and Elliott (Ref. 3) (b, c).
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(a)
(b)
8.0
6.0
6.0
g(r)
g(r)
4.0
4.0
2.0
2.0
0.0
0.0
0.0
1.5
3.0
4.5
r/Å
6.0
7.5
0.0
1.5
3.0
4.5
r/Å
6.0
7.5
Figure S8 Partial radial distribution functions (RDFs) centered on Mn (purple) and Zn (orange) in the amorphous (a) and
crystalline (b) phases. These RDFs were computed by averaging over 4000 configurations, extending over 20 ps, at the
end of the quench/annealing periods. The color-coding of the lines is as follows: Mn - purple, Zn - orange.
(b)
30
30
25
25
20
20
MSD / Å2
MSD / Å2
(a)
15
10
5
15
10
5
0
0
30
35
40
45
50
Quench Time / ps
55
60
0
50
100
150
200
Annealing Time / ps
250
Figure S9 Comparison of the Mn (purple) and Zn (orange) mean-square displacements (MSDs) during (a) quenching and
(b) annealing. In (b), the crystallisation times are marked by arrows. The color-coding of the lines is as in Figure S6.
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(a)
35
30
MSD / Å2
25
20
15
10
5
0
0
100
150
200
Annealing Time / ps
(c)
35
30
25
25
20
15
20
15
10
10
5
5
0
250
35
30
MSD / Å2
MSD / Å2
(b)
50
0
0
50
100
150
200
Annealing Time / ps
250
0
50
100
150
200
Annealing Time / ps
250
Figure S10 Atomic mean-square displacements (MSDs) during annealing in (a) undoped and (b) Mn-/(c) Zn-doped
Ge2Sb2Te5. The color-coding of the lines is: Ge - blue, Sb - red, Te - green, Mn - purple, Zn - orange.
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(b)
120
120
110
110
100
100
Ave. Angle
Ave. Angle
(a)
90
80
70
90
80
70
60
60
0
50
100
150
200
Annealing Time / ps
250
0
50
100
150
200
Annealing Time / ps
250
Figure S11 Variation in the four smallest bond angles around the Mn (a) and Zn (b) atoms during annealing. A fairly
sharp reduction in the magnitude of the fluctuations occurs following crystallisation (marked by an arrow on the time
axis). The bond angles considered are those for the six nearest neighbors of the TM atom.
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(a)
(b)
0.75
(c)
0.50
Average Charge
Average Charge
0.50
0.25
0.00
Ge
Sb
Te
-0.25
0.25
0.00
TM
-0.50
-0.75
-0.75
(d)
0.75
Te
-0.25
-0.50
0.75
0.50
0.25
0.00
Ge
-0.25
Sb
Te
Mn
Average Charge
0.50
Average Charge
0.75
0.25
0.00
Ge
Sb
Te
Zn
-0.25
-0.50
-0.50
-0.75
-0.75
Figure S12 Average Bader charges (Ref. 4) on atoms in the (a) undoped and (c) Mn-/(d) Zn-doped Ge2Sb2Te5 systems.
The charges in the amorphous (blue) and crystalline (red) phases are compared. The charges on the TM atoms may be
compared to those in the telluride minerals (b), MnTe (purple) and ZnTe (orange), computed from models of the unit
cells of these systems.
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Set 1
ρ / g cm-3
aGST
5.73
cGST
5.88
aGST:Mn
5.80
cGST:Mn
5.88
aGST:Zn
5.73
cGST:Zn
5.88
Set 2
Δρ
ρ / g cm-3
Δρ
5.64
-2.504%
5.98
-6.025%
5.84
-1.343%
5.81
0.447%
5.52
-2.602%
5.73
-3.840%
Table SII Densities of the relaxed amorphous (a-) and crystalline (c-) models of the undoped and Mn/Zn-doped systems,
together with the density change on crystallisation.
∆E / meV per atom
Set 1
Set 2
GST
-57
-48
GST:Mn
-65
-54
GST:Zn
-66
-55
Table SIII Energy changes per atom on going from amorphous (a-) to crystalline(c-) phases in the undoped and Mn/Zndoped systems. The total energies compared are for relaxed configurations obtained at the end of the quench (amorphous)
and annealing (crystalline) periods, and were calculated using a 2x2x2 Gamma-centred Monkhorst-Pack (Ref. 5) k-point
mesh and 1.3x the plane-wave energy cutoff used during the MD runs.
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4. References
1
W. Humphrey, A. Dalke, and K. Schulten, Journal of Molecular Graphics 14 (1), 33 (1996).
2
J. Hegedus and S. R. Elliott, Nature Materials 7 (5), 399 (2008).
3
T. H. Lee and S. R. Elliott, Physical Review Letters 107 (14), 145702 (2011).
4
R. F. Bader, Atoms in Molecules: A Quantum Theory. (Oxford University Press, Oxford, 1990).
5
H. J. Monkhorst and J. D. Pack, Physical Review B 13 (12), 5188 (1976).
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