Combined density functional and RMC simulations of phase change materials

Combined density functional and RMC simulations of phase change materials

Jaakko Akola

1Department of Physics, Tampere University of Technology, Finland

2CoE of Computational Nanoscience (COMP), Aalto University, Finland

3PGI-1 and GRSS, Forschungszentrum Jülich, Germany

E-mail: jaakko.akola@tut.fi

RMC-5, 20.9. 2012 Budapest, Hungary

Phase change materials (PCM): Operation principle of phase change memory, PC-RAM

  Structural transition between amorphous and crystalline phases

  Heating above glass-

transition temperature (set pulse)  crystalline state

  Heating above melting point and quenching (reset pulse)

 amorphous state

  electrical resistivity and optical reflectivity change

M. Wuttig, Nature Materials 4, 265 (2005).

Phase change materials (PCM) diagram

  Pseudobinary line

  Ternary alloys with significant number of vacancies

  Three phases: amorphous,

metastable and stable crystalline

  Ge₂Sb₂Te₅ (GST, in Group 1) was invented 1987  DVD-RAM  PC-RAM (future?)

  Doped AgInSbTe compounds (AIST, in Group 2) are used for DVD±RW

”The local structural order of ternary GST glasses is not

well established.”

J.K. Olson et al., J. Ovonic Res. 1, 1 (2005).

What is known of the atomic structure of a-GST and Group 1 materials (from theory)?

  Local coordination of atoms predominantly (defective) octahedral

  Ge in octahedral and tetrahedral (minority) configurations

  Strong alternation of atomic types A (Ge, Sb) and B (Te)  AB

  Ring structure points to abundant four-membered rings  ABAB squares  link to c-GST

  Cavities (voids) frequent, analogous to vacancies in c-GST

  Poor glass former

  Sb and Te overcoordinated with respect to 8-N rule

[1] J. Akola and R. O. Jones, PRB 76, 235201 (2007);

JPCM 20, 465103 (2008); PRL 100, 205502 (2008).

[2] S. Caravati et al., APL 91, 171906 (2007).

[3] J. Hegedüs and S. R. Elliott, Nat. Mater. 7, 399 (2008).

[4] K. B. Borisenko et al., Chem. Mater. 21, 5244 (2009).

[5] J. Akola and R.O. Jones, PRB 79, 134118 (2009).

[6] J. Akola et al., PRB 80, 020201 (2009).

[7] M. Micoulaut et al., PRB 81, 174206 (2010).

+ many others…

Simulation method

  Density functional theory (DFT) of electronic structure

  CPMD with periodic boundary conditions (www.cpmd.org)

  Born-Oppenheimer MD driver (time step 3-6 fs), Nosé-Hoover-chain thermostat, NVT ensemble, predictor-corrector algorithm

  Scalar-relativistic TM91 pseudopotentials¹ (+ NLCCs occasionally)

  PBEsol² for the exchange-correlation energy functional (+ PBE, TPSS)

  Plane wave basis set, cut-off energy 20-60 Ry

  Melt-quench down to 300 K (process duration ~0.2-0.5 ns)

  Simulations on IBM Blue Gene/P (JUGENE) and Intel Xeon 5570

(JUROPA) supercomputers in FZ Jülich  IBM Blue Gene/Q (JUQUEEN)

  RMC-refinement with respect to x-ray diffraction data (in some cases)

1N.L. Troullier and J.L. Martins, PRB 43, 1993 (1991).

2J.P. Perdew et al., PRL 100, 136406 (2008).

Our simulations of amorphous structure are not guided by intuition!

IBM Blue Gene/P and Q supercomputers

  Jülich Supercomputing Centre (JSC), FZ Jülich, Germany

  72 Racks with 32 nodecards x 32 compute nodes (total 73728 nodes, 294 912 cpus)

  Compute node: 4-way SMP processor

  Processortype: 32-bit

PowerPC 450 core 850 MHz

  Linpack peak performance:

825.5 TFLOPS  1 PFLOP

  Typical production run: 1 rack

= 4096 cpus for 24/7

  The new IBM Blue Gene/Q

(JUQUEEN) installed in May-

June 2012; running 

  512 atomic sites, rocksalt (NaCl) structure (c-GST)

  Te occupies Cl sites (256 atoms)

  Ge, Sb, and vacancies occupy Na sites randomly

 10% vacancies  460 atoms altogether

  Box size 24.6 Å (ρ=5.9 g/cm³)

Metastable ordered (”crystalline”) phase

Amorphous

disordered phase

Example 1: Melt-quench procedure of GST

J. Akola and R.O. Jones, PRB 76, 235201 (2007).

Example 2: Computer-aided deposition of GST

  Fixed template of randomly placed 36 atoms (magenta spheres), area 27.6×27.6 Ų

  Randomly generated sparse layers (“gas”) of 36 atoms placed on top of the sample sequentially

  Each configuration relaxed at 300 K for 5-10 ps (DF/MD simulation)

  17 added layers  648 atoms

  Vertical box dimension adjusted  vacuum of 10 Å for each system

After 5 added layers After 10 added layers

After 15 added layers

As-deposited sample: surface (2D slab)

  Tetrahedral Ge atoms visible  red tetrahedra (many)  EXAFS

  Tellurium has a tendency to be topmost  lowest coordination

  More wrong bonds, less ABAB squares  re-crystallization speed slower (?)

Top Side

J. Akola, J. Larrucea, and R.O. Jones, PRB 83, 094113 (2011)."

Structure factor and DOS

  S(Q) very similar for AD and MQ samples

  Deviation from experiment due to functional

  RMC-refinement leads to excellent agreement with experiment (Akola, Jones, Kohara, et al. PRB 2009)

  DOS very similar, again

  Band gap 0.2-0.3 eV

  Most visible differences

observed at lower energy, -10 eV (Te-Te bonds)

xrd: S. Kohara et al., APL 89, 201910 (2006)."

GST-225 (Group 1) has been studied extensively by DFT simulations.

How about the other technologically interesting material, AIST (Group 2)?

11

DF simulations of liquid AIST:!

J. Akola and R.O. Jones, APL 94, 251945 (2009)."

Main topic: Amorphous Ag/In/Sb/Te

Recent work: Amorphous structure of AIST

12

Finnish-Japanese programme:!

T. Matsunaga, J. Akola, S. Kohara et al., Nature Materials 10, 129 (2011)."

Experiment & Theory

(DFT + RMC-refinement)

  EXAFS

  HXPS

  TEM

  High-energy x-ray diffraction (HEXRD)

  Reverse Monte Carlo (RMC)

  Density functional / molecular dynamics simulations (DF/MD)

13

Amorphous AIST: Unit cell (+ periodicity)

14

640 atoms

(melt-quenched) Ag: 3.5%; In: 3.8 % (dopants)

Sb: 75.0%

Te: 17.7%

Cavities in red: 7% of box volume (only)

Structure factor and radial distribution function

15

Q (Å^-1)

S(Q)

r (Å)

T(r)

a b

AIST

GST

AIST

GST

Red: cryst.

Black: amorph.

Blue: theory (DFT-RMC)

T. Matsunaga, J. Akola, S. Kohara et al., Nature Materials 10, 129 (2011)."

PDFs

DF/MD:

am. - 300 K liquid - 850 K cryst. (ref.)

Ag/In prefer Te  AgInTe₂ (chalcopyrite)  segregation?

DF/MD of liquid AIST: J. Akola and R.O. Jones, APL 94, 251945 (2009)."

No Te-Te bonds

Coordination numbers, a-AIST

Atom N_EXAFS r_EXAFS (Å) N_DF/MD r_DF/MD(Å) N_bond Ag 3.3 ± 0.5 2.768 ± 0.006 4.4 2.80±0.05 1.9 (2.0)

In 4.3 ± 0.6 2.826 ± 0.006 3.1 2.85±0.05 2.5 (2.9) Sb 3.7 ± 0.3 2.872 ± 0.006 3.3 2.85±0.05 3.1 (3.2) Te 2.4 ± 0.4 2.827 ± 0.006 2.5 2.85±0.05 2.5 (2.6)

17

Crystalline phase (A7) displays 3+3 coordination

75.0%

17.7%

3.5%

3.8%

Angles and dihedral angles

•  Bond cutoff distance varied

•  Distorted cubic (A7) structure visible, effects of short and long bonds

•  Clear similarities between c-AIST and a-AIST!

18

Red, < 3.1 Å Blue, < 3.3 Å Black, < 3.5 Å

Electronic density of states, DOS

19

Photoelectron intensity (arb. units) Photoelectron intensity (arb. units) Sb 5s

Ag 4d Ag 4d

Sb 5s

Sb 5p Sb 5p

Te 5s

Te 5s Te 5p

Te 5p

Energy (eV) Energy (eV)

Band gap

increases upon amorphization;

typical for PCMs

Crystalline AIST Amorphous AIST

Chemical bond orders in AIST

  Bond orders have been computed from the overlap of wavefunctions

  Bond order = “bond strength”

  Reference value 1 for covalent single-bond

  Chemical coordination : 3.1/3.2 (Sb) and 2.5/2.6 (Te) for a-/c-AIST

  Bonding is less covalent in c-AIST (“resonance effect”) Bond order

Weight (arb. units)

Bond order

Weight (arb. units)

Sb-Sb bonds " " Sb-Te bonds

crystalline

K. Shportko et al., Nature Materials 7, 653 (2008).

B. Huang and J. Robertson, PRB 81, 081204(R) (2010).

Bond interchange model

21

T. Matsunaga, J. Akola, S. Kohara et al., Nature Materials 10, 129 (2011)

  chemical bond interchange

  S

2 reaction (Walden inversion)

  theory of liquid crystals

  6-vertex model (a.k.a. ice model  Ising model)

hv

c-axis

Bond interchange: DFT simulation

23

  300 K simulation, 30 ps, constrained MD

  Barrier height 0.42 eV (for selected Sb atom)

Ring statistics: amorphous phases

  Crystalline AIST comprises only 6-fold rings

  4-fold rings dominant in GST, 6-fold rings also present in c-GST

24

n-fold ring

Fraction (%)

a-AIST

+

n-fold ring

Fraction (%)

a-GST

+

25

15.10.2012

4R

3R 6R

8R

7R 5R

5R

6R

Ring reconstruction via! bond interchange

8R

6R

9R

4R 4R

4R 5R

3R 7R

6R

3R 4R

Bond formation around nuclei

6R 6R

A. B.

AIST

GST

Conclusions: PCMs

Rapid amorphous-to-crystalline transition of GST can be viewed as a reorientation of ABAB squares ( NaCl structure), which is

supported by the cavities  nucleation driven crystallization.

AIST recrystallizes via an avalanche of individual bond interchanges of Sb atoms (3+3 octahedron). The collective “director” is set by

crystalline surrounding (perimeter of a bit) or a large nucleus (template)  growth dominated crystallization.

The effect of dopants (Ag, In) is to hinder the spontaneous

recrystallization of Sb by introducing defects in the bond network.

The dopants prefer Te which affects the recyclability of AIST.

GST AIST

laser scanning direction

Recent work: glassy Ga ₁₁ Ge ₁₁ Te ₇₈

•  540 atoms (60 Ga, 60 Ge, and 420 Te)

•  Three initial RMC models (differences in Ga-Ga, Ga-Ge, and Ge-Ge bonds), DF/MD for each of them

•  50 ps of DF/MD for the most promising model (all bond types allowed) and final structure optimization

•  RMC refinement:

(1) Minimum interatomic distances of 2.35 (Ga- 145 Te), 2.45 (Ge-Te, Te-Te), and 2.30 Å (Ge-Ge, Ge-Ga, and 146 Ga-Ga)

(2) No constraints on coordination

(2) Bond angle distribution constraints (Te-Ga-Te, Te-Ge-Te, Te-Te-Te, Te-Te-Ge, and Te-Te-Ga)

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15.10.2012

28

I. Voleska, J. Akola, P. Jovari, J. Gutwirth, T. Wagner, Th. Vasileiadis, S. N. Yannopoulos, and R. O. Jones, Phys. Rev. B 86, 094108 (2012), published last week…

Amorphous Ga ₁₁ Ge ₁₁ Te ₇₈ : DFT-RMC

Acknowledgements

•  R.O. Jones (Forschungszentrum Jülich)

•  J. Larrucea and J. Kalikka (University of Jyväskylä)

•  S. Kohara and K. Kobayashi (SPring-8, Japan)

•  T. Matsunaga and N. Yamada (Panasonic, Japan)

•  P. Jovari (RISSPO, Hungary)

Financial support:

•  Academy of Finland

•  JST, Japan

Computational resources:

•  Forschungszentrum Jülich, Germany

•  CSC, Espoo, Finland

T. Matsunaga, J. Akola, S. Kohara et al., Nature Materials 10, 129 (2011).

Additional slides

31

Oma nimi ja esityksen aihe vaihdettava mastersivulla 15.10.2012

Principle of amorphization (via cooling)

M. Wuttig and N. Yamada, Nature Mater. 6, 824 (2007)."

  Rapid quench from the liquid phase enables amorphization (melt-quench)"

  Time scale depends on the material in question (~1 ns for PCMs, fortunately…)"

  Amorphous-to-crystalline

transition occurs below the melting point (referred to as the glass

transition, T

)"

GST: Bulk sample (3D system, AD)

  Gradual compression necessary for obtaining a 3D sample

  19 steps of 3-4 ps at 300 K (molecular dynamics)  scaling of vertical box side

  Resulting sample almost pressure-free  good relaxation

  Cavities comprise 16% of total volume (cyan regions, our definition)

J. Akola and R.O. Jones, PRL 100, 205502 (2008)."

J. Akola and R.O. Jones, PRB 76, 235201 (2007)."

Atomic structure – visualization (slabs)

34

Fragment of NaCl lattice ABAB square

AIST GST

What is a “cavity’’?

Vacancy-vacancy RDF!"

  Cavities (voids) are regions of empty space, analogous to vacancies!

  Cavity domain (red area I) determined by inserting spherical test particles (R>2.8 Å, dashed circle) in real space mesh (spacing 0.08 Å)"

  Cavity volume (yellow area II) determined via Voronoi construction (Wigner-Seitz cell) with respect to cavity domain (not center alone)"

a-GST, 300 K"

l-GST, 900 K"

Cavity volumes"

J. Akola and R.O. Jones, PRL 100, 205502 (2008)."

J. Akola and R.O. Jones, PRB 76, 235201 (2007)."

Example: Cavities in PbO-SiO ₂

Reverse Monte Carlo

4000 atoms, 34% of PbO

S. Kohara et al., Phys. Rev. B 82, 134209 (2010).

Freeware software pyMolDyn with GUI to be

published in soon

Finnish-Japanese programme:!

J. Akola, R.O. Jones, S. Kohara, S. Kimura, K.

Kobayashi, M. Takata, T. Matsunaga, R. Kojima, and N. Yamada, PRB 80, 020201(R) (2009)."

DFT & reverse Monte Carlo refinement of a-GST:"

Structure factor S(Q), and x-ray weighted radial distribution function"

Red, experiment!

Blue, theory (DFT-RMC, 460 atoms, melt-quench)!