Coupling molecular dynamics and first- principle ... · Coupling molecular dynamics and first-principle electronic structure modeling of disordered heterostructures Olle$Heinonen$

Coupling molecular dynamics and first-principle electronic structure modeling of disordered heterostructures Olle Heinonen Materials Science Division, Argonne Na6onal Laboratory Chicago Center for Hierarchical Materials Design University of Chicago Computa6on Ins6tute

Argonne Na6onal Laboratory is supported by DOE Office of Science

Acknowledgements

Olle Heinonen Singapore 2015-‐02-‐12

2

Xiaoliang Zhong (ANL) Peter Zapol (ANL)

Ivan Rungger (TCD) Ketan Mahashweri (UC/ANL)

Subramanian Sankanayaranyan (ANL)

Mike Welland (ANL)

Dima Karpeyev (UC/ANL)

Mike Wilde (UC/ANL) Serge Nakhmanson (Uconn)

John Mangeri (Uconn)

Badri Narayanan (ANL) (no picture)

Outline

§  Resis6ve switching in transi6on metal oxides §  SIESTA/smeagol and self-‐interac6on correc6ons §  Combining molecular dynamics and first-‐principle calcula6ons: Swi[,

Galaxy, and eMa]er workflow §  Meso-‐scale defects: Li intercala6on in ba]ery electrodes §  Core-‐shell nanopar6cles §  Outlook


3

Resistive switching


4

Many complex oxides (perovskites such as Pr0.7Ca0.3MnO3), or transi6on metal oxides such as TiO2, NiO switch reversibly between a high-‐resistance state and a low-‐resistance state.

A. Sawa et al., APL 85, 4073 (2004) – bipolar switching Pt/NiO/Pt unipolar switching

~10nm

metal

TMO (insulator)

Substrate – Xtor


5

Resistive switching in metal oxides

(a) Au/Ti/SrZr0.998Cr0.002O3/SrRuO3; (b) Ag/CeO2/La0.67Ca0.33MnO3; (c) Ag/Bi2Sr2CaCu2O8+y heterojunction; (d) Pt/NiO/Pt; (e) Al/“Rose Bengal”/ITO; (f) Al/DDQ/ITO; (g) Au/porus Si/p-type Si; (h) Double barrier AlAs/GaAs heterostructure.

Typical structures


6

TiOx, HfOx, ~10nm

metal

TMO (insulator) V Substrate – Xtor Au, Ag, Pt, TiN

•  Early work used a host of oxides – PrCaMnO, TaOx, NiO, TiOx,… •  More recent work has focused in TiOx, HfOx insulator, TiN electrodes: more

stable switching, compa6bility with back-‐end-‐of-‐line semiconductor processing

•  Low programming voltage ~3 V •  High speed (~1 ns) •  Intensive ongoing research and development for applica6ons as Resis6ve

Random Access Memories (RRAM) – scalable beyond 20 nm node

What causes the switching?


7

•  Transi6on-‐metals have many oxida6on states •  Crea6on energy of (charged) oxygen defects is rela6vely small •  Oxygen defects have rather high mobility •  Mo6on of oxygen defects can change local electronic conduc6on proper6es: •  8TiO2 è2Ti4O7+O2. TiO2 is an insulator (bandgap ~3 eV), Magnéli phase Ti4O7 is a

metal

Top electrode

Bo]om electrode

Forming – so[ dielectric breakdown

Top electrode

Bo]om electrode

Oxygen moves to electrode interface – vacancies le[ behind form conduc6ng paths or phases

Reset Top electrode

Bo]om electrode

Oxygen moves into oxide – annihilates vacancies and conduc6ng paths

Can be restricted to interface only ~1 nm

Modeling goal


8

•  Use electronic structure calcula6ons and non-‐equilibrium Green’s func6ons (NEGF) methods to calculate •  Oxygen diffusion barriers using nudged elas6c band (NEB) methods under

applied bias voltage •  Electronic conduc6on for different oxygen vacancy concentra6ons

•  We use SIESTA/smeagol for electronic structure and NEGF •  Need to be able to capture the right electronic proper6es for off-‐stochiometric

systems.

DFT stuff


9

HΨ = EΨ

Hψi = εiψi

H = −12∇2 + vext + vxc + dr '∫ ρ(r ')

| r − r ' |ρ(r) = ψi

occupied∑

2

Use Hohenberg-‐Kohn theorem, Kohn-‐Sham formula6on: map system onto a non-‐interac/ng system with the same ground state density as the interac6ng one:

Approxima6on: exchange-‐correla6on energy and poten6al must contain all correc6ons to single-‐par6cle kine6c energy and Coulomb interac6ons Usual approxima6ons: L(S)DA (local), GGA (semi-‐local)

Problem


10

•  Transi6on metal oxides (incl. HfO2) have rather strong electronic correla6ons – exchange-‐correla6on energy/poten6al is a bad approxima6on.

•  Only using standard density func6onal theory methods (local density approxima6on, generalized gradient approxima6on) gives incorrect results – must go beyond to include correla6ons

•  LDA+U, hybrid func6onals,… •  Here: self-‐interac6on correc6ons implemented in smeagol (remove self-‐interac6ons

of localized orbitals) – Self-‐Interac6on Correc6ons (SIC)

Problem


11

•  Usual DFT implementa6ons include electronic self-‐interac/ons: an electron interacts with itself •  OK for metals – electrons really spread out so error ~1/Ne •  Really bad for atoms, small molecules – error ~1 •  Not good if material contains ~localized electronic states (eg transi6on metal 3d

states, 4f states….) •  Need to correct by subtrac6ng out self-‐interac6ons

or the orbital kinetic energy density, are on the third rung,and so on. The higher its position on the ladder the moreaccurate a functional becomes, but at the price of increasingcomputational overheads. Therefore it is worth investigatingcorrections to the functionals of the lower rungs, which pre-serve most of the fundamental properties of DFT and do notgenerate massive additional numerical overheads.

One of the fundamental problems intrinsic to the semilo-cal functionals of the first three rungs is the presence ofself-interaction !SI".16 This is the spurious interaction of anelectron in a given KS orbital with the Hartree and XC po-tential generated by itself. Such an interaction is not presentin the Hartree-Fock method, where the Coulomb self-interaction of occupied orbitals is canceled exactly by thenonlocal exchange. However, when using semilocal func-tionals such a cancellation is not complete and the rigorouscondition for KS-DFT,

U#!n"$ + Exc#!n

",0$ = 0, !2"

for the orbital density !n"= %#n

"%2 of the fully occupied KSorbital #n

" is not satisfied. A direct consequence of the self-interaction in LDA/GGA is that the KS potential becomestoo repulsive and exhibits an incorrect asymptotic behavior.16

This “schizophrenic” !self-interacting" nature of semilocalKS potentials generates a number of failures in describingelementary properties of atoms, molecules, and solids. Nega-tively charged ions !H!, O!, F!" and molecules are predictedto be unstable by LDA,17 and transition-metal oxides aredescribed as small-gap Mott-Hubbard antiferromagnets!MnO, NiO",18 or even as ferromagnetic metals !FeO,CoO",18 instead of charge-transfer insulators. Moreover, theKS highest occupied molecular orbital !HOMO", the onlyKS eigenvalue that can be rigorously associated to a single-particle energy,19–21 is usually nowhere near the actual ion-ization potential.16

Finally XC functionals affected by SI do not present aderivative discontinuity as a function of the occupation.19,20

Semilocal functionals in fact continuously connect the orbitallevels of systems of different integer occupation. This means,for instance, that when adding an extra electron to an openshell N-electron system the KS potential does not jump dis-continuously by IN!AN where IN and AN are, respectively,the ionization potential and the electron affinity for theN-electron system. This serious drawback is responsible forthe incorrect dissociation of heteronuclear molecules intocharged ions22 and for the metallic conductance of insulatingmolecules.23

The problem of removing the SI from a semilocal poten-tial was acknowledged a long time ago when Fermi and Am-aldi proposed a first crude correction.24 However, the moderntheory of self-interaction corrections !SICs" in DFT is due tothe original work of Perdew and Zunger from almost threedecades ago.16 Their idea consists in removing directly theself-Hartree and self-XC energy of all the occupied KS or-bitals from the LDA XC functional !the same argument isvalid for other semilocal functionals", thus defining the SICfunctional as

ExcSIC#!!,!"$ = Exc

LDA#!!,!"$ ! &n"

occupied

!U#!n"$ + Exc

LDA#!n",0$" .

!3"

Although apparently simple, the SIC method is more in-volved than standard KS DFT. The theory is still a density-functional one, i.e., it satisfies the Hohenberg-Kohn theorem,however, it does not fit into the Kohn-Sham scheme, sincethe one-particle potential is orbital dependent. This meansthat one cannot define a kinetic energy functional indepen-dently from the choice of Exc.16 Two immediate conse-quences are that the #n

" are not orthogonal, and that theorbital-dependent potential can break the symmetry of thesystem. This last aspect is particularly important for solidssince one has to give up the Bloch representation.

In this paper we explore an approximate method for SICto the LDA, which has the benefit of preserving the localnature of the LDA potential, and therefore maintains all ofthe system’s symmetries. We have followed in the footstepsof Filippetti and Spaldin,1 who extended the original idea ofVogel and co-workers25–27 of considering only the atomiccontributions to the SIC. We have implemented such ascheme into the localized atomic-orbital code SIESTA,28 andapplied it to a vast range of molecules and solids. In particu-lar we have investigated in detail how the scheme performsas a single-particle theory, and how the SIC should be res-caled in different chemical environments.

II. REVIEW OF EXISTING METHODS

The direct subtraction proposed by Perdew and Zunger isthe foundation of the modern SIC method. However, theminimization of the SIC functional !3" is not trivial, in par-ticular for extended systems. The main problem is that Excitself depends on the KS orbitals. Thus it does not fit into thestandard KS scheme and a more complicated minimizationprocedure is needed.

Following the minimization strategy proposed by Levy,29

which prescribes to minimize the functional first with respectto the KS orbitals #n

" and then with respect to the occupationnumbers pn

", Perdew and Zunger derived a set of single-particle equations,

'!12

!2 + veff,n" !r"(#n

" = $n",SIC#n

", !4"

where the effective single-particle potential veff,n" !r" is de-

fined as

veff,n" !r" = v!r" + u!#!$;r" + vxc

",LDA!#!!,!"$;r" ! u!#!n$;r"

! vxc",LDA!#!n

!,0$;r" , !5"

and

u!#!$;r" =) d3r!!!r!"

%r ! r!%, !6"

vxc",LDA!#!!,!"$;r" =

%

%!"!r"Exc

LDA#!!,!"$ . !7"

PEMMARAJU et al. PHYSICAL REVIEW B 75, 045101 !2007"

045101-2



U#!n"$ + Exc#!n

",0$ = 0, !2"








ExcSIC#!!,!"$ = Exc

LDA#!!,!"$ ! &n"

occupied

!U#!n"$ + Exc

LDA#!n",0$" .

!3"










'!12

!2 + veff,n" !r"(#n

" = $n",SIC#n

", !4"


fined as

veff,n" !r" = v!r" + u!#!$;r" + vxc

",LDA!#!!,!"$;r" ! u!#!n$;r"

! vxc",LDA!#!n

!,0$;r" , !5"

and

u!#!$;r" =) d3r!!!r!"

%r ! r!%, !6"

vxc",LDA!#!!,!"$;r" =

%

%!"!r"Exc

LDA#!!,!"$ . !7"


045101-2

Condi6on on SIC

Unitary transforma6on connec6ng KS orbitals with localized atomic orbitals that minimize ExcSIC – vary canonical KS orbitals and unitary transforma6on

Orbital-‐dependent poten6als……

These are solved in the standard KS way for atoms, withgood results in terms of quasiparticle energies.16 In this par-ticular case the KS orbitals !n

" show only small deviationsfrom orthogonality, which is re-imposed with a standardSchmidt orthogonalization.

The problem of the nonorthogonality of the KS orbitalscan be easily solved by imposing the orthogonality conditionas a constraint to the energy functional, thus obtaining thefollowing single-particle equation:

!!12

!2 + veff,n" "r#$!n

" = %m

#nm",SIC!m

" . "8#

Even in this case where orthogonality is imposed, two majorproblems remain: the orbitals minimizing the energy func-tional are not KS-type and in general do not satisfy the sys-tem’s symmetries.

If one insists in minimizing the energy functional in a KSfashion by constructing the orbitals according to the symme-tries of the system, the theory will become size-inconsistent,or in other words it will be dependent on the particular rep-resentation employed. Thus one might arrive at a paradox,where in the self-interaction of N hydrogen atoms arrangedon a regular lattice of large lattice spacing "in such a way thatthere is no interaction between the atoms# vanishes, since theSIC of a Bloch state vanishes for N!$. However, the SICfor an individual H atom, when calculated using atomiclikeorbitals, accounts for essentially all the ground-state energyerror.16 Therefore a size-consistent theory of SIC DFT mustlook for a scheme where a unitary transformation of the oc-cupied orbitals, which minimizes the SIC energy, is per-formed. This idea is at the foundation of all modern imple-mentations of SICs.

Significant progress towards the construction of a size-consistent SIC theory was made by Pederson, Heaton, andLin, who introduced two sets of orbitals: localized orbitals%n

" minimizing ExcSIC and canonical "Kohn-Sham# de-

localized orbitals !n".30–32 The localized orbitals are used for

defining the densities entering into the effective potential "5#,while the canonical orbitals are used for extracting the La-grangian multipliers #nm

",SIC, which are then associated to theKS eigenvalues. The two sets are related by unitary transfor-mation !n

"=%mMnm" %m

" , and one has two possible strategiesfor minimizing the total energy.

The first consists in a direct minimization with respect tothe localized orbitals %n

", i.e., in solving Eq. "8# when wereplace ! with % and the orbital densities entering the defi-nition of the one-particle potential "5# are simply &n

"= &%n"&2.

In addition the following minimization condition must besatisfied:

'%n"&vn

SIC ! vmSIC&%m

"( = 0, "9#

where vnSIC=u")&n* ;r#+vxc

",LDA")&n" ,0* ;r#. An expression for

the gradient of the SIC functional, which also constrains theorbitals to be orthogonal, has been derived33 and applied toatoms and molecules with a mixture of successes and badfailures.34–36

The second strategy uses the canonical orbitals ! andseeks the minimization of the SIC energy by varying both theorbitals ! and the unitary transformation M. The corre-sponding set of equations is

Hn"!n

" = "H0" + 'vn

SIC#!n" = %

m#nm

",SIC!m" , "10#

!n" = %

mMnm%m

" , "11#

'vnSIC = %

mMnmvm

SIC%m"

!n" , "12#

where H0" is the standard LDA Hamiltonian "without SIC#.

Thus the SIC potential for the canonical orbitals appears as aweighted average of the SIC potential for the localized orbit-als. The solutions of the set of equations "10# is somehowmore appealing than that associated to the localized orbitalssince the canonical orbitals can be constructed in a way thatpreserves the system’s symmetries "for instance, translationalinvariance#.

A convenient way for solving Eq. "10# is that of using theso-called “unified Hamiltonian” method.30 This is defined as"we drop the spin index "#

Hu = %n

occup

P̂nH0P̂n + %n

occup

"P̂nHnQ̂ + Q̂HnP̂n# + Q̂H0Q̂ ,

"13#

where P̂n= &!n"('!n

"& is the projector over the occupied orbital

!n", and Q̂ is the projector over the unoccupied ones Q̂=1

!%noccupP̂n. The crucial point is that the diagonal elements of

the matrix #nm",SIC and their corresponding orbitals !n

" are, re-spectively, eigenvalues and eigenvectors of Hu, from whichthe whole #nm

",SIC can be constructed. Finally, and perhapsmost important, at the minimum of the SIC functional, thecanonical orbitals diagonalize the matrix #nm

",SIC, whose eigen-values can now be interpreted as an analog of the Kohn-Sham eigenvalues.32

It is also interesting to note that an alternative way forobtaining orbital energies is that of constructing an effectiveSI-free local potential using the Krieger-Li-Iafrate method.37

This has been recently explored by several groups.38–40

When applied to extended systems the SIC method de-mands considerable additional computational overheads overstandard LDA. Thus for a long time it has not encounteredthe favor of the general solid-state community. In the case ofsolids the price to pay for not using canonical orbitals isenormous since the Bloch representation should be aban-doned and in principle infinite cells should be considered.For this reason the second minimization scheme, in whichthe canonical orbitals are in a Bloch form, is more suitable.In this case for each k-vector one can derive an equationidentical to Eq. "10#, where #nm

",SIC=#nm",SIC"k# and n is simply

the band index.41 The associated localized orbitals %, for

ATOMIC-ORBITAL-BASED APPROXIMATE… PHYSICAL REVIEW B 75, 045101 "2007#

045101-3




!!12

!2 + veff,n" "r#$!n

" = %m

#nm",SIC!m

" . "8#








"=%mMnm" %m




"= &%n"&2.


'%n"&vn

SIC ! vmSIC&%m

"( = 0, "9#





Hn"!n

" = "H0" + 'vn

SIC#!n" = %

m#nm

",SIC!m" , "10#

!n" = %

mMnm%m

" , "11#

'vnSIC = %

mMnmvm

SIC%m"

!n" , "12#




Hu = %n

occup

P̂nH0P̂n + %n

occup


"13#















045101-3




!!12

!2 + veff,n" "r#$!n

" = %m

#nm",SIC!m

" . "8#








"=%mMnm" %m




"= &%n"&2.


'%n"&vn

SIC ! vmSIC&%m

"( = 0, "9#





Hn"!n

" = "H0" + 'vn

SIC#!n" = %

m#nm

",SIC!m" , "10#

!n" = %

mMnm%m

" , "11#

'vnSIC = %

mMnmvm

SIC%m"

!n" , "12#




Hu = %n

occup

P̂nH0P̂n + %n

occup


"13#















045101-3

Atomic-orbital-based approximate self-interaction correction scheme for molecules and solids

C. D. Pemmaraju,1 T. Archer,1 D. Sánchez-Portal,2 and S. Sanvito1

1School of Physics, Trinity College, Dublin 2, Ireland2Unidad de Fisica de Materiales, Centro Mixto CSIC-UPV/EHU and Donostia International Physics Center (DIPC), Paseo Manuel

de Lardizabal 4, 20018 Donostia-San Sebastián, Spain!Received 14 September 2006; published 2 January 2007"

We present an atomic-orbital-based approximate scheme for self-interaction correction !SIC" to the local-density approximation !LDA" of density-functional theory. The method, based on the idea of Filippetti andSpaldin #Phys. Rev. B 67, 125109 !2003"$, is implemented in a code using localized numerical atomic-orbitalbasis sets and is now suitable for both molecules and extended solids. After deriving the fundamental equationsas a nonvariational approximation of the self-consistent SIC theory, we present results for a wide range ofmolecules and insulators. In particular, we investigate the effect of re-scaling the self-interaction correction andwe establish a link with the existing atomiclike corrective scheme LDA+U. We find that when no re-scaling isapplied, i.e., when we consider the entire atomic correction, the Kohn-Sham highest occupied molecular orbital!HOMO" eigenvalue is a rather good approximation to the experimental ionization potential for molecules.Similarly the HOMO eigenvalues of negatively charged molecules reproduce closely the molecular affinities.In contrast a re-scaling of about 50% is necessary to reproduce insulator band gaps in solids, which otherwiseare largely overestimated. The method therefore represents a Kohn-Sham based single-particle theory andoffers good prospects for applications where the actual position of the Kohn-Sham eigenvalues is important,such as quantum transport.

DOI: 10.1103/PhysRevB.75.045101 PACS number!s": 71.15.Mb, 71.20.Nr, 75.50.Ee, 71.15.Dx

I. INTRODUCTION

Density-functional theory !DFT", in both its static2 andtime-dependent3 forms, has become by far the most success-ful and widely used among all the electronic structure meth-ods. The most obvious reason for this success is that it pro-vides accurate predictions of numerous properties of atoms,inorganic molecules, biomolecules, nanostructures, and sol-ids, thus serving different scientific communities.

In addition DFT has a solid theoretical foundation. TheHohenberg-Kohn theorem2 establishes the existence of aunique energy functional E#!$ of the electron density !which alone is sufficient to determine the exact ground stateof a N-electron system. Although the energy functional itselfis not known, several of its general properties can be dem-onstrated rigorously. These are crucial for constructing in-creasingly more predictive approximations to the functionaland for addressing the failures of such approximations.4

Finally, but no less important, the Kohn-Sham !KS" for-mulation of DFT !Ref. 5" establishes a one-to-one mappingof the intrinsically many-body problem onto a fictitioussingle-particle system and offers a convenient way for mini-mizing E#!$. The degree of complexity of the Kohn-Sham!KS" problem depends on the approximation chosen for thedensity functional. In the case of the local-density approxi-mation !LDA",5 the KS problem typically scales as N,3

where the scaling is dominated by the diagonalization algo-rithm. However, clever choices with regard to basis sets andsophisticated numerical methods make order-N scaling areality.6,7

The energy functional E#!! ,!"$ !!", "= ! ," is the spindensity, !=%"!"" can be written as

E#!!,!"$ = TS#!$ +& d3r!!r"v!r" + U#!$ + Exc#!!,!"$ ,

!1"

where TS is the kinetic energy of the noninteracting system,v!r" is the external potential, U is the Hartree electrostaticenergy, and Exc is the exchange and correlation !XC" energy.This last term is unknown and must be approximated. Theconstruction of an approximated functional follows two strat-egies: empirical and “constraint satisfaction.”

Empirical XC functionals usually violate some of the con-straints imposed by exact DFT, and rely on parametrizationsobtained by fitting representative data. One includes in thiscategory XC functionals which borrow some functional de-pendence from other theories. This is, for instance, the caseof the celebrated LDA+U scheme,8,9 where the Hubbard-Uenergy takes the place of the LDA energy for certain“strongly correlated” atomic orbitals !typically d and fshells". The method, however, depends on the knowledge ofthe Coulomb and exchange parameters U and J, which varyfrom material to material, and can also be different for thesame ion in different chemical environments.10,11

In contrast, the construction based on constraint satisfac-tion proceeds by developing increasingly more sophisticatedfunctionals, which, nevertheless, satisfy most of the proper-ties of exact DFT.12 It was argued that this method constructsa “Jacob’s ladder,”13 where functionals are assigned to dif-ferent rungs depending on the number of ingredients theyinclude. Thus the LDA, which depends only on the spin den-sities, is on the first rung, the generalized gradient approxi-mation !GGA",14 which depends also on !!", is on the sec-ond rung, the so-called meta-GGA functionals,15 which inaddition to !" and !!" depend on either the Laplacian !2!"

PHYSICAL REVIEW B 75, 045101 !2007"

1098-0121/2007/75!4"/045101!16" ©2007 The American Physical Society045101-1



U#!n"$ + Exc#!n

",0$ = 0, !2"








ExcSIC#!!,!"$ = Exc

LDA#!!,!"$ ! &n"

occupied

!U#!n"$ + Exc

LDA#!n",0$" .

!3"










'!12

!2 + veff,n" !r"(#n

" = $n",SIC#n

", !4"


fined as

veff,n" !r" = v!r" + u!#!$;r" + vxc

",LDA!#!!,!"$;r" ! u!#!n$;r"

! vxc",LDA!#!n

!,0$;r" , !5"

and

u!#!$;r" =) d3r!!!r!"

%r ! r!%, !6"

vxc",LDA!#!!,!"$;r" =

%

%!"!r"Exc

LDA#!!,!"$ . !7"


045101-2




!!12

!2 + veff,n" "r#$!n

" = %m

#nm",SIC!m

" . "8#








"=%mMnm" %m




"= &%n"&2.


'%n"&vn

SIC ! vmSIC&%m

"( = 0, "9#





Hn"!n

" = "H0" + 'vn

SIC#!n" = %

m#nm

",SIC!m" , "10#

!n" = %

mMnm%m

" , "11#

'vnSIC = %

mMnmvm

SIC%m"

!n" , "12#




Hu = %n

occup

P̂nH0P̂n + %n

occup


"13#















045101-3

Filipeq and Spaldin

SIC in SIESTA


12

See, for example, C.D. Pemmaraju, T. Archer, D. Sanchez-‐Portal, and S. Sanvito, PRB 75, 045101 (2007)

α is parameter that sets the level of SIC. α=1 is full SIC, α=0 is LDA. Empirically, α=0.5 works well for oxides; α=1 for strongly ionic compounds (NaCl).

•  Implemented in SIESTA (Atomic Self-‐interac6on correc6ons) •  Uses parameter (or fudge factor) α

SIC calculations of Ti-oxides


13

Predicted band gap vs. empirical parameter α for LT-‐Ti4O7, TiO2 and Ti2O3. α=0.5 captures the bandgaps reasonably well across the Ti oxide series (and high-‐temperature phase Ti4O7 comes out metallic)

Scaling of SIC


14

•  Paralleliza6on: parallel over rows (SIESTA); k-‐points, energy grid (MPI) and threading (OpenMP) over orbitals (smeagol)

•  Have op6mized the code and run trials of large unit cells on 16384 cores using 256 energy points for the SMEAGOL NEGF calcula6on at an applied bias of 0.5 V using the ANL BG/Q.

•  Can go up to ~64k cores for a finite-‐bias calcula6on at 1 V, and do different bias voltages in parallel

Pt-TiOx-Pt heterostructures

§  Calculate conduc6vity using DFT+SIC and non-‐equilibrium Green’s func6ons §  Must first set up the structure…..


15

Ti4O7 Pt (111) Pt (111)

2.2 A

TiO2 (110)

Pt (111) Pt (111)

Xiaoliang Zhong

Interfacial disorder

§  Thin film deposi6on in industrial applica6ons is done using spu]ering (physical vapor deposi6on)

§  The interfaces will not be epitaxial but will have some degree of disorder §  Conduc6vity – especially near insulator-‐conductor transi6on will be very sensi6ve

to local structure at interfaces metal electrode-‐oxide §  Need to include some realis6c disorder. How?

–  Can generate structures “by hand” and relax using electronic structure methods – tedious and slow, cannot sample many configura6ons


16 ! &A&different&phase&with&conical&shape&was&observed&aher&SET&process.&! 5~10nm&diameter&Magnéli&phase&(TinO2n,1)&is&confirmed&by&electron&diffracMon&measurements&.&

• In,situ&local&I,V&in&TEM&using&conducMve,AFM&(C,AFM)&

Nano5Filament$FormaKon$in$Pt/TiO2/Pt$

SET SET (different site)

Incomplete filament (growing from TE)

X,ray&absorpMon&spectromicroscopy&and&TEM$$$J.P.&Strachan&et&al.,&Adv.&Mat.&22,&2010.&&&

HRTEM&and&electron&diffracMon&analysis$$&D.,H.&Kwon&et&al.,&Nat.&Nanotech.,&5,&148,153,&2010.&

Observation of electric-field induced Ni filament channels in polycrystallineNiOx film

Gyeong-Su Parka! and Xiang-Shu LiAnalytical Engineering Center, Samsung Advanced Institute of Technology, Suwon 440-600, Korea

Dong-Chirl Kim, Ran-Ju Jung, Myoung-Jae Lee, and Sunae SeoSemiconductor Device Laboratory, Samsung Advanced Institute of Technology, Suwon 440-600, Korea

!Received 10 September 2007; accepted 26 October 2007; published online 26 November 2007"

For high density of resistive random access memory applications using NiOx films, understandingof the filament formation mechanism that occurred during the application of electric fields isrequired. We show the structural changes of polycrystalline NiOx !x=1–1.5" film in the set !lowresistance", reset !high resistance", and switching failed !irreversible low resistance" statesinvestigated by simultaneous high-resolution transmission electron microscopy and electronenergy-loss spectroscopy. We have found that the irreversible low resistance state facilitates furtherincreases of Ni filament channels and Ni filament density that resulted from the grain structurechanges in the NiOx film. © 2007 American Institute of Physics. #DOI: 10.1063/1.2813617$

The electric-field controlled resistance switchingmemory using metal oxides has been projected in the form ofmetal/oxide/metal structures1–5 and attracted considerable at-tention because it can be grown at low temperatures and iscompatible with three-dimensional stack structures.6 It iswell known that polycrystalline NiOx films have shown thedistinct behavior of unipolar resistance switching.7,8 Themain issues concerning the realization of resistive randomaccess memory !ReRAM" using the NiOx film are reducingthe reset current and the resistance fluctuations during theswitching cycles.9

Despite its early discovery, as for the cyclic resistanceswitching of the crystalline NiOx thin film,10–12 the physicalorigins of the resistive switching phenomena have not beenfully clarified. According to the literature reviews for theproposed resistance switching mechanisms of the NiOx filmin a ReRAM cell, it has been most commonly believed thatthe voltage stress creates multiple filamentary conductingpaths in the NiOx film due to the nonnegligible Joule heatingeffect.9,13,14 They have strongly suggested that the formationand rupture of the filamentary conducting paths in the NiOxfilm are directly related to the low and high resistance prop-erties of the ReRAM cell. Interestingly, the “filament anod-ization model”13 and the “electric faucet model”15 have re-cently been suggested as possible explanations for localizedfilament formation and its contribution to the memoryswitching close to the anodic !positively biased" electrode.16

However, further experimental evidence and theoretical in-vestigations are needed to understand the origin of the resis-tance switching phenomena in the NiOx film and to optimizethe performance of ReRAM devices.

Structural changes of a polycrystalline NiOx !x=1–1.5",observed in the varied voltage-biased states, were character-ized in detail using simultaneous high-resolution transmis-sion electron microscopy !HR-TEM" and electron energy-loss spectroscopy !EELS". Direct imaging of Ni atoms in theNiOx film was obtained by recording a high-angle annulardark-field scanning transmission electron microscopy!HAADF-STEM" image with atomic resolution.17,18 The sto-

ichiometric ratio x of NiOx film was determined using anenergy dispersive x-ray spectroscopy.

We deposited a top Pt electrode !TE" /NiOx !x=1–1.5"film on a Pt bottom electrode !BE" /SiO2 /Si substrate by dcmagnetron reactive sputtering. In order to measure electricalproperties and investigate the structural changes of the NiOxfilm as well as the top Pt electrode in varied voltage-biasedstates, a 0.25 !m2 cell area with a thin top Pt electrode!about 5–7 nm thickness" was deposited at room tempera-ture using a complementary metal-oxide semiconductor pro-cess. For thin TEM sample preparation of locally switchedcell areas, we carefully applied the focused ion beam tech-nique, reducing sample damages by using low energy ions.19

After the forming process on a pristine memory cell, weobserved the reversible bistable resistive memory switchingthrough a voltage sweep as indicated in Fig. 1!a". As theapplied voltage increases, the resistive transition from astable low resistance Ron state to a stable high resistance Roffstate, the reset, appears at %3.5 V. The resistive transition

a"Author to whom correspondence should be addressed. Electronic mail:[email protected].

FIG. 1. !a" Current vs voltage characteristics of a Pt /NiOx !x=1%1.5" /Ptcapacitor structure with a 0.25 !m2 top electrode area, !b" Cross-sectionalTEM image of the as-grown NiOx film showing a fine columnar structure.Cross-sectional TEM images of the NiOx film after the set !c" and reset !d"processes showing the changes in grain shapes, particularly, near the top Ptelectrode. The dotted lines, indicated in !c" and !d", denote the boundary ofrandomly deformed areas in the NiOx film.

APPLIED PHYSICS LETTERS 91, 222103 !2007"

0003-6951/2007/91"22!/222103/3/$23.00 © 2007 American Institute of Physics91, 222103-1Downloaded 10 Sep 2009 to 146.139.150.34. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp

Pt/TiO2/Pt Pt/NiO/Pt

But what do the interfaces really look like?


17

Need be]er interface models – use reac6ve force-‐field molecular dynamics to generate structures with quenched disorder

900 K 300 K

•  Molecular dynamics (LAMMPS) è generate quenched structure (equilibrate) è send output atomic posi6ons to SIESTA/Smeagol first principle/NEGF code

•  Can do this manually – cut and paste output .xyz file, input .fdf file….

Badri Narayanan, Subramanian Sankanayaranyan, Xiaoliang Zhong, Ivan Rungger, Dima Karpeyev, Peter Zapol, OGH

Smarter way….

§  Each of these examples has a well-‐defined set of parameters or coupling constants that can (in principle) be calculated directly from atomis6c models and transferred to the mesoscale model

§  Simplest: MD to SIESTA •  Cut and paste LAMMPS output (*.xyz) into SIESTA/Smeagol input (*.fdf) •  Can do because atomic posi6ons are direct output from LAMMPS and input to SIESTA

–  Smarter way: •  Write a script that reads LAMMPS output file, pulls out atomic posi6ons, opens a SIESTA file

and pastes the atomic posi6on

–  Even smarter way: •  Write a program or python script that reads some input parameters (number of atoms, ini6al

posi6ons, other simula6on parameters,…), then launches LAMMPS, does post-‐processing, grabs the output (atomic posi6ons), creates a SIESTA input file, launches SIESTA, and gathers the output, does post-‐processing.


18

Even Smarter Way….

§  Write a Web-‐interface to a program that generates a workflow and launches it –  Reads an input file (type of atoms, number of runs, etc)

–  Generates appropriate LAMMPS input files

–  Launches parallel LAMMPS runs on some pla9orm(s)

–  Gathers output, does post-‐processing, generates SIESTA input

–  Lauches parallel SIESTA/Smeagol runs on some pla9orm(s)

–  Gathers output, does postprocessing


19

Dima Karpeyev, Ketan Maheshwari, Mike Wilde

Workflow using Swift parallel scripting language


20

Input files (input and mesh)

Galaxy-based web interface for workflow


21

Drag and drop


22

Pt-TiOx system Transmission coefficients with quenched disorder

TiN-Ta-HfO2-TiN system


23

604 atoms

1368 atoms

TiN-Ta-HfO2-TiN system – transmission coefficients


24

604 atoms

1368 atoms

Future work


25

•  Calcula6on of conductance for different values of oxygen concentra6ons moved from HfO2 to Ta, different realiza6ons of quenched disorder (ongoing)

•  Explore PEXSI diagonaliza6on (thanks to Dr. Yang and his talk!) •  Use Swi[ workflow to calcula6on oxygen diffusion barriers using NEB •  New direc6on:

•  Construc6on of semi-‐empirical molecular orbitals for transi6on-‐metals and transi6on metal oxides added to MOPAC code; construc6on of density func6onal theory-‐based 6ght-‐binding (DFTB) parameters (A. Wagner, D. Dixon, P. Zapol)

•  Combine with Shi[-‐and-‐Invert Parallel Spectral Transforma6ons (SIPs) to exploit sparsity of Hamiltonian, rapid and scalable method

Strong scaling plots of nanotube (le[), diamond nanowire (center), diamond nanocluster (right) with different numbers of atoms (N in the legend). Straight lines correspond to a linear decrease in solu6on 6me with respect to number of cores.

Future work


26

•  Use Swi[ workflow to combine molecular dynamics (reac6ve force-‐field) with MOPAC/DFTB

•  Generate transi6on-‐oxide nanoclusters using MD •  Calculate electronic proper6es using MOPAC/DFTB

Documents

Coupling molecular dynamics and first- principle ... · Coupling molecular dynamics and first-principle electronic structure modeling of disordered heterostructures Olle$Heinonen$