FIRST PRINCIPLES COMPUTATIONS

First principles calculations of oxygen vacancy-ordering effectsin resistance change memory materials incorporating binarytransition metal oxides

Blanka Magyari-Kope • Seong Geon Park •

Hyung-Dong Lee • Yoshio Nishi

Received: 2 March 2012 / Accepted: 4 June 2012 / Published online: 22 June 2012

� Springer Science+Business Media, LLC 2012

Abstract Resistance change random access memories

based on transition metal oxides had been recently pro-

posed as promising candidates for the next generation of

memory devices, due to their simplicity in composition and

scaling capability. The resistance change phenomena had

been observed in various materials, however the funda-

mental understanding of the switching mechanism and of

its physical origin has not been agreed upon. We have

employed first principles simulations based on density

functional theory to elucidate the effect of oxygen vacan-

cies on the electronic structure of rutile TiO2 and NiO

using the local density and generalized gradient approxi-

mations with correction of on-site Coulomb interactions

(LDA ? U for TiO2 and GGA ? U for NiO). We find that

an ordered oxygen vacancy filament induces several defect

states within the band gap of both materials, and can lead to

the defect-assisted electron transport. This state may

account for the ‘‘ON’’-state low resistance conduction

observed experimentally in rutile TiO2 and NiO. As the

filament structure is perturbed by oxygen ions moving into

the ordered chain of vacancies under applied electric field,

charges are trapped and the conductivity can be signifi-

cantly reduced. We predict this partially disordered

arrangement of vacancies may correspond to the ‘‘OFF’’-

state of the resistance change memories.

Introduction

Resistive switching devices for data storage are currently

considered a high-risk, but possibly a high-payoff solution

for an embedded non-volatile memory (NVM) module.

Along this line, the switching devices based on the resis-

tance change induced in a metal–insulator–metal (MIM)

stack, received increased interest lately. As for materials,

the binary metal oxides, e.g., TiOx, NiOx, HfOx, AlOx,

TaOx were considered, with the prospect of low cost, high

scalability, and low power consumption characteristics. In

terms of resistance-switching models for these memory

cells, there is no general consensus about how the

switching occurs. Based on experiments performed for

various MIM stacks, several models had been proposed:

e.g., charge trapping mechanism [1], conductive filament

formation [2], Schottky barrier modulation [3], electro-

chemical migration of point defects [4], ionic transport and

electrochemical redox reactions [5]. The role of defects in

the resistance-switching, in particular oxygen vacancy

diffusion effects describing the transition between the high

and low resistive state has been recently a topic of interest

[6–10]. The oxygen vacancies have been shown to induce a

metal–insulator transition in SrTiO3 (STO) single crystals

[11], and the aggregation of these dopants into an extended

defect network was postulated to drive the generation of

conductive filaments during the resistive switching [5].

Before the bi-stable switching can be achieved, an elec-

troforming step is required for most of the samples. On the

surface of STO single crystals, Janousch et al. [12] iden-

tified the existence of a channel of oxygen vacancies (VO)

after electroforming.

Both the crystalline and thin film reduced TiO2-x, have

been found to have substantially higher n-type conductivity

than their stoichiometric structures. For the reduced TiO2

B. Magyari-Kope (&) � H.-D. Lee � Y. Nishi

Department of Electrical Engineering, Stanford University,

Stanford, CA 94305, USA

e-mail: blankamk@stanford.edu

S. G. Park

Department of Materials Science and Engineering,

Stanford University, Stanford, CA 94305, USA

123

J Mater Sci (2012) 47:7498–7514

DOI 10.1007/s10853-012-6638-1

there are, however, several stable titanium–oxygen phases

between Ti2O3 and TiO2, in the phase diagram of the Ti–O

system. An oxygen vacancy created in stoichiometric TiO2

behaves as a positively charged double donor [13, 14], and

with increasing concentration of vacancies, vacancy-

ordering trends had been identified theoretically by Park

et al. [15] using ab initio simulations of vacancies in bulk

TiO2. Yang et al. [16] also studied the vacancy formation

mechanisms in Pt/TiO2/Pt devices. A positive electro-

forming voltage applied to the top electrode was found to

induce the formation of an oxygen gas composed of O2-

ions, which drift towards the anode. Simultaneously the

oxygen vacancies (VO) are drawn to the cathode and

decrease the field in this region [5].

For nanoscale filaments inside vertical Pt/TiO2/Pt devi-

ces, in a recent study, Kwon et al. [17] identified the fila-

ments to be of TinO2n-1 composition, which are known as

room temperature conducting Magneli phases. Using high-

resolution transmission electron microscopy (HRTEM) and

electron diffraction they observed that the filaments form a

bridge between the two electrodes in the SET state. Direct

probing of the filaments using conductive atomic force

microscopy revealed that the filaments were both localized

and conducting. The character changed abruptly from

metallic to semiconducting near 130 K. Conversely, after

RESET, no Magneli phases were observed in the regions

previously occupied by the conducting filaments. Thus,

TiO2 is believed to spontaneously order into Ti4O7 when

the concentration of oxygen vacancies reaches a critical

density.

The nature of nanofilament formation [7–9, 18, 19] and

that of electronic charge injection [20] had also been the

subject of intense discussion over the past years. In addi-

tion, it was pointed out that electrode–oxide interfaces may

play an important role in the forming and switching, and

the properties can be material and/or deposition controlled.

Jameson et al. [21], and Dong et al. [22], identified that

oxygen vacancies were responsible for TiO2 bipolar

switching through field-driven drift, which alters the

Schottky barriers at the electrode interfaces. The atomic

interactions at the interfaces between the metal oxide and

reactive electrodes can influence the filament formation, as

addressed by Jeong et al. [23].

The NiO-based RRAM has also been extensively

investigated, in particular due to its unipolar switching

characteristics. The filament model discussed above has

been found to give qualitative explanation for unipolar

switching as well [24]. Up to date, various models had been

proposed to explain the switching phenomena in this

material i.e., migration of oxygen into the Pt anodic elec-

trode after the forming process [25], metallic nickel defects

in NiO [26], oxygen migration [27], thermal energy con-

siderations [28], crystal disorder, and electrode interface

effects [29–31]. An atomistic description of the filament

has been recently proposed [32], with a detailed investi-

gation of the role of oxygen vacancies in the switching.

In this article, we review and discuss the fundamental

aspects of the switching mechanism models developed

based on first principles calculations. A nanofilament for-

mation model is constructed and its implications for ‘‘ON’’

and ‘‘OFF’’ state conduction in TiO2 and NiO are

predicted.

Computational details

The structures and energies of oxygen deficient rutile TiO2

and cubic NaCl-type NiO were calculated using density

functional theory. In the past decade, several theoretical

investigations employed the local density (LDA) and the

gradient-corrected approximations (GGA), to calculate the

electronic band structure of transition metal oxides [33–

35]. Going beyond LDA and GGA, however, was neces-

sary, to correct for some of the most severe shortcomings

of the conventional LDA and GGA, i.e., the accurate pre-

diction of the energy band gap and the position of the

electronic defect states in the band gap. Recent theoretical

developments, as the addition of the on-site Coulomb

correction within LDA/GGA ? U [36], dynamical mean

field theory approaches [37], hybrid functional [38] and

GW implementations [39], have been very successful in

predicting realistic properties for these materials.

In this study, the electronic interactions are described

within the LDA/GGA ? U formalism for TiO2 and NiO,

where on-site Coulomb corrections are applied. While for

NiO the GGA ? Ud approach yields an acceptable band

structure, for TiO2 is necessary to go beyond LDA ? Ud

[14]. The on-site Coulomb corrections are applied on the

3d orbital electrons of Ti or Ni ions (Ud) for TiO2 and NiO,

respectively, and in addition on the 2p orbital electrons of

the O ions (Up), in the case of TiO2.

The density functional calculations were done using the

Vienna ab initio program package, (VASP) [40, 41], and

the projector augmented-wave (PAW) pseudopotentials

[42, 43]. An energy cutoff of 353 eV for TiO2, and 500 eV

for NiO was employed for the plane wave expansion. The

supercells size was chosen to minimize the spurious elec-

trostatic interactions between defect images. All the

structures were optimized at T = 0 K and vibrational and

entropic effects were not included. For k-point integration,

a Monkhorst–Pack grid of 8 9 8 9 12 grid for the TiO2

primitive cell, 4 9 4 9 4 for the Ti72O144 supercell, and a

2 9 2 9 2 grid for the supercell of Ni64O64 was used. The

O 2s22p4, Ti 3s23p63d24s2, and Ni 3d84s2 states were

considered valence electrons. All ions were allowed to

relax with energy convergence tolerance of 10-6 eV/atom

J Mater Sci (2012) 47:7498–7514 7499

123

and by minimizing the force on each atom to be less than

0.01 eV/A.

Oxygen vacancy-ordering effects in TiO2

Single oxygen vacancy in TiO2

The unit cell of rutile TiO2 is shown in Fig. 1. TiO2 n-type

semiconducting behavior was attributed to extra electrons

generated by intrinsic defects, such as oxygen vacancies

[44, 45]. The oxygen vacancy is found to induce a defect

state in the band gap, and the semiconducting behavior

depends on the position of the defect state relative to the

conduction band minimum (CBM). The determination of

the exact position of the oxygen vacancy defect state in

reduced transition metal binary oxides has been however a

long standing challenge of theoretical methods based on

density functional theory (DFT) [46–50]. The level of

accuracy in describing the electronic interactions is crucial

to obtain reasonable results. On the other hand, the com-

putational cost of more accurate methods such as GW [39]

or HSE [38, 49] for large supercells is a limiting factor for

their usage. Here we use the computationally efficient

LDA ? U approach and apply corrections on both the Ti

3d and O 2p electrons. The LDA ? Ud method with cor-

rections on the 3d electrons of Ti, had been employed in a

couple of earlier studies with different choices of the

optimal value of Ud. Calzado et al. [50] used the Ueff-d = Ud-J of 5.5-0.5 eV within the LDA ? U implemen-

tation the VASP code to correct the description of the

defect state. On the other hand, Deskins and Dupuis [51]

used a Ueffd value of 10 eV with the same code and found a

band gap in satisfactory agreement with experiment for

rutile TiO2. In most LDA ? Ud studies of transition metal

oxides, Ud values are fitted in an empirical way, but

schemes based on theoretical determination of the

U parameter had been also performed [52]. Within the

LDA ? Ud approach the Ud parameter was shown to affect

only the character of the conduction band and values higher

than 8 eV produce an unphysical description of the elec-

tronic interactions in TiO2 [14], partly because the con-

duction band states are rigidly moved up with increasing

Ud value (Fig. 2a). The results are dramatically improved,

when corrections are introduced additionally on the O

2p orbitals by employing the LDA ? Ud ? Up approach,

and we observe systematic shifts for both the valence and

Fig. 1 Unit cell structure of rutile TiO2 (P42/mnm)

Fig. 2 Energy band structure

and density of states calculated

by a LDA ? Ud and

b LDA ? Ud ? Up

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conduction bands (Fig. 2b). This combined approach pro-

duces a corrected band structure and the band gap energy is

in very good agreement with experimental data for TiO2. In

the oxygen deficient structure with a neutral oxygen

vacancy, Ti d electrons become localized and induce defect

states within the band gap. These electronic states are

strongly localized on the three Ti ions surrounding the

oxygen vacancy, composed of two equatorial and one

apical Ti. In Fig. 3, we show the partial density of states

corresponding to Ti ions for the Ud parameter of 7 and

8 eV. For Ud = 7 eV the defect states appear in the band

gap, but since the band gap is still underestimated their

relative position is not correct (Fig. 3a, b). Values above

8 eV for Ud induce additional defect states in the band gap,

and at the same time still underestimate the band gap, as

depicted in Fig. 3b, d for equatorial and apical Ti ions in

the vicinity of the oxygen vacancy. Electron localization

function [53] and interatomic distances between the nearest

Ti ions to an oxygen vacancy shown in Fig. 4a for

Ud = 7 eV and Fig. 4b for Ud = 8 eV point to the source

of this error, the unphysical repulsive interaction as the Ud

value is larger than 8 eV, from 3.58 A Ti–Ti distance to

3.82 A. When Up = 6 eV is introduced to correct for O

p orbital repulsion in addition to Ud = 8 eV for the

d orbitals of Ti the description is improved as shown in

Fig. 5a–b for the partial density of states and Fig. 5c

electron localization function. The interatomic distances

between nearest Ti–Ti ions become 3.54 A. With this

Fig. 3 Partial density of state of

two equatorial and one apical Ti

ions surrounding an oxygen

vacancy calculated by

LDA ? Ud (Ud = 7 eV and

8 eV). a Equatorial Ti

(Ud = 7 eV). b Equatorial Ti

(Ud = 8 eV). c Apical Ti

(Ud = 7 eV). d Apical Ti

(Ud = 8 eV). An additional

defect states is observed for

Ud = 8 eV

Fig. 4 Electron localization

function and corresponding

structural relaxation around

neutral oxygen vacancy

calculated by a LDA ? Ud

(Ud = 7 eV) and b LDA ? Ud

(Ud = 8 eV)

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combination of Ud and Up the band gap (Eg * 2.9 eV,

Exp. Eg = 3 eV), lattice parameters and the position of the

defect states are greatly improved.

The localization of electrons on the oxygen vacancy site,

occupying the defect state in the band gap is illustrated by

the band-decomposed charge density in Fig. 6. The defect

states are found to originate only from the nearest neigh-

boring Ti ions as stated above and also supported by the

partial density of states of Ti ions in the nearest and next

nearest neighbor shell around the oxygen vacancy (Fig. 7).

Within this method the defect state induced by an isolated

oxygen vacancy is at 0.4 eV below the CBM, in very good

agreement with experimental observations [45].

Positively charged vacancies in rutile TiO2 are found to

increase the interatomic Ti–Ti distance to 3.78 A for VO1?

and 3.98 A for VO2?, thus the extraction of electrons from

the vacancy site enhances the ionic character of Ti ions

(Fig. 8a, b). In the case of negatively charged vacancies the

interatomic distances first slightly decrease for VO1- at

3.53 A, then increase for VO2- to 3.59 A, with increasing

electronic electrostatic repulsion (Fig. 8c, d).

The doubly positively charged oxygen vacancy is found

to be stable over the neutral oxygen vacancy in a large

range of Fermi energy values (Fig. 9), with a transition to

singly positively charged vacancy around 0.7 eV and to the

neutral state around 0.5 eV below the CBM. The vacancy

formation energies show significant dependence on the

deposition conditions, i.e., Ti or O-rich environments

(Fig. 9b, c).

As the isolated oxygen vacancy induces a defect state

around 0.4 eV below the CBM, these states are too deep to

elevate electrons to the conduction band at room temper-

ature. Thus, to describe the n-type semiconductivity

observed experimentally in this material, the concentration

of vacancies needs to be increased and we investigated

their ordering trends.

Filament of ordered vacancy configurations in TiO2

A number of oxygen vacancy configurations had been

considered, ranging from di-vacancies, tri-vacancies to

four, five, six and eight vacancies in a supercell of

3 9 3 9 4 TiO2 (Fig. 10) to investigate the effect of

vacancy-ordering on the conduction properties of reduced

TiO2. Previously, Szot et al., [54] have examined the effect

of dislocations containing oxygen vacancies on the con-

duction properties in SrTiO3. More recently, the switching

between an insulating and conductive TiO2-x was associ-

ated with a phase transition to a Magneli phase in a fila-

ment that showed metallic conduction behavior [17].

Therefore, our investigation is directed towards character-

izing vacancy-ordering mechanisms, in which certain

configurations are found to exhibit properties of increased

metallic conductivity. Figure 11 shows the electron local-

ization function corresponding to the structures in Fig. 10.

By adding more oxygen vacancies, the localization of

electrons on the vacancy sites can be significantly altered,

based on the coordination number of vacancies. It is found

Fig. 5 Partial density of states of Ti ions surrounding the oxygen vacancy for a equatorial Ti and b apical Ti. c Electron localization function for

the same structure calculated with LDA ? Ud ? Up (Ud = 8 eV and Up = 6 eV)

Fig. 6 Band decomposed partial charge density distribution in TiO2

(110) plane containing one isolated single oxygen vacancy

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that 8 vacancies in a supercell, periodically repeated along

the [001] direction, stabilize the formation of a conductive

chain (Fig. 11b). The formation energy of these structures

(Fig. 12) decreases with the number of ordered vacancies,

and the [001] direction is energetically preferred. The

conductivity implications are shown in Fig. 13 for the 8

vacancies along [001] (Fig. 13a) and 6 vacancies along

[110] (Fig. 13b). The electron localization function, partial

density of states and band-decomposed charge density

corresponding to Ti ions in the first nearest neighbor shell

around the vacancy clusters along [001] are found to be

responsible for the increased conductivity. The equatorial

Ti ions induce discrete defect states with partial overlap

between them covering the entire band gap, and yielding

the metallic behavior. These Ti–Ti bonds involve strong

overlap of t2g-t2g type orbitals. We note that the [001]

direction with 8 vacancies/supercell has two rows of oxy-

gen vacancies, while [110] direction has 6 vacancies/

supercell in a single row. The single row of vacancies

along the [110] direction (Fig. 13b) induces defect states

from mid gap up to the conduction band. The band-

decomposed partial charge density including all the

vacancy induced defect states in the band gap is shown in

the lower row of Fig. 13 with an iso-surface of 0.1 e/A.

In order to investigate the thermodynamic stability of

ordered vacancy configurations along the [001] direction

with 8 vacancies/supercell, three randomly distributed

vacancy configurations R1, R2, and R3 containing also 8

vacancies/supercell were considered (Fig. 14a, b, c). In R1

the vacancies are randomly distributed in the supercell, in

R2 and R3 the vacancies are randomly distributed in the

same plane.

Fig. 7 a Schematic picture of

the (110) plane in rutile TiO2.

The partial density of states for

the nearest neighboring Ti ions.

b, c, d Ti ions as next nearest

neighbors from the oxygen

vacancy. e, f Nearest

neighboring O ions

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The vacancy formation energy was determined using the

following formula:

Evf ¼ E TiO2�xð Þ � E TiO2ð Þ þ nlO

where E(TiO2-x) is the total energy of a supercell con-

taining the oxygen vacancy, E(TiO2) is the total energy of a

perfect TiO2 in the same size of supercell, lO is the oxygen

chemical potential, and n is the number of oxygen

vacancies.

From Fig. 15, the ordered vacancy structure has the

lowest vacancy formation energy relative to all three ran-

domly configured vacancy structures of percolative nature.

The iso-surface of the band-decomposed charge density of

all defect states within the band gap for the random and

ordered oxygen vacancy configurations presented in

Fig. 14 are shown in Fig. 16. Entropic effects not included

in the present calculations may alter the relative stability of

these structures, however the random configurations had

been found to be less conductive than the ordered chain of

vacancies and behaving very similarly to the isolated

vacancy cases. The random vacancy configurations can be

stabilized during the material deposition, however once an

electric field is applied the vacancy-ordering process will

be favored to form a conductive filament. Then, for the

Fig. 8 Electron localization

function and structural

relaxations around a charged

oxygen vacancy using

LDA ? Ud ? Up (Ud = 8 eV,

Up = 6 eV). a VO1?, b VO

2?,

c VO1-, and d VO

2-

Fig. 9 Charged oxygen

vacancy formation energies in

rutile TiO2. a Unrelaxed in

Ti-rich condition, b relaxed in

Ti-rich condition, and c relaxed

in O-rich condition

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repetitive switching process of the memory, an order–

disorder transition can involve large diffusion barriers, thus

in the present study a filament cohesion–disruption

model supported by experimental observations [17] is

investigated.

We conclude that the oxygen vacancies act as mediators

of electron conduction, which is achieved through the

successive metallic Ti ions in the channel. Most of the

defect states originate from the Ti ions in the vacancy

chains, and the electronic charge density around them is

considerably enhanced compared to the stoichiometric

TiO2.

Fig. 10 Schematic picture of

oxygen vacancy clusters in

reduced rutile TiO2 (110).

a Vacancy-ordering in the [110]

plane, and b vacancy-ordering

in the [001] plane

Fig. 11 Electron localization function calculated for the structures shown in Fig. 10. a Vacancy-ordering in the [110] plane, and b vacancy-

ordering in the [001] plane

Fig. 12 Oxygen vacancy cluster formation energies along the [110]

and [001] directions in reduced rutile TiO2

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Fig. 13 Electron localization

function, partial density of

states of equatorial and apical Ti

ions surrounding oxygen

vacancies and partial charge

densities for the a vacancy-

ordered structure along [001],

and b vacancy-ordered structure

along [110]

Fig. 14 Schematic picture of the a R1, b R2 and c R3 random

configurations of oxygen vacancies and d the [001] ordered vacancy

chain in the 3 9 3 9 4 supercell of rutile TiO2. Red spheres denote

O; blue spheres are for Ti, and the black spheres represent the oxygen

vacancies (Color figure online)

7506 J Mater Sci (2012) 47:7498–7514

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Disruption of the ordered filament in TiO2

Considering the vacancy filament model incorporating an

ordered array of two rows of oxygen vacancies as the

model describing the conductive ‘‘ON’’ state of the mem-

ory operation, we further investigated how a transition to

the ‘‘OFF’’ state might take place during the switching

process of a memory operation. The proposed models are

shown in Fig. 17. The number of oxygen vacancies placed

away from the ordered filament is gradually increased from

1 VO-off (Fig. 17b) to 2 adjacent VO-off (Fig. 17c), and 4

adjacent VO-off (Fig. 17c). The implication of these

geometries to the conductivity is explored. For the 1 VO-off

structure the band-decomposed charge density corre-

sponding to the occupied defect states in the band gap

indicates that electronic conduction is still possible,

although the total number of defects states is reduced in the

band gap (Fig. 18e) compared to the ordered filament

(Fig. 18d). This arrangement corresponds to a conductive

‘‘imperfect filament’’, which might serve as a more realistic

model for the ‘‘ON’’ state, depending on the degree of

ordering and materials properties. For the 2 VO-off struc-

ture the band-decomposed partial charge density point to a

totally disrupted filament (Fig. 18c) and in the density of

states a small bandgap is observed. The electron

Fig. 15 Total energies calculated for the structures in Fig. 14

Fig. 16 Band decomposed charge density of defect states for the a R1; b R2; c R3 and d vacancy chain structure. The iso-surface corresponds to

0.1 e/A3

Fig. 17 Schematic picture of

the a the filament structure in

the [001] direction, b disrupted

filament obtained with one

vacancy away from the filament

(1 VO-off), c disrupted filament

with two vacancies away from

the filament (2 VO-off), and d 4

vacancies away from the

filament (4 VO-off)

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localization function for the filament and 1 VO-off and 2

VO-off structures are shown for the most stable charge state

corresponding to each configuration (Fig. 18g, h, i). The

degree of electron delocalization is decreasing as a more

vacancies are placed away from the filament structure.

The vacancy formation energies corresponding to the

arrangements presented in Fig. 17 are shown in Fig. 19. As

the number of vacancies placed away from the ordered

filament is increased, the stability of the charge states

changes from 1? to 2? for a wide range of the chemical

potential, i.e. Fermi level of the system. The filament and

the 1 VO-off arrangement are most stable in the 1? state.

Here and in the following the 1? notation refers to the

average charge per vacancy, i.e., all eight vacancies are

depleted by one electron. However, when more than two

vacancies are placed away from the filament the transition

state between the 2? and 1? states falls closer to mid gap

and yields a larger range of stability for the 2? state/

vacancy. We note that the isolated vacancies were also

found to be stable in the 2? state for a wide range of the

chemical potential, up to 0.7 eV below the CBM (Fig. 9).

Thus, the transition between an ordered and disrupted fil-

ament is found to be accompanied by a change in the

charge state that can be induced by the applied electric field

during the memory operation. A schematic picture of the

‘‘ON’’ to ‘‘OFF’’ transition [20] based on charge state

change is depicted in Fig. 20a. The calculated cohesive

energies of a filament formation relative to isolated

vacancies in bulk TiO2, in the three charge states, as

defined in Ref. 20, are shown in Fig. 20b, further confirm

Fig. 18 Upper row band decomposed partial charge density for the

neutral oxygen vacancy chain in: a the filament, b 1 VO-off and c 2

VO-off structures. Middle row total density of states corresponding to

the most stable charge state of each structure d 1? for filament e 1?

for 1 VO-off and f 2? for 2 VO-off. Lower row electron localization

function for the most stable charge state for each structure g 1? for

filament, h 1? for 1 VO-off and i 2? for 2 VO-off

7508 J Mater Sci (2012) 47:7498–7514

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the finding that the filament formation is energetically

preferred if the average charge per vacancy is neutral or 1?

[20].

Oxygen vacancy-ordering effects in NiO

Single oxygen and nickel vacancies in NiO

The unit cell of NiO has cubic symmetry and is of NaCl-

type (Fig. 21). NiO had been proposed to have p-type

conductivity. Isolated single oxygen and nickel vacancies

in a supercell Ni64O64 were considered to elucidate the

nature of this property. GGA ? Ud was employed in all the

calculations for NiO, and the Ud was chosen in accordance

with previous studies [56]. Partial densities of states are

shown in Fig. 22 for neutral, 1- and 2- charge states for Ni

Fig. 19 Oxygen vacancy

cluster formation energies for

a a connected vacancy filament,

b 1 VO-off, c 2 VO-off and d 4

VO-off structures, in the neutral,

1? and 2? charge states

Fig. 20 a Schematic picture describing a possible ‘‘ON’’ to ‘‘OFF’’

transition by the cohesion and disruption of the conducting channel

formed by charged oxygen vacancies. b Cohesive energy as a

function of the charge state of the oxygen vacancy chain model

relative to the isolated oxygen vacancy configurations

Fig. 21 Unit cell for NiO (NaCl-type, Fm-3 m)

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Fig. 22 Partial density of states for a Ni vacancies and b O vacancies in NiO

Fig. 23 Band gaps and defect

states positions of a Ni

vacancies and b O vacancies, in

reduced NiO

Fig. 24 Formation energy of

charged vacancies in reduced

NiO a VNi, b for VO

Fig. 25 Schematic picture of the disrupted filament obtained by moving one oxygen atom into a vacancy site. The considered positions for the

vacancy 1 VO-off away from the filament are a A position, b B position, or c D position

7510 J Mater Sci (2012) 47:7498–7514

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vacancies (Fig. 22a) and neutral, 1? and 2? charge states

for O vacancies (Fig. 22b). Defect states near the valence

band maximum are observed for Ni vacancies, while the

oxygen vacancies induce gap states closer to the mid gap.

With the introduction of charge defects the band gap is

slightly altered ranging from 3.41 eV for neutral Ni

vacancies to 3.14 eV for the 2- state (Fig. 23a). For the

neutral Ni vacancy there is an additional perturbation close

to the conduction band. A defect state in the proximity of

the valence band maximum at *0.37 eV is depicted. For

the neutral oxygen vacancies defect states are found around

1.3 eV above the valence band maximum and at 0.3 eV

below the CBM. As the vacancy becomes more positively

charged several defect states are created throughout the gap

and the band gap is decreased from 3.66 eV (neutral) to

3.41 eV (2?) (Fig. 23b).

The as-deposited NiO samples had been found nickel

deficient. We show that the vacancy states of charged

nickel vacancies are stable for EF near the valence band

maximum as shown in Fig. 24a. The transition states of

nickel vacancies are 0.04 eV for q = -1 and 0.16 eV for

q = -2. These low energies for acceptor-like states support

the possibility of p-type conductivity in Ni-deficient NiO

films observed in experiments [56]. After the forming

process, oxygen vacancies were shown to generate [25] and

cluster due to the favorable interaction between oxygen

vacancies [55]. Based on formation energy calculations

(Fig. 24b), the stable charge state of oxygen vacancy is

found to be 2? closed to the valence band, then a neutral

vacancy is stabilized in the mid gap region and a transition

is observed to 1- around 3 eV below the CBM.

Filament formation and disruption in NiO

To describe the ‘‘ON’’ state conduction in NiO a filamen-

tary arrangement of six ordered oxygen vacancies in two

Fig. 26 Total density of states for the reduced NiO supercell structures with vacancy off configurations shown in Fig. 25

Fig. 27 Band decomposed

partial charge density for the

(110) plane, within (EF,

EF ? 0.3 eV) window for the

a ‘‘ON’’ state (filament),

b ‘‘OFF’’ state (vacancy off

structure). Total density of

states corresponding the

c ‘‘ON’’ state and d ‘‘OFF’’ state

J Mater Sci (2012) 47:7498–7514 7511

123

rows along the h110i direction were chosen. For the

‘‘OFF’’ state, we investigate the possibility of the oxygen

vacancy sites in the filament becoming occupied by oxygen

ions diffusing from adjacent sites [41]. We have considered

three different positions of diffusing oxygen ions denoted

A (Fig. 25a), B (Fig. 25b) and D (Fig. 25c) in the neigh-

boring shells around the filament arrangement. The oxygen

vacancy coordination number varies for these structures.

These positions are similar to the 1 VO-off arrangement

type described in the section for TiO2. In this section

however, we have also explored the effect of various

oxygen vacancy coordination shells on the conduction and

filament stability. The structures corresponding to the A

and B positions from Fig. 25 for the 1 VO-off arrangement,

induce a semiconducting band gap of 0.25 eV (A) and

0.6 eV (B) and exhibit reduced conductivity based on the

total densities of states plotted in Fig. 26a, b. On the other

hand, a weak metallic character is observed for the oxygen

vacancy in position D (Fig. 26c). While in the nearest

neighbor shell of the oxygen vacancy in position A there is

only one vacancy, in the B position there are two oxygen

vacancies and for the D position there are four nearest

neighbor oxygen vacancies. The vacancy–vacancy inter-

actions in NiO had been previously found to be stronger in

nearest neighbor di-vacancies [55] and stabilize these

configurations. Therefore, the position in D may corre-

spond to an intermediate state in the switching process and

could be similar to the ‘‘imperfect filament’’ observed in

TiO2 showing reduced conductivity, but being still weakly

metallic.

Electron localization functions and total density of states

for the ‘‘ON’’ state and the ‘‘OFF’’ state with the largest

band gap (A) are shown in Fig. 27. The charge integrated

around Ni ions in the filament case has 9.8 e/Ni around the

vacancies in the middle of the supercell, which also have

the largest nearest neighbor vacancy coordination. The

Fermi level is positioned in a band dominated by the spin-

down electron component (Fig. 27a). The 4 metallic nickel

ions surrounded by oxygen vacancies dominate the density

of states near EF for the proposed ‘‘ON’’ state configura-

tion. In average there are 9.8 electrons localized near each

Ni site, which account for the metallic conduction observed

through the metallic nickel ions. On the other hand, when

one oxygen atom is moved into a vacancy site in the

middle of the supercell, the neighboring Ni ions reduced

their charges to 9.6 e/Ni, while those placed between the

filament and the new vacancy site increased their charge to

9.2 e/Ni. These Ni ions contribute to the defect states

below the Fermi level in the band gap, while those with

only one vacancy in the nearest neighbor shell contribute to

the states below the CBM.

The calculated band decomposed charge density for the

‘‘ON’’ state is shown in Fig. 28a, and for the ‘‘OFF’’ state

in Fig. 28b. Figure 28 shows the band-decomposed partial

charge density for different regions in the band gap (EF,

EF ? 0.3 eV), (EF - 0.25 eV, EF) and (EF - 0.45 eV,

EF - 0.28 eV) describing the formation (a) and disruption

(b) of the filament. In the case of ordered oxygen vacancy

chain (Fig. 28a) the metallic type Ni ions have a strong

contribution to the defect states at the Fermi level.

Fig. 28 Band decomposed

partial charge density

corresponding to the various

regions in the band gap around

the EF a for the ‘‘ON’’ state,

b for the ‘‘OFF’’ state

7512 J Mater Sci (2012) 47:7498–7514

123

As mentioned above, the Ni ions outside the filament, but

within the first coordination shell around the vacancies

induce the low-lying defect states close to the valence

band. With an applied voltage if the Fermi level is repo-

sitioned in the band gap towards the conduction band, the

Ni ions from the center of the filament may have the most

significant contribution. In contrary, for a disrupted fila-

ment (Fig. 28b) the Ni ions participating in the filament do

not retain a main role in their neutral charge state, however

localized conductive clusters are observed around the Ni

ions outside of the filament with a coordination of at least

two oxygen vacancies. The filamentary Ni ions show a

more localized nature and would contribute to the con-

duction if the system becomes negatively charged under an

applied electric field. Based on an experimental investi-

gation of NiO, Jung et al. [57] had shown evidence that

weak metallic conduction and correlated barrier polaron

hopping coexist in the high-resistance off state.

As a general remark on elucidating the role of oxygen

vacancies in the resistive switching, assuming that the

transition between ‘‘ON’’ and ‘‘OFF’’ states is described by

oxygen migration in and out of the filament for materials

like TiO2 and NiO, we have found that a very small amount

of oxygen migration may change the conductivity drasti-

cally. Also, the possible variation of the exchanged oxygen

site during the memory operation may induce randomness

in the switching process, and influence the retention time of

the memory.

Conclusions

The ‘‘ON’’ and ‘‘OFF’’-state implications of vacancy-

ordering/disordering on the conduction mechanism were

discussed based on first-principle calculations for rutile

TiO2 and cubic NiO incorporating oxygen vacancies. The

formation and disruption of a conductive channel between

nearest metals (i.e. Ti or Ni ions in the filament) were

investigated. It was found that the oxygen vacancy chains

could mediate the conduction. When the oxygen vacancy

concentration is further increased and the vacancies

become nearest neighbors significant charge redistribution

is observed, which ultimately enhances the metallic nature

of the interaction between nearest Ti and Ni ions, respec-

tively. We predict that the electronic transport can be

described as defect-assisted tunneling through the channel

of Ti and Ni ions in these binary metal oxides.

Acknowledgements The Stanford Non-Volatile Memory Technol-

ogy Research Initiative (NMTRI), and the Marco Focus Center

(MSD) sponsored this study. The computational study was carried out

using the National Nanotechnology Infrastructure Network’s Com-

putational Cluster at Stanford.

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