Reduction of Monoclinic HfO2: A Cascading Migration of Oxygen and

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On the Reduction of Monoclinic HfO: A Cascading Migration of Oxygen and Its Interplay with a High Electric Field Boubacar Traoré, Philippe Blaise, and Benoit Sklénard J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b06913 • Publication Date (Web): 07 Oct 2016 Downloaded from http://pubs.acs.org on October 12, 2016

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The Journal of Physical Chemistry

On the Reduction of Monoclinic HfO 2: A Cascading Migration of Oxygen and Its Interplay with a High Electric Field

Boubacar Traoré,

†,‡,¶,§

Philippe Blaise,

∗,¶,§

and Benoît Sklénard

¶,§

†Fondation Nanoscience, 25 rue des Martyrs, 38000 Grenoble, France ‡Institut de Microélectronique Electromagnétisme et Photonique, Laboratoire

d'Hyperfréquences et de Caractérisation (IMEP-LAHC); Grenoble Institut Polytechnique (INP), Grenoble 38000, France ¶Univ. Grenoble Alpes, F-38000 Grenoble, France §CEA, LETI, MINATEC campus, F-38054 Grenoble France E-mail: [email protected]

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Abstract Using density functional theory, we investigated the formation of an extended Frenkel pair (EFP) in monoclinic m-HfO2 which we propose to be a prototype defect in oxide reduction by an intense electric eld. We studied an emission mechanism that involves the cascading migration of 3-fold coordinated O atoms along the [00¯1] direction leading to a well separated pair of oxygen vacancy (VO )/oxygen interstitial (Oi ). For the neutral case, the calculated energy barrier at 5.2 eV is in good agreement with the activation energy value extracted from time to breakdown tests supporting a thermochemical model for oxygen extraction from HfO2 . An associated net dipole develops itself along the calculated emission path leading to an estimated critical electric eld of 10 MV/cm. The role of charge injection on EFP formation and diusion is also studied and shows a consequent lowering of the activation energy to 2.9 eV. The electroforming of an oxygen poor lament is commented in the framework of resistive random access memories.

Introduction Hafnium dioxide is widely used in microelectronic industry as a gate dielectric for complementary metal oxide semi-conductor (CMOS) devices 1 and more recently as a resistive layer in resistive random access memory (RRAM) technology. HfO 2 is deposited in thin nanometric layers via chemico-physical techniques which produce a stoichiometric insulating layer of a very good quality: large forbidden band gap of around 5.6 eV, high dielectric constant (22-25) and low leakage current. Practically, HfO 2 is fabricated between two electrodes made of a metal (Pt, Ti, TiN etc.) or a semiconductor (Si, Ge). Based on the electrodes chemical reactivity with oxygen, the quality of HfO 2 may be modulated at the interfaces while its bulk properties are usually preserved. Under operating conditions, by applying a few volts to the electrodes, the thin oxide layer is subjected to an intense electrical stress which can permanently modify its properties due to the appearance of new defects inside 2


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the dielectric. Hence, oxide degradation is intimately related to reliability issues of CMOS devices. Moreover, the emergence of oxide based resistive memories (OxRRAM) has intensied the interest in bringing sound microscopic details on the processes leading to oxide reduction. The reason being that qualitatively the operation of an OxRRAM relies on the quasi-reversible breakdown of the oxide layer sandwiched between two metal electrodes involving the creation and rupture of oxygen poor conductive paths generally referred to as

conductive laments (CF). 27 For RRAM, this quasi-reversible breakdown, usually referred as electroforming or just

forming, has been attributed to a combined eect of temperature and electric eld. 2 More specically, in order to explain the valence change of Hafnium atoms experimentally observed during the forming step, 8 two scenarios cohabit: 7 one is based on oxygen Frenkel pair emission inside the dielectric layer, 3 while the other is based on an oxygen transport mechanism related to the oxygen vacancy exchange layer between the dielectric and the anode. 7,9 Thus, understanding the redox mechanisms behind oxide degradation and OxRRAM electroforming is of major concern. With regards to device physics coming mainly from time dependent dielectric breakdown (TDDB) tests, a thermochemical breakdown model suggesting a strong relationship between the breakdown eld, the oxide formation enthalpy and the dielectric constant was proposed by McPherson et al. 10 while a model based on hole generation due to impact ionization was proposed by Chen et al. 11 Although both models were capable of explaining to some extent dierent TDDB data, they obscure any redox phenomena and do not provide a convincing mechanism for oxide breakdown at the atomic level. Among HfO2 defects, we propose to study the oxygen Frenkel pair (FP) in monoclinic hafnia (m-HfO2 ) as the prototype defect that leads to oxide degradation related to oxygen loss. This defect consists of an oxygen atom that leaves behind an oxygen vacancy (V O ) and sits in an interstitial (O i ) position resulting in a V O /Oi pair. Both intimate (IFP) and extended (EFP) Frenkel pair terminologies have been used in the literature. IFP refers to

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closely distanced V O and Oi (0.9 - 1.7 Å). 12,13 EFP refers to largely separated V O and Oi with either Oi going to an interface electrode 14,15 or Oi remaining at a distance greater than a unit cell parameter. Both scenarios involve a diusion mechanism before any recombination. 16 Öttking et al. 12 investigated IFP formation and diusion in m-HfO 2 and found that neutral IFPs are not stable with O i snapping back into V O while charged IFP could have metastable energy states, as latter conrmed by Bradley et al. 13 However, IFP position is an intermediate state towards EFP formation, the latter being required to push oxide degradation toward dielectric breakdown or lament formation. On another side, Demkov 14 showed that EFP formation is favored across Mo/HfO 2 interface but did not investigate its generation in the oxide bulk. Thus, we propose to investigate EFP formation in HfO 2 which could be at the heart of redox mechanisms under a high electric eld. Moreover, the role of carrier injection in oxide degradation is of major importance and has also to be dealt with microscopically.

Method For the calculations, we used Density Functional Theory (DFT) 17,18 as implemented in SIESTA 19 with numerical atomic orbitals. We used the Generalized Gradient Approximation (GGA) with Perdew-Burke-Ernzerhof (PBE) functional to describe the exchange-correlation term. 20 Hf and O species are described with Troullier-Martins pseudopotentials 21 with 6s2 5d2 and 2s2 2p4 conguration respectively. Relativistic and non linear core corrections were applied to Hf pseudopotential. Optimized Double Zeta Doubly Polarized (DZPP) basis sets with an energy shift of 50 meV and a Mesh cut-o of 400 Rydberg were used for the calculations. A monoclinic HfO 2 supercell with 2 × 2 × 4 dimensions, space group P2 1 /c, with 192 atoms was considered for all the calculations in order to minimize image charge interaction and allow for long range migration of EFP in the [00 ¯ 1] direction. The Brillouin zone was sampled with a 2 × 2 × 1 mesh. For the optimization of the supercells geometry and atomic positions, the maximum residual forces and stresses were 0.02 eV/Å and 200 MPa

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respectively. Defects diusion barriers were calculated using the climbing image nudged elastic band (CI-NEB) technique 22 as implemented in Atomistic Simulation Environment (ASE) package 23 with more than 20 intermediate images converged below 0.1 eV/Å. Charge analysis was carried out with the Bader charge decomposition method. 24

Results and discussion Frenkel Pair Stability The thermodynamic stability of point defects related to O and Hf has been largely studied for the m-HfO2 ground state 16,2527 using eq. 1 obtained from standard thermodynamics analysis,

∆HD f

±q

= U(D±q ) − U(HfO2 ) + µD ± q(∆V + V B + F )

(1)

where U(D±q ) is the total energy of the supercell with a defect D charged ±q , U(HfO2 ) the energy of pristine HfO 2 , µD the chemical potential associated to the defect, ∆V the valence band oset between the pristine and the defective system, V B the top of valence band, F the Fermi level measured from the top of valence band and q the net charge in number of electrons. An EFP can be formed by an oxygen atom or a hafnium atom. In both cases, the system can minimize its Coulombic energy by maximizing the charge exchange between 4− vacancy and interstitial forming an O i2− /VO2+ pair or a Hfi4+ /VHf pair. Using the formation

energies we obtained for point defects in Table 1 (our results are similar to those reported by Zheng et al. 25 ), the corresponding energies of formation for a neutral EFP consisting of well separated defects are respectively ∆Hf (EFPHf ) = 10.71 eV and ∆Hf (EFPO ) = 4.97 eV. For Hf vacancies, the positions are all equivalent while for O the lowest energy is obtained for a 3-fold coordinated oxygen atom. Together with the strong oxygen mobility experimentally

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Table 1: Point defects and oxygen extended Frenkel pair (EFP) formation energies ∆Hf in m-HfO2 at valence band maximum, (without image charge correction). For point defects, the chemical potential of oxygen µO corresponds to molecular O2 while µHf corresponds to hcp-Hf. For EFP, ∆Hf is obtained for a Oi /VO pair separated by ∼ 10Å and δE is the energy dierence between EFP and corresponding sum of individual point defect energies. Defect

∆Hf (eV) µ = µO

µ = µHf

V0o3 (V0o4 )

6.54 (6.46)

1.12 (1.04)

1+ V1+ o3 (Vo4 )

3.66 (4.08)

-1.76 (-1.34)

2+ V2+ o3 (Vo4 )

1.09 (1.80)

-4.33 (-3.62)

O0i

1.50

6.92

O1− i O2− i 4− VHf Hf4+ i

2.93

8.35

3.88

9.30

6.48

17.32

4.23

-6.62

∆Hf (eV) 30

δ E (eV)

10.38 7.64 5.15 4.11 2.53

-0.04 +0.10 +0.18 +0.09 -0.06

EFP2− → V0o3 + O2− i 2− EFP1− → V1+ + O o3 i 2− EFP0 → V2+ + O o3 i 1− EFP1+ → V2+ o3 + Oi 0 EFP2+ → V2+ o3 + Oi

observed in HfO2 , 28,29 the large energy obtained for Hf EFP supports a degradation scenario solely based on oxygen. In order to evaluate the oxygen EFP stability and the eect of carrier injection, we generated an EFP inside the 2 × 2 × 4 m-HfO2 supercell with 3-fold coordinated O i and VO , separated by a distance of approximately 10 Å as shown in Fig. 2c. By relaxing the EFP with various charge states, we evaluated its formation energy using the following formula:

∆HEFP f

±q

= U(EFP±q ) − U(HfO2 ) ± q(∆V + V B + F )

6


(2)

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where U(EFP±q ) is the total energy of the supercell with EFP charged ±q , and other quantities are as previously dened except the oxygen chemical potential which cancels out. The results obtained at F = 0 are shown in Table 1 together with the dierence in energy δ E between EFP and the sum of corresponding point defect energies. The residual interaction energy δ E lower than 0.2 eV validates the extended character of our conguration, where VO and Oi can recombine or move further away as independent charged point defects inside HfO2 , (see the following paragraphs). The EFP stability over the whole forbidden gap is shown in Figure 1. Due to a well known deciency in GGA, the gap is underestimated at 3.7 eV against the experimental 5.6 eV. This leaves uncertain the formation enthalpy and position of transition levels for charged defects. +2

10

EFP +1 EFP 0 EFP -1 EFP -2 EFP

9

7

EFP

(eV)

8

6

∆Hf

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


5 4 3 2

0

0.5

1 2 1.5 2.5 Fermi level (eV from VB)

3

3.5

Figure 1: Formation enthalpy of charged oxygen EFP inside m-HfO 2 using DFT/GGA as a function of the Fermi level obtained with eq. 2. The EFP charged ±2 are the most favorable states when F is close to m-HfO2 valence band and conduction band respectively. Otherwise, neutral EFP is the most probable charged state. Nevertheless, the qualitative result obtained in Figure 1 shows that EFP ±2 are more favorable nearby the band edges thanks to the following oxidation and reduction reactions:

2− 0 2− − EFP2− = EFP0 + 2.e− = V2+ O + Oi + 2.e → VO + Oi

(3)

2− 2+ 0 − EFP2+ = EFP0 − 2.e− = V2+ O + Oi − 2.e → VO + Oi

(4)

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The charge exchange considered here is adiabatic and in equilibrium with a reference level F . In real device operating conditions, carrier injection is related to device polarization with a high electric eld in MV/cm. This usually triggers a tunneling current which dramatically increases up to the breakdown of the dielectric. Therefore, carrier injection is an out-of-equilibrium process which is actually thought to be related to polaronic eects inside HfO2 . 31 Taking into account such a non equilibrium condition goes beyond the scope of our contribution. Here, we treat the eect of a charge exchange in equilibrium with defects with a level of carrier injection localized nearby the band edges which is compatible with a permanent high electric eld applied to a thin dielectric. Therefore, in the following, we will focus on the neutral EFP case and the injection of two electrons which can be favored in the case of metallic electrodes usually employed in OxRRAM technology, (see discussion section).

Charge Analysis Knowing that HfO2 is an ionic insulator, in order to understand qualitatively its charge partition, Table 2 gives the Bader charge values obtained for the atomic sites and point defects of interest. Note that the Bader charge analysis which is fully justied for atoms and molecules has to be adapted for a solid: for a vacancy, the reported value is a mean of the rst neighbors of the corresponding removed atom. As can be seen, the Bader charge of V 2+ O diers notably from V 0O and approaches that of an on-site Hf. Reciprocally, the charge of diers from O0i and approaches that of an on-site O. This will allow us to interpret the O2− i charge exchange that takes place along the emission path of an oxygen EFP.

Neutral EFP Emission For m-HfO2 , O atomic diusion is known with a low energy of activation below 0.8 eV in the neutral case and as low as 0.1 eV and 0.2 eV when O is negatively charged with one and two electrons respectively. 28,32 This diusion process involves an oxygen interstitial that 8


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Table 2: Bader charge analysis of site atoms and point defects in m-HfO 2 . The charge on VO corresponds to the mean charge of neighbor Hf atoms around V O . O3 and O4 are for 3-fold and 4-fold coordinated O atoms in m-HfO 2 . Perfect HfO2

HfO2 with defects

Site atom

Bader charge |e− |

Defect

Bader charge |e− |

Hf

+2.71 (+2.73 4 )

V0o3 (V0o4 )

+2.33 (+2.36)

O3

-1.28 (-1.34 4 )

1+ V1+ o3 (Vo4 )

+2.60 (+2.57)

O4

-1.43 (-1.39 4 )

2+ V2+ o3 (Vo4 )

+2.67 (+2.64)

O0i

-0.76

O1− i

-1.04

O2− i

-1.34

migrates through the bulk system by an exchange mechanism between neighboring oxygen atoms of the same 3-fold coordination for each charge state. We propose an oxygen emission process based on this mechanism illustrated in Figure 2 with ve 3-fold oxygen atoms that are involved in long range diusion along the [00 ¯ 1] direction. The rst oxygen atom O 1 replaces the site O2 leaving behind an oxygen vacancy. Then, the O 2 atom takes the site of O3 which subsequently pushes O 4 and O5 into an interstitial position. The corresponding cascade of displacements obtained by successive NEB calculations is highlighted in Fig. 2b with the nal conguration obtained shown in Fig. 2c. Fig. 2b,c corresponds to the neutral case knowing that by injecting 2 electrons, the structure of the other charge state diers mainly by local displacements around the moving oxygen atoms. The full energy barrier prole obtained for the long range emission of an oxygen EFP 0 is shown Figure 3. The reaction coordinate is the cumulative norm of the global displacement vector computed for all the atoms of the supercell. 33 The maximum of the reaction coordinate is of the order of the distance between O 1 and O4 atoms (∼ 8 Å) and can be more or less expanded depending on the local rearrangements that occur during diusion. As pointed out by the arrow in Fig. 3a, the barrier height for EFP 0 emission is close to its formation enthalpy from Figure 1. Close to the maximum of the reaction coordinate, we 9



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Figure 2: Diusion path for the emission of an oxygen EFP along the [00 ¯ 1] direction in m-HfO2 . The ve (3-fold) oxygen atoms involved are labeled in the top panel, the cascade of displacements is visualized in the middle panel with a dierent orientation, the nal conguration after EFP emission is shown in the bottom panel. O atoms are in red, Hf in blue. obtain a relatively at energy prole insuring that a transition state has been reached (we veried that the tangential force is almost null for the energy extremum). In this way O 5 , which is located at the end of the cascade of displacements, loses its mechanical and electrostatic interactions with the generated V O and can, in principle, pursue its migration with a low activation energy as low as 0.1-0.2 eV as expected for a negatively charged interstitial, (see below for the charge analysis). The diusion prole also shows that recombination is almost spontaneous requiring no more than 0.1 eV in order to diuse the interstitial back to 10


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6.0 0

EFP

Energy (eV)

5.0

a)

4.0 3.0 2.0 1.0

-

Oi charge |e |

0.0

b)

-1.1 -1.2 -1.3 -1.4

c)

-

VO charge |e |

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2.7

2.6

0

1

2

3

4

5

6

7

8

9

Reaction Coordinate in Å

¯] Figure 3: Diusion energy prole for the emission of a neutral oxygen EFP along [00 1 direction in m-HfO 2 (top panel). An arrow is positioned at the corresponding enthalpy of formation for EFP0 . The Bader charge analysis along the diusion path is also shown for the O4 interstitial position noted O i (middle panel) and for the vacancy position V O (bottom panel). Relevant bader charges obtained from Table 2 are indicated by dotted lines. the oxygen vacancy. In the case of EFP0 , an activation energy of 5.23 eV is calculated. This value is remarkably compatible with the experimental zero-eld activation energy of 4.6 eV extracted from time to breakdown measurements and statistical analysis with a percolation model applied to HfO2 samples as reported by Padovani et al. 34 The smooth energy curve obtained for EFP0 is supported by the fact the O i and VO sites keep their respective charge states −2 and +2 all along the cascade of displacements as supported by the charge analysis in the 2+ middle and bottom panels of Figure 3. Therefore, O 2− i and VO develop a long range electro-

static interaction inside the dielectric medium which is akin to a dipole with a characteristic distance of one nanometer. An external electric eld applied to the dielectric would then be

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able to couple with this dipole by generating an EFP.

Dipolar moment A rough evaluation of the dipole associated to EFP 0 emission using Bader charges would be possible. Nevertheless the atomic movements are correlated as illustrated Figure 2 with two electrons traveling along the cascade of displacements from O 1 to O5 , (see next paragraph). Therefore, it seems more relevant to use a direct evaluation of the dipolar moment using eq.5:

P~ =

Z ρ(~r).~r d~r V

(5)

where V is the volume of the supercell and ρ(~r) is the total charge density. Due to periodic boundary conditions this standard formula can not be used as it is, see for example Martin. 35 Knowing that we want to extract the contribution coming essentially from the EFP 0 creation which contributes as a localized dipole inside the supercell volume, we replace the standard formulation by eq.6:

∆P~ =

Z ˜ V

(ρ(~r) − ρ0 (~r)).~r d~r

(6)

˜ indicates that where ρ0 (~r) is the total charge density of the initial conguration and V the calculation is done by xing the coordinates of all the atoms on the edges of the supercell in order to get rid of relaxation eects as if the periodic images of the supercell were not aected by the EFP. Note that this procedure looks like a Lorentz-Lorenz analysis used in dielectric response and eectively employed by McPherson 10 in order to model dielectric breakdown. Fixing the atomic positions on the edges of the supercell modies a priori the diusion mechanism. Indeed we obtained a diusion prole which is almost the same with a slight increase of the activation energy at 5.58 eV instead of 5.23 eV. The obtained result for the Z component of the dipole is shown Figure 4 knowing that the contributions from X and 12


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Y components remain small as expected due to an elongation axis along the [00 ¯ 1] direction. 6.0 5.0

-

PZ (e .Å)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


4.0 3.0 2.0 1.0 0.0 0

1

7 2 3 4 5 6 Reaction Coordinate in Å

8

9

Figure 4: Evolution of the Z component of the dierential dipolar moment along the reaction coordinate, see eq.6, for EFP 0 . The dipole increases up to a maximum value corresponding to O-2 i emission. The extracted dipole increases almost monotonically along the reaction path, reaching a maximum value of 5.6 e− .Å at the saddle point of the barrier. This value is in good agreement with the estimated value of McPherson 36 in between 4.4 and 10.2 e− .Å using an empirical approach rather than ab initio. Moreover, using a Lorentz relation for the local electric eld that couples with the dipolar moment the breakdown eld can be estimated by 36

EBD =

Ea p0 . 2+3 k

(7)

with Ea the activation energy at 5.23 eV, p 0 the maximum of PZ at 5.6 e− .Å, k the dielectric constant of m-HfO 2 at 25. This leads to a breakdown electric eld of 10 MV/cm in good agreement with what is known from experimental measurements for capacitors made with HfO2 thin lms. 37 Therefore, the breakdown eld can be seen as the eld intensity required to extract an oxygen atom from its equilibrium position inside HfO 2 , suciently far away, to avoid its instantaneous recombination with the formed oxygen vacancy, leading to a well separated Frenkel pair.

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Electron Injection We further analyze the electron injection which is favored for a Metal-Insulator-Metal MIM structure as implemented in RRAM technology. For the non neutral case, the activation energy for EFP 2− is 2.92 eV as a result of charge injection, Fig. 5a. By looking at the Bader charge analysis in Fig. 5b,c a global charge 2− rearrangement is visible along the diusion paths: EFP 2− starts with a V2+ pair and O /Oi

ends up with a V0O /O2− pair. An inection is detected at 2 Å which corresponds to the i injection of the two electrons from the conduction band towards the oxygen vacancy with an energy around 1.8 eV similar to the barriers of 1.61 12 and 1.96 13 eV calculated for the intimate IFP2− . Then, the resulting O −2 is able to pursue its diusion with a 0.17 eV nal i step in between 7.2 and 9.2Å related to the diusion of an oxygen interstitial anion with an activation energy of 0.2 eV as expected for an isolated defect. 28,32 To conrm our charge injection analysis, Figure 6 shows the evolution of the density of states (DOS) along the EFP 2− emission path. Right after the inection point in energy detected in Figure 5, several pics appear right below the conduction band and above the valence band. At rst look, they can eectively be attributed respectively to a neutral oxygen vacancy and a negatively charged oxygen interstitial. 25,26 We also drew the contour plot of the square module of the wave functions for the last occupied states in Figure 7 at the point where the pics appear inside the forbidden gap of HfO2 . As can be seen, the two highest occupied states are localized on the newly created oxygen vacancy (in pink) and the following two occupied states are localized on O 1 and O2 oxygen atoms (in blue) that constitute the beginning of the cascade of displacements. First, this explains the overall energy reduction of the EFP 2− emission as compared to EFP 0 due to the screening of neutralized V O and the equivalent O 2− i . Then, by performing the same wave function analysis along the diusion path (not shown), the negative charge is shared and drifts along the O 1 , O2 , O3 , O4 up to O5 interstitial during the cascade displacement. Eventually, by looking at the tangential component of the force Figure 5, we have to 14


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4.0

Energy (eV)

3.0

Oi charge |e |

-2

-1.1

a)

EFP Force

2.0 1.0

-

0.0

-

b)

-1.2 -1.3 -1.4

VO charge |e |

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


c)

2.7 2.6 2.5 2.4 2.3

0

1

2

3

4

5

6

7

8

9

10

Reaction Coordinate in Å

¯] direction combined with the correFigure 5: Diusion energy prole for EFP 2− along [001 sponding tangential force on each NEB image during the emission process in red, (same scale but in eV/Å). At the inection point around 2 Å electrons localization occurs on V O , but the maximum force on the image is not close to zero as expected for a transition state. The Bader charge analysis along the diusion path is also shown for the O 4 interstitial position noted Oi (middle panel) and for the vacancy position V O (bottom panel). Relevant bader charges obtained from Table 2 are indicated by dotted lines. point out that the energy extremum at 1.8 eV corresponding to the inection point at 2 Å is not a standard transition state due to a discontinuity related to the adiabatic transition of two electrons from the conduction band toward the localized states of the oxygen vacancy as illustrated Figure 6 and Figure 7.

Discussion and Conclusion In summary, we presented an atomistic view of processes related to the electroforming of m-HfO2 through the formation and diusion of an oxygen extended Frenkel pair. We studied

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60 40 20

R = 0 Å

0 60

-

DOS (e /eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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40

R = 2.0 Å

20 0 60

-

e injection

40

R = 2.6 Å

20 0 60 40 20 0 -5

R = 9.2 Å -4

-3

-2

-1

Oi 0

2-

VO 1

2

0

3

4

5

Energy (eV)

Figure 6: Evolution of the density of states along the emission path of an oxygen EFP 2− in m-HfO2 . The reaction coordinate is indicated at each step. The zero in energy correspond to the top of the valence band and the Fermi level is visualized by dotted lines that shift when two electrons move from the conduction band toward the oxygen vacancy newly created. An arrow is positioned where states typical of a neutral V O appear inside the forbidden gap near the conduction band at R = 2.6Å. The pics close to the valence band are related to an O 2− i .

Figure 7: Probability density of localized electrons along the emission path of an oxygen EFP2− in m-HfO2 . The reaction coordinate is equal to 2.6Å, see Figure 5 and Figure 6. The two highest occupied levels related to the neutral oxygen vacancy are visualized by the contour plot in pink whereas the two following levels related to the oxygen interstitial emission are visualized in blue. The orientation is the same as in Fig. 2a with oxygen in red and hafnium in gold. an EFP emission mechanism that involves the cascading migration of ve 3-fold coordinated oxygen atoms along the [00 ¯ 1] direction on a characteristic distance of one nanometer. Although dierent EFP emission paths may be possible in m-HfO 2 , the path that we have 2− investigated is very likely due to somehow favorable V 2+ formation enthalpies and difO /Oi

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fusion of O2− through concerted migration of the same coordination. In particular, our i atomistic model allowed us to extract the neutral EFP activation energy and its dipolar moment using an original dipole extraction method for EFP 0 in DFT. These results can then be directly exploited to sustain a thermochemical view of HfO 2 breakdown. In particular, one should be able to sustain the hypotheses used to interpret the experimental behavior of OxRRAM devices during the forming step. 3,34 The calculated activation energy of 5.2 eV for EFP 0 is in good agreement with the experimental extracted value of 4.6 eV from time to breakdown tests obtained by Padovani et. al 34 for the case of a non-reactive electrode with oxygen like Pt or TiN. This energy is also in relative agreement with the phenomenological model of McPherson 10 with an estimated energy barrier of 6.2 eV for HfO 2 . Moreover, the dipolar moment we estimated to 5.6 e− .Å is in very good agreement with the experimental value of 5.2 e− .Å. 34 However this value is almost two times lower than 10.2 e− .Å reported by McPherson. Note that McPherson has further derived another set of values: 1.5eV for E a and 4.4 e− .Å for the dipole. The latter value tends to reconcile the dipolar moment with what we obtained but with a lower activation energy. Our EFP emission mechanism also points out a clear dierence with the McPherson phenomenological approach: rst, unlike McPherson we did not consider a cation but an 2− anion. Moreover the dipole extension for V 2+ is long range associated with a complex O /Oi

charge rearrangement. To put it another way, one can not correctly estimate at the same time the dipolar moment and the activation energy by assigning point charges to defects inside the dielectric layer. Therefore, for OxRRAM electroforming, our ab initio simulation results sustain the kinetic Monte-Carlo model derived by Padovani 38 where oxygen Frenkel pairs are emitted statistically by the combined eect of temperature and intense electric eld applied to the dielectric thin layer. Under this scenario, we do not consider any interaction with the electrode: the electric eld intensity has to reach a maximum value in order to emit an EFP 0

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avoiding its recombination. In the case of a reactive electrode with oxygen, like titanium, Padovani 34 extracted another activation energy of 2.8 eV keeping the same dipolar moment of 5.2 e − .Å. Based on our calculations, this could be due to charge injection eect: when two electrons neutralize the oxygen vacancy, the activation energy drops from 5.2 eV to 2.9 eV for EFP 2− emission which is in very good agreement with the calculated 2.8 eV value. Nevertheless, for electrons injection the dipole vanishes after a global displacement of 2Å, leading to the diusion of a single oxygen interstitial O 2− i under temperature and electric eld eect, while the remaining VO quickly looses its inuence as compared to V 2+ O . Note also that the underestimation of the band gap by GGA/PBE functional brings uncertainties in quantifying the eect of adiabatic charge injection on the calculated energy barriers. This result contrasts with the most accepted scenario currently used for a reactive electrode, where the conductive region or lament are related to a reservoir of oxygen vacancies. Indeed, oxygen vacancies are easily created at the interface when a metal like titanium is put in contact with HfO 2 due to the high solid solubility of oxygen in hcp-Ti. 32 Thus, facilitated by the reactive electrode, a transport mechanism via already formed oxygen vacancies at a low chemical potential, would allow for the electroforming of the lament at a lower energy cost than direct EFP emission. 7,9 Depending on the electric eld strength, and especially for low voltages well below two volts applied to a few nanometers of HfO 2 , it is assumed that the oxygen vacancies transport will overtake the EFP emission mechanism. Moreover, by employing a reactive electrode, the better thermal stability observed for the conductive state right after the forming step, indicates that no oxygen interstitial is easy to diuse inside the dielectric or close to the dielectric interface. Therefore, for a reactive electrode, the electroforming scenario requires an additional chemico-physical interpretation. Recently, Bradley and co-workers 13 showed that the initial presence of oxygen vacancies allows for an easier charge injection, a lower activation energy for intimate Frenkel pair emission, which is in turn stabilized by the pre-existing oxygen vacancies. These new results

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seem to pave the way for a unied scenario built between the previous hypotheses taking into account already formed V O 's. Eventually, for a metal with a low work function and high oxygen reactivity in contact with the dielectric layer, (note that both eects are usually related), an analysis at the atomic level would deserve another study by employing a suitable Ti/HfO2 interface model with a realistic amount of oxygen vacancies.

Acknowledgement This work was nancially supported by the Nanosciences Foundation, under UJF Foundation, in Grenoble, France. Part of the calculations were performed on CEA/Grenoble "Summer" cluster and Stanford University's "Baymax" cluster. The authors thank Prof. Yoshio Nishi, Blanka Magyari-Köpe and Jimmy Wu from Stanford University.

References (1) Robertson, J. High Dielectric Constant Oxides. Eur. Phys. J. Appl. Phys.

2004, 28,

265291. (2) Waser, R.; Dittmann, R.; Staikov, G.; Szot, K. Redox-Based Resistive Switching Memories - Nanoionic Mechanisms, Prospects, and Challenges. Adv. Mat.

2009, 21, 2632

2663. (3) Bersuker, G.; Gilmer, D. C.; Veksler, D.; Kirsch, P.; Vandelli, L.; Padovani, A.; Larcher, L.; McKenna, K.; Shluger, A.; Iglesias, V. et al. Metal Oxide Resistive Memory Switching Mechanism Based on Conductive Filament Properties. J. Appl. Phys.

2011,

110, 124518. (4) Xue, K.-H.; Blaise, P.; Fonseca, L. R. C.; Nishi, Y. Prediction of Semimetallic Tetragonal Hf 2 O3 and Zr2 O3 from First Principles. Phys. Rev. Lett.

19


2013, 110, 065502.


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 24

(5) McKenna, K. P. Optimal Stoichiometry for Nucleation and Growth of Conductive Filaments in HfOx. Model. Simul. Mater. Scienc. Eng.

2014, 22, 025001.

(6) Traoré, B.; Blaise, P.; Vianello, E.; Grampeix, H.; Jeannot, S.; Perniola, L.; Salvo, B. D.; Nishi, Y. On the Origin of Low-Resistance State Retention Failure in HfO 2 -Based RRAM and Impact of Doping/Alloying. IEEE Trans. Elec. Dev.

2015, 62, 40294036.

(7) Menzel, S.; Bottger, U.; Wimmer, M.; Salinga, M. Physics of the Switching Kinetics in Resistive Memories. Adv. Func. Mat.

2015, 25, 63066325.

(8) Jiang, R.; Du, X.; Han, Z.; Sun, W. Investigation of Chemical Distribution in the Oxide Bulk Layer in Ti/HfO2/Pt Memory Devices using X-Ray Photoelectron Spectroscopy.

Appl. Phys. Lett. 2015, 106, 173509. (9) Clima, S.; Govoreanu, B.; Jurczak, M.; Pourtois, G. HfOx as RRAM Material: First Principles Insights on the Working Principles. Micro. Eng.

2014, 120,

13 18,

MAM2013, March 10-13, Leuven, Belgium. (10) McPherson, J. W.; Mogul, H. C. Underlying Physics of the Thermochemical E Model in Describing Low-Field Time-Dependent Dielectric Breakdown in SiO2 Thin Films. J.

of Appl. Phys. 1998, 84, 15131523. (11) Chen, I.-C.; Holland, S.; Hu, C. Electrical Breakdown in Thin Gate and Tunneling Oxides. IEEE J. of Sol.-State Circ.

1985, 20, 333342.

(12) Öttking, R.; Kupke, S.; Nadimi, E.; Leitsmann, R.; Lazarevic, F.; Plänitz, P.; Roll, G.; Slesazeck, S.; Trentzsch, M.; Mikolajick, T. Defect Generation and Activation Processes in HfO2 Thin Films: Contributions to Stress-Induced Leakage Currents. Phys. Stat. Sol.

(a) 2015, 212, 547553. (13) Bradley, S. R.; Shluger, A. L.; Bersuker, G. Electron-Injection-Assisted Generation of Oxygen Vacancies in Monoclinic HfO2 . Phys. Rev. Applied 20


2015, 4, 064008.

Page 21 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(14) Demkov, A. A. Thermodynamic Stability and Band Alignment at a Metal High-k Dielectric Interface. Phys. Rev. B

2006, 74, 085310.

(15) Sharia, O.; Tse, K.; Robertson, J.; Demkov, A. A. Extended Frenkel Pairs and Band Alignment at Metal-Oxide Interfaces. Phys. Rev. B

2009, 79, 125305.

(16) Xue, K.-H.; Traoré, B.; Blaise, P.; Fonseca, L. R. C.; Vianello, E.; Molas, G.; Salvo, B. D.; Ghibaudo, G.; Magyari-Köpe, B.; Nishi, Y. A Combined Ab Initio and Experimental Study on the Nature of Conductive Filaments in Pt / HfO2 / Pt Resistive Random Access Memory. IEEE Trans. Elec. Dev.

2014, 61, 13941402.

(17) Hohenberg, P.; Kohn, W. Inhomogeneous Electron Gas. Phys. Rev.

1964, 136, B864

B871. (18) Kohn, W.; Sham, L. J. Self-Consistent Equations Including Exchange and Correlation Eects. Phys. Rev.

1965, 140, A1133A1138.

(19) Soler, M.; Artacho, E.; Gale, J. D.; Garc, A.; Junquera, J.; Ordejon, P.; Daniel, S. The SIESTA Method for ab initio Order- N Materials. J. Phys.: Condens. Matter

2002,

14, 2745. (20) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett.

1996, 77, 38653868.

(21) Troullier, N.; Martins, J. L. Ecient Pseudopotentials for Plane-Wave Calculations.

Phys. Rev. B 1991, 43, 19932006. (22) Henkelman, G.; Uberuaga, B. P.; Jónsson, H. A Climbing Image Nudged Elastic Band Method for Finding Saddle Points and Minimum Energy Paths. J. Chem. Phys.

2000,

113, 9901. (23) Bahn, S.; Jacobsen, K. An Object-Oriented Scripting Interface to a Legace Electronic Structure Code. Comput. Scienc. Eng.

2002, 4, 5666. 21



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 24

(24) Tang, W.; Sanville, E.; Henkelman, G. A Grid-Based Bader Analysis Algorithm Without Lattice Bias. J. of Phys. Cond. Matt.

2009, 21, 084204.

(25) Zheng, J.; Ceder, G.; Maxisch, T.; Chim, W.; Choi, W. First-Principles Study of Native Point Defects in Hafnia and Zirconia. Phys. Rev. B

2007, 75, 104112.

(26) Broqvist, P.; Pasquarello, A. Oxygen Vacancy in Monoclinic HfO 2 : A Consistent Interpretation of Trap Assisted Conduction, Direct Electron Injection, and Optical Absorption Experiments. Appl. Phys. Lett.

2006, 89, 262904.

(27) Jain, M.; Chelikowsky, J. R.; Louie, S. G. Quasiparticle Excitations and Charge Transition Levels of Oxygen Vacancies in Hafnia. Phys. Rev. Lett.

2011, 107, 216803.

(28) Hou, Z. F.; Gong, X. G.; Li, Q. Al-induced Reduction of the Oxygen Diusion in HfO 2 : an ab initio Study. J. of Phys.: Cond. Matt.

2008, 20, 135206.

(29) Capron, N.; Broqvist, P.; Pasquarello, A. Migration of Oxygen Vacancy in HfO 2 and across the HfO2 /SiO2 Interface: A First-Principles Investigation. Appl. Phys. Lett.

2007, 91, 192905. (30) For extended Frenkel pairs, we compared the calculated formation enthalpies using plane waves and projector augmented planewave (PAW) pseudopotentials as implemented in Quantum Espresso. Our SIESTA results are in good agreement with those of Quantum Espresso within a dierence of tenths of eV. (31) Muñoz Ramo, D.; Shluger, A. L.; Gavartin, J. L.; Bersuker, G. Theoretical Prediction of Intrinsic Self-Trapping of Electrons and Holes in Monoclinic HfO2 . Phys. Rev. Lett.

2007, 99, 155504. (32) Traoré, B.; Blaise, P.; Vianello, E.; Perniola, L.; De Salvo, B.; Nishi, Y. HfO 2 -Based RRAM: Electrode Eects, Ti/HfO 2 Interface, Charge Injection, and Oxygen (O) De-

22


Page 23 of 24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


fects Diusion Through Experiment and Ab Initio Calculations. IEEE Trans. Elec.

Dev. 2016, 63, 360368. (33) The global displacement vector is a 3N dimensions vector in phase space where N is the number of atoms. It is evaluated as the dierence of atomic positions between two succesive NEB images. Its norm is updated for each image and summed along the diusion path. For a sucient number of intermediate images, it can serve as a well dened reaction coordinate. (34) Padovani, A.; Larcher, L.; Bersuker, G.; Pavan, P. Charge Transport and Degradation in HfO2 and HfOx Dielectrics. IEEE Elec. Dev. Lett.

2013, 34, 680682.

(35) Martin, R. M. Comment on Calculations of Electric Polarization in Crystals. Phys. Rev.

B 1974, 9, 19981999. (36) McPherson, J.; Kim, J.-Y.; Shanware, A.; Mogul, H. Thermochemical Description of Dielectric Breakdown in High Dielectric Constant Materials. Appl. Phys. Lett.

2003,

82, 21212123. (37) Sire, C.; Blonkowski, S.; Gordon, M. J.; Baron, T. Statistics of Electrical Breakdown Field in HfO2 and SiO2 Films from Millimeter to Nanometer Length Scales. Appl. Phys.

Lett. 2007, 91, 242905. (38) Padovani, A.; Larcher, L.; Pirrotta, O.; Vandelli, L.; Bersuker, G. Microscopic Modeling of HfOx RRAM Operations: From Forming to Switching. IEEE Transa. Elec. Dev.

2015, 62, 19982006.

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Reduction of Monoclinic HfO2: A Cascading Migration of Oxygen and

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