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A New Theoretical Insight Into ZnO NWs Memristive Behavior Federico Raffone, Francesca Risplendi, and Giancarlo Cicero Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b00085 • Publication Date (Web): 29 Feb 2016 Downloaded from http://pubs.acs.org on March 1, 2016
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Nano Letters
A New Theoretical Insight Into ZnO NWs Memristive Behavior Federico Raone,∗ † Francesca Risplendi,‡ and Giancarlo Cicero† ,
†Dipartimento
di Scienza Applicata e Tecnologia, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino 10129, Italy
‡Department
of Materials Science and Engineering, Massachusetts Institute of Technology, 77
Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
Received February 29, 2016; E-mail: federico.ra
[email protected] Recently, nanostructured materials in particular in the
Resistive switching memory operation is generally described in terms of formation and rupture of a conductive lament connecting two metal electrodes. Although this model was reported for several device types, its applicability is not guaranteed to all of them. Based on Density Functional Theory calculations, we propose a novel switching mechanism suitable to nanowire-based resistive switching memories. Expecially for thick devices the current is highly unlikely to ow through a metallic lament connecting the electrodes. We demonstrate that, in the case of ZnO nanowires, metal adatoms, spread on the nanowire surface, locally dope the insulating oxide allowing surface conductance even for small metal concentrations.
form of nanowires (NWs) have been exploited as insulat-
Abstract:
ing layer between the metallic electrodes due to bene ts in device performance such as endurance and LRS/HRS ratio.
1315
For example, Yang and al.
employed ZnO NWs
sandwiched between two dierent metal contacts, Cu/ZnONW/Pd.
16
Unexpectedly, in these devices memristive be-
havior is observed even though the NWs (i.e.
the initially
insulating lm) have lengths of the order of microns. It is argued that, in this case, the active electrode atoms move on the surface of the wires rather than in their bulk, allowing faster percolation
16
and giving rise to a current ow through
formation of a surface conductive channel.
These ndings
open new questions about the validity of the conventional RRAM switching mechanism. Does lamentary conduction In last few years an extensive research activity has been
hold for such large devices? Do we really need a continuous
focusing on resistance switching memories (RRAMs), also
metallic lament? Could it be that a lower density of metal
referred as memristors, both for their application as non-
ions is enough to bridge the electrodes?
volatile data memory
1
and as component of neuromorphic
In this paper we analyze the switching mechanism between
RRAM operation consists into a voltage-controlled
high and low resistive state of ZnO NWs based memristors
switch between two resistive states: a high resistance state
via DFT calculations: we study the extraction and diusion
(HRS) and a low resistance state (LRS). Researchers pro-
of copper metal atoms from the electrode to the ZnO NWs
posed new designs and materials to achieve subnanosecond
surface and compare our results with recently published ex-
switching time,
perimental data.
circuits.
2
retention
5
3
picoJoule switching energy,
6
and trillion cycles endurance.
4
year-lasting
In the vast class
16
To this aim, we estimated the energy
needed to extract a Cu atom from the metal contact and
of RRAM, the so-called electrochemical metallizations cells
the potential energy surface (PES) for the adsorption of Cu
(ECMs) are one of the most studied. These are asymmet-
on the ZnO NWs surfaces.
ric structures composed by an electrochemically active elec-
the adatom preferential binding sites, mobility and possi-
trode (Cu,
7,8
Ag
9,10
), an inorganic thin lm that functions
as an electrolyte (inorganic oxides, and an inactive electrode (Pt,
7,9
810
Au,
Ge chalcogenides
8,10
7
PES provides information on
ble migration paths along the NWs surface plane. Based on )
our results we propose a novel switching mechanism relying
Pd ). ECM SET
on ZnO surface doping eects of single Cu adatoms rather
8
process (switch from a HRS to a LRS) is usually described
than on the formation of a continuous metallic lament, at
as a three step process: dissolution, drift and reduction of
variance with other studies where current has been consid-
the active electrode metal atoms.
ered a result of the electron ow through metallic nanoparti-
11
First, atoms of the ac-
1720
tive electrode dissolve into the insulating lm by means of
cles (NPs) separated by nanometric gaps.
a high voltage that also turns them into charged species.
in agreement with experimental evidences and qualitatively
These charged metal atoms are then dragged through the
consistent with the reported values of RRAM electronic fea-
insulator bulk by the electric eld and drift toward the op-
tures such as V set and V reset .
posite electrode. Once the inactive electrode is reached, ions are reduced and start nucleating till a metallic lament con-
Our model is
16
Calculations have been carried out within the Density Functional Theory (DFT)
21
in the PBE
23
22
formulation of
necting the two contacts is formed. The opposite transition
the general gradient approximation.
(RESET process) is achieved either by reversing the polar-
set with 28 Ry (280 Ry) cuto was employed to represent
ity of the voltage, leading to the partial oxidation of metallic
the electronic wavefunctions (densities). Electron-ion inter-
ions back into the contact, or by lament rupture through
action has been described by ultrasoft pseudopotentials.
Joule eect, which randomly spreads the metal particles. In
Within this scheme, the calculated ZnO unit cell parameters
order for this process to occur and to observe a fast switch
are a bulk =3.29 Å, c bulk =5.32 Å, u bulk =1.64 Å, in agreement
between the conductive and insulating state, the electrolyte
with other theoretical works.
layer (often an oxide) must have a thickness of few tens of
generally grow along the [0001] direction and present non-
nanomenter.
polar (1 ¯ 100) surfaces.
12
Diusion and formation of a metallic la-
28
2527
A plane-waves basis
24
Single-crystal ZnO NWs
To study adsorption and mobility of
ment through thicker lms would be unlike and kinetically
Cu on NWs, surfaces were represented by symmetric slabs
hindered.
containing 12 ZnO layers with a 2
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×2
surface supercell.
29
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at low coverage (one atom per supercell). The corresponding PES is represented in Fig.
1.
This gives information
on Cu adsorption minima and diusion barrier along the ZnO non-polar surface. As seen in Fig 2, in the lowest energy con guration (darkest region of the PES) the adatom forms strong bonds with the substrate atoms as indicated by the large value of the adsorption energy calculated with respect to an isolated Cu atom (-1.7 eV) and by the short distances with the underlying surface species, 2.47 Å and 1.90 Å with Zn and O respectively.
In this con guration,
the adatom is strongly polarized as demonstrated by an analysis in Fig.
2 where the electron density dierence
ρdif f = ρCu/ZnO − (ρZnO + ρCu )
is plotted. Being
the density of the interacting system and
ρZnO
ρCu/ZnO ρCu
and
the densities of the bare ZnO surface and isolated Cu atom
PES of a single Cu adatom on top of the ZnO NW surface. Potential energy varies between 0 and 2 eV as indicated by the color bar. The zero of energy has been set to the lowest energy adsorption con guration. Zinc and oxygen atoms are respectively colored in gray and red.
Figure 1.
respectively,
ρdif f
highlights charge rearrangements occur-
ring upon surface/adatom interaction (the blue isosurface highlights charge depletion while the yellow isosurface represents charge accumulation). It is apparent that there is a charge transfer from the right-hand side of the Cu atom towards the surface Zn atoms, thus, the surface acts as a Lewis acid accepting partial negative charge (electrons) from the adatom. As a consequence the Cu atom is partially ionized by the interaction with ZnO and can drift in the presence of an electric eld, if the intensity of the applied eld is high enough to make the adatom overcome the diusion barrier present in the PES reported in Fig. 1. An analysis of the above mentioned gure, highlights that Cu mobility is highly anisotropic since the PES presents a diusion barrier (white stripe of Fig. 1) of, at least, 1.67 eV for diusion along the [0001] direction and a small diusion barrier of 0.21 eV in the perpendicular [11
¯ 20]
direction.
Notably the [0001] di-
rection corresponds to the NWs growth axes and thus it is also the direction along which the electric eld is applied during memristive measurements. From the point of view of lament formation, this barrier has a double eect. On one
Charge dierence density isosurface for a Cu adatom adsorbed on ZnO (1¯100) surface. Density accumulation is depicted in yellow while depletion in blue. Zinc, oxygen and copper atoms are respectively colored in gray, red and orange. Figure 2.
side, it allows for ionic drift under high voltage stresses. On the other, it prevents diusion in absence of external stimuli, ensuring long-lasting retention of the resistance state.
We
also highlight that single atom drift toward the inactive electrode would not proceed in straight line but it would be characterized by hops in both the [0001] and [11
¯ 20]
directions.
A vacuum layer of 15 Å between periodic replicas was in-
The eect of the presence of a Cu adatom on the electronic
cluded. A (3 ×3×1) Monkhorst-Pack grid was used for the
properties of the ZnO non-polar surface can be understood
Brillouin zone sampling. The PES was obtained by placing a
by analyzing the density of states (DOS) and the projected
Cu adatom at several (15 evenly spaced grid points) inequiv-
DOS of the system (see Fig.
alent positions in the irreducible part of the (2
×2)
surface
3 (b)).
Due to presence of
the Cu atom, occupied electronic states appear at bottom of
cell at an initial distance from the surface atoms of 2.5 Å, as
the ZnO conduction band that shift upwards the Fermi level
proposed by Aliano et al.
(EF ). This suggests that a single adatom locally dopes the
30
At each position, the z coordi-
nate (perpendicular to the surface plane) of the adatom was
insulating ZnO surface turning it into conductive.
relaxed together with each coordinate of the atoms in the
density at
substrate until forces were smaller than 26 meV/Å. To ana-
as well as on surrounding oxygens indicating that electrons
lyze the electronic properties of the Cu covered ZnO surfaces,
are partially delocalized over the surface atoms. This analy-
a Hubbard-U correction was applied to the relaxed systems.
sis suggests that Cu adatoms act as dopant species for ZnO
For Zn, the correction is set to U=12.0 eV, whereas for O
allowing the current to ow on the surface and not in a l-
U=6.5 eV.
The accuracy of these parameters in predicting
ament as it would be in a conventional RRAM. To con rm
surface properties has been already previously
these results two adatoms/cell were adsorbed at the ZnO
Spin-polarization has been taken into account
surface by placing them in the two lowest energy minima
ZnO
31
(1 ¯ 100)
reported.
26,32
for systems with odd number of Cu atoms.
33
All compu-
tation were performed with the QUANTUM ESPRESSO
34
EF
Charge
(Fig. 4) is localized on top of the copper atom
presented by the PES. In this con guration the Cu atoms are separated by a high energy barrier and do not move upon relaxation, i.e. their interaction is negligible. The correspond-
software package. To understand if a single Cu atoms can drift on the
ing DOS is similar to the one obtained for a single adatom,
100) surface under the eect of an external applied ZnO(1 ¯
since both atoms act as n-type dopants (see Figure S1 of the
electric eld we have rst considered the adsorption of Cu
Supporting Information).
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In order to understand how the
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Isosurface electron density plot of a state located at Fermi energy when a Cu adatom is adsorbed at the ZnO (1 ¯100) surface. Zinc, oxygen and copper atoms are respectively colored in gray, red and orange. Figure 4.
a continous lament (see Fig.
S2 of the Supporting Infor-
mation for an example of a larger particle DOS). In the nal relaxed geometry both odd and even number of Cu nanoparticles are found at the ZnO surface and, since odd atoms NPs have an odd number of electrons they generate lled donor states degenerate with the conduction band minimum of ZnO responsible for surface metallic character. In Panel (d) of Fig.
3 we report the results for the case of a
Cu3 NP adsorbed at the ZnO surface: the system is indeed metallic.
Densities of states (DOS) of the bare ZnO-NW surface (a) and of the adsorbed Cu adatom (b), Cu dimers (c) and 3atoms Cu NP (d) on the same surface. The total DOS is depicted in black while the projected DOS of Cu and a innermost ZnO dimer inside the surface are respectively represented in red and blue. Valence band top of the bulk ZnO dimer is set at 0 eV while Fermi level is indicated by a vertical dash-dot line.
Figure 3.
The nanoparticle moves Fermi level upward into
ZnO conduction band. Based on the results presented above we can summarize the memristive switching mechanism of ZnO NWs with Cu metal contact as follows. Depending on the voltage polarity, the switching mechanism and, consequently, the rate limiting step dier. In the pristine form NWs are in a high resistive state, but, as the positive bias increases, copper ions of the metal contact get enough energy to detach from the contact and drift along the NW surface. We estimate the energy
ZnO NWs conductivity changes with increasing coverage of
required to extract a Cu atom from the metal contact and
Cu atoms and to verify if the formation of a continuos metal-
place it on the ZnO NWs surface by calculating the quan-
Eext = ECu/ZnO − EZnO − µCu ,
tity
the HRS and LRS (as commonly accepted), we have consid-
total energy of the ZnO slab with adsorbed a Cu adatom,
ered ZnO surfaces with larger amount of adsorbed adatoms,
EZnO
namely 0.5 and 0.75 ML (4 and 6 atoms/supercell). When
chemical potential of metallic Cu bulk.
four Cu are adsorbed at the surface in an initial geometry
lated
forming a single atom chain lament, the Cu atoms rear-
(1.67 eV), Cu atom extraction represents a higher obstacle
range so to form two atom clusters (bond distance 2.30 Å)
to the device switch ON. With this respect, we can regard
rather than remaining in single chain con guration. Inter-
electrode dissolution as the rate limiting step.
estingly, the corresponding DOS (see Fig.
3 (c)) reveals a
voltage magnitudes in real NW ZnO device agree with this
semiconducting behavior, and as such, copper dimers do not
conclusion. During forming stage voltage has to be risen up
have a n-type dopant eect at the ZnO surfaces. The reason
to at least 3 V to ensure electrode dissolution.
behind this nding is that Cu dimers are closed shell par-
high electric eld is removed, ions do not have enough kinetic
ticles characterized by and even number of electrons and a
energy to overcome the diusion barrier, thus they remain
large band gap energy. Upon Cu-Cu dimer formation, the
spread on the surface and cannot aggregate.
unpaired electrons of the single adatoms are shared among
the ones that most of all contribute to conduction due to
the two Cu atoms and correspondingly the dimer HOMO
their mobility.
state is pushed downward in energy.
ductive channel that leads to LRS: electrons can ow along
These electrons are
where
ECu/ZnO
lic lament is necessary to achieve enhanced switch between
is the total energy of the ZnO slab and
Eext
µCu
is the is the
Our DFT calcu-
value is 2.05 eV. Compared to diusion barriers
Switching
16
Once the
Adatoms are
Once spread, adatoms form a surface con-
not anymore free in the ZnO conduction band and do not
the ZnO NW surfaces connecting the two electrodes.
contribute to electronic conduction.
density of particles required to switch the device is lower
At higher coverage, we observed a general trend of the Cu adatoms to form clusters at the ZnO surface rather than
compared to a conventional RRAM in accordance with the large dimensions of the NWs (
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∼ 1 µm
in height and a diam-
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eter of 150 nm). Identifying adatoms as most active species
under the ISCRA initiative and HPC@POLITO, for the
for the conduction is also consistent with the experimental
availability of high performance computing resources and
observation that the ON current is reduced when the device
support. The authors declare no competing nancial inter-
is exposed to air.
ests.
16
Adatoms are highly reactive species due
to the presence of an unpaired electron, therefore they are easily oxidized by oxygen molecules. In this process the unpaired adatom electron participates in the bonding and it does not contribute to conduction, as already reported for other noble metals.
35
Moreover direct adsorption of oxygen
molecules at ZnO NW surfaces would further lower the position of the Fermi level of the oxide nanostructure (see Ref.
36
) decreasing device conductivity.
e.g
When the polarity
is inversed, the metal ions, already populating the NW surface, have to be dragged away from cathode, so a voltage lower than the set one (about 1.6 V in Ref.
16
) is needed to
overcome the diusion barriers. In this stage, it is then drift the rate limiting step, in accordance with experimental device V reset .
16
Not all adatoms have to be moved back to the
contact. It is su cient to create a small region free of doping metal atoms to interrupt the surface conductive channel and recover the HRS. As adatoms are transfered back they can aggregate into NPs. These NPs can be divided into two categories: odd and even numbered NPs. When the number of ions forming the NP is odd, metallic conduction occurs on ZnO surface like reported for Cu3 case in Fig.
3 (d).
Odd-NPs are generally the least stable clusters and easier to break.
37
As opposed to them, even-NPs do not participate
in conduction like dimers in Fig. 3 (c), since their tendency is to deform their structure to maximize the band gap.
37
We
can expect aggregated NPs to be hardly moved by electric eld and adatom detachment to be much more probable. It is known in literature that cohesion energy in nanoparticles is lower than in bulk making easier for a high electric eld to extract adatoms.
38
It is than explained why V set is
slightly lower than the voltage required to form the device. Experimental evidences con rm that there is not trace of a lament connecting the two electrodes in ZnO NW memristors in the ON state.
16
Energy dispersive X-ray spectroscopy
(EDX) identi es only spots of Cu on the surface representing particles agglomerates. Moreover, theoretical studies report that on ZnO copper nucleates in three dimensional islands even at small coverages.
39
These results show that in ZnO
based memristive devices, switching to a high conductive state does not require the formation of a continuos Cu lament at the NW surface, but rather relies on the doping eects of single adatoms (or odd atoms nanoparticles). We nally highlight that the Cu surface diusion mechanism that we propose would not be aected by ZnO piezoelectric properties. Indeed, it has been recently shown that surface piezoelectric response in ZnO NWs is negligible.
40
To conclude in this letter we demonstrated by means of DFT calculations that lament formation/rupture model does not apply to NW RRAMs, where surface diusion is possible, as agglomeration into stable nanoparticle is more likely to occur. A more suitable mechanism has been proposed. Contact atoms, rather than arranging together into a lament, spread on the surface. Especially when in form of adatom, adsorbed Cu dope the NW surface forming a conductive channel and thus a percolation path for the electrons.
Cu adatoms are easily moved by electric eld once
the diusion barrier is overcome thanks to the ionizing effect of the surface. In absence of external stimuli clustering is impaired by the same barrier.
Acknowledgement
Supporting Information Available: Additional information and gures (DOSs of the double adatom and the Cu6 NP on ZnO surface). This material is available free of charge via the Internet at http://pubs.acs.org/ .
References (1) Yang, J. J.; Strukov, D. B.; Stewart, D. R. Nat. Nanotechnol. 2013, 8, 13. (2) Chua, L. Nanotechol. 2013, 24, 383001. (3) Torrezan, A.; Strachan, J.; Medeiros-Ribeiro, G.; Williams, R. Nanotechology 2011 , 22, 485203. (4) Miao, F.; Strachan, J. P.; Yang, J. J.; Zhang, M.; Goldfarb, I.; Torrezan, A. C.; Eschbach, P.; Kelley, R. D.; MedeirosRibeiro, G.; Williams, R. S. Adv. Mater. 2011, 23, 5633. (5) Chen, A.; Haddad, S.; Wu, Y. J.; Fang, T.; Lan, Z.; Avanzino, S.; Pangrle, S.; Buynoski, M.; Rathor, M.; Cai, W. D.; Tripsas, N.; Bill, C.; VanBuskirk, M.; Taguchi, M. IEEE Int. El. Devices Meet. 2005 , 765. (6) Lee, M.; Lee, C. B.; Lee, D.; Lee, S. R.; Chang, M.; Hur, J. H.; Kim, Y.; Kim, C.; Seo, D. H.; Seo, S.; Chung, U.; Yoo, I.; Kim, K. Nat. Mater. 2011, 10, 625. (7) Soni, R.; Meuels, P.; Staikov, G.; Weng, R.; Kügeler, C.; Petraru, A.; Hambe, M.; Waser, R.; Kohlstedt, H. J. Appl. Phys. 2011, 110, 054509. (8) Singh, B.; Mehta, B. Thin Solid Films 2014, 569, 35. (9) Yang, Y.; Gao, P.; Gaba, S.; Chang, T.; Pan, X.; Lu, W. Nat. Commun. 2012 , 3, 732. (10) Song, J.; Zhang, Y.; Xu, C.; Wu, W.; Wang, Z. L. Nano Lett. 2011, 11, 2829. (11) Waser, R.; Dittmann, R.; Staikov, G.; Szot, K. Adv. Mater. 2009, 21, 2632. (12) Onofrio, N.; Guzman, D.; Strachan, A. Nat. Mater. 2015, 14, 440. (13) Chiang, Y.; Chang, W.; Ho, C.; Chen, C.; Ho, C.; Lin, S.; Wu, T.; He, J. IEEE T. Electron Dev. 2011, 58, 1735. (14) Huang, Y.; Luo, Y.; adn G.g Yuan, Z. S.; Zeng, H. Nanoscale Res. Lett. 2014 , 9, 381. (15) Nagashima, K.; Yanagida, T.; Oka, K.; Taniguchi, M.; Kawai, T.; Kim, J.; Park, B. H. Nano Lett. 2010, 10, 1359. (16) Yang, Y.; Zhang, X.; Gao, M.; Zeng, F.; Zhou, W.; Xie, S.; Pan, F. Nanoscale 2011, 3, 1917. (17) Hsiung, C. P.; Liao, H. W.; Gan, J. Y.; Wu, T. B.; Hwang, J. C.; Chen, F.; Tsai, M. J. ACS Nano 2010, 4, 5414. (18) Yang, Y.; Gao, P.; Gaba, S.; Chang, T.; Pan, X.; Lu, W. Nat. Commun. 2012 , 3, 732. (19) Gao, S.; Song, C.; Chen, C.; Zeng, F.; Pan, F. Appl. Phys. Lett. 2013, 102, 141606. (20) Tian, X.; Yang, S.; Zeng, M.; Wang, L.; Wei, J.; Xu, Z.; Wang, W.; Bai, X. Adv. Mater. 2014, 26, 3649. (21) Hohemberg, P.; Kohn, W. Phys. Rev. 1964, 136, 864. (22) J. P. Perdew, K. B.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865. (23) Langreth, D. C.; Perdew, J. P. Phys. Rev. B 1980, 21, 5469. (24) Vanderbilt, D. Phys. Rev. B 1990, 41, 7892. (25) Pham, A.; Zhang, Y. B.; Assadi, M. H. N.; Yu, A. B.; Li, S. J. Phys.: Condens. Matter 2013 , 25, 116002. (26) Risplendi, F.; Cicero, G. J. Phys. Chem. C 2015, 119, 27348. (27) Cicero, G.; Ferretti, A.; Catellani, A. Phys. Rev. B 2009, 80, 201304. (28) Nikoobakht, B.; Davydov, A.; Stranick, S. J. Mat. Res. Soc. Symp. Proc. 2004 , 818 , M8.25.1. (29) Considering only the surface rather than representing the whole NW is a reasonable approximation since their typical diameter for RRAM applications is around 150 nm 16 . (30) Aliano, A.; Catellani, A.; Cicero, G. App. Phys. Lett. 2011, 99, 193106. (31) Vogel, D.; Krüger, P.; Pollmann, J. Phys. Rev. B 1996, 54, 5495. (32) Calzolari, A.; Ruini, A.; Catellani|, A. J. Am. Chem. Soc. 2011, 133 , 5893. (33) As a test an U correction was put also on Cu. 41 However, the only eect was a down-shift of the Cu occupied levels which does not aect our considerations. Therefore this correction was not included in the results presented in the paper. (34) Giannozzi, P. et al. J. Phys. Condens. Mat. 2009, 21, 395502. (35) Chen, Y.; Crawford, P.; Hu, P. Catal. Lett. 2007, 119, 21. (36) Korir, K. K.; Catellani, A.; Cicero, G. J. Chem. Phys. C 2014, 118 , 24533. (37) Larsen, A. H.; Kleis, J.; Thygesen, K. S.; Nørskov, J. K.; Jacobsen, K. W. Phys. Rev. B 2011, 84, 245429. (38) Fernández, E. M.; Soler, J. M.; Garzón, I. L.; Balbás, L. C. Phys. Rev. B 2004 , 70, 165403. (39) Patterson, M. C.; Nie, X.; Wang, F.; Kurtz, R. L.; Sinnott, S. B.;
We acknowledge the CINECA award
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Asthagiri, A.; Sprunger, P. T. J. Phys. Chem. C 2013, 117, 18386. (40) Korir, K. K.; Cicero, G.; Catellani, A. Nanotechnology 2013, 24, 475401. (41) Himmetoglu, B.; Wentzcovitch, R. M.; Cococcioni, M. Phys. Rev. B 2011 , 84, 115108.
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