Statistics-Based Analysis of the Evolution of Structural and Electronic

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Statistics-Based Analysis of the Evolution of Structural and Electronic Properties of Realistic Amorphous Alumina During the Densification Process: Insights from First-Principles Approach Vanessa Riffet, and Julien Vidal J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b06887 • Publication Date (Web): 06 Sep 2017 Downloaded from http://pubs.acs.org on October 20, 2017

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The Journal of Physical Chemistry

Statistics-Based Analysis of the Evolution of Structural and Electronic Properties of Realistic Amorphous Alumina during the Densification Process: Insights from First-Principles Approach. Vanessa Riffet,§* Julien Vidal¶,¥* §

Institut Photovoltaïque d’Ile de France (IPVF), 8 rue de la Renaissance 92160 Antony, France

¶

Institute for Research and Development of Photovoltaic Energy (IRDEP), UMR 7174 CNRS /

EDF R&D / Chimie ParisTech-PSL, 6 quai Watier, 78401 Chatou, France ¥

EDF R&D, Departement EFESE, 6 quai Watier, 78401 Chatou, France

ABSTRACT. Based on the melt and quench strategy, over 3000 structurally different AlOx structures have been generated using ab initio Molecular Dynamics. Unlike other previous studies where defects were introduced into some crystalline polymorph of Al2O3, variety of defects emerged directly from this approach. A new way to probe the short (distances between first neighbors and coordination numbers) and medium (atom rings, bond-angles, and distances between second neighbors) range structural properties of H- and/or O-rich AlOx have been defined. The evolution of such structural properties during the densification process with mass loss have been studied using averaged data at fixed chemical composition. A good agreement is observed between experimental and theoretical structural data, validating the methodology. In

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particular, the profile of the total experimental neutron pair correlation function has been rationalized. At fixed composition, the Spearman correlations have been calculated in order to reveal monotonic relationships between properties: a correlation between the structure and bandgap energy of different stoechiometries of AlOx could not be clearly inferred. Finally, we may speculate that the O22- and Al-H defects could explain the origin of negative fixed charges in AlOx because of their effects on electronic properties of AlOx and their structural characteristics.


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INTRODUCTION. Amorphous alumina (AlOx) have been considered in several technological applications ranging from microelectronic devices,1 resistive coating2-4 or passivation layer in photovoltaic solar cell.5,6 In the case of silicon solar cell, AlOx is often used as a thin passivation layer at the silicon surface, not only because of its isolating properties and high transparency in the visible, but also owing to its passivating properties. [For a recent review, see [6]] Indeed, the silicon surface presents a large amount of defects, linked to impurities and dangling bonds, leading to electronic recombination losses for solar cells. The AlOx monolayers, deposited on silicon via a variety of techniques ranging from vacuum to non-vacuum, allow a chemical passivation of dangling bonds and a field-effect passivation induced by its native negative fixed charges.6 So far, experimental studies have been mostly devoted to understand the structuration and the disorder in AlOx. In particular, the analysis techniques such as X-ray and neutron diffractions, Extended X-ray Absorption Fine Structure (EXAFS) and Extended Electron Energy Loss Fine Structure (EXELFS) spectroscopies,

27

Al NMR and Rutherford backscattering spectrometries

provide local structural informations such as bond lengths and/or coordination numbers. However, the origin of the native negative fixed charges in AlOx and the understanding of the link between the structural, optoelectronic and passivating properties are far from being achieved.6 This is a real challenge because structural properties of AlOx depend strongly on deposition techniques and conditions as precursor chemical species, temperature, atmosphere or annealing time.7-18 The profusion of experimental parameters make difficult to obtain a unique amorphous structure, as shown by different experimental structural properties reported in Table 1.


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Table 1. Experimental [n]Al (%) where n represents the number of coordination of Al, average number of coordination of Al (CNAl) and Al-O, O-O and Al-Al distances (Å) of AlOx thin films. deposition methods O/Al = 1.5

MOCVD

Ref.

[19]a

T°dep (°C)

[3]

Al (%)

480 550 600 360b 420b 200 200

ALD [20]a PVD [20]a Experiment average Experimental standard deviation deposition methods O/Al = 1.5

Ref.

T°dep (°C)

[21]c,d 300 [22]c 10 [22]c 15 Anodic oxidation [23]c 500 of Al foils [24]a rt [25]e rt [26]e rt Experiment average Experimental standard deviation O/Al = 1.53 ±0.054 MOCVD [27]a rt a 1D MAS and 2DMQ MAS 27Al NMR b assumed hydrogen content c X-ray diffraction d neutron diffraction e EXAFS and EXELFS rt = room temperature

[3]

Al(%)

[4]

coordination number of Al [5] [6] Al (%) Al (%) Al (%)

53.0±0.6 53.3±0.6 46.5±0.3 32.9±0.8 45.6±0.7 54.3±0.4 56.4±0.4 48.9±0.5 8.1

41.6±0.4 39.2±0.5 37.6±0.3 40.9±0.7 42.9±0.5 40.6±0.4 36.2±0.4 39.9±0.4 2.3

5.4±0.4 7.5±0.3 15.9±0.2 26.2±0.7 11.5±0.6 5.1±0.4 7.4±0.4 11.3±0.4 7.6

[4]

[5]

[6]

Al (%)

Al (%)

Al (%)

20

56

22

/

/

25

30

45

dAlO (Å)

bond lengths dOO (Å)

dAlAl (Å)

CNAl

dAlO (Å)

dOO (Å)

dAlAl (Å)

4.1 4.64 4.81 4.3 5.2

1.8±0.21 1.85 1.85 1.87±0.05

2.8±0.58 / / /

3.2±0.55 / / 3.08

1.89 1.90 1.86 0.04

/ / 2.8±0.58 /

/ / 3.14 /

CNAl 4.52±0.07 4.54±0.07 4.69±0.04 4.93±0.11 4.66±0.09 4.51±0.06 4.51±0.06 4.62±0.07 0.15

4.61 0.43

55±3

42±3

3±2

4.48±0.39

Moreover, experimental evidences on films slightly O-rich and partially hydroxylated are reported in the literature,6-8,15,17 but O-poor films have also been characterized by XPS analyses.28 The H-, O- and Al-based defect states within AlOx films have been reported at least once in several theoretical and experimental studies, such as O-H,1,6,7,9,13,28,32 Al-Al,9,32 O-O,31,32 H-H29,32 and Al-H30,32. The existence of large scatterings of the experimental measurements is therefore evident, such as bandgap energy6,33,34 or refractive index.6,7,10,13,28,35,36 Comprehensive insight into the behavior of AlOx is possible only if experimental structural informations are coupled with computation of the corresponding amorphous structures. From


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such observation, the computational approach to explore the potential energy surface of AlOx should be sufficiently exhaustive and accurate, in order to obtain structural diversity. In the literature, the theoretical melt and quench approach have been proven successful to generate structures with significant structural disorder, such as amorphous37 or glasses.38 In the AlOx case, empirical potentials of Al and O parameterized on crystalline phases were mostly used, probably because of the less time-consuming calculations (but less accurate than the ab initio Molecular Dynamic (MD)), allowing for larger simulation boxes (up to 22000 atoms) and slower quenching rates (ranging from few K/fs to 10-3 K/fs).39-47 Yet in the case of the ternary system Al-O-H, H is parameterized only as part of an OH bond, i.e. proton-like.43 To our knowledge, AlOx structures of the literature from classical MD do not allow to explain the origin of experimental peak around 1.5 Å (not attributed) of total neutron scattering curves.21 Using stochastic method, Århammar et al. have shown that structures of AlOx displaying trapped O-O pairs (= hole traps) describe better the measured NEXAFS spectrum.31 But, no peroxide group in AlOx have been highlighted in studies using classical MD. This illustrates the importance to ensure a sufficient structural diversity in terms of atomic arrangements and nature of the defect states to understand the experimental properties of AlOx. Furthermore, this cast some doubts about the ability of empirical potentials fitted on selected structure to describe properly such variety of environments. These reasons prompt us to prefer the use of the computationally expensive ab initio MD over classical MD in order to avoid any bias. Recently, in the literature, the dependence between the refractive index and the mass density has been studied in the case of AlO1.5, AlO1.625H0.278, AlO2H and AlO3H3.32 The effects of H-, O- and Al-based defects, revealed by the Bader analysis, on the refractive index have been studied, which allowed to decouple their effects from those of mass density.32 The published study has


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been realized using 2010 amorphous structures of AlOx generated by the melt and quench strategy presented in this paper. In the present contribution, a new way to probe the structural, electronic and passivating properties of AlOx is defined using a large set of realistic amorphous structure. Indeed, over 3000 structurally different AlOx structures are first generated by a strategy of type melt and quench using the ab initio MD applied to simulation box of around 200 atoms/cell. This approach differs significantly from the strategy employed to investigate the defect physics of amorphous materials. Usually, defect formation energies are computed from the low energy crystal phase (αAl2O3)48-51 or a crystal phase structurally closed to the amorphous one (γ-Al2O3).52-53 In the methodology presented here, the defects emerged directly from the melt and quench strategy. One important aspect is the setting of the simulation box: in all compositions, the charge balance (or semiconducting nature of the electronic structures) is ensured by the addition of a specific number of H2(g), O2(g) and H2O(g) molecules (typical precursor chemical species) in a cell of AlO1.5. For instance: (i) 12O2(g) + 24H2(g) in a 120 atoms cell of AlO1.5 allowed to obtain a 192 atoms cell of AlO2H and (ii) AlO1.625H0.278 is a semiconducting material obtained as 8H2(g) + 4O2(g) + H2O(g) + H2(g) in a 180 atoms cell of AlO1.5. On the other hand, the melt and quench procedure does not guarantee that the semiconducting properties are kept. Actually, certain number of structures generated by melt and quench has to be discarded due to their metallic nature. In the most extreme cases, only few semiconducting structures are obtained and retained from the fastest quench rate. Then, structural properties of these structures at short (distances between first neighbors and coordination numbers) and medium-range order (atom rings, bondangles, and distances between second neighbors) regardless of the states of defects are discussed. The experimental mass densities ranging from 2.1 to 3.5 g.cm-3,8,16,54-56 the evolution of these


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structural properties is exclusively analyzed in this range of mass density. Two densification processes are considered in this study, and different statistical approaches allow to analyze them: -

For a fixed chemical composition of AlOx, the increase of the mass density is so-called “densification process without mass loss”. The statistical analysis based on the Spearman correlation has been realized in this case in order to highlight the monotonic relationships (also not linear) of type structure – structure and structure – electronic property.

-

As oxygen and hydrogen contents decrease in AlOx (AlO3H3 → AlO2H → AlO1.625H0.278 → AlO1.5), the mass density range increase (2.11-2.75 → 2.50-3.25 → 2.70-3.35 → 2.753.45 g.cm-3, respectively). The overall increase of the mass density in changing the chemical composition is so-called “densification process with mass loss”. In this case, our data have been averaged using all structures of a fixed chemical composition, regardless of density. Experimental and theoretical data are compared in order to validate our methodology and to understand and rationalize the experimental data sometimes disparate (Table 1). Thus, based on this statistical approach, averaged theoretical structural parameters characterizing the amorphous structure are proposed.

Then a section is dedicated to the structural analysis of defects. The remainder of the article involves a description of electronic and passivating properties of AlOx: especially, the hydrogen role combined or not with an O-excess have been highlighted. METHODS. Density Functional Theory (DFT) calculations have been performed with the Vienna Ab-initio Simulation Package (VASP) 5.2 code.57-59 The supercell approach has been performed considering around 200 atoms/cell (AlO1.5 = Al72O108, AlO1.625H0.278 = Al72O117H20, AlO2H =


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Al48O96H48 and AlO3H3 = Al28O84H84). The neutral O-rich and/or H-rich AlOx are considered as AlO1.5 in which O2(g), H2(g) and H2O(g) molecules (precursor chemical species) are added. Only valence electrons are explicitly treated by a plane wave basis set (Al: 3s23p1, O: 2s22p4, H: 1s1). The projector augmented wave (PAW) formalism replacing the core electrons60,61 and the Perdew-Burke-Ernzerhof (PBE) functional62,63 have been used as implemented in VASP 5.2. The Melt and quench procedure. The ab initio MD has been performed using a soft version for the PAW of O and a cutoff of 320 eV64 for the plane wave basis set. The electronic convergence were performed for a threshold of 1.10-4 eV. The canonical ensemble (NVT) with the Nosé-Hoover thermostat have been considered in this study.65 The Nosé-mass has been set on the frequency of H2 molecule (νHH,exp = 4401 cm-1 → νNose = 8.28.1014 Hz). The spin polarization and the dispersion effects are not taken into account in calculations. During the procedure, the cell shape and the volume are frozen. A Γ point only have been considered to sample the Brillouin zone. The melt phase: After a 2 ps equilibration step, ab initio MD of 10 ps have been done at 6000K using a time step of 0.2 fs (see supporting information for complementary informations). For each composition of AlOx, two randomly generated structures of mass density 2.70 and 3.34 g.cm-3 have been used as starting point. Verifying that two successive structures are sufficiently different, one structure is extracted every 0.25 ps, i.e. a total of 41 structures by ab initio MD. The quenching/cooling phase: 6 different melts quenching/cooling have been carried out on structures previously extracted from melt for AlO1.5, AlO1.625H0.278, AlO2H and AlO3H3, given a total of 1968 structures. The associated characteristics are reported in Table 2. Other compositions have also been investigated to better understand the optic and passivating


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properties of AlOx such as AlO1.5H0.056, AlO1.5H0.139, AlO1.5H0.194, AlO1.5H0.278, AlO1.625, AlO1.625H0.056, AlO1.625H0.139, AlO1.625H0.222, AlO1.75, AlO1.875 and AlO2. For these latter, the melt quenching Q∞ have been performed yielding a total of 220 semiconducting structures. Table 2. Characteristics of melt quenching and cooling used in the procedure: temperature (K), quenching rate (rq, K.fs-1) and time of simulations.

melt quenching Q∞ a Q 1b Q 2b

T (K)

rq (K.fs-1)

time (ps)

0 6000 → 300 6000 → 300

/ -1.425 -0.475

/ 4 12

melt cooling C1b C2b b C3 = C1+C2

1000 / 4 300 / 4 (i) 1000 and / 8 (ii) 300 a Q∞ consists to relax the structures from the melt phase at low precision without geometric constraint: cutoff 320 eV, threshold 1.10-4 eV, soft version for the PAW potential of O. b The last snapshot is optimized following parameters of Q∞.

Amorphous structures. All structures from the melt and quench procedure are then reoptimized using a harder PAW for O with an increased plane wave basis set with cutoff 500 eV. The cell shape, the volume and the ionic positions were all optimized until atomic forces are smaller than 3 meV.Å-1. The electronic convergence were performed for a threshold of 1.10-7 eV. The van der Waals interactions have been considered using the DFT-D2 method of Grimme.66 The structural features at short-range have been investigated using (i) the total and partial radial distribution functions (RDF), (ii) [n]Al, [m]O for the Al-O pair only, where n and m represent the number of coordination of Al and O, respectively, (iii) the average coordination numbers of Al and O (CNAl and CNO) for the Al-O pair only, (iv) the bond lengths (dAlO, dAlAl and dOO), and then compared to experimental data available in the literature. Unfortunately, experimental mass


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densities of AlOx are rarely provided together with the previous structural features. The mediumrange order have also been studied in term of atom rings for the Al-O pair using the ANELLI program package.67,68 All atoms not belonging to any atom rings or any paths between atom rings are so-called dangling structures and have also been considered. The dangling structures corresponding always to an oxygen atom, the terms dangling atom and dangling oxygen have been used in this study. This program uses the Balducci-Pearlman-Mancini algorithm to bring out atom rings linearly independent while eliminating the redundancies.67-70 ANELLI has been successfully used on glasses, such as xPbO(1-x)SiO267 or PbGeOx71. CN values are also been extracted from ANELLI. The distribution of CN for the Al-O pair have been calculated using a cut-off radius of around 2.25-2.30 Å associated to the first crossing of partial RDF of Al-O and O-O pairs. Statistical analysis. During the densification process without mass loss, for a fixed chemical composition of AlOx, the Spearman’s rank correlation coefficients (rs) are thus calculated to highlight the monotonic relationship between two properties. A perfect correlation exists when rs = ±1, (the sign + or - indicates the direction of variation). This statistical analysis were carried out using the open source package OpenTURNS.72 Formation energy. The formation energy of each structure has been evaluated with respect to the lowest energy structure (AlOx,ref) at a given composition: Ef = Etot[AlOx] – Etot[AlOx,ref]. The formation energy in the case of amorphous structures is an ill-defined quantity as amorphous structures are meta-stable: a high formation energy does not necessarily infer that the amorphous structure cannot be synthesized by out of equilibrium. Nevertheless, the formation energy allows to classify amorphous structures and to qualitatively assert the energy cost of the formation of point defects.


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Electronic properties. The total and partial density of states (DOS and p-DOS, respectively) have been calculated as in [32]. Non-Covalent interactions Index (NCI). The Al2O2 ring interactions has been investigated using the NCI topological tool. This tool is based on the so-called reduced electron density gradient s(ρ) =

|∇ఘ| ஼ಷ ఘర/య

where CF, ρ and ∇ρ are the Fermi constant, the electron density and the electron

density gradient, respectively.73,74 The s isosurfaces (NCI region) allow to highlight the different types of interaction. The NCI analysis has been performed using the CRITIC2 code.75 RESULTS AND DISCUSSION. In the following section, the main results of this study are presented. Complementary informations on the relative energy of structures versus mass density for different quench rate are reported in Supporting Informations. First, the analysis of short- and medium-range order of AlOx are described. Short-range order. The distance between first neighbours is the simplest structural information. Thus, in the Figure 1 the shapes of average RDF (averaged data using all structures at a fixed composition) for AlO1.5, AlO1.625H0.278, AlO2H and AlO3H3 are reported, allowing to characterize partially the local environment of Al and O atoms. For the Al-O pair in AlOx, the first peaks at 1.80±0.06, 1.80±0.07, 1.83±0.08 and 1.87±0.08 Å, respectively are rather sharp (see Table 3). During the densification process with mass loss, i.e. when the O/Al ratio decreases from 3 to 1.5, the Al-O distances decrease slightly and the full width at half maximum (FWHM) of Al-O distances also decrease. However, the average Al-O distances for AlO1.5 and AlO1.625H0.278 are the same, so not enough to discriminate O/Al ratios. We can simply assume that a large excess of


11


O and H in AlO1.5 (AlO1.5 → AlO2H →AlO3H3) induces a slight dispersion of Al-O bond lengths in addition to an elongation of Al-O distances. To better understand the evolution of distances during the densification process with mass loss, [n]Al, [m]O, CNAl and CNO have been analysed.

a)

b) AlO1.5

0.012

0.05

0.0005 0.0004 0.0003 0.0002 0.0001 0.0000

AlO2H

0.04 1.40

0.008

1.50

RDFav [O-O]

RDFav [Al-O, O-O, Al-Al]

0.016

1.60

AlO1.625H0.278 AlO3H3

0.004

0.03 0.02 0.01

0.000

0 1

2

3

4

1

2

3

4 5 r [Å]

6

7

1

2

3

4 5 r [Å]

6

7

r [Å]

c)

d) 0.04

0.12

RDFav [Al-Al]

0.10

RDFav [Al-O]

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0.08 0.06 0.04

0.03 0.02 0.01

0.02 0.00

0 1

2

3

4

r [Å]

Figure 1. a) Total and b-d) partial average radial distribution function (RDFav), normalized to unit, associated to b) O-O, c) Al-O and d) Al-Al pairs. All structures at a fixed composition are considered. The dashed line serves as a guide to the eye. The total experimental neutron PDF extracted from [21] is reported in Supporting Information. Table 3. Mean Value of Theoretical Structural Parameters of AlOx at short-range order.


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O/Al 1.500 1.625 2.000 3.000 a b

bond length (Å) O-Oa Al-Ala 2.83±0.26 3.18±0.26 1.80±0.06 ~2.47 2.78 2.78±0.27 3.18±0.27 1.80±0.07 ~2.53 2.78 3.23±0.27 1.83±0.08 2.73±0.27 2.83 1.87±0.08 2.68±0.21 3.38±0.26 2.88

CNAlb

Al-Oa

CNOb

4.61±0.17

3.07±0.11

4.68±0.20

2.88±0.12

4.93±0.24

2.48±0.12

5.30±0.21

1.79±0.06

data extracted from Figure 1 ± FWHM ± standard deviation

The Figure 2 plots the variation of [n]Al and [m]O as a function of O/Al ratio. For the O/Al ratio of 1.5, a good correlation is observed between experimental (Table 1) an theoretical (Figure 2) [4]Al (48.9±8.1 % versus 46.5±12.2 %) ,

[5]

Al (39.9±2.3 % versus 46.0±9.0 %) and

[6]

Al (11.3±7.6 %

versus 7.4±5.4 %). During the densification process with mass loss, the content of {[4]Al and [6]

Al} and {[1]O,

[2]

O and

[3]

O} sites vary dramatically. In particular,

[4]

Al and

[6]

Al vary in

opposite directions and a similar behaviour has already been observed experimentally (see Figure 2a).19 More precisely, when AlOx grows denser, the content of [6]Al decreases from 40.9±13.7 to 7.4±5.4 %, whereas the number of

[4]

Al increases from 10.6±8.8 to 46.5±12.2 %. The

[5]

Al

content is around of 48.9±9.0 % for all O/Al ratio, which is consistent with the experimental results (41.9±0.6%, Figure 2a).19 Thus, it is not [5]Al and of CNAl, but rather

[6]

Al and

[4]

[4]

Al which imposes the average value

Al. In the Table 3 the average CNAl and CNO is reported for

different stoechiometries of AlOx: CNAl is of 5.30±0.21, 4.93±0.24, 4.68±0.20 and 4.61±0.17 for AlO3H3, AlO2H, AlO1.625H0.278 and AlO1.5, respectively. During the densification process with mass loss, the decrease of CNAl is consistent with that of Al-O bond length. Furthermore, the average CNAl values for O/Al ratios < 2 are fully consistent with the experimental average value (4.62±0.07, Table 1). Concerning [m]O, the [3]O content increases spectacularly from 16.2±3.5 to 82.2±5.1 %, whereas

[2]

O evolves according to two regimes: a slight decrease from 47.2±5.6 to

41.2±5.5 % for AlO3H3 → AlO2H, then a rapid decreases from 41.2±5.5 to 5.3±4.0 % for AlO2H → AlO1.625H0.278 → AlO1.5. No content of

[1]

[1]

O has been revealed in AlO1.5. However, a non-negligible

O (29.2±4.4 %) is present within AlO3H3 and decreases down to 0 % in AlO1.5.

Considering AlO3H3 as AlO1.5 + O1.5H3, it becomes obvious that the average CNO increases during the densification process with mass loss (Table 3): CNO = 1.79±0.06, 2.48±0.12, 2.88±0.12 and 3.07±0.11, for AlO3H3, AlO2H, AlO1.625H0.278 and AlO1.5, respectively. As a


13


reminder, the n and m values do not consider the hydrogen environment. The hydrogen atoms are fixed essentially on [1]O and [2]O.

a)

b) 60

100

[5]Al

[4]Al

+ [6]Al 80 [6]Al

40

20

content [%]

content [%]

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 14 of 56

[4]Al

1.5

2

2.5

[1]O

+ [2]O

60 [2]O

40

[1]O

20

[3]Al

0

[3]O

[4]O

[O]O

0 3

1.5

O/Al

2

2.5

3

O/Al

Experimental data extracted from [19]

Figure 2. Percentage of a)

[n]

Al and b)

[m]

O sites as a function of the O/Al ratio associated to

AlO1.5, AlO1.625H0.278, AlO2H and AlO3H3. At fixed composition, data are averaged using all structures and the standard deviations are also reported. Experimental data of [n]Al extracted from [19] are plotted in the panel a). The evolution of CNAl and CNO during the densification process without mass loss have also been investigated in order to look if the trends extracted from the densification process with mass loss can be transposed. Thus, CNAl and CNO of all structures of different stoechiometries of AlOx are plotted as a function of mass density (see Figure 3) During the densification process without mass loss, it appears from the Figure 3 that CNAl and CNO increase ([CNAl,min, CNAl,max]: [4.32, 5.01], [4.33, 5.09], [4.46, 5.42] and [4.64, 5.75] for AlO1.5, AlO1.625H0.278, AlO2H and AlO3H3, respectively; and [CNO,min, CNO,max]: [2.88, 3.34], [2.67, 3.15], [2.25, 2.73] and [1.56, 1.92], respectively). For CNAl and CNO, the Spearman’s rank correlation coefficients (rs = 0.807-0.924


14

Page 15 of 56

and 0.714-0.926, respectively) allow to highlight a clear monotonic relationship between these latter structural parameters and the mass density (Figure 3). CNO decrease during two densification processes (Figures 2 and 3), whereas the evolution of CNAl is different. Thus, the study of CNAl parameter allow to assert that the trends during the densification process with mass loss could not be necessarily transposed to those during the densification process without mass loss. Moreover, a good Spearman correlation between

[4]

Al ([6]Al) and the mass density is

revealed for the different stoichiometries of AlOx (-0.71 < rs < -0.90 and 0.73 < rs < 0.84 for [4]Al and [6]Al, respectively). But surprisingly, a good correlation between [5]Al and the mass density is true only for AlO1.5 and AlO1.625H0.278 (rs = 0.77 and 0.75, respectively). Similar correlations are also observed between [6]

[n]

Al and CNAl: (i) -0.77 < rs < -0.97 and 0.88 < rs < 0.95 for

Al, respectively and (ii) for

[5]

[4]

Al and

Al: rs = 0.83, 0.79, 0.33 and -0.58 for AlO1.5, AlO1.625H0.278,

AlO2H and AlO3H3, respectively. The weak correlations between AlO3H3 allowed to confirm that the

[6]

Al and

average CNAl. Finally, considering the higher

[4]

[m]

[5]

Al and CNAl for AlO2H and

Al contents are key criteria determining the

O contents in each composition, a correlation

between [m]O and the mass density could not be inferred (|0.19| < rs < |0.65|).

a)

b) 6.0

3.5 rs = 0.807

rs = 0.926

3.0

rs = 0.897

5.5

rs = 0.916 rs = 0.923

2.5

CNO

CNAl

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


5.0

rs = 0.874 2.0

4.5

rs = 0.714

1.5

rs = 0.924 4.0

1.0 2.0

2.5

3.0 ρ [g.cm-3]

3.5

2.0

2.5

3.0 ρ [g.cm-3]

3.5


15


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Page 16 of 56

Figure 3. a) CNAl and b) CNO of all structures of different stoechiometries of AlOx as a function of mass density (g.cm-3). The associated rs values are reported in this Figure. Medium-range order. The Al-O ring analysis allow to have additional informations on the structuration of AlOx (Figure 4a-b). First, the nature and the content of dangling atoms have been identified, then the structures have been described in atom rings (atom rings, bond-angles and distances between second neighbours). The evolutions during the densification process with mass loss are first discussed (averaged data using all structures at a fixed composition), then a discussion for the densification process without mass loss closes this part (Spearman correlation between atom rings and mass density). The largest graphs of connected atoms contain 100, 99.99±0.08, 99.78±0.40 and 95.61±7.36 % of Al and O atoms for AlO1.5, AlO1.625H0.278, AlO2H and AlO3H3, respectively. Thus, the identified rings are highly connected between them, indicating the existence of a medium-range order in AlOx. In these connected graphs, some O atoms are dangling atoms (0, 0.57±0.58, 5.20±0.02 and 23.79±7.01 %, respectively), the remaining of Al and O atoms belonging to rings or paths between rings. These dangling atoms correspond mainly to

[1]

O, because their content

and their evolution as a function of O/Al ratio are very similar (see Supporting Informations). These latter have a destructuring effect on AlOx. Thus, for strongly O- and H-rich AlOx, a nonnegligible content of oxygen is not involved in the medium-range arrangement (for example: at least 22.75 % of total oxygen within AlO3H3). The dangling oxygen are passivated by hydrogen atoms. In Figure 4b is reported the content of atom rings as a function of O/Al ratio. The four-, six- and eight-member rings clearly dominate, followed by ten-member rings. During the densification


16

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process with mass loss, the distribution of rings shifts towards shortest rings, except fourmember rings which remains approximately constant (see Figure 4b). The atom rings do not exceed 12 atoms, except for AlO3H3 (14 atoms). More precisely, during this densification process with mass loss, around 36 % of atom rings have four-members, whereas the proportion of six-members rings increase from 25.50±6.38 to 44.10±5.56 %. The curves crossing takes place towards O/Al ratio of 2 indicating a structural reconstruction. Cyclic structures display commonly steric clashes in the center of the ring (red isosurface),73,74,76 constraining especially rings at three and four-members. Thereby, this is in contradiction with the high content of four-member rings revealed by ANELLI (~36%). In a previous work based on the chemical bonding within vanadia layers, Riffet et al. have shown that polarization effects stabilize the V2O2 rings.77 This interaction results especially from the bonding combination of two lobes from the 2p atomic orbital of two oxygen. Using the NCI topological tool, a similar stabilizing interaction is revealed by the presence of a blue isosurface between two oxygen within Al2O2 (see Figure 4c). Thus, the polarization effects in the Al2O2 units could explain the unexpected important quantities of four-member rings in AlOx.


17


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Page 18 of 56

Figure 4. a) Example of Al2O2, Al3O3 and Al4O4 rings identified within AlOx. b) Evolution of atom rings content as a function of O/Al ratio: at fixed composition, data are averaged using all structures and the standard deviations are also reported. c) NCI isosurfaces for s=0.5 a.u. A color code is used to visually identify the NCI region: red for steric clashes, green for van der Waals interactions and blue for strong attractive interactions.


18

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The bond-angle distribution function using the Al-O pair gives us further indications about the atom rings. For AlO1.5 and AlO1.625H0.278, the distribution of Al-O-Al (Figure 5) and O-Al-O (Figure 6) bond-angles in Al2O2 have a prominent peak at 93±6° and 81±5°, respectively. In the Al3O3 case, (i) the O-Al-O bond-angles have a peak at 97±14° for AlO1.5 and 94±13° for AlO1.625H0.278 and (ii) the Al-O-Al bond-angles have a main peak at 120±13° and 117±13°, respectively. However, a small shoulder appears at ~ 93° in the distribution of Al-O-Al bondangles of Al3O3 rings, bond-angle similar to those of Al2O2 rings. For Al4O4 and Al5O5 rings, the profile of the Al-O-Al distribution is similar to that of Al3O3 (main peak at ~123° and shoulder at ~93°), whereas a difference appears in the O-Al-O bond-angles case. Indeed, in addition to the main peak around 105°, a flat band appears between 150-180°. Gutiérrez et al. have shown that the Al-O-Al bond-angle distribution allows to describe the connectivity of elementary units in amorphous alumina.40 Two types of connectivity have been highlighted: (i) the corner-sharing configuration where the AlOx elementary units are linked either and share one oxygen, and (ii) the edge-sharing configuration where two oxygen are shared between two AlOx elementary units. In this study, the AlOx units forming the Al2O2 rings are edge-sharing configurations (peak at ~90°), and the corner-sharing configurations are associated to the peak at ~123° (Figure 5).40 For the longer rings (> Al2O2), a minority includes motifs of type edge-sharing. In other words, multicyclic motifs exist within AlOx explaining the low peak around 90° for rings longer than Al2O2. The profile of total O-Al-O bond-angles for different O/Al ratio allowed us to highlight which

[n]

Al contribute mainly to the ring formation of given length. Indeed, the total O-Al-O

angle distribution of AlO1.5 and AlO1.625H0.278 are very similar and have a main peak at 83° and a shoulder around 99°. This shoulder is attenuated in AlO2H and disappears in AlO3H3, consistent trend with the evolution of [4]Al. Thus, contrary to what is indicated in [40], [4]Al contribute very


19


few to Al2O2 rings (edge-sharing configurations). Furthermore, the

[6]

Al content being low for

AlO1.5 and AlO1.625H0.278, the peak at ~ 82° is mainly due to the presence of [5]Al. In the AlO3H3 case, the top of the curve is flat from 80° to 91° and the content of

[5]

Al and

[6]

Al is close

(40.9±13.7 and 48.4±10.6 %, respectively). Thus, the peak around 91° is associated mainly to [6]

Al. Bergmański et al. have shown that the peaks at ~90° and ~180° associated to O-Si-O are

related to the geometry of SiO5 (square pyramids and triangular bi-pyramids) within PbSiO3.78 A similar profile having been identified in this study, the flat band (150-180°) is thus attributed to [5]

Al. In summary, (i) [5]Al is mainly linked to another [5]Al, and to [6]Al to form the Al2O2 rings,

and (ii) the longer rings (> Al2O2) are formed by a sequence of corner-sharing configurations linking [4]Al, [5]Al and [6]Al between them.

0.05

0.10

0.03

Al3O3

Al2O2

0.02

0.01

0.00

0.08

angle distribution

angle distribution

Total angle distribution

0.06 0.04 0.02

70

90 110 130 150 170 angle [°]

0.04 0.03 0.02 0.01 0.00

0.00 50

50

70

50

90 110 130 150 170 angle [°] 0.05

0.05

AlO1.5 AlO1.5

Al4O4 0.04

angle distribution

angle distribution

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 56

0.03 0.02 0.01

AlO1.625H0.278 AlO1.625H0.278

0.04

70

90 110 130 150 170 angle [°]

Al5O5

AlO2H AlO2H

0.03

AlO3H3 AlO3H3

0.02 0.01 0

0.00 50

70

90 110 130 150 170 angle [°]

50

70

90 110 130 150 170 angle [°]

Figure 5. Bond-angles distribution of type Al-O-Al, normalized to unit, in Al2O2, Al3O3, Al4O4 and Al5O5 rings for different stoechiometries of AlOx. All structures of a fixed composition are considered.


20

Page 21 of 56

0.08

0.04 0.14

Total

Al2O2

Al3O3

0.03

0.02

0.01

angle distribution

0.12

angle distribution

angle distribution

0.10 0.08 0.06 0.04

0.06

0.04

0.02

0.02 0.00

0.00 50

70

90

110 130 150 170 Angle [°]

0.00 50

70

90

110 130 150 170 angle [°]

0.05

50

70

90

110 130 150 170 angle [°]

0.06

Al4O4

AlO1.5 AlO1.5 AlO1.625H0.278 AlO1.625H0.278 AlO2H AlO2H AlO3H3 AlO3H3

Al5O5 angle distribution

0.04

angle distribution

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


0.03 0.02

0.04

0.02

0.01 0.00

0.00 50

70

90

110 130 150 170 angle [°]

50

70

90

110 130 150 170 angle [°]

Figure 6. Bond-angles distribution of type O-Al-O, normalized to unit, in Al2O2, Al3O3, Al4O4 and Al5O5 rings for different stoechiometries of AlOx. All structures of a fixed composition are considered. In order to complete the description of atom rings during the densification process with mass loss, the distances between second neighbours are also considered. The total experimental neutron PDF extracted from [21] presents a second peak around 2.8 Å with a clear shoulder situated around 2.4-2.5 Å. This structural feature has not been observed in the previous works using the classical MD.40,79 Two hypotheses have been proposed by authors of [79]: (i) the existence of intermixed crystalline phases in the experimental mixture, and (ii) many-body effects not parameterized in the empirical potential. Århammar et al. have reproduced this shoulder for one structure using a stochastic quenching method, but no interpretation has been proposed to explain it.31 In this study, the shoulder at ~2.47 and ~2.53 Å (Figure 1 and Table 3)


21


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Page 22 of 56

is clearly identified for AlO1.5 and AlO1.625H0.278, respectively and is attributed unequivocally to the O-O distances of Al2O2 rings. Thus, these analyses prove unambiguously that the experimental amorphous structures have a non-negligible content of 4-members rings of type Al2O2. During the densification process with mass loss, the O-O distances increase from 2.68±0.21 to 2.83±0.26 Å, which is consistent with the [6]Al → [4]Al transition, i.e. AlO6 → AlO4 (Figure 2). Thus, these O-O distances are shifted up and tend to move away from those of Al2O2 rings, justifying the appearance of the shoulder for the low O/Al ratios. This upward shift of O-O distances is consistent with the increase of O-Al-O bond-angles in all rings (Figure 6). Turning to the Al-Al distances, the shoulders at 2.78, 2.78, 2.83 and 2.88 Å (Figure 1 and Table 3) for AlO1.5, AlO1.625H0.278, AlO2H and AlO3H3 correspond to the Al-Al distances within Al2O2 rings. During the densification process with mass loss, the Al-Al distances decrease from 2.88 to 2.78 Å in the Al2O2 rings, and from 3.38±0.26 to 3.18±0.26 Å in others rings being mainly Al3O3 and Al4O4. This evolution is compatible with the slight decrease of Al-O-Al bond angles (Figure 5). Moreover, the shorter O-O distances in the Al3O3 and Al4O4 rings and the Al-Al distances in Al2O2 are all included in a broad band around 2.7-2.9 Å, disrupting the experimental measurements of the O-O distances and can explain the large experimental incertitude of ±0.58 Å.21 The experimental Al-Al distances (3.2±0.55 Å) are fully consistent for all chemical composition. However, the value of 3.08 Å measured using X-ray diffraction is underestimated,23 but corresponds to an intermediate value between the two maxima identified for the Al-Al pair. During the densification process without mass loss, the analysis of the atom rings evolution is compromised (see supporting information). Indeed, there is no good correlation between atom rings of higher content in AlOx (Al2O2 and Al3O3) and the mass density (0.02 < rs < 0.67 and


22

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0.34 < rs < 0.70 for Al2O2 and Al3O3, respectively): for example, two structures having densities very close, the content for a given ring length can vary up to 20 % (see supporting information). However, some trends can be extracted in the case of AlO1.5 and AlO1.625H0.278: for mass density ranging from 2.7 to 3.0, the content of atom rings at 4-, 6 and 8-members are almost constant (AlO1.5: 34.18±3.40, 40.8±4.12 and 23.48±3.68 %; AlO1.625H0.278: 32.93±3.72, 38.25±4.32 and 24.01±3.55 %, respectively). Then, as mass density goes on increasing towards 3.5, the content of 8-member rings decreases towards 10 %, whereas 6-members rings increases towards 50 % and 4-members rings trend slightly towards 40 %. Defects. In this part, structural properties (bond lengths) of defects are studied and a comparison with experimental data is done when available. Then, a discussion on the formation energies of defects is reported. Considering the total hydrogen content, 94.4±4.4, 97.8±2.8 and 97.9±2.1 % of hydrogen are of type H+ for AlO1.625H0.278, AlO2H and AlO3H3, respectively, i.e. forming an hydrogen bond donor (O-H), the remaining being either as H-H (charge state 0) or hydrogen bond acceptor (charge state -1, Al-H). Das et al. have shown using a simple cluster model of type [H2O+AlOx-] that the hydroxide form is favoured if the clusters are O-rich, whereas the Al-H bond formation is favoured for clusters O-poor.30 Because the chemical compositions of AlOx are O-rich, it is not surprising that the Al-H bonds are seldom compared to Al-OH bonds. The Al-OH groups are detected experimentally by X-ray photoelectron spectroscopy of the O(1s) core level at around 534 eV.7 As mentioned earlier in this paper, a part of O-H groups stems from the passivation of dangling oxygen by hydrogen. For the O-H pair, the first peak at 0.98±0.02 Å is rather sharp. Concerning the Al-H pair (noted H-), 3.7±3.4, 0.7±1.2 and 0.1±0.4 % of hydrogen are under this charge state for AlO1.625H0.278, AlO2H and AlO3H3, respectively. The first peak from partial RDF


23


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Page 24 of 56

of the Al-H pair has a very low intensity and is broad, and the Al-H bond length is estimated at 1.62±0.03 Å for AlO1.625H0.278 and AlO3H3, and 1.62±0.09 Å for AlO2H. To our knowledge, no experimental evidence on the presence of Al-H bond in AlOx has been highlighted. For H2 defects, 2.0±4.1, 1.5±2.6 and 2.0±2.6 % of hydrogen have a charge state close to 0 for AlO1.625H0.278, AlO2H and AlO3H3, respectively. An experimental study suggested that the blistering phenomena at the interface Al2O3/Si are due to the accumulation of H2, highlighting indirectly the possible existence of H2 within AlOx.29 In the present contribution, the shortest intramolecular H-H distances identified are of 0.755±0.009 Å, respectively. As comparison, the freely rotating H2 molecules in molecular solids (hexagonal-close-packed phase at 1 atmosphere and low temperatures) have experimental and theoretical (PBE functional) length bonds of 0.741 Å and 0.751 Å, respectively.80,81 Thus, the average H-H bond length (0.755 Å) is very close of the theoretical reference value (∆d(H-H) = 0.004 Å). However, the obtained values are dispersed of ±0.01 Å. This dispersion is prima facie low, but the evolution of the chemical bond of the hydrogen under high pressure indicates otherwise. In the [1 atm – 500 GPa] pressure range, the associated intramolecular H-H bonds range from 0.736 to 0.780 Å.81 In a recent study, Riffet et al. have shown that the behaviour of H2 molecules during the polymerization process under high pressure takes place in three different steps: dipolar attraction (1 atm to ~3GPa), repulsion (~3 GPa to ~250 GPa) and bond formation (~250 GPa to ~500 GPa).82 By direct comparison of intramolecular H-H distances, the H2 systems in AlOx are true molecules localized in interstitial sites (regimes of repulsion and dipolar attraction), except for the H-H bond lengths superior to 0.76 Å where their molecular identities are lost (bond formation regime). In this last case only, H2 is coordinated at one Al3+ site (i.e. two hydrogen bonds of type Al+3…H0) passivating thereby this Al3+ site.


24

Page 25 of 56

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In AlO1.625H0.278, AlO2H and AlO3H3, 95.6±10.0, 94.5±6.6 and 95.6±4.2 % of oxygen have a charge state of -2, respectively. The remaining of oxygen is essentially under form of peroxide groups, noted O22-, and seldom ozone groups, noted O32-. So, O22- constitute essentially the Obased defects and are characterized by intramolecular O-O distances of 1.49±0.02 Å. To compare, the O2, O2- and HO-OH experimental bond lengths are of 1.21, 1.35 and 1.47 Å (isolated molecules), respectively. The O-O bond lengths are fully consistent with the position of the experimental peak around 1.5 Å of total neutron scattering curves from [21]. Furthermore, as mentioned in the introduction, structures including trapped O-O pairs explain better the measured NEXAFS spectrum.31 All this information indicates that the O22- defects are highly probable in AlOx. Local oxygen vacancies with two electron (ܸைଶି ) have been also identified within AlOx. The consequence of this defect is the decrease of the distance between two Al sites creating interactions of type Al…Al (in our previous work, three types of Al…Al motifs by dint of the distribution of two electrons have been distinguished: Al~1.25+-Al~2.2+, Al~1.5+-Al~2.0+ and Al~1.7+-Al~1.8+, noted here ܸைଶି [1], ܸைଶି [2] and ܸைଶି [3], respectively).32 The number of structures having ܸைଶି increases with the oxygen depletion within AlOx (0, 0.56 and 6 % of structures for AlO3H3, AlO2H and AlO1.5, respectively). For these latter chemical compositions, ܸைଶି defects are coupled with O22- defects. Surprisingly, a last type of defect is identified in AlO1.625H0.278 as two electrons occupying the conduction band minimum (CBM), a delocalized state formed of O2- and Al3+ s orbitals. For such cases, the Bader analysis do not reveal any charge anomaly on any atoms in the simulation box. In the supporting information, the wave functions corresponding to the CBM occupied by the 2 electrons and the empty CBM for a structure of AlO1.625H0.278 with H2 defect which does not affect the CBM32 are drawn and show no significant difference. The origin of such charges is


25


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Page 26 of 56

still unclear and might not be related to the fixed negative charges observed in AlOx.6 Indeed, the state occupied by the two electrons is highly dispersed and would imply that such structures are nearly metallic. The structures of AlO1.5, AlO2H and AlO3H3 having the lowest formation energies have all their O, Al and H elements assimilated to O2-, Al3+ and H+, respectively. For the sake of clarity, these structures are classified in a set so-called Σ0. Thus, the formation of OH groups are favored compared to other defects and this can explain that more than 94 % of hydrogen are in form of H+, i.e. O-H bond. The range of formation energies of H2 and Al-H is equivalent in all compositions (defined by the blue dashed-lines in Figure 7): yet, the out-of-equilibrium nature of the formation of amorphous phase may render the accessibility of such configuration difficult due to the presence of energy barrier (untreated in this paper): the formation energy is still required to identify the most probable defects. Considering AlO1.625H0.278, it is noticeable that the H-based defects are energetically more favorable than those of type ܸைଶି (∆Ef = 0.014 eV/atom using the most stable structure containing H2 or H- and that containing ܸைଶି ), which is coherent with the fact that studied AlOx in this paper are O- and H-rich. As mentioned previously, the O22- defects are not only coupled to the ܸைଶି defects, but also with H2 and Al-H defects to respect the charge balance. In particular, the couple {O22-; H-based} defects are much more frequent in AlO1.625H0.278, AlO2H and AlO3H3 and are energetically more favourable than {O22-; ܸைଶି }. Indeed, in each composition, the most stable structure containing the couple {O22-+ ܸைଶି } have a formation energy ~0.08 eV/atom compared to the reference structure from Σ0, whereas in the case of {O22- + H2 or H-} this is of ~0.03, 0.04 and 0.02 eV/atom for AlO1.625H0.278, AlO2H and AlO3H3, respectively. For AlO1.625H0.278 compound, the 2 electrons in CBM have similar formation energies to ܸைଶି and {O22- + 2H-}/{O22- + H2 + H-} but significantly


26

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higher than H2 and H-. In assuming that all structures from Σ0 can be energetically accessible, so others structures having a similar formation energies should also be accessible (see under the red dashed-lines in Figure 7). Thus, {O22- + H2} or {O22- + H-} are potential defects in AlOx respecting the charge balance (AlO2H and AlO3H3), whereas for the non-stoichiometric composition AlO1.625H0.278 (over-excess of hydrogen), H2, Al-H, O22-, ܸைଶି [1], ܸைଶି [2], ܸைଶି [3] and 2 electrons in CBM are also accessible.


27


0.20

0.16

AlO1.5

0.14

AlO1.625H0.278

0.12 Ef (eV/atom)

Ef (eV/atom)

0.16 0.12 0.08

0.10 0.08 0.06 0.04

0.04

0.02 5

6

0.00

7

H2 H[1] [2] [3] H2 + H- + O222H- + O222H2 + O22H2 + 2H- + 2O223H- + 2O224H- + 3O22H2 + [1] + O222H- + [1] + 2O222 [1] + O22H +2 [1] + 2O22H- + [2] + O22[1] + [2] + O22H- + [3] + O22H2 + H- + [3] + 2O222e-

ø4

[2] + 2O22-

3

[1] + O32-

2

ø

[1] +

2

1

[3] + O22-

[1] + O22-

Σ0

0

[2] + O22-

0.00

0.20

AlO2H

AlO3H3

0.14

0.16

0.12 Ef (eV/atom)

Ef (eV/atom)

0.12 0.08

0.10 0.08 0.06 0.04

0.04 0.02 12

+ 2O22- + O32-

10

14

3H2 +

8

4H2 + 4O22-

ø

H-

6

H2 + 2H- + O22- + O32-

4

3H2 + O22- + O32-

2

2H2 + H- + 3O22-

0

3H2 + 3O22-

12

H2 + H- + O32-

10

2H2 + O32-

ø

8

2H2 + 2O22-

6

H2 + H- + 2O22-

4

H- + O22-

2

H2 + O22-

0

Σ0

0.00

0.00 Σ0 H2 + O22H- + O22H2 + H- + 2O222H- + 2O222H2 + 2O22[1] + O22H2 + 2H- + 3O223H2 + 3O222H2 + 2H- + 4O222H2 + H- + 3O22-

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 28 of 56

Figure 7. AlO1.5, AlO1.625H0.278, AlO2H and AlO3H3 formation energies (Ef, eV/atom) computed at PBE level, the most stable amorphous structure of each composition is used as reference. Structures are classified with respect to the nature of defects. Blue and red dashed-lines serve as a guide to the eye.


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Electronic and chemical passivation properties. A complete description of AlO1.5, AlO1.625H0.278, AlO2H and AlO3H3 DOS has been reported in our previous work.32 This property is important to understand the following of this paper, a brief description of the DOS is thus presented: For Σ0, the 2p orbitals of O2- sites constitute mainly the localized states forming the top of valence band (VB), whereas the delocalized states forming the bottom of conduction band (CB) are constituted of Al 3s atomic orbitals and O 2s orbitals. In the case of structures with defects, the DOS analyses have shown that the defects O22- (O32-) and ܸைଶି are responsible for introducing electronic states inside the band gap. Indeed, ܸைଶି generates one filled electronic state towards VB edge, whereas the internal O-O bond of O22- introduces in most cases non-degenerate filled π*-states at the top of VB and one empty σ*-state at the bottom of CB.32 In the present contribution, in order to understand the effects of hydrogen impurities and oxygen excess on the electronic properties of AlOx, other chemical compositions are studied (as mentioned in the METHODS section). Three sets are thus defined as follows: Γ1 → {AlO1.5; AlO1.625; AlO1.75; AlO1.875; AlO2}, Γ2 → {AlO1.5; AlO1.5H0.056; AlO1.5H0.139; AlO1.5H0.194; AlO1.5H0.278} and Γ3 → {AlO1.625; AlO1.625H0.056; AlO1.625H0.139; AlO1.625H0.222; AlO1.625H0.278}: -

The OH, ܸைଶି , H2 and Al-H defects are identified in the case of Γ2. Among these defects, only ܸைଶି affects significantly the band gap. However, the most stable identified structure has only H-based defects (OH, H2 and Al-H), thereby no electronic state is present in the gap. The most stable identified structure containing only ܸைଶି + H-based defect is situated at 4 meV/atom higher in energy. When several ܸைଶି occurs in the simulation box, corresponding to a high density of such defect, a set of bands appears inside the band gap.


29


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Page 30 of 56

But, the optical transitions of type ܸைଶି s and p orbitals → O2- and Al3+ s orbitals (conduction band) are strong, thereby the refractive index associated to this type of defect is higher than the experimental refractive index.32 Thus, ܸைଶି is not a good candidate to explain the origin of negative fixed charges. -

In the case of Γ1, only O22- and O32- groups are identified. These latter introduce many empty σ*-states inside the gap in the vicinity of the CB. In order to quantify the defect ఌ

electronic states localized in the bandgap, the quantity Ndefect = ‫׬‬ఌ ೎ ݊ሺߝሻ݀ߝ is calculated ೡ

using the lowest-energy structure of each composition, and where εv and εc represent the energies of the highest filled valence band and of the lowest empty conduction band not associated with defects, respectively. During the densification process with mass loss (AlO2 → AlO1.875 → AlO1.75 → AlO1.625 → AlO1.5), the O22- and O32- groups disappear progressively from structures, and Ndefect decreases thus towards 0 (Figure 8a). For Γ3, a progressive increase of hydrogen content in AlO1.625 allows to supress some or all electronic states inside the gap through the passivating reaction O22- + 2H → 2OH-. Such trend is also highlighted by the decrease of Ndefect towards 0 as the hydrogen content increases (Figure 8b). In [32], structures having defects of type O22-, OH, H2 and/or Al-H have bandgap energies fully consistent with the experimental data range (5.60±0.49, 5.96±0.29, 6.33±0.38 and 5.71±0.48 eV at PBE0 level for AlO1.5, AlO1.625H0.278, AlO2H and AlO3H3, respectively), and the refractive index are sparsely disturbed by their presence. Considering all structural and electronic properties studied in the present study and in [32], we can speculate on the fact that O22- and Al-H are good candidates to explain the origin of negative fixed charges.


30

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a)

b)

80

AlO2

15 AlO1.625 AlO1.625H0.056

60 Ndefect

10 Ndefect

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


40 AlO1.875 20

AlO1.625

5 AlO1.625H0.222

AlO1.75

AlO1.5

0 1.5

1.6

AlO1.625H0.139

AlO1.625H0.278

0 1.7 1.8 ratio O/Al

1.9

2

0

2.5

5 % H atomic

7.5

10

Figure 8. Integration of defect electronic states localized in the bandgap from DOS (Ndefect): a) Effect of excess O in AlO1.5 (Γ1), and b) effect of % H atomic in AlO1.625 (Γ3). In order to identify correlations of type structure – property, the rs values are calculated between the bandgap energy and structural parameters (ρ, CNAl, CNO,

[n]

Al, [m]O and atom rings) (Figure

9). For the sake of simplicity, only structures from the Σ0 for AlO1.5, AlO2H and AlO3H3 are considered. The bandgap energy is calculated as the difference of energy between the highest filled band from the valence band and the lowest empty band from the conduction band.32 The normal distribution function associated to bandgap energy for each compound is reported in Supporting Information: the distribution becomes significantly narrower as the H content increases (variance = 0.09, 0.06 and 0.04, respectively). The rs parameters for AlO1.5, AlO2H and AlO3H3 have all values lower than |0.7|, which prevents any strong correlation between the bandgap energy and short- and medium-range structural properties from being inferred. One should notice however some weak correlation between the mass density and the band gap is observed for AlO1.5 (rs = 0.66). Besides, the content of

[4]

Al (rs = -0.63) and

[2]

O (rs = -0.70) in

AlO1.5 correlate with the band gap: however, these latter also strongly correlate with the mass


31


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

density (rs = -0.89 and -0.89 for

[4]

Al and

[2]

Page 32 of 56

O, respectively). One should notice much less

correlations between band gap and structural parameters are found when the H content increases which is a combined effect of the narrowing of the band gap distribution for both AlO2H and AlO3H3 (see Supporting Information) and a slight widening of the distribution of the structural parameters (see error bars in the Figures 2, 4 and Table 1 of this paper).

Figure 9. Mapping of the Spearman’s correlation coefficients for structures from Σ0 of a) AlO1.5, b) AlO2H and c) AlO3H3. CONCLUSIONS. Based on the melt and quench strategy, over 3000 structurally different AlOx structures have been generated using ab initio MD. For a large number of structures, the defects considered in this study (OH, O22-, ܸைଶି , H2, Al-H and 2 electrons) emerged directly from the melt and quench strategy, which made the originality of this approach. Because of the large number of data, the evolution of structural properties during the densification process with mass loss have been studied using averaged data at fixed chemical composition. Thus, structural parameters at short-range for AlO1.5, AlO1.625H0.278, AlO2H and


32

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AlO3H3 may be proposed: dAlO = 1.80, 1.80, 1.83, 1.87 Å; dOO = 2.83, 2.78, 2.73, 2.68 Å; dAlAl = 3.18, 3.18, 3.23, 3.38 Å; [3]Al = 0.1, 0.7, 0.2, 0.1 %; [4]Al = 46.5, 40.5, 27.0, 10.6 %; [5]Al = 46.0, 48.9, 52.5, 48.4 %;

[6]

Al = 7.4, 9.9, 20.2, 40.9 %; CNAl = 4.61, 4.68, 4.93, 5.30. The atom rings

(ring length, bond-angles and distance between second neighbors) allowed to describe the medium-range structuration. In particular, in all compositions of AlOx, Al2O2 representing ~36 % of the ring population are mainly composed of

[5]

Al, Al2O2 being stabilized by polarization

effects. The others rings are formed by a sequence of corner-sharing configurations linking [n]Al between them. The and

[5]

[5]

Al content (~ 50%) is the most important, except for AlO1.5 where

Al contents are sensibly the same (~ 45%). The

[6]

[4]

Al

Al/[4]Al ratio is a key criteria

determining the average CNAl. Moreover, during this densification process, a strong restructuration of AlOx is observed around O/Al ratio = 2: the {[4]Al and [2]

[6]

Al} and {[3]O,

O+[1]O} contents vary in opposite directions and becomes equal around O/Al = 2. Then, the

structural parameters (atomic distance, CN, ring length) of AlO1.5 and AlO1.625H0.278 remain close. This observation allowed to highlight that the use of simple structural parameters criteria alone do not always allow to discriminate between many AlOx slightly O-rich of different chemical composition. Experimental and theoretical structural data are in good agreement, validating the methodology. In particular, the profile of the total experimental neutron PDF and the existence of large scatterings of the experimental measurements (such as dOO) have been rationalized. The evolution of structural properties during the densification process without mass loss have also been investigated. The Spearman correlations have been explored in order to obtain monotonic relationships of type structure – structure and structure – electronic property. A good correlation between the mass density and coordination number (CNAl,

[4]

Al,

[6]

Al and CNO) is


33


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Page 34 of 56

observed. But a correlation of type bandgap energy – structural properties could not be clearly inferred. Dangling oxygen, passivated by hydrogen (forming an OH group), appear mainly in O-rich AlOx and have a destructuring effect. Moreover, the bond length of O22- (1.495 Å) is fully consistent with the position of experimental peak around 1.5 Å of total neutron scattering curves from [21], explaining thus its origin. Surprisingly, a last type of defect has been identified in the AlO1.625H0.278 compound as two electrons occupying the CBM. The origin of such charges is still unclear and might not be related to the fixed negative charges observed in AlOx. However, the analysis of structural properties of defects and their effects on electronic properties of AlOx allowed to speculate that the O22- and Al-H defects are good candidates to explain the origin of negative fixed charges. ASSOCIATED CONTENT Supporting Information. Additional content related to the melt and quench procedure (choice of melt temperature, energy versus mass density for all obtained structures after the quenching/cooling melt). Total experimental neutron pair correlation function extracted from [21]. Spearman correlation between (i) [n]Al and mass density, (ii) [m]O and mass density and (iii) atom rings and mass density at fixed chemical composition. Mean values and standard deviations of theoretical structural parameters extracted from Figure 2 and 4. Evolution of dangling atoms as a function of the

[1]

O content. Wave functions of CBM. Normal distribution function

associated to bandgap energy for the Σ0 set of AlO1.5, AlO2H and AlO3H3. Spearman rank correlation matrix associated to the Σ0 set of AlO1.5, AlO2H and AlO3H3. This material is available free of charge via the Internet at http://pubs.acs.org.


34

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AUTHOR INFORMATION Corresponding Author * [email protected] and [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ‡These authors contributed equally. Notes The authors declare no competing financial interest. ACKNOWLEDGMENT This work was carried out in the framework of a project of IPVF (Institut Photovoltaïque d’Ilede-France). This project has been supported by the French Government in the frame of the program of investment for the future (Programme d’Investissement d’Avenir – ANR-IEED-00201). We thank Etienne Drahi and Fabien Lebreton for illuminating discussions about AlOx experimental data. We also thank Giorgio Mancini for valuable discussions about ANELLI program package. REFERENCES (1) Avice, M.; Diplas, S.; Thøgersen, A.; Christensen, J. S.; Grossner, U.; Svensson, B. G. Rearrangement of the Oxide-Semiconductor Interface in Annealed Al2O3/4H-SiC Structures. Appl. Phys. Lett. 2007, 91, 052907-3. (2) Potts, S. E.; Schmalz, L.; Fenker, M.; Díaz, B.; Światowska, J.; Maurice, V.; Seyeux, A.; Marcus, P.; Radnόczi, G.; Tόth, L.; et al. Ultra-Thin Aluminium Oxide Films Deposited by


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TOC Graphic


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a) Total and b-d) partial average radial distribution function (RDFav), normalized to unit, associated to b) OO, c) Al-O and d) Al-Al pairs. All structures at a fixed composition are considered. The dashed line serves as a guide to the eye. The total experimental neutron PDF extracted from [21] is reported in Supporting Information. 122x119mm (96 x 96 DPI)



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Percentage of a) [n]Al and b) [m]O sites as a function of the O/Al ratio associated to AlO1.5, AlO1.625H0.278, AlO2H and AlO3H3. At fixed composition, data are averaged using all structures and the standard deviations are also reported. Experimental data of [n]Al extracted from [19] are plotted in the panel a. 1720x833mm (96 x 96 DPI)


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a) CNAl and b) CNO of all structures of different stoechiometries of AlOx as a function of mass density (g.cm-3). The associated rs values are reported in this Figure. 1790x761mm (96 x 96 DPI)



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a) Example of Al2O2, Al3O3 and Al4O4 rings identified within AlOx. b) Evolution of atom rings content as a function of O/Al ratio: at fixed composition, data are averaged using all structures and the standard deviations are also reported. c) NCI isosurfaces for s=0.5 a.u. A color code is used to visually identify the NCI region: red for steric clashes, green for van der Waals interactions and blue for strong attractive interactions. 1231x2138mm (96 x 96 DPI)


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Bond-angles distribution of type Al-O-Al, normalized to unit, in Al2O2, Al3O3, Al4O4 and Al5O5 rings for different stoechiometries of AlOx. All structures of a fixed composition are considered. 1858x1016mm (96 x 96 DPI)



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Bond-angles distribution of type O-Al-O, normalized to unit, in Al2O2, Al3O3, Al4O4 and Al5O5 rings for different stoechiometries of AlOx. All structures of a fixed composition are considered. 2065x1294mm (96 x 96 DPI)


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AlO1.5, AlO1.625H0.278, AlO2H and AlO3H3 formation energies (Ef, eV/atom) computed at PBE level, the most stable amorphous structure of each composition is used as reference. Structures are classified with respect to the nature of defects. Blue and red dashed-lines serve as a guide to the eye. 165x175mm (96 x 96 DPI)



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Integration of defect electronic states localized in the bandgap from DOS (Ndefect): a) Effect of excess O in AlO1.5 (Γ1), and b) effect of % H atomic in AlO1.625 (Γ3). 1749x723mm (96 x 96 DPI)


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Mapping of the Spearman’s correlation coefficients for structures from Σ0 of a) AlO1.5, b) AlO2H and c) AlO3H3. 165x51mm (96 x 96 DPI)



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TOC graphic 1652x906mm (96 x 96 DPI)


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Statistics-Based Analysis of the Evolution of Structural and Electronic

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