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Letter

Decoupling the Effects of Mass Density and Hydrogen-, Oxygen- and Aluminum-based Defects on Optoelectronic Properties of Realistic Amorphous Alumina. Vanessa Riffet, and Julien Vidal J. Phys. Chem. Lett., Just Accepted Manuscript • Publication Date (Web): 17 May 2017 Downloaded from http://pubs.acs.org on May 21, 2017

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The Journal of Physical Chemistry Letters

Decoupling the Effects of Mass Density and Hydrogen-, Oxygen- and Aluminum-based Defects on Optoelectronic Properties of Realistic Amorphous Alumina.

Vanessa Riffeta,b,* Julien Vidalc,b,a AUTHOR ADDRESS. a

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

b

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

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

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

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] 1 ACS Paragon Plus Environment


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ABSTRACT. The search for functional materials is currently hindered by the difficulty to find significant correlation between constitutive properties of a material and its functional properties. In the case of amorphous materials, the diversity of local structures, chemical composition, impurities and mass densities makes such connection difficult to be addressed. In this letter, the relation between refractive index and composition has been investigated for amorphous AlOx materials, including non-stoichiometric AlOx, emphasizing the role of structural defects and the absence of effect of the band gap variation. It is found that the Newton-Drude (ND) relation predicts the refractive index from mass density with a rather high level of precision apart from some structures displaying structural defects. Our results show especially that O- and Al-based defects act as additive local disturbance in the vicinity of band gap, allowing us to decouple the mass density effects from defect effects (n = n[ND] + ∆ndefect).

TOC GRAPHICS

2 ACS Paragon Plus Environment

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Amorphous alumina (AlOx) has been considered in several technological applications, not only because of passivating and insulating properties, but also because of its high dielectric constant and reflectivity in the visible.1-6 The AlOx thin layer can be deposited via a variety of techniques ranging from vacuum to non-vacuum techniques such as sputtering, chemical vapor deposition or atomic layer deposition.6 However, it is well-known that these processes introduce impurities from precursor chemical species used during film deposition, as hydrogen.6-8 Unfortunately, it is difficult to quantitatively probe the H content in a film,7 particularly unbounded H formed during annealing under H2 atmosphere and incorporated within AlOx bulk or at the interface AlOx/Si creating blistering phenomena.9 Furthermore, precise experimental knowledge of O/Al ratio of such material is hampered by thickness dependence of the composition, the experimental estimation yielding O/Al ratio ranging from 1.5 to 8.8,10-15 Inexplicably, despite the experimental evidence on films slightly O-rich, only AlO1.5 is considered in the theoretical studies.16,17 Large scatterings of the experimental measurements of optoelectronic quantities of interest have been observed for amorphous AlOx materials: mass density from 2.5 to 3.5 g.cm-3,7,8,14,15,18,19 band gap energy from 5 to 7 eV,6,20,21 refractive index at 633 nm from 1.51 to 1.67.6,10,15,18,22-24 In order to fine tune some given properties, the understanding of the link between structures and properties is essential. Such relations may guide the deposition process towards more effective AlOx layer with improved performances. In particular, relationships between mass density (ρ) and refractive index (n) are reported in the literature: the empirical Gladstone-Dale (GD) relation (n-1)/ρ = C1,25 the Newton-Drude (ND) relation (n²-1)/ρ = C2, the Lorentz-Lorenz (LL) relation (n²-1)/(n²+2)ρ = C3 and the general Anderson and Schreiber (AS) relation 4π/(n²-1) = 1/(C4ρ) – b with (Ci=1,2,3,4 constant and b the electronic overlap parameter: for b = 0 → ND and b = 4π/3 → LL). They are found to be applicable to large classes of crystalline materials (non-opaque,26-28 3 ACS Paragon Plus Environment


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allotropic29,30 and polymorphs31,32) as long as the nature of the electronic states involved in the optical transitions remains unchanged, no significant change of band gap is observable and the change in mass density is confined to a narrow range. Taking advantage of the existence of these relations, we propose here to investigate an extended family of realistic amorphous materials: (i) AlO1.5,6 AlO2H15 and AlO3H3,1,10 the overall stoichiometry following charge balance, and (ii) the new non-stoichiometric compound AlO1.625H0.278 whose the stoichiometry respects experimental observations (O/Al > 1.5 and hydrogen content < 13 atomic %).7-9,15,24,33 For the first time, the effects of defects on the refractive index have been investigated in order to decouple them from the effects of mass density, quantitative data being proposed. Results from ND relation are presented in this letter (GD, LL and AS are reported in supporting informations, LL was found not to be adapted to AlOx). All calculations have been done using PBE functional,34,35 but the band gap energies being underestimated by DFT calculations, the popular hybrid functional PBE0 has been used to refined them.36 Structures. To ensure a sufficient statistical sampling, a set of 2010 amorphous structures has been generated using a strategy based on the ab initio melt and quench approach. A large mass density range ranging from 2.11 to 3.45 g.cm-3 is obtained indicating a good sampling of structural parameters (2.75-3.45, 2.70-3.35, 2.50-3.25 and 2.11-2.75 g.cm-3 for AlO1.5, AlO1.625H0.278, AlO2H and AlO3H3, respectively). A good match with experimental data, ranging from 2.5 to 3.5 g.cm-3,7,8,14,15,18,19 is obtained for O/Al ratio from 1.5 to 2. A Bader analysis37 reveals anomalous charge states of atoms drastically deviating from Al2.48+, O1.59-,1.52- and H0.63+ (taking α-AlO(OH) as reference), being qualified in the following as defects.


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Concerning H-based defect, H2 molecules are always localized in interstitial positions (total charge ≈ 0 and d(H-H) ≈ 0.75 Å). Besides the O-H hydrogen bond donor,1,6,10,15 some structures also display Al-H hydrogen bond acceptor, i.e. H is in the substitutional O site (H~0.75- and d(AlH) ≈ 1.65 Å, noted H-). Turning to the oxygen-based defects, most of them are composed of the peroxide group (O2~1.65- and d(O-O) ≈ 1.45 Å, noted O22-), while ozone group (noted O32-) have been seldom identified. In addition, an oxygen vacancy between two Al sites leads to a local lattice distortion. The distance between these two Al sites decreases creating an Al-Al defect, the associated charge states being Al~1.25+-Al~2.2+, Al~1.5+-Al~2.0+ and Al~1.7+-Al~1.8+, noted Al-AlI, AlAlII and Al-AlIII, respectively. We show in Figure 1 the distribution of obtained defects. The case of AlO1.625H0.278 allows us to analyze separately H- and Al-based defects. Overall, the relative energies tend to increase with the number of defects. The Al-based defects are less frequent with the increase of O/Al ratio, H- and O-based defects being clearly favored. Finally, it is clear that the energetic cost of H2 molecule in an interstitial environment is equivalent to the energy cost to form H- or Al-based defects. All these defects have been mentioned at least once in the experimental literature.1,6,9,10,15,22,38-40 We have defined three sets: Σ1 for structures without defects, Σ2 for those with H- and/or O-based defects, and Σ3 for those including at least Al-based defects.



a)

b) 0.20

0.16

AlO1.5 ∆Erel (eV/atom)

∆Erel (eV/atom)

AlO1.625H0.278

0.14

0.16 0.12 0.08 0.04

0.12 0.10 0.08 0.06 0.04 0.02

0.00

0.00

7

0

d)

0.20

AlO2H

ø

10

15

20

AlO3H3

0.14

0.16

5

H2 HAl-AlI Al-AlII Al-AlIII H2 + H- + O222H- + O222H2 + O22H2 + 2H- + O223H- + 2O224H- + 3O22H2 + Al-AlI + O222H- + Al-AlI + 2O222Al-AlI + O22H + 2Al-AlI + 2O22H- + Al-AlII + O22Al-AlI + Al-AlII + O22H- + Al-AlIII + O22H2 + H- + Al-AlIII + 2O22-

6

Al-AlI + AlAlII + 2O22-

ø

5

2Al-AlI + O32-

4

Al-AlIII + O22-

3

Al-AlII + O22-

Al-AlI + O22-

2

∆Erel (eV/atom)

0.12

0.12 0.08 0.04

0.10 0.08 0.06 0.04 0.02 10

12

+ 2O22- + O32-

8

14

3H2 +

ø

4H2 + 4O22-

6

H-

4

H2 + 2H- + O22- + O32-

2

3H2 + O22- + O32-

0

2H2 + H- + 3O22-

ø

3H2 + 3O22-

12

H2 + H- + O32-

10

2H2 + O32-

8

2H2 + 2O22-

6

H2 + H- + 2O22-

4

H2 + O22-

2

without defect H2 + O22H- + O22H2 + H- + 2O222H- + 2O222H2 + 2O22Al-AlI + O22H2 + 2H- + 3O223H2 + 3O222H2 + 2H- + 4O222H2 + H- + 3O22-

0

H- + O22-

0.00

0.00

without defect

c)

1

without defect

0

∆Erel (eV/atom)

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Figure 1. a) AlO1.5, b) AlO1.625H0.278, c) AlO2H and d) AlO3H3 relative energies (∆Erel) computed at PBE level in eV/atom, the most stable amorphous structures of each composition being used as reference. Structures are classified with respect to the nature of defects. Structures from Σ1, Σ2 and Σ3 are represented in blue, black and red, respectively. 6 ACS Paragon Plus Environment

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Optoelectronic properties. Figure 2 plots the ND relation applied to Σ1, Σ2 and Σ3. For Σ1, all compositions have distinct ND-related lines. The coefficients of determination are close to 1 (R² = 0.978-0.990) showing that the ND relation can be effectively used to describe properly the refractive index of AlOx. The non-stoichiometric AlO1.625H0.278 verifies also the ND relation. ND[Σ2] deviates from ND[Σ1] by being shifted upward by ~0.02 and data points are more dispersed as evidenced by the decreasing of R² (0.968-0.985). This indicates H and O-based defects slightly disturb the ND relation. In the Σ1 and Σ2 case, as oxygen and hydrogen contents decrease further (mass loss) and consequently AlOx grows denser, the refractive index increases. This trend is consistent with experimental observations on the densification of thin AlOx film.15,33 Thereby, great caution must be taken on the interpretation of experimental linear fits because different AlOx composition (+ impurities) are obtained upon annealing. Figure 2 c) reveals that ND[Σ3] deviates more from ND[Σ2] and ND[Σ1] for AlO1.625H0.278 and AlO1.5, respectively by being shifted upward by ~0.045 and ~0.08, respectively. Data points are more dispersed (R² = 0.861-0.954) and the line of AlO1.5 merges with the line of AlO1.625H0.278. The interpretation of these observations constitutes the main result of this letter.



a) 3.2

AlO1.5 (n²-0.944)/ρ = 0.654

ND[Σ1]

n²

3.0

2.8

AlO2H (n²-0.911)/ρ = 0.696

2.6

AlO3H3 (n²-0.868)/ρ = 0.762

2.4 2.0

2.5

b) 3.2

ND[Σ2]

3.0 ρ [g.cm-3]

3.5

AlO1.625H0.278 (n²-0.952)/ρ = 0.665

n²

3.0

2.8

AlO2H (n²-0.912)/ρ = 0.704

2.6

AlO3H3 (n²-0.918)/ρ = 0.749

2.4 2.0

2.5

3.0 ρ [g.cm-3]

3.5

c) ND[Σ3] 3.2

3.0

AlO1.625H0.278[Σ2]

(n²-0.951)/ρ = 0.680 (n²-0.866)/ρ = 0.707

n²

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2.8

AlO1.5[Σ1]

2.6 2.5

2.7

2.9

3.1

3.3

ρ [g.cm-3]

Figure 2. ND relation for a) Σ1, b) Σ2 and c) Σ3 groups, computed at PBE level. The fits to the data points are indicated with the solid lines. For c), the fits from Σ1 and Σ2 for AlO1.5 and AlO1.625H0.278, respectively are reported to guide the eye. A succinct diagram of theoretical etalon model using the refractive index calculated at the PBE0 level for some key structures of AlOx is


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reported in Figure S2, data extracted from [15], [18] and [33] are plotted as an example of application. In the case of anisotropic volume change of a crystalline allotropic material based on the optical

building block TiO6, Rocquefelte et al. have shown that the quantity I(ε2) =

is

proportional to refractive index (see Ref [29,30] for further details and ε2 imaginary part of the electronic dielectric constant). In the following sections, we will discuss the use of I(ε2) in a novel approach to decouple the effects of defects from mass density effects. As ε2 depends on optical transitions, we have first investigated the density of states (DOS), bandgap energies (Eg) and the

average optical transition matrix elements estimated as follows αi,j = ∑,, | < | | > | at Γ only. In order to draw some general conclusion on the nature of electronic states in the vicinity of the band gap for structures without defect, we have first focus on the DOS obtained from the Σ1 set. The top states forming valence band (VB) are localized on 2p orbitals of O2- sites (noted 2p (O2)i), while the bottom states of conduction band (CB) are very delocalized, mainly formed of Al 3s atomic orbitals and O 2s and 2p orbitals (noted s,p (Al3+, O2-)j, except the lowest vacant band (LV) on O2- and Al3+ s orbitals, noted s (Al3+, O2-)). In supporting information, the corresponding total and partial DOS for each composition are reported. Switching to the Σ2 and Σ3 sets, because of the presence of anomalous charge states of O and Al, electronic states are introduced inside the band gap, resulting at first sight in an apparent reduction of the bandgap (Figure 3). The filled electronic states of Al-based defects (noted s,p (Al-Al)) are located towards VB edge, whereas the internal O-O bond of O22- induces in most cases non-degenerate filled π*-states at the top of VB (different chemical environment of both O-) and one empty σ*-state in the bottom of CB,



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noted 2p (O22-)i and 2p (O22-)j, respectively.41 On the contrary, H-based defects do not affect the bandgap because (i) the H- defect induces localized states at the VB edge, but their contributions to the DOS are negligible in these states compared to O2-, and (ii) the electronic states of H2 molecule lie deep inside the VB.

Figure 3. Atomic density of states of a) H (1s), O (2s2p) -based defects and b) Al (3s3p) -based defects computed at PBE level and extracted from two amorphous structures AlO1.625H0.278. To quantify the perturbation of defects in the bandgap, we have calculated Eg using the highest occupied (HO) and the lowest vacant bands. The values being dispersed within a large range of circa 1 eV, we revisited the way to process this optical property. Indeed, following a normal distribution (as shown in supporting information), the mean value and the variance of bandgap energies have been calculated and reported in Table 1. It appears clearly that the O-based defects reduce the bandgap by less than 0.4 eV, while Al-based defects reduce it by more than 1.5 eV (consistent with the increase of n observed in the ND relation for Σ2 and Σ3). For Σ1 and Σ2, the


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mean value of Eg increases with the O/Al ratio (good match with the experimental data for all compositions, 6,20,21 except Σ3). Table 1. The mean value (Eg,mean) and the variance (σg) from the probability density of the normal distribution for AlOx, computed at PBE0 level. Values correspond to Eg,mean[σg]. AlOxHy AlO1.5 [AlO1.625H0.25+H2] AlO2H AlO3H3 exp.

Σ1 5.69[0.30] / 6.44[0.28] 6.91[0.20]

Σ2 / 5.96[0.29] 6.23[0.45] 6.57[0.56]

Σ3 4.09[0.56] 4.09[0.54] 4.14[/] / 5-76,20,21

Σ1+Σ2 5.60[0.49] 5.96[0.29] 6.33[0.38] 6.71[0.48]

Σ1+Σ2+Σ3 5.60[0.49] 5.57[0.84] 6.32[0.42] 6.73[0.40]

Based on the relation I(ε2) ∝ n, we show in Figure 4 a) how I²(ε2) evolves for Σ1, noted I²(ε2)[Σ1], with the mass density (at fixed and variable Eg). As mass density increases, I²(ε2)[Σ1] increases independently of Eg, implying that Eg has not a significant impact on optical transitions and so the refractive index (consistent with ND relation). It is found in the vicinity of bandgap that optical transitions 2p (O2-)i to s (Al3+, O2-) are the most favorable with αi→LV ≈ 0.1-0.2, while for others transitions αi→j ≈ 10-2-5.10-2 : the data of Σ1 serve as reference for the study of Σ2 and Σ3.

a)

b)

1795 1545

AlO2H

45

AlO1.5

2.5 3.0 ρ [g.cm-3]

3.5

2 Al-based defects

0.80

44

1295 2.0

1.00 I(ε2)[Σ1] I(ε2)

43

∆Idefect

2045

at 5.7 eV 6.96 AlO3H3 5.72 at 6.4 eV 6.72 6.80 at 6.82 eV 7.24 6.55 5.50 6.30 7.03 6.24 6.71 5.90 6.15 7.11 4.09 6.30 6.63 5.28 5.44 5.72 6.47

c)

46

I(ε2)

2295

I²(ε2)[Σ1]

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42

0.60

AlO2H[Σ2]

0.40

41 0.20

40 39 1.66

Icor(ε2)

AlO1.5[Σ3]

AlO1.5

1.70

1.74

1.78

n

0.00 0.000

0.025 ∆ndefect

0.050



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Figure 4. a) Effect of Eg on I²(ε2) vs ρ, illustrated for AlO2H. Dotted lines are linear fits, and in all cases, R² > 0.998. Values correspond to bandgap energies. (The shapes of ε2 vs energy are reported in Figure S7-9: the peak around 11 eV of AlOx is associated to 2p (O22-)i → s,p (Al3+, O2-)j, whereas the peak around 15 eV involve hydrogen as evidenced by the absence of this peak .

for AlO1.5). b) Comparison of I(ε2), I(ε2)[Σ1] and Icor(ε2) = I(ε2) –

.

+

[Σ1] in function of refractive index, dotted lines are linear fits: I(ε2) = 59,291n –

59,717 (R² = 0.881), I(ε2)[Σ1] = 75.403n – 86.128 (R² = 1.00) and Icor(ε2) = 77.045n – 88.95 (R² = 0.997); and c) ∆Idefect vs ∆ndefect. Dotted lines are linear fits: AlO1.5[Σ3]: ∆Idefect = 19.21∆ndefect + 0.004 (R² = 0.954) and AlO2H[Σ2]: ∆Idefect = 25.277∆ndefect – 0.0527 (R² = 0.962). For b-c), note that the values I(ε2)[Σ1] and √" [Σ1] at given ρ are extracted from fits of Figure 4 a) and 2, respectively. 16 and 13 amorphous structures representing different couples of defects from AlO1.5[Σ3] and AlO2H[Σ2], respectively have been used. Interestingly, for Σ2 and Σ3 the global shapes of (ω) are similar to those of Σ1, except additional bands that can appear in the vicinity of the bandgap (Figure 5 a) and b)). In the Σ3 case, these bands are associated unequivocally to strong optical transitions of type s,p (Al-Al) → s,p (Al3+, O2-)j (αHO,j>LV ≈ 0.1-0.5) (Figure 5 a)). At the opposite, O-based defect contributes very slightly in this energy window because optical transitions 2p (O22-)i → 2p (O22-)j, 2p (O22-)i → s,p (Al3+, O2-)j and 2p (O2-)i → 2p (O22-)i are not favored (α ≈ 1-5.10-2) compared to 2p (O2-)i to s (Al3+, O2-) (α ≈ 0.1-0.2). We display in Figure 5 b) the case of multiple O-based defects. Contrarily to Al-based defects, there are no apparent additive effects on the transition intensities in the vicinity of bandgap.


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Figure 5. a) Effects of Al-, O- and H-based defects in the case of AlO1.625H0.278. The maximum of bands are associated to following transitions: δ1 = s,p (Al-Al) → s,p (Al3+, O2-)LV+1 (αHO,LV+1 ≈ 0.42, ∆EHO,LV+1 = 3.06 eV); δ2 = s,p (Al-Al) → s,p (Al3+, O2-)LV+7 (αHO,LV+7 ≈ 0.26, ∆EHO,LV+7 = 3.97 eV); δ3 = s,p (Al-Al) → s,p (Al3+, O2-)LV+1 (αHO,LV+1 ≈ 0.45, ∆EHO,LV+1 = 3.64 eV); δ4 = s,p (Al-Al) → s,p (Al3+, O2-)LV+4 (αHO,LV+4 ≈ 0.25, ∆EHO,LV+4 = 4.17 eV); δ5 = s,p (Al-Al) → s,p (Al3+, O2-)LV+1 (αHO,LV+1 ≈ 0.29, ∆EHO,LV+1 = 3.93 eV); b) Effects of H- and O-defects, in the case of AlO2H. δ6 = 2p (O2-)HO-3 → 2p (O22-)LV (note that O2- and O22- are in the same coordination 13 ACS Paragon Plus Environment


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shell of one Al3+, αHO-3,LV ≈ 0.05, ∆EHO-3,LV = 3.46 eV); δ7 = 2p (O22-)HO-3 → 2p (O22-)LV+1 (type π* → σ*, αHO-3,LV+1 ≈ 0.05, ∆EHO-3,LV+1 = 4.05 eV). Data are computed at PBE level.

To acquire quantitative information about defect contributions on the refractive index, we have #$

#$

calculated corrected transition intensities Icor(ε2) = I(ε2) – + [Σ1], where the two last terms account for optical transitions from 0 to ω’ (i.e. in the vicinity of the #$

bandgap, and includes also the optical transitions associated to defects), the aim being to eliminate the contribution of defects in this energy window. This has been illustrated in the following using ND[Σ3] of AlO1.5 because it deviates more dramatically from ND[Σ1] than other sets. In Figure 4 b), we show that Icor(ε2) is very close to I(ε2)[Σ1] (relative deviation < 0.5 %) indicating that the main optical transitions due to defects are clearly in the vicinity of the bandgap. Thus, we can quantify the contribution of defects as ∆Idefect = I(ε2) – Icor(ε2) ≈ I(ε2) – I(ε2)[Σ1]. We display these quantities as a function of ∆ndefect = √" [Σi=2,3]-√" [Σ1] at given ρ in Figure 4 c), a linear relation being obtained (R² = 0.954). The same observation is done for ND[Σ2] of AlO2H (R² = 0.962). Based on these observations, we show that Σ2 and Σ3 have overall a bulk-like behavior (depending on ρ) to which is added a local disturbance (depending on defects). Thus, refractive index of AlOx can be written as n[Σi=2,3] = n[Σ1] + ∆ndefects. We now return in Figure 2 to extract ∆ndefect, we have calculated ∆nO ≈ 0.006 (using Σ1 and Σ2) and ∆nAl ≈ 0.015 (using AlO1.625H0.278). In summary, we propose a study dealing with refractive index of AlOx, and for the first time the case of non-stoichiometric composition is considered. We show the success of the Newton-Drude (ND) relation on AlOx using a set of 2010 amorphous structures. The presence of O- (Σ2) and Al14 ACS Paragon Plus Environment

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based (Σ3) defects, introducing electronic states inside the band gap, shift upward n² of ~ 0.02 and 0.04, respectively. At the opposite, H-based defects seem to have negligible effects on the refractive index. The electronic states of O- and Al-based defects being present in the vicinity of the band gap, we were able to decouple the effects of mass density with those of O- and Al-based defects. The relation n[Σi=2,3] = n[Σ1] + ∆ndefect can be used, with n[Σ1] (without defect) depending on mass density only (ND relation), and quantitative data of ∆ndefect were obtained (∆nO ≈ 0.006 and ∆nAl ≈ 0.015). Contrarily to O-based defects, Al-based defects have additive effects on the optical transitions in the vicinity of band gap and which can strongly modify the refractive indices of AlOx. Of course, the present study can be extended to other intrinsic or extrinsic defects and even other functional materials of interest.

AUTHOR INFORMATION Notes The authors declare no competing financial interests. 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 Philippe Baranek and Xavier Rocquefelte for valuable discussions.



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ASSOCIATED CONTENT Supporting Information. Additional content related to computational details. Empirical Gladstone-Dale, Lorentz-Lorenz and generalized Anderson and Schreiber relations for AlOx structures from Σ1. Succinct diagram of theoretical etalon model. Total and partial DOS. Eg vs ρ at the PBE0 level. Normal distribution function associated to Eg at the PBE0 level. ε2 vs energy calculated at the PBE level for key amorphous structures. Choice of the ω’ value. 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 Plasma-Enhanced Atomic Layer Deposition for Corrosion Protection. J. Electrochem. Soc. 2011, 158, C132-C138. (3) Díaz, B.; Härkönen, E.; Światowska, J.; Maurice, V.; Seyeux, A.; Marcus, P.; Ritala, M. LowTemperature Atomic Layer Deposition of Al2O3 Thin Coatings for Corrosion Protection of Steel: Surface and Electrochemical Analysis. Corros. Sci. 2011, 53, 2168-2175. (4) Borylo, P.; Lukaszkowicz, K.; Szindler, M.; Kubacki, J.; Balin, K.; Basiaga, M.; Szewczenko, J. Structure and Properties of Al2O3 Thin Films Deposited by ALD Process. Vacuum 2016, 131, 319-326. (5) Hezel, R.; Jaeger, K. Low-Temperature Surface Passivation of Silicon for Solar Cells. J. Electrochem. Soc. 1989, 136, 518-523. (6) Dingemans, G.; Kessels, W. M. M. Status and Prospects of Al2O3-Based Surface Passivation Schemes for Silicon Solar Cells. J. Vac. Sci. Technol. A 2012, 30, 040802-27. 16 ACS Paragon Plus Environment

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