Electronic Supplementary Material (ESI) for: Optoelectronic properties and color chemistry of native point defects in Al:ZnO transparent conductive oxide

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eV, so to obtain the experimental value.Qualitatively, a larger bandgap is ascribable to an increase of the internal bond polarization and a higher localization of the electron density, thus an enhancement of the resulting Us is not surprising.A detailed set of accuracy tests on the effect of DFT+U (same set of parameters) on the electronic structure of both ZnO bulk and surfaces can be found in Refs [7,8].It is important to note that the inclusion of Hubbard potential, by correcting the Zn-O hybridization, properly describes not only the electronic structure but also the vibrational and dielectric properties of ZnO, in agreement with the experimental results (e.g.Raman, IR) [9].
In order to show the effect of inclusion of U in the case of undefective AZO, we compared the density of states (DOS) obtained with and without the inclusion of U. The results are summarized in Fig. S1.The effect of the Hubbard correction is firstly to decouple the Zn(3d) and O(2p) band and consequently to open the gap exactly of the same extent of the undoped ZnO case.We note also that the inclusion of U does not modify or the n-doping process due to Al impurities, which donates their 3p electrons to the host, filling the bottom of the ZnO conduction band.
Evidently, since in the case of pure DFT (no U correction) the dramatic underestimation of gap makes the original ZnO unphysically absorbing light in the IR-vis range (rather than in the UV), also the corresponding Al-doped system does not represent a transparent material.This explains the need for introducing the bandgap correction described above to describe the optoelectronic properties of the compound.
Simulations of AZO (1.6%) and simulations with different Al-to-vacancy ratio (see next section) have been performed doubling the cell along the x direction.The XYZ coordinates for all AZO (3.2%) structures are listed at the end of this file.
Labels refer to main text.Open circles identify the position of vacant atoms.Grey, red, and pink spheres represent Zn, O and Al atoms, respectively.

Modification of Al and defect contents
We checked the robustness of our results with respect to the modification of the Al amount and/or the ratio between Zn vacancies and Al impurities.Figure S3 shows the comparison between AZO with 3.2% (as in the main text) and 1.6% of Al content, in the presence of oxygen vacancies, in the close and far configurations (see main text for labels).AZO (1.6%) has been obtained by using the same simulation cell (64 atoms), but in the presence of a single Al/Zn substitution (1/64∼ 1.6%).The structures are then fully relaxed.
For both close and far systems, the results confirm what observed for the 3.2% case (Figure 1, main text): oxygen vacancies introduce deep and fully occupied in-gap state, while they do not directly interact with the Al dopant that donates its valence electron to the ZnO conduction band, imparting a TCO character to the system.The only expected differences observed between the two doping cases is the final position of the Fermi level that results deeper inside the conduction band in the case of higher Al amount (3.2 %), because higher is the free electron charge injected in the host.Figure S4a shows the analogous case for AZO bulk in the presence of V Zn , at different Al dosages (1.6 and 3.2%), but keeping fixed the ratio (1:2) between the number of Zn vacancies and of Al impurities.In this case the system has been simulated by using a doubled cell (128 atoms), including 2 Al ions in Zn-subsitutional sites (2/128∼ 1.6%) and a single Znvacancy.As the compensation ratio (1:2) is maintained, the picture remains essentially the same, with the system that behaves as a semiconductor rather than a TCO.
Panels b and c display instead the case in which the formal doping is maintained at 3.2% (as in the main text), while the compensation ratio is changed.In one case (panel b) the number of V Zn is reduced with respect to the Al dopant, in the other (panel c) the reciprocal ratio is inverted.The former case (1:4), which physically corresponds to a high quality grown sample, is simulated by using a doubled cell (128 atoms), including 4 Al impurities (4/128∼ 3.2%) and a single Zn vacancy.The latter, which corresponds to a highly defective sample, is obtained from the same simulation cell (128 atoms), including 4 Al impurities and three Zn vacancies.
The modification of the compensation ratio radically modifies the electrical character of the system that results semiconducting in vacancy rich conditions (panel c) while it restores the intrinsic TCO behavior of undefective AZO in Al rich conditions.
FIG. S1: DOS of undefective AZO bulk without (a) and with (b) the inclusion of Hubbard U correction.Black lines represent the total DOS, while blue shaded areas and red thin lines identify the contribution of 3d electrosn of zinc and the 2p electrons of oxygen, respectively.Zero energy reference is set to the top of valence band of the pristine ZnO host.Dashed vertical lines mark the energy gap (E g ) and thick black lines the resulting Fermi levels (E F ) of AZO system.
FIG. S3: DOS plots for AZO bulk in the presence of oxygen vacancies (V O ) in (a) close and (b) far configurations at different Al content, namely 3.2% (black line) and 1.6% (cyan line).Black lines are the same of Fig. 1b, and reported for sake of clarity.Vertical lines identify the position of the corresponding Fermi levels.Zero energy reference is set at the top of valence band of the ZnO host.
FIG. S4: DOS plots for AZO bulk in the presence of Zn vacancies (V Zn ).(a) Comparison between 1.6% (cyan)and 3.2% (black) Al content at fixed compensation ratio (1:2).(b-c) Comparison between different Zn vacancy-Al ratio, at fixed formal doping level (3.2%).Black line is the same of Fig. 1c (namely, one V Zn in AZO (3.2%)), and reported in each panel for sake of clarity and comparison.Vertical lines identify the position of the corresponding Fermi levels.Zero energy reference is set at the top of valence band of the ZnO host.