Prueba de hipótesis específica

From∆G(SHE) = 0 [cf. eq. 2.20], we obtain

µ(SHE) = ∆dpAH3O+− ∆zpEH3O+− E

q=+1

corr + µH− ²v. (2.32)

2.5 Computational details

In this research, all the calculations are carried out with the freely availableCP2Ksuite of codes, except the GW calculations of band gaps of semiconductors, which are performed with theABINITcode [131]. TheCP2Kcode features a combined atomic basis set/plane-wave approach: atom-centered Gaussian-type basis functions are used to describe the orbitals and an auxiliary plane-wave basis set is employed to re-expand the electron density. Here, analytical Goedecker-Teter-Hutter pseudopotentials [132, 133] are used to account for core- valence interactions. We use a triple-ζ correlation-consistent polarized basis set (cc-pVTZ) [134] for O, H, C, P, N, and S atoms, and the shorter range molecularly optimized double-ζ basis set with one polarization function [135] for Al, Ti, Ga, As, Cd, Zn, and Sn atoms. For the plane- waves, a cutoff of 500 Ry is employed. The Brillouin zone is sampled at the soleΓ point. In this thesis, all structural relaxations are carried out with the PBE functional under a force tolerance of 10−4_{hartree/bohr. All molecular dynamics (MD) simulations are performed in the NVT}

ensemble with the rVV10 functional [136] for systems containing H2O water molecules and

the PBE functional for the other systems. The temperature is controlled by a Nosé−Hoover thermostat [137, 138]. In order to overcome the band gap underestimation associated with the use of the PBE, the electronic properties of various defects in am-Al2O3are finally evaluated at

the HSE level [116, 118] with the fraction of Fock exchangeα = 0.44 and the range-separation parameterω = 0.11 bohr−1.

2.5.1 Molecular dynamics simulations of semiconductor-water interfaces

Molecular dynamics (MD) simulations of the semiconductor-water interfaces are performed with the rVV10 functional, which accounts for nonlocal van der Waals interactions [139, 140]. The parameter b of the rVV10 functional is set to the value of 9.3, in order to correctly reproduce the density and the structural properties of liquid water [136]. The MD simulations are carried out in the NVT ensemble with a time step of 0.5 fs. The temperature is set at 350 K to ensure a frank diffusive motion of liquid water and is controlled by a Nosé−Hoover thermostat [137, 138].

3

Defects in amorphous Al

₂

O

₃

This chapter first introduces the method for generating model structures of the defects of interest in Section 3.1. Then, intrinsic (e.g. oxygen vacancy and interstitial) and extrinsic defects (e.g. interstitial hydrogen, carbon and nitrogen) in am-Al2O3are discussed in Sections

3.2 and 3.3, respectively. Next, the possible electrical activity of the defect levels identified in this work is discussed in Section 3.4. The conclusions of this chapter are drawn in Section 3.5.

3.1 Model generation

We use the model of am-Al2O3generated in Ref. [52], which features an orthorhombic su-

percell containing 64 Al and 96 O atoms, with lattice constants of 11.47, 11.24, and 12.78 Å, corresponding to a mass density of 3.29 g/cm3 in accord with the experimental range (3.05−3.65 g/cm3) [141, 142, 143]. This bulk model was produced via ab initio MD simulations through a quench from the melt. The obtained structure shows good agreement with neutron diffraction experiments [52, 141]. With the setting of the fraction of Fock exchangeα = 0.44 and the short-range parameterω = 0.11 bohr−1, the HSE functional reproduces well the exper- imental band gap of 9.13 eV ofα-Al2O3and also gives a bandgap of 6.63 eV for this am-Al2O3

model in accord with the experimental range 6.1−7.0 eV [33, 34, 35]. For the native defects (e.g. interstitial oxygen) and the extrinsic impurities (e.g. hydrogen, carbon and nitrogen), defect structures are generated by a two-step procedure. First, we identify available voids in the amorphous structure, in which the defect atom (O, H, C, and N) is placed. For this, we carry out a Voronoi analysis, which determines the position and the size of the available voids. For each defect atom and for each considered charge state, ten such voids with radii between 1.7 and 2.5 Å are selected and ten different initial configurations are generated by placing the defect atom at their center. Next, each initial configuration is allowed to evolve through

ab initio MD simulations in the NVT ensemble for a duration of 3 ps. The temperature is set at

1000 K through a Nosé-Hoover thermostat [138, 137]. In this way, the defect atom can optimize its structural configuration on an affordable time scale. It should be noted that the barriers that can be overcome with such a temperature are just of the order of 0.1 eV. In our simulations, these barriers are overcome in a couple of picoseconds. Hence, on the macroscopic time

scales of typical experimental conditions, the system would easily undergo such structural rearrangements, independently of the adopted growth method. We then sample structural configurations at simulation times of 1, 1.5, 2, 2.5, and 3 ps of every MD trajectory and fully relax the structures, until the forces are smaller than 10−4Ha/bohr. Among these 5 relaxed configurations, only the lowest-energy one is kept for further investigation, resulting in 10 models for each defect atom in a given charge state. During the MD runs, the structural rearrangement induced by the defect is always accompanied by a general relaxation of the amorphous structure. To minimize the influence of this effect on the defect formation energy, we carry out a cycling procedure, as proposed earlier in the study of defects in amorphous HfO2(Ref. [14]) and Al2O3(Ref. [15]). In this procedure, we first remove the inserted defect

atom from its relaxed configuration and relax the resulting structure. Hence, we reinsert the defect atom and relax the structures again. The cycling is continued until the total energies of both the defective and the pristine bulk systems converge within 10−3eV. In this procedure, we only retain the model when the final configuration for the pristine amorphous system shows an energy that is lower than its initial energy and a band gap that does not differ by more than 0.2 eV from the initial one.