Impact of Charge Transitions at Atomic Defect Sites on Electronic Device Performance

List of Figures

1.1 Schematic state diagram of a hydrogen bride (HB) defect in the three charge states.

2.1 1D configuration coordinate diagram for the optical transitions between an electron localized at an aluminum split vacancy in $α$ -Al $_{2}$ O $_{3}$ and the conduction band minimum.

2.2 Sketch of an 1D configuration coordinate diagram for a charge transition governed by a non-radiative multi phonon process.

2.3 Schematics of the potential energy curves (PECs) in the harmonic approximation of an electron trap in two charge states within the context of an Si/Si $_{3}$ N $_{4}$ band diagram.

2.4 Schematic PECs of a four-state oxide defect as a function of the configuration coordinate $Q$ for $0 / - 1$ charge transitions in the context of a Si/SiO $_{2}$ band diagram.

2.5 Two different stable configurations of the same hydrogen bridge defect in $a$ -SiO $_{2}$ in the neutral charge state.

2.6 Renderings of different material systems investigated in this thesis.

3.1 Schematics of the GAP algorithm.

3.2 Training and re-training procedure of a GAP potential.

3.3 Correlation plot of (a) energies and (b) forces of 1000 different Si $_{3}$ N $_{4}$ structures as calculated with the final version of a GAP and DFT.

4.1 Normalized distributions of geometrical parameters of 20 amorphous SiO $_{2}$ structures created with molecular dynamics and cell optimized with density functional theory.

4.2 Structure factor $S$ as a function of the scattering vector $Q$ of the structure used for defect calculations compared to $S$ from neutron scattering experiments [213].

4.3 Schematic potential energy curves of a four-state oxide defect as a function of the configuration coordinate $Q_{i}$ for (a) the $0 / + 1$ and (b) $0 / - 1$ charge transitions in the context of a Si/SiO $_{2}$ band diagram.

4.4 Example of an unpuckered oxygen vacancy in different charge states with the respective HOMO (blue) shown for the neutral (a) and negative (c) charge state and the LUMO (red) for the positive charge state (b) at an isovalue of 0.05 e/Å $^{3}$ .

4.5 An example HB in different charge states with its HOMO (blue) or LUMO (red) at an isovalue of $0.05$  e/Å $^{3}$ ; Charge states from left to right: (a) neutral, (b) positive, (c) negative.

4.6 H-E′ center in different charge states with its HOMO (blue) or LUMO (red) at an isovalue of 0.05 e/Å $^{3}$ . Charge states: neutral (a), positive (b), negative metastable (c-e) and the minimum energy configuration of the negatively charged H-E′ center (f).

4.7 Transition barriers from metastable negatively charged H- $E^{'}$ configuration to the H- $E^{'}$   $_{\min}^{-}$ configuration.

4.8 Distributions of formation energies for unpuckered and puckered defects of type OV, HB and H- $E^{'}$ .

4.9 Total energy differences between unpuckered and puckered configurations of oxygen vacancies in different charge states.

4.10 (a) Typical energy profiles for the charge conserving transitions between stable and metastable negatively charged states of the three defect types as a function of the configuration coordinate. (b) Energy barrier distribution for the transition from stable to metastable states.

4.11 State diagram of an oxygen vacancy with the corresponding distributions of charge transition levels shown in the context of a Si/SiO $_{2}$ (black) and a SiC/SiO $_{2}$ (grey) band diagram.

4.12 State diagram of a hydrogen bridge in three charge states with the calculated charge transition level distributions shown in the context of a Si/SiO $_{2}$ and a SiO $_{2}$ /SiC band diagram.

4.13 State diagram of a hydroxyl- $E^{'}$ center with the calculated charge transition level distribution shown in the context of a Si/SiO $_{2}$ and a SiO $_{2}$ /SiC band diagram.

4.14 Potential energy curves of a single H- $E^{'}$ defect in different charge states obtained from parabolic fits to the equilibrium (full circles) and relaxation energies (empty circles for 0/ $q$ and squares for $- q / q$ transitions).

4.15 Classical energy barriers for different NMP charge transitions at H- $E^{'}$ defect sites extracted from potential energy curves according to Fig. 4.14 for different Fermi levels.

4.16 Energy differences of classical NMP transitions barriers between (a) $- 1 / + 1$ and $- 1 / 0$ charge transitions and (b) $+ 1 / - 1$ and $+ 1 / 0$ charge transitions of 78 H- $E^{'}$ defects.

4.17 CTLs for emitting (a) and capturing (b) electrons of the three defect types plotted against each other.

4.18 Charge transition levels of unpuckered SiO $_{2}$ defects as a function of their formation energy.

4.19 Atomic structure of a tungsten vacancy ( $V_{W}$ ) in a WSe $_{2}$ monolayer geometry optimized with DFT.

4.20 Atomic structure of a selenium antisite ( ${Se}_{W}$ ) in a WSe $_{2}$ monolayer geometry optimized with DFT.

4.21 Electronic Kohn-Sham (KS) levels and CTLs from hybrid functional DFT in the WSe $_{2}$ band gap introduced by a $V_{W}$ and an ${Se}_{W}$ .

5.1 Structural properties of amorphous Si $_{3}$ N $_{4}$ model structures compared with experimental data.

5.2 Hole trapping near intrinsic sites in $a$ -Si $_{3}$ N $_{4}$ with the localized wave functions and the PDOS of the structure.

5.3 Electron trapping near intrinsic sites in $a$ -Si $_{3}$ N $_{4}$ with the localized wave functions and the respective projected density of states.

5.4 Energy levels of the electronic defect states introduced in the band gap after an electron (occupied state) or a hole (unoccupied state) is trapped in $a$ -Si $_{3}$ N $_{4}$ .

5.5 Charge transition levels of intrinsic hole and electron traps of several $a$ -Si $_{3}$ N $_{4}$ structures.

5.6 Relaxation energies according to the NMP model for different charge transfer processes with the fitting parameters of a normal distribution given in the plots.

5.7 Energy barriers in logarithmic scale from minimum energy configurations to the crossing point of the PECs for electron emission vs. electron capture with the CBM of a Si substrate acting as an electron reservoir.

5.8 Structure factor $S$ as a function of the scattering vector magnitude $Q$ of a Si $_{3}$ N $_{4}$ :H model structure compared with experimental data [213].

5.9 Inverse participation ratio (IPR) of a model $a$ -Si $_{3}$ N $_{4}$ :H structure showing the increased degree of localization of electronic states near the band edges.

5.10 Hole polaron formation in amorphous $a$ -Si $_{3}$ N $_{4}$ :H.

5.11 Distributions of structural and electronic properties of the combined $a$ -Si $_{3}$ N $_{4}$ :H sample structures plotted as normalized histograms.

5.12 Electron polaron in $a$ -Si $_{3}$ N $_{4}$ :H.

5.13 Electronic density of states (DOS) of a single $a$ -Si $_{3}$ N $_{4}$ model structure before and after passivating the dangling bonds with H.

5.14 Hole trapping in Si $_{3}$ N $_{4}$ :H near a Si–H bond.

5.15 Electron polaron formation in the same $a$ -Si $_{3}$ N $_{4}$ :H sample at different sites, one formed spontaneously and one after perturbing the neutral system.

5.16 Energetic properties of electron (bi)polarons (a, b) and hole polarons (d) in $a$ -Si $_{3}$ N $_{4}$ :H.

6.1 Formation energy of the investigated vacancy configurations in $α$ -Al $_{2}$ O $_{3}$ as a function of the Fermi level and rendering of $α$ -Al $_{2}$ O $_{3}$ with a $V_{Al, s}$ defect relaxed in charge state $q = - 3$ .

6.2 Absorption line shapes for compared with absorption spectroscopy data.

6.3 Luminescence line shapes compared with spectroscopy measurements of the $F$ and $F^{+}$ centers.

B.1 Potential energy curves $V_{1} (Q)$ and $V_{2} (Q)$ of a model defect system in two different charge states for different $Δ Q$ .

List of Tables

4.1 Mean and standard deviation of characteristic distances (Si–Si for the OV, Si–H for the HB and Si–O for the H- $E^{'}$ ) of relaxed unpuckered defects OV ( $N = 124$ ), HB ( $N = 131$ ) and H- $E^{'}$ ( $N = 92$ ) in different charge states.

4.2 Fitting parameters for charge transition levels of oxygen vacancies, hydrogen bridges and hydroxyl- $E^{'}$ centers (normal and Weibull-distributions) relative to $E_{V} ({SiO}_{2})$ .

4.3 Normal distribution fitting parameters for relaxation energies of oxygen vacancies, hydrogen bridges and hydroxyl- $E^{'}$ centers. $E_{Relax}$ of OVs including a positive charge state follow a bimodal distribution.

4.4 Energetic configurations of the hole trapping defect types ${Se}_{W}$ and $V_{W}$ from hybrid functional DFT. CTLs for hole transitions ( $ε (0 / + 1)$ ) are given with respect to the valence band maximum of the pristine monolayer.

5.1 Relaxation energies of hole polarons, electron polarons and bipolarons and hole traps at Si–H bonds in $a$ -Si $_{3}$ N $_{4}$ :H.

6.1 Calculated CTLs of vacancies in $α$ -Al $_{2}$ O $_{3}$ . Results obtained with PBE0_TC_LRC are from this work; for comparison, results from previous work are listed, labeled with the functional used (in the case of LDA additional corrections were applied). All energy levels (in eV) are referenced to the VBM.

6.2 Migration barriers between $V_{Al}$ and $V_{Al, s}$ configurations in different charge states.

6.3 Effective parameters of the optical transitions within the 1D approximation for vacancies in $α$ -Al $_{2}$ O $_{3}$ .

D.1 Comparison of average band gaps and CTLs for hole ( $ε (0 / + 1)$ ) and electron ( $ε (0 / - 1)$ ) polarons in $a$ -Si $_{3}$ N $_{4}$ :H obtained from DFT calculations employing PBE and PBE0_TC_LRC