Dissertation

D I S S E R T A T I O N

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

ausgeführt zum Zwecke der Erlangung des akademischen Grades
Doktor der technischen Wissenschaften

eingereicht an der Technischen Universität Wien
Fakultät für Elektrotechnik und Informationstechnik
von

Dipl.-Ing. Christoph Wilhelmer, BSc
Matrikelnummer: 01326677

unter der Betreuung von

Univ.Prof. Dipl.-Ing. Dr.techn. Tibor Grasser

Wien, im Oktober 2024

Contents

Acknowledgements

1.1.1 Hydrogen-related defects in amorphous silicon dioxide ( $a$ -SiO₂)

1.1.2 Intrinsic charge trapping sites in amorphous silicon nitride ( $a$ -Si $_{3}$ N $_{4}$ :H)

1.1.3 Vacancies in corundum aluminum oxide ( $α$ -Al $_{2}$ O $_{3}$ )

1.2 Outline of the thesis

2 Theoretical Background

2.1 Charge transition model

2.1.1 Fermi’s golden rule

2.1.2 Charge transition at a defect site

2.1.3 Radiative transitions

2.1.4 Non-radiative multi-phonon transitions

2.1.5 Thermal transitions

2.2 Defect calculations

2.2.1 Supercell approach

2.3 Material structures

2.3.1 Crystalline

2.3.2 Amorphous

2.3.3 2D materials

3 Computational Methods

3.1 Density functional theory (DFT)

3.1.1 Hohenberg-Kohn theorems

3.1.2 Kohn-Sham equations

3.1.3 Exchange-correlation functionals

3.1.4 Solving the equation

3.2 Molecular dynamics

3.2.1 Newton’s equation of motion

3.2.2 Controlling the temperature

3.2.3 Interatomic potentials

4 Charge Trapping in Field Effect Transistors

4.1 Defects in amorphous silicon dioxide ( $a$ -SiO₂)

4.1.1 SiO $_{2}$ structure creation

4.1.2 Structural analysis

4.1.3 Multi-state defect PECs

4.1.4 Defect types

4.1.5 Formation energy

4.1.6 Transitions without charge transfer

4.1.7 Charge transition level

4.1.8 Non-radiative multi-phonon transitions

4.1.9 Defect correlations

4.1.10 Discussion

4.2 Charge trapping in monolayer tungsten diselenide (1L-WSe $_{2}$ )

4.2.1 Defect types

5 Charge Trap Flash Memories

5.1 Structural defects – over- and undercoordinated atoms in $a$ -Si $_{3}$ N $_{4}$

5.1.1 Structure creation of amorphous silicon nitride

5.1.2 Electronic structure of intrinsic defects

5.1.3 Kohn-Sham defect states

5.1.4 NMP characterization of intrinsic defect sites

5.2 Polarons in the amorphous hydrogenated silicon nitride $a$ -Si $_{3}$ N $_{4}$ :H

5.2.1 Structure creation of $a$ -Si $_{3}$ N $_{4}$ :H

5.2.2 Electronic structure of $a$ -Si $_{3}$ N $_{4}$ :H

5.2.3 Charge transition levels of polarons

6 Optical Properties of Vacancies in Corundum ( $α$ -Al $_{2}$ O $_{3}$ )

6.1 Charge transition levels

6.1.1 Oxygen vacancy

6.1.2 Aluminum vacancy

6.2 Optical properties

6.2.1 Configuration coordinate diagrams

6.2.2 Absorption

7 Summary, Conclusions and Outlook

7.2 Conclusions

7.3 Outlook and future investigations

A Limitations of the 1D configuration coordinate diagram

B Crossing points of PECs from relaxation energies

C Weibull distribution

D Stability of polarons: PBE vs. PBE0_TC_LRC

E Computational setup

List of Publications

List of Figures