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

1.2 Outline of the thesis

The charge trapping processes at defect sites in different materials as discussed in the previous sections have in common that their underlying physics have to be described within a many-body quantum-mechanical framework. This is because atomic defects are embedded in an intricate network of atoms, where every particle is interacting with each other. Such complex problems can only be addressed through numerical methods that involve carefully selected approximations and employ extensive computational resources.

In this thesis, computational implementations of density functional theory (DFT), molecular dynamics (MD) and machine learning interatomic potentials (MLIPs) trained with the Gaussian approximation potential (GAP) method will be used to analyze the structural and electronic properties of defects in various materials. The focus will lie on the characterization of charge capture and emission processes at different defect sites. In particular, charge trapping sites in crystalline, amorphous and two-dimensional (2D) material systems employed in semiconductor technologies will be identified and characterized based on their structural, thermodynamic and electronic properties. The studied mechanisms include electron and hole transitions at vacancies, intrinsic atomic irregularities such as over- and undercoordination and defect sites involving H atoms. Furthermore, it is demonstrated that polarons can form in amorphous materials at fully coordinated atoms, highlighting the variety of possible charge trapping sites that must be considered for a comprehensive understanding of charge localization in electronic devices.. A brief overview of the thesis follows.

Chapter 2 discusses the general theory behind charge transitions at atomic defect sites. Important basic concepts for the quantum mechanical description of charge transition processes including Fermi’s golden rule, the Born-Oppenheimer approximation and the Franck-Condon principle are outlined. Subsequently, the probability of radiative and non-radiative charge transitions at defect sites is discussed in the context of effective phonon modes. Thermally activated transitions between two different defect configurations are discussed including practical approaches to calculate the corresponding activation energy barriers. Finally, practical approaches and implications for defect calculations in crystalline, amorphous and two-dimensional materials are described.

Chapter 3 gives details about the utilized computational methods. The basic concepts of density functional theory, including the Hohenberg-Kohn theorems, the Kohn-Sham equation and the necessity of hybrid functionals to study the localization of charge are discussed. The chapter also describes molecular dynamics, focusing on its application for creating amorphous structures. Finally, the concept and training process of an machine learning interatomic potential for amorphous structure creation is described.

Chapter 4 presents results of defect calculations and relates them to charge trapping phenomena in field effect transistors. A multi-state defect model for electron and hole trapping at oxygen vacancies and hydrogen related defects in amorphous silicon dioxide ( $a$ -SiO₂) is proposed and related to reliability degrading phenomena in Si/SiO $_{2}$ and SiC/SiO $_{2}$ devices. The defects are studied in a statistical manner, as every defect in the amorphous network can exhibit different properties related to charge transitions, depending on the respective local atomic environment. Furthermore, hole trapping properties of the tungsten vacancy ( $V_{W}$ ) and the selenium antisite ( ${Se}_{W}$ ) in 2D monolayer tungsten diselenide (1L-WSe $_{2}$ ) are evaluated to investigate the origin of random telegraph noise (RTN) signals in scaled FETs.

Chapter 5 focuses on various intrinsic charge trapping sites in amorphous silicon nitride ( $a$ -Si₃N₄). The structure creation of $a$ -Si $_{3}$ N $_{4}$ with the MLIP is discussed and the structural and electronic properties of the resulting samples validated against spectroscopy data. Electron and hole trapping at under- and overcoordinated sites in the amorphous network are analyzed. Subsequently, dangling bonds are passivated with H and the polaron formation in the hydrogenated amorphous Si₃N₄ ( $a$ -Si₃N₄:H) is studied. It will be emphasized that the localization of charge at intrinsic sites gives a crucial contribution to the memory effect in charge trap flash devices.

Chapter 6 explores the vibrational broadening of optical transitions at Al and O vacancies in alumina ( $a$ - ${Al}_{2} O_{3}$ ) from first-principles. The resulting line shapes are related to experimental data to back their identification with the $F$ and $F^{+}$ centers in this material. Furthermore, the Al split vacancy configuration is analyzed based on formation energies and migration barriers to the single Al vacancy in different charge states.

Chapter 7 finally gives a summary of the thesis and discusses the conclusions that can be drawn from the first-principles investigations related to the performance of electronic devices. Additionally, possible future investigations are outlined.