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

Abstract

Over the last decades, enormous efforts have been devoted to optimizing the performance of electronic devices. One of the most prevalent ways to improve the computational power is the downscaling of the semiconductor based material systems, which allows for the integration of an increasing number of electronic components on the same area. Nowadays, the dimensions of single transistors have already reached the low nanometer regime. At this scale, the reliability, and in some cases even the functionality, of electronic devices depend on small irregularities, such as defects, in the atomic structure of the utilized materials. This is because atomic defects can induce strain and lead to the localization of charge which alters the electrostatics of a device.

Identifying and characterizing electrically active defect sites is thus a promising approach to gain insights into charge trapping dynamics and to continue the optimization of electronic devices. Experimentally, defects can be studied by various spectroscopy techniques or electrical and optical measurements. On the theoretical side, density functional theory (DFT) in particular has been established as a reliable and accurate quantum mechanical method to predict material properties based on first-principles calculations. In this thesis, DFT is used to investigate phonon-driven and optical charge transitions at atomic defects and intrinsic charge trapping sites in crystalline, amorphous and two-dimensional (2D) material systems as employed in modern electronics.

The impact of hydrogen-related defects in amorphous silicon dioxide (a-SiO $_{2}$ ) on reliability degrading effects as detected in Si and SiC based metal-oxide-semiconductor field-effect transistors (MOSFETs) is statistically investigated. It is demonstrated that H atoms introduce defects in the amorphous network that can trap both electrons and holes from Si substrates, following a non-radiative multi-phonon (NMP) transition. Such charge trapping processes have been suspected to be the cause for phenomena like bias temperature instability (BTI) and random telegraph noise (RTN). Furthermore, it is shown that defects can exist in metastable configurations, which can lead to anomalous behavior and vanishing electrically active defects. The results of the DFT calculations are used to propose a multi-state defect model, providing statistical insights into the complex charge trapping mechanisms in a-SiO $_{2}$ .

Recently, the use of two-dimensional (2D) semiconductors in electronic devices has been recognized as a promising approach for the production of ultra-scaled FETs. As such devices still lack the reproducibility needed for industrial fabrication, physical models are required to interpret measurements and to give guidance for experimentalists for further developments. In this thesis, the charge trapping properties of the tungsten vacancy ( $V_{W}$ ) and the selenium antisite ( ${Se}_{W}$ ) in two-dimensional monolayer WSe $_{2}$ are characterized. In agreement with measurements and device simulations, it is demonstrated that both defect types can be responsible for detected RTN signals by capturing and emitting holes following an NMP process.

In silicon nitride (Si $_{3}$ N $_{4}$ ), charge trapping sites are essential for the functionality of charge trap flash (CTF) devices, where Si $_{3}$ N $_{4}$ is commonly used as the charge storage layer in the utilized material stacks. To study the atomic nature of the responsible charge trapping sites, first a machine learning interatomic potential (MLIP) is developed to generate realistic amorphous silicon nitride thin films (a-Si $_{3}$ N $_{4}$ and a-Si $_{3}$ N $_{4}$ :H) with molecular dynamics (MD). By analyzing the electronic structure of the nitrides, it is demonstrated that both electrons and holes can localize at over- and undercoordinated sites in the amorphous network and form polarons at fully coordinated sites. It is thus argued, that these intrinsic sites can contribute to the memory effect of CTFs.

Furthermore, optical properties of vacancies in the high- $κ$ insulator $α$ -Al $_{2}$ O $_{3}$ are investigated within the general theory of luminescence. The vibrational broadening of emission and absorption spectra are predicted based on effective phonon modes, which were modeled with parameters from first-principles calculations. The luminescence and absorption line shape function of the neutral and singly charged oxygen vacancy show good agreement with spectroscopy data of the $F$ and $F^{+}$ center. Migration barriers between the aluminum vacancy and the aluminum split vacancy are calculated for different charge states of the defect and the vibrational broadening of their optical spectra is evaluated.

Kurzfassung

Im Laufe der letzten Jahrzehnte wurden erhebliche Anstrengungen unternommen, um die Leistungsfähigkeit elektronischer Geräte zu optimieren. Eine der am häufigsten genutzten Methoden zur Steigerung der Rechenleistung ist die Verkleinerung der halbleiterbasierten Materialsysteme, was die Integration einer wachsenden Anzahl elektronischer Bauteile auf derselben Fläche ermöglicht. Durch diese Bemühungen können heutzutage Transistorabmessungen von wenigen Nanometern erreicht werden. In dieser Größenskala hängen die Zuverlässigkeit und in manchen Fällen sogar die Funktionalität elektronischer Geräte von kleinen Unregelmäßigkeiten, wie etwa Defekten, in der atomaren Struktur der verwendeten Materialien ab. Solche atomaren Defekte können mechanische Spannungen induzieren und die Lokalisierung von Ladungsträgern begünstigen, was in der Folge die Elektrostatik eines Gerätes verändert.

Die Identifizierung und Charakterisierung elektrisch aktiver Defektstellen ist daher ein vielversprechender Ansatz, um physikalische Prozesse, die zum Einfangen von Ladungen führen, besser zu verstehen und daraufhin die Optimierung elektronischer Geräte voranzutreiben. Experimentell können Defekte durch verschiedene spektroskopische Techniken oder elektrische und optische Messungen untersucht werden. Aus theoretischer Sicht hat sich insbesondere die Dichtefunktionaltheorie (DFT) als eine zuverlässige und genaue quantenmechanische Methode etabliert, um Materialeigenschaften basierend auf ab-initio-Berechnungen vorherzusagen. In der vorliegenden Arbeit wird DFT angewendet, um phononengetriebene und optische Ladungsübergänge an atomaren Defekten und intrinsischen Ladungsfallen in kristallinen, amorphen und zweidimensionalen (2D) Materialsystemen, wie sie in der modernen Elektronik eingesetzt werden, zu untersuchen.

Der Einfluss von wasserstoffhaltigen Defekten in amorphem Siliziumdioxid ( $a$ -SiO $_{2}$ ) auf Zuverlässigkeitseffekte, die in Si- und SiC-basierten Metall-Oxid-Halbleiter-Feldeffekttransistoren (MOSFETs) beobachtet wurden, wird statistisch analysiert. Die Untersuchungen dieser Arbeit zeigen, dass wasserstoffhaltige Defekte sowohl Elektronen als auch Löcher von Siliziumsubstraten durch einen nicht-strahlenden Multiphononenübergang (NMP) einfangen können. Solche Ladungsprozesse werden als Ursache für Phänomene, wie Bias-Temperatur-Instabilität (BTI) und stochastisches Telegrafenrauschen (RTN), betrachtet. Darüber hinaus wird gezeigt, dass Defekte in metastabilen Konfigurationen existieren können, was zu anomalem Verhalten und zu schlagartig nicht mehr detektierbaren Defekten führen kann. Die Ergebnisse der DFT-Berechnungen dienen als Grundlage für ein Mehrzustands-Defektmodell, welches statistische Einblicke in die komplexen Prozesse der Ladungslokalisierung in $a$ -SiO $_{2}$ ermöglicht.

Zuletzt hat sich die Implementierung zweidimensionaler Halbleiter in elektronische Geräte als vielversprechender Ansatz für die Herstellung von ultraskalierten FETs etabliert. Da solche Geräte noch nicht die für die industrielle Fertigung erforderliche Reproduzierbarkeit erreichen, sind physikalische Modelle notwendig um Messungen zu interpretieren und folgend experimentelle Entwicklungen zu unterstützen. In dieser Arbeit werden die Ladungszustände der Wolfram-Vakanz ( $V_{W}$ ) und der Selen-Antiseite (Se $_{W}$ ) in einer zweidimensionalen Einzelschicht von Wolframdiselenid (1L-WSe $_{2}$ ) charakterisiert. Übereinstimmend mit Messungen und Gerätesimulationen wird dargelegt, dass beide Defekttypen für gemessene RTN-Signale verantwortlich sein können, da sie in der Lage sind, Löcher einem NMP-Prozesses folgend einzufangen und wieder freizusetzen.

Für Charge Trap Flash (CTF)-Geräte sind hingegen Ladungsfallen in Siliziumnitrid (Si $_{3}$ N $_{4}$ ) von zentraler Bedeutung für ihre Funktionalität, da Si $_{3}$ N $4$ hier üblicherweise explizit als die Ladungsspeicherschicht der Geräte implementiert wird. Um die atomare Natur der verantwortlichen Strukturen zu untersuchen, wird zunächst mithilfe von maschinellem Lernen ein interatomares Potential (MLIP) entwickelt, um daraufhin realistische amorphe Siliziumnitrid Strukturen ( $a$ -Si $_{3}$ N $_{4}$ und $a$ -Si $_{3}$ N $_{4}$ :H) mittels Molekulardynamik (MD) Simulationen zu erzeugen. Die Analyse der elektronischen Struktur der Nitride ergibt, dass sich sowohl Elektronen als auch Löcher an über- und unterkoordinierten Atomen im amorphen Netzwerk lokalisieren können. Zudem wird argumentiert, dass Elektronen und Löcher Polarone an vollständig koordinierten Atomen bilden können, was zum Memory-Effekt von CTFs beitragen kann.

Des Weiteren werden die optischen Eigenschaften von Vakanzdefekten im Hoch- $κ$ -Isolator $α$ -Al $_{2}$ O $_{3}$ im Rahmen der allgemeinen Theorie der Lumineszenz untersucht. Die durch atomare Schwingungen hervorgerufene Verbreiterung von Emissions- und Absorptionsspektren wird mittels effektiver Phononenmoden, die mit Parametern aus ab-initio-Berechnungen modelliert wurden, vorhergesagt. Die berechneten Lumineszenz- und Absorptionsspektren der neutralen und einfach geladenen Sauerstoffvakanz sind in guter Übereinstimmung mit Spektroskopiedaten der $F$ und $F^{+}$ Zentren. Energiebarrieren für die Migration zwischen der Aluminium-Vakanz und der Aluminium-Teilvakanz werden für verschiedene Ladungszustände des Defekts berechnet und die Verbreiterung der optischen Spektren beider Konfigurationen wird ausgewertet.

Acknowledgements

As the final days of my formal education are rapidly approaching, at last the time has come to thank all the wonderful people who supported me during those exciting years, and ultimately made the completion of this thesis possible.

First, I want to express my deep gratitude to Tibor Grasser for granting me the opportunity to pursue my PhD in his microelectronics reliability group. Under his proficient supervision, I have enjoyed the freedom to follow my research interests, knowing that I could always rely on his valuable advice, comments and mentoring. Thank you Tibor for your constant support and for creating a working environment that is carried by trust, enthusiasm and appreciation.

I would also like to thank Lukas Cvitkovich, not only for his scientific mindset that encouraged me to explore new directions, but also for the deep connection we share and all the challenges we faced together. Next, I want to thank Dominic Waldhör for engaging discussions, thoughtful comments and for his competent advice over the course of my PhD. I also want to thank Markus Jech for patiently introducing me into the world of scientific computing and his support and guidance in my first year. Additionally, I thank Michael Waltl for his valuable support throughout my PhD and Alex Shluger for inspiring comments and questions. Furthermore, many thanks to Diego Milardovich, Al-Moatassem El-Sayed, Franz Fehringer, Theresia Knobloch, Mina Bahrami, Mohammad Davoudi, Pedram Khakbaz and Rittik Ghosh for delightful collaborations and for being awesome colleagues. I would also like to express my gratitude to Georg K. H. Madsen and Matt B. Wattkins for their time and commitment to serve as examiners for my doctoral defense.

I would like to thank Chris G. Van de Walle for warmly welcoming me into his computational materials group during my research visit in Santa Barbara. I immensely profited from his tireless motivation for scientific discussions and his keen eye for details, which undoubtedly influenced my critical thinking and scientific approaches. Thank you Chris for granting me this opportunity. My sincere thanks also goes to Mark E. Turiansky for sharing his profound knowledge with me and mentoring me through the theoretical background. I have learned a lot from working with you. Furthermore, I want to thank Mathilde Franckel, Woncheol Lee, Kevin Nangoi, Akash Ram and Haochen Wang for making my time abroad so enjoyable.

My deepest gratitude goes to my parents, Birgit and Christian. Your unwavering support and constant encouragement throughout my life has been crucial for my personal and professional development. I also want to thank my sister Lisa with Lukas for their kindness and interest in my work and progress. Furthermore, I would like to thank my late grandmother, Irmi, who I knew I could always rely on from my youngest days, and my grandfather Sepp, for being my first friend and teacher. I would also like to express my appreciation to my friends who no only supported me during my PhD, but also constantly reminded me about all the wonderful things one can spend time on besides scientific writing. Thank you Aaron, Chris, Flo, Jonathan, Martin and Peter for being by my side throughout the years and my Jimmies for all the unforgettable moments on tour. At last, to my wife Lisa, thank you for your selfless support and empowerment over all those years. This thesis would not have come to life without your love, inspiration and understanding.

Acronyms

2D two-dimensional.

3D three-dimensional.

BTI bias temperature instability.

CBM conduction band minimum.

CCD configuration coordinate diagram.

CI-NEB climbing image nudged elastic band.

CP crossing point.

CTF charge trap flash.

CTL charge transition level.

CVD chemical vapor deposition.

DFT density functional theory.

GAP Gaussian approximation potential.

GGA generalized gradient approximation.

GPW Gaussian plane wave.

GTO Gaussian type orbital.

H-E′ hydroxyl-E ′ .

HB hydrogen bridge.

HOMO highest occupied molecular orbital.

IP interatomic potential.

IPR inverse participation ratio.

JJ Josephson junction.

KS Kohn–Sham.

LDA local density approximation.

LUMO lowest unoccupied molecular orbital.

MD molecular dynamics.

MEP minimum energy path.

MLIP machine learning interatomic potential.

MO molecular orbital.

MOSFET metal-oxide-semiconductor field-effect transistor.

NEB nudged elastic band.

NMP non-radiative multi-phonon.

OV oxygen vacancy.

PDOS projected density of states.

PEC potential energy curve.

PES potential energy surface.

PVD physical vapor deposition.

RTN random telegraph noise.

SOAP smooth overlap of atomic positions.

TCAD technology computer aided design.

TLS two-level system.

TST transition state.

VBM valence band maximum.

WF Wannier function.