Efficient Physical Modeling of
Bias Temperature Instability

zur Erlangung des akademischen Grades
Doktor der technischen Wissenschaften
eingereicht an der Technischen Universität Wien
Fakultät für Elektrotechnik und Informationstechnik

Matrikelnummer 0625735
Berg 3, 3071 Böheimkirchen, Österreich
Betreuer: Ao.Univ.Prof. Dipl.-Ing. Dr.techn. Tibor Grasser

Wien, im Juni 2018


Metal-oxide-semiconductor (MOS) devices are a key driver of modern technologies. Of particular importance are MOS field-effect transistors (MOSFETs), which act as binary switches for electrical currents by exploiting the field effect. It is through the embedding of billions of these devices into single chips that the extensive computation that underpins modern life is made possible. A major design challenge within these technologies is to ensure maximal performance while simultaneously guaranteeing reliable behavior throughout the entire projected lifetime of the device. Of chief importance are instabilities which are sensitive to the gate bias voltage and the temperature. This phenomenon is termed bias temperature instability (BTI) and is one of several reliability issues related to charge trapping in the oxide layer of these devices.

The first reports of BTI were presented more than 50 years ago, but despite ongoing research efforts and continual economic interest, the fundamental physics is still not fully understood. From early on, diffusive processes and thermally activated reactions have been deemed responsible for BTI, and since then, the question as to which of these two processes governs the degradation kinetics remains controversial. Recent technology advancements have shed some light on these processes, and it has since been shown that many reliability phenomena can be consistently described through non-radiative multi-phonon (NMP) theory. In particular, the 4-state NMP model was successfully applied to describe degradation due to pre-existing oxide defects. In addition to these pre-existing defects, there is some evidence of a more elusive degradation mechanism, which is believed to be related to defect generation and transformation involving the relocation of hydrogen in the oxide.

In this work, the 4-state NMP model will be employed to reproduce a broad range of experimental degradation data. Starting with an analysis of pre-existing defects in simple SiO2 oxides at negative bias temperature instability (NBTI) conditions, a unified modeling approach will be presented for such defects in devices with high-κ gate stacks at NBTI and positive bias temperature instability (PBTI) conditions.

Furthermore, it will be shown that the essential physics of these rather complex degradation mechanisms can be captured with high accuracy through a more simplified model. This condensed physical description is implemented within a new modeling framework called Comphy, short for “compact-physics”. With this framework, the key physical properties of oxide defects in SiO2 and HfO2 oxides for various device processes are extracted and consistent results for both NBTI and PBTI stress are obtained. For transparency, all parameters used in the Comphy-based studies will also be listed in this work.

The detailed insights into the governing physics of pre-existing oxide defects developed here can aid future studies of the still elusive degradation mechanisms within oxides in MOS devices. Furthermore, by complementing the physical model for pre-existing oxide defects with a phenomenological description of defect generation and transformation, fast and accurate predictions of device lifetimes can be obtained. Thus, the Comphy framework presented in this thesis can contribute to the continuing improvement of MOS technology.


Metal-Oxid-Halbleiter (MOS)-Bauelemente sind Schlüsselfaktoren moderner Technologien. Vor allem ihre Eigenschaft, Ströme mittels Feldeffekt ein- und auszuschalten, wird in nahezu allen elektronischen Geräten verwendet und das Zusammenspiel von Milliarden dieser MOS-Feldeffekttransistoren (MOSFETs) auf kleinen Computerchips ermöglicht die komplexen Berechnungen, die nunmehr Teil unseres Alltags sind. Eine der größten Herausforderungen dieser Technologien ist es, Geräte bei höchstmöglicher Leistung, aber zugleich auch ausreichender Zuverlässigkeit über die vorgesehene Lebensdauer hinweg zu betreiben. Besonders entscheidend sind dabei Instabilitäten die stark von der Biasspannung und der Temperatur abhängen. Dieses Phänomen wird Bias-Temperaturinstabilität (BTI) genannt und stellt eines von mehreren Zuverlässigkeitsproblemen dar, die auf das Einfangen von Ladungen in den Oxiden dieser Bauelemente zurückzuführen sind.

BTI wurde bereits vor mehr als 50 Jahren dokumentiert, aber trotz andauernder Forschung und wirtschaftlichem Interesse sind die grundlegenden physikalischen Mechanismen nicht zur Gänze geklärt. Schon früh wurden diffusive Prozesse und temperaturaktivierte Reaktionen für BTI verantwortlich gemacht, kontrovers ist jedoch, welcher dieser beiden Mechanismen den zeitlichen Verlauf der Degradation dominiert. Moderne Technologien erlauben detailliertere Studien dieser Prozesse und es wurde gezeigt, dass die Theorie der nichtstrahlenden Multiphononen (NMP) viele dieser Zuverlässigkeitsprobleme widerspruchsfrei beschreibt. Speziell mittels des 4-State-NMP-Modells konnte die Degradation aufgrund von präexistenten Defekten erfolgreich beschrieben werden. Zusätzlich zu diesen präexistenten Defekten wird ein schwerer zu erfassender Mechanismus beobachtet. Es wird vermutet, dass dieser Mechanismus mit der Defektgeneration und -transformation und einer damit einhergehenden Umverteilung von Wasserstoff in Verbindung steht.

In dieser Arbeit wird eine Vielzahl von verschiedenen experimentellen Degradationsdaten mittels des 4-State-NMP-Modells untersucht. Nach der Analyse von präexistenten Defekten in einfachen SiO2 -Oxiden unter BTI-Bedingungen mit negativer Biasspannung (NBTI) wird eine einheitliche Modellierung solcher Defekte in high-κ-Gate-Schichtstapeln bei negativen und positiven BTI-Bedingungen (PBTI) präsentiert.

Weiters wird gezeigt, dass die Essenz dieser durchaus komplexen Degradationsmechanismen mit hoher Genauigkeit und unter weitgehender Beibehaltung des physikalischen Gehalts abstrahiert werden kann. Diese auf das Wesentliche beschränkten Beschreibungen werden in einem neuen Modellierungssystem namens Comphy, einer Kurzform von „compact-physic“, eingebettet. Mit diesem Modellierungssystem werden die grundlegenden physikalischen Eigenschaften von Defekten in SiO2 - und HfO2 -Oxiden bestimmt und konsistente NBTI- und PBTI-Simulationen für verschiedenartige Prozessierungen durchgeführt. Um diese Studien nachvollziehbar zu machen, werden alle Parameter der Comphy-Simulationen aufgelistet.

Das detaillierte Verständnis der Physik und der Eigenschaften präexistenter Oxiddefekte kann zukünftige Studien der noch ungeklärten Degradationsmechanismen von Oxiden in MOS-Bauelementen erleichtern. Darüber hinaus erlaubt die Ergänzung des physikalischen Modells für präexistente Defekte mit einem phänomenologischen Modell zur Beschreibung der Defektgeneration und -transformation eine sehr genaue und performante Berechnung der Lebensdauer von MOS-Bauteilen. Damit kann das in dieser Dissertation dargestellte Comphy-Modellierungssystem zu der Entwicklung und Verbesserung von MOS-Technologien beitragen.


Prof. Tibor Grasser is by far the most passionate and eager researcher I know and surely it is this passion which, at the same time, provides him the energy to maintain and encourage a large group of researchers in such a peaceful and productive way. Often I have benefited from his relentless commitment to fostering collaborations around the world and I am also truly grateful to you, Tibor, for inspiring me with your enthusiasm for research and for all that I have learned from you in the last years.

While studying at TU Wien, I have always appreciated the university’s administrative efficiency, and this has remained the case even during my final days as a PhD student. Dietlinde Egger has helped to arrange my defense on short notice, and I am proud and thankful to have Prof. Felice Crupi, Prof. Luca Larcher and Prof. Wolfgang Gawlik on the examination committee.

Certainly, my deepest gratitude goes to those whom I have befriended and with whom I share so many good memories. Unfortunately, there is not enough space to thank each of you, and even if there was, I am not sure I could find the words to adequately express my gratitude. Instead, I shall thank each of you in person and limit my acknowledgments below to the more technical aspects of this thesis’ development.

I would like to thank Prof. Siegfried Selberherr and Prof. Erasmus Langer, together with Diana Pop, Renate Winkler, Ewald Haslinger, and Manfred Katterbauer for fostering a professional, productive, and enjoyable working environment at the Institute for Microelectronics. The experimental studies I have conducted at this Institute would never have been possible without the equipment developed and guidance offered by Michael Waltl. The basis for the development and implementation of the BTI models was provided by Wolfgang Goes and Franz Schanovsky, while Theresia Knobloch, Markus Jech, Al-Moatsaem El-Sayed, Mischa Thesberg, Lado Filipovic, Yannick Wimmer and Alexander Grill always found time for helpful technical discussions and to proofread my thesis. Prof. Hans Kosina, Stanislav Tyaginov, Robert Kosik, Bernhard Stampfer, Bianka Ullmann, Yury Illarionov, and Johann Cervenka also contributed their expertise to this thesis.

My first contact with imec and KU Leuven, Belgium was through Ben Kaczer and, from the very start, this enriching and fruitful collaboration could not have been more pleasant. During my PhD studies, I have spent more than a half year in the Device Reliability (DRE) group of imec and the exchange with the researchers there was indispensable for my work. For me Dimitri Linten is the most outstanding team leader and together with Guido Groeseneken he enables the

achievements of this research group. I am deeply grateful to Ben Kaczer who broadened my technical and cultural horizons and contributed to this thesis like no other. His ideas served as the initial impetus of the Comphy framework and he coined its name. The technical comprehension of Jacopo Franco is beyond striking and he contributed extensively to this modeling framework and to my wonderful time at imec. Philippe J. Roussel and his mathematical expertise was important for the efficiency of Comphy and he is gratefully acknowledged for establishing Eq. (4.36), (4.37), (4.55), and (4.56). When it comes to the efficiency of Comphy, the refactoring of the Python code by Geert Hellings exceeded all expectations and enabled its success. I am truly grateful to my colleagues at the DRE group for the good times and their contributions to this thesis through experimental work and technical discussions. Thank you Simon Van Beek, Roman Boschke, Erik Bury, Adrian Vaisman Chasin, Shih-Hung Chen, Kent Chuang, Robin Degraeve, Myriam Janowski, Mirko Scholz, Vamsi Putcha, Marko Simicic, Alexandre Subirats, Barry O’Sullivan, Bart Vermeulen, and Pieter Weckx.

Markus Karner and Christian Kernstock welcomed me at Global TCAD Solutions when I was looking for a job during my master’s studies, and I was pleased to find there a group of unconventional but nonetheless driven and dedicated developers and researchers, some of whom also supported me during my PhD studies. These include Ferdinand Mitterbauer, Philipp Prause, Oliver Triebl, Franz Schanovsky, Hui-Wen Karner, Klaus Schnass, Zlatan Stanojević and Oskar Baumgartner. Thank you, Markus and Christian, for this opportunity and for being truly kind supervisors.

Furthermore, I would like to thank Hans Reisinger, Wolfgang Gustin, Katja Puschkarsky, and Gunnar Rott from Infineon, Munich for sharing their experimental insights and providing measurement data. In the course of the European project “MoRV” I was lucky enough to collaborate with Domenik Helms and Reef Eilers from Offis, Oldenburg, with Roland Jancke and Kay-Uwe Giering from Fraunhofer, Dresden, and with Dan Alexandrescu from IROC, Grenoble. All of them did an outstanding job and the close collaboration within the consortium made this project such a successful and enjoyable one.

I am grateful to Martin Tomitsch, Daniela Rzepa, and Victoria Haykin for additional comments and proofreading. In large part the template for this thesis was provided by Michael Waltl and Vel (www.LaTeXTemplates.com) and this research made use of the Python libraries NumPy, SciPy, and matplotlib. Finally, I would like to express my gratitude to those who motivated me through their interest and encouragement. It were the sincere words of Shinya Yamakawa from Sony, Runsheng Wang from Peking University, Kevin Huang from TSMC, and many other kind colleagues which spurred me to finish the work for this thesis.