Contents

Abstract

Kurzfassung

Acknowledgment

List of Acronyms

1 Introduction

1.1 Research Goals

1.2 Research Setting

1.3 Outline of the Thesis

2 Heteroepitaxy and Selective Epitaxial Growth

2.1 Fundamentals of Epitaxy

2.1.1 Microscopic Processes During Epitaxial Growth

2.1.2 Crystal Facets and Miller Indices

2.1.3 Equilibrium Epitaxial Growth

2.1.4 Kinetic Epitaxial Growth

2.1.5 Selective Epitaxy of SiGe

2.2 Modeling Epitaxy

2.2.1 Atomistic Lattice-Gas Models

2.2.2 Burton-Cabrera-Frank Theory

2.2.3 Island Dynamics Models

2.2.4 Multiscale Approach

2.2.5 Continuum Models

2.3 Summary

3 Anisotropic Wet Etching

3.1 Fundamentals of Anisotropic Wet Etching

3.1.1 Microscopic Processes During Anisotropic Wet Etching

3.1.2 Wet Etchants and Characterization

3.2 Modeling Anisotropic Wet Etching

3.2.1 Atomistic Methods

3.2.2 Continuum Approaches

3.3 Summary

4 Level-Set Method for Anisotropic Wet Etching and Selective Epitaxy

4.1 The Level-Set Method for Anisotropic Semiconductor Processes

4.1.1 The Level-Set Method for Process Simulations

4.1.2 Crystal Direction-Dependent Surface Propagation

4.2 Stencil Lax-Friedrichs Scheme

4.2.1 Derivation of the Scheme

4.2.2 Implementation and Analysis

4.3 Multi Level-Set Scheme for Non-Planar Selective Epitaxy

4.3.1 Deposition Top Layer

4.3.2 Implementation and Analysis

4.4 Summary

5 Applications

5.1 Sigma-Cavity for Embedded-SiGe MOSFETs

5.1.1 Hubbard Interpolation for Octahedral Symmetry

5.1.2 Modeling and Results

5.2 Selective Epitaxy of SiGe

5.3 Heteroepitaxy of 3C-SiC on Si(111) Micro-Pillars

5.3.1 Growth Rates in Tetrahedral Symmetry

5.3.2 Modeling and Results

5.4 Anisotropic Wet Etching of Patterned Sapphire Substrates

5.4.1 Etch Rates in Trigonal Symmetry

5.4.2 Modeling and Results

5.5 Summary

6 Process TCAD and Semiconductor Device Design

6.1 Linking Process and Device Simulation

6.2 Light Extraction Efficiency of GaN-Based LEDs

6.2.1 Ray Optics Approximation

6.2.2 Light Extraction Efficiency

6.2.3 Coupled Process and Device Simulations

6.3 Summary

7 Summary and Outlook

Bibliography

Own Publications

Curriculum Vitae

Abstract

The development of semiconductor device fabrication techniques which operate on complex three-dimensional topographies strongly benefits from technology computer-aided design (TCAD). Particularly important for intricate topographies and at the center of the research presented in this thesis are selective epitaxial growth and anisotropic wet etching processes, which are essential for fabricating fin field-effect transistors (fin FETs), substrate patterning for efficient light emitting diodes (LEDs), and micro-electro-mechanical systems (MEMS). The introduction of alternative materials to silicon (e.g., silicon carbide and sapphire) with their unique processing requirements further intensifies the need for specialized TCAD algorithms and models.

In this thesis, to set the stage, the fundamental phenomena causing strong anisotropy in selective epitaxy and wet etching are presented and various modeling approaches are reviewed. Since continuum modeling approaches are particularly attractive for TCAD, process simulations based on the level-set method are discussed in depth. However, the computational treatment of anisotropic processes with level-sets poses several challenges involving numerical stability and sensitivity to the accuracy of the geometry description. Hence, numerical methods for the level-set method, namely a novel finite difference Stencil Lax-Friedrichs scheme and the deposition top layer method, which are tailored to selective epitaxy and anisotropic wet etching are proposed and assessed with respect to high accuracy and physical relevance.

The thus advanced level-set method enables the simulation of strongly anisotropic steps manifesting in a variety of state-of-the-art semiconductor fabrication processes, including source-drain engineering of FETs and LEDs. The involved crystalline materials (e.g., silicon-germanium, silicon carbide, and sapphire) exhibit different crystal symmetries and induce complex topographies, which need to be accounted for by computational methods. Hence, a general etch/deposition rate interpolation procedure which respects the associated symmetry operation is proposed and evaluated. Moreover, a continuum model for anisotropic wet etching of sapphire with phosphoric and sulfuric acid, which covers different etchant mixtures and etching temperatures is presented. The capability of the modeling approach is demonstrated by comparing the simulation results with experimental observations from the literature.

Furthermore, closely coupled process and device simulations are investigated, which allow to link process parameters with the resulting device characteristics. By way of example, the impact of post-implantation annealing parameters on silicon carbide power transistor characteristics are studied. Additionally, the sapphire wet etching model is utilized to study geometrically patterned gallium nitride-based LED structures and characterize the light extraction efficiency with ray-tracing calculations. These simulations reveal the subset of the process parameter space resulting in optimal device characteristics and thus corroborate the merits of level-set based process simulation.

Kurzfassung

Die Entwicklung der Fertigungstechniken von Halbleiterbauelementen, die auf komplexen dreidimensionalen Topographien basieren, profitiert stark von rechnerunterstütztem Technologie-Design. Selektive Epitaxie und anisotropes nasschemisches Ätzen sind hervorragend geeignet, um komplizierte Topographien zu realisieren. Diese Prozesse sind essentiell für die Herstellung von flossenähnlichen Feldeffekttransistoren (fin FETs), geometrisch strukturierten Substraten für effiziente Leuchtdioden (LED), sowie mikroelektromechanische Systeme. Durch die Einführung von alternativen Materialien (z. B. Siliziumkarbid und Saphir) mit ihren besonderen Anforderungen an die Prozessierung gewinnen spezialisierte TCAD Algorithmen und Modelle zunehmend an Bedeutung.

In dieser Dissertation werden zunächst die fundamentalen Phänomene, die der ausgeprägten Anisotropie von selektiver Epitaxie und nasschemischen Ätzen zugrunde liegen, präsentiert und verschiedene Modellierungsansätze besprochen. Da Kontinuummodelle gut geeignet sind im Kontext von TCAD, werden Prozesssimulationen mithilfe der Level-Set Methode im Detail behandelt. Die rechnerische Behandlung von anisotropen Prozessen mit der Level-Set Methode ist herausfordernd, insbesondere die numerische Stabilität und die hohe Sensitivität der Methode auf numerische Ungenauigkeiten in der Geometriebeschreibung. Daher werden numerische Verfahren für die Level-Set Methode, im Speziellen ein neues Finite-Differenzen Stencil Lax-Friedrichs Verfahren und die Abscheidungsdeckschicht-Methode, die auf das Rechenproblem der selektiven Epitaxie und des anisotropen nasschemischen Ätzens zugeschnitten sind, vorgeschlagen und bezüglich Simulationsgenauigkeit und physikalischer Relevanz evaluiert.

Die damit weiterentwickelte Level-Set Methode ermöglicht die Simulation von stark anisotropen Prozessschritten in vielfältigen hochmodernen Halbleiterherstellungsprozessen, einschließlich der Source-Drain Optimierung von FETs und der Herstellung von LEDs. Die hier benötigten kristallinen Materialien (z. B. Silizium-Germanium, Siliziumkarbid und Saphir) zeigen unterschiedliche Kristallsymmetrien und erzeugen daher komplexe Topographien. Die Kristallsymmetrien müssen folglich in den Rechenmodellen akkurat abgebildet sein. In dieser Arbeit wird ein allgemeines Interpolationsverfahren für Ätz- und Abscheidungsraten, das die jeweiligen Symmetrieoperationen respektiert, vorgeschlagen und evaluiert. Daneben wird ein Kontinuummodel für anisotropes nasschemisches Ätzen von Saphir mit Phosphor- und Schwefelsäure präsentiert, das verschiedene Ätzgemische und Ätztemperaturen beschreibt. Die Eignung des Modellansatzes wird demonstriert, indem die Simulationsergebnisse mit experimentellen Beobachtungen aus der wissenschaftlichen Literatur verglichen werden.
Außerdem werden gekoppelte Prozess- und Bauelementsimulationen behandelt, welche die enge Verknüpfung von Prozessparametern und der resultierenden Bauelementcharakteristiken ermöglichen. Beispielshaft wird zum einen der Einfluss von Prozessparametern der Post-Implantations-Wärmebehandlung auf die Bauelementcharakteristiken von Siliziumkarbid Leistungstransistoren untersucht. Zum anderen wird das Saphir Ätz-kontinuumsmodell verwendet, um geometrisch strukturierte Galliumnitrid LED-Strukturen zu untersuchen und die Lichtextraktionseffizienz mit Strahlverfolgungsberechnungen zu bestimmen. Diese Simulationen legen den Teilraum der Prozessparameter offen, der zu optimalen Bauelementverhalten führt und demonstrieren damit die Vorzüge der Level-Set Halbleiter-Prozesssimulation.

Acknowledgment

Writing a dissertation is a substantial task and is only made possible with the support of many people. I am grateful for having the opportunity to be part of the Christian Doppler Laboratory (CDL) for High Performance TCAD at the Institute for Microelectronics ( ), TU Wien.

I would like to thank my supervisors Josef Weinbub, who is the head of the CDL, and Prof. Siegfried Selberherr for providing an excellent environment for research. Their continuous support, willingness to give me the freedom to pursue my ideas, and remarkable eye for detail, formed the foundation for all scientific achievements presented in this work.

The outbreak of the COVID-19 pandemic has abruptly changed many facets of our lives and has also significantly affected the scientific world. It is a considerable challenge to organize research activities during these difficult times of social distancing and increased uncertainty. I want to thank the head of the institute, Prof. Tibor Grasser, and all members of the for their efforts to sustain the high-quality working environment our institute is known for.

Special thanks go to Paul Manstetten, who proofread this dissertation and frequently offered advice during the entire project, and Michael Quell, who always had the patience to listen to my not yet fully conceived ideas. I also want to highlight Xaver Klemenschits: His constant optimism and ambition to develop elegant simulation software are extraordinarily inspiring. Many thanks go to Luiz Felipe Aguinsky, Frâncio Rodrigues, Alexander Scharinger, and Christoph Lenz for the numerous fruitful discussions we had.

An important facet of this work was the close collaboration with our industry partner, Silvaco Europe Ltd., which gave me the opportunity to spend time in their Vienna office. In particular, I want to thank Andreas Hössinger, who provided many research ideas and was always open for valuable discussions, but also Vito Šimonka and Wolfgang Gös for their support. The elaborate simulations for light-emitting diodes presented in this thesis were only possible due to Silvaco’s openness to quite ambitious ideas. Silvaco’s developers and engineers were helping me to overcome the technical challenges of connecting several software tools and I would like to thank Artem Babayan, Carlos Bedregal, Mark Eastlick, David Green, Matthias Roschke, and Slim Chourou.

Finally, I want to express my deep gratitude to my family for always supporting my academic ambitions.

List of Acronyms