Computer Simulation of ElectroMigration in Microelectronics Interconnect by Xiaoxin Zhu Centre of Numerical Modelling and Process Analysis, School of Computing and Mathematical Sciences,The University of Greenwich, London, U.K. A thesis submitted in partial fulfillment of the requirements of the University of Greenwich for the Degree of Doctor of Philosophy July 2014 DECLARATION I certify that this work has not been accepted in substance for any degree, and is not concurrently being submitted for any degree other than that of Doctor of Philosophy being studied at the University of Greenwich. I also declare that this work is the result of my own investigations except where otherwise identified by references and that I have not plagiarised the work of others. …………………………………………………………………. Xiaoxin Zhu (PhD student) …………………………………………………………………. Hua Lu (Supervisor) …………………………………………………………………. Christopher Bailey (Supervisor) Abstract Electromigration (EM) is a phenomenon that occurs in metal conductor carrying high density electric current. EM causes voids and hillocks that may lead to open or short circuits in electronic devices. Avoiding these failures therefore is a major challenge in semiconductor device and packaging design and manufacturing, and it will become an even greater challenge for the semiconductor assembly and packaging industry as electronics components and interconnects get smaller and smaller. According to the assembly and packaging section of the International Technology Roadmap for Semiconductor (ITRS) developed in 2007 and 2009 [1] [2], EM was a near term threat for the interconnecting part of semiconductor, devices and packaging methods such as flip chip, and Ball Grid Array (BGA). In the industry, EM-aware designs are mainly based on design rules that are derived from empirical laws which do not help understand complicated EM processes and therefore can’t be used to carry out accurate predictions for EM failures of sophisticated components in varied environmental conditions. In this work, novel numerical modelling methods of EM in micro-electronics devices have been developed and the methods have been used to analyse EM process in a lead free solder thin film, and to optimize the design of electronic components in order to reduce the risk of EM relative failure. EM is an atomic diffusion process that is driven by a high density electric current, but it is strongly affected by temperature and its gradient as well as stress distribution. In order to model EM accurately, the interacting electrical, thermal, and mechanical phenomena must all be solved simultaneously. In this work, a novel multi-physics modelling method has been proposed and developed to include all of the above mentioned physical phenomena using unstructured Finite Volume (FV) and Finite Element (FE) techniques. The methods have been implemented on the multi-physics software package PHYSICA. Comparing with existing methods, this fully coupled solution method is a significant improvement that will facilitate further development of electronics design and optimization tool as well as new research work that helps understand EM phenomenon. The developed models can be used to i simulate the whole process of EM, predict voids initiation lifetime of electronics products or test specimens. In today’s electronics manufacturing, lead-free solder alloys are used as interconnect. As in copper or aluminium interconnect EM has become a threat to device reliability as current density increase in solder joints with diminishing sizes. In this work, computer simulation methods have been used to analyse the experimentally observed EM process in a thin film solder. The experiment was designed in such a way that effects of temperature and stress gradients can be avoided. The advantage of this experimental method is that the electric current effect is isolated which makes analysis and model validation easier. In this work, the predicted voids locations are consistent with experimental results. In this work, numerical examples are given to illustrate how interconnect designs can be made more EM failure resistant. The ultimate aim of the research is to understand EM and to develop techniques that predict EM accurately so that EM-aware designs can be made easier. ii ACKNOWLEDGEMENTS Firstly, I would like to express my gratitude to my supervisors Dr. Hua Lu and Professor Christopher Bailey for their kind advice, encouragement and guidance throughout my PhD studies. I would like to acknowledge Professor Samjid H. Mannan and Dr. Hiren Kotadia from King’s College, London, Professor Y.C. Chan and Ms Sha Xu from the City University of Hong Kong for their advice and help in experiments. I would also like to acknowledge Dr. Georgi Djambazov for helping me understand the structure of PHYSICA. I would like to thank my parents for their understanding and complete support and also my friends for their entertaining distractions and polite interest. Finally, I would like to acknowledge the University of Greenwich without its financial support I could not have carried out my research. iii Table of Contents Declaration Abstract .................................................................................................................................................................... i Acknowledgements ......................................................................................................................................... iii List of Figures .................................................................................................................................................... vii List of Tables ..................................................................................................................................................... xiii List of Publication ........................................................................................................................................... xiv Chapter 1 INTRODUCTION ............................................................................................................................ 1 1.1 Electromigration and Microelectronics Reliability ........................................................................ 1 1.2 Electronic Packaging and Its Trend ............................................................................................... 3 1.3 Aims and Objectives of This Research .......................................................................................... 9 1.4 Challenges and Methodologies ..................................................................................................... 9 1.5 Contribution of This Study .......................................................................................................... 10 1.6 The Structure of The Thesis ........................................................................................................ 11 Chapter 2 A REVIEW ON ELECTROMIGRATION PHENOMENON AND RESEARCH METHODOLOGY ............................................................................................................................................... 13 2.1 Overview of The Chapter ............................................................................................................ 13 2.1.1 The EM Phenomenon........................................................................................................... 13 2.1.2 The Thermomigration Phenomenon ................................................................................... 14 2.1.3 The Stressmigration Phenomenon ...................................................................................... 15 2.1.4 EM and Conductor Materials ............................................................................................... 15 2.1.5 The Effects of Interfacial Chemical Reactions ...................................................................... 16 2.1.6 AC or DC? ............................................................................................................................. 16 2.2 EM Modelling Approaches .......................................................................................................... 21 2.2.1 Empirical Approaches of EM Analysis .................................................................................. 21 2.2.2 Numerical Approaches of EM Analysis ................................................................................ 24 2.2.2.1 EM and Mechanical Stress Effect ...................................................................................... 25 iv 2.2.2.2 EM and Thermal Effect...................................................................................................... 27 2.2.2.3 Generation /Annihilation Term ......................................................................................... 28 2.2.2.4 Void Nucleation ................................................................................................................ 29 2.2.2.5 Damage Mechanics/Measurement .................................................................................. 31 2.2.2.6 Molecular Dynamics Model .............................................................................................. 33 2.2.3 EM Modelling Methodologies .............................................................................................. 35 2.2.3.1 Atoms/Vacancies Condensation at Boundary .................................................................. 36 2.2.3.2 Atomic/Vacancy Flux Divergence Based Analysis ............................................................