The effect of the pore topology on the elastic modulus of organosilicate glasses
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Malgorzata Kopycinska-Mueller Fraunhofer Institute for Nondestructive Testing, 01109 Dresden, Germany; and Dresden University of Technology, Faculty of Electrical and Computer Engineering, 01068 Dresden, Germany
Lei Chen Queensland University of Technology, School of Chemistry, Physics and Mechanical Engineering department, Brisbane, Queensland 4001, Australia
Yu Chen National University of Singapore, Department of Mechanical Engineering, 117576 Singapore
Marco Jungmann and Reinhard Krause-Rehberg Martin Luther University Halle, Department of Physics, 06120 Halle, Germany
Sukesh Mahajan SBA Materials, Inc., NE Albuquerque, New Mexico 87113
Joost Vlassak Harvard University, School of Engineering and Applied Sciences, Cambridge, Massachusetts 02138
Martin Gall Fraunhofer Institute for Nondestructive Testing, 01109 Dresden, Germany
Ehrenfried Zschecha) Fraunhofer Institute for Nondestructive Testing, 01109 Dresden, Germany; and Dresden University of Technology, Faculty of Electrical and Computer Engineering, 01068 Dresden, Germany (Received 2 January 2013; accepted 20 March 2013)
Optimization of the pore topology in organosilicate glass (OSG) is crucial in the development of dielectrics with an extremely low k-value and a relatively high Young’s modulus. In this paper, a finite-element modeling strategy is applied to develop a general understanding of the relationship between porosity, pore topology, and elastic modulus for the porous OSG thin films. This relationship in combination with the experimental elastic modulus data from nanoindentation (NI) studies is used to predict the pore structure of various OSG films. In addition, positron annihilation spectroscopy measurements are performed to determine the threshold porosity for the transition from nonoverlapping to overlapping porous structure. A similar threshold value is determined based on the finite-element modeling and experimental NI data.
I. INTRODUCTION
Meso-, Micro-, and nanoporous dielectrics used as insulating materials between on-chip interconnects are a crucial component in the leading-edge microelectronic products to reduce electrical signal delay and power loss.1 Beyond the current state-of-the-art 22 nm complementary metal oxide semiconductor technology, the insulating materials need a dielectric constant, k, below 2.2 and elastic modulus, E, above 5 GPa. These stringent requirements for dielectric properties and mechanical stability can be achieved for porous organosilicate glass (OSG) by
optimizing molecular2 and pore3 structures. However, the structure–property relationship for porous OSG is highly complex and not fully understood yet. The relationship between elastic modulus (E) and porosity (p) for OSG films is conventionally described by a simple power law equation2,4: E ¼ Cð1 pÞn q=qs ¼ 1 p
;
;
ð1Þ
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2013.79
where C is a constant dependent on the stiffness of the solid matrix, q and qs are the density of the composite and th
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