Papers by Author: Wolfgang H. Müller

Abstract: We consider a silicon nanopowder based anode for a lithium ion battery cell. We present the design of the battery cell ready for in situ Raman and X-ray experiments and a technical procedure for the cell manufacturing. From the continuum mechanics point of view, this type of anode can be represented by a spherical nanoparticle surrounded by viscoelastic matrix. During the charging process this nanoparticle undergoes a chemical reaction. Based on the chemical affinity concept we describe how the mechanical properties of the matrix material influence the kinetics of the charging process. We study spherically symmetry problems numerically for different sets of matrix material parameters and show their influence on the reaction front kinetics.

Abstract: Damage of metals subjected to large plastic deformations typical for forming processes is mainly governed by void nucleation, growth and coalescence. An opposite process may occur in deformation processes with negative stress triaxialities: the closure of strain-induced defects under large hydrostatic pressure. Understanding the mechanisms of damage growth and healing under plastic deformation of metals is still an urgent problem. In order to solve it a theoretical framework for anisotropic ductile damage based on a physically motivated concept for changes in the void volume and shape was recently developed [6]. Strain-induced damage was experimentally determined during uniaxial compression of cylindrical metallic specimens with artificial voids represented by fully-trough drilled holes. It was revealed that the governing physical mechanism of failure is a change in void shapes due to compressive stresses at low negative stress triaxialities in contrast to the growth of voids volume due to high positive stress triaxialities in the processes with dominating tensile stresses. The tensorial model presented in [6] proved to be able to describe kinetics of ductile damage, failure as the ultimate damage, and the closure of voids at negative stress triaxialities.

Abstract: The fabrication of microelectronic and micromechanical devices leads to the use of only very small amounts of matter, which can behave quite differently than the corresponding bulk. Clearly, the materials will age and it is important to gather information on the (changing) material characteristics. In particular, Young’s modulus, yield stress, and hardness are of great interest. Moreover, a complete stress-strain curve is desirable for a detailed material characterization and simulation of a component, e.g., by Finite Elements (FE). However, since the amount of matter is so small and it is the intention to describe its behavior as realistic as possible, miniature tests are used for measuring the mechanical properties. In this paper two miniature tests are presented for this purpose, a mini-uniaxial-tension-test and a nanoindenter experiment. In the tensile test the axial load is prescribed and the corresponding extension of the specimen length is recorded, both of which determines the stress-strain- curve directly. The stress-strain curves are analyzed by assuming a non-linear relationship between stress and strain of the Ramberg-Osgood type and by fitting the corresponding parameters to the experimental data (obtained for various microelectronic solders) by means of a non-linear optimization routine. For a detailed analysis of very local mechanical properties nanoindentation is used, resulting primarily in load vs. indentation-depth data. According to the procedure of Oliver and Pharr this data can be used to obtain hardness and Young’s modulus but not a complete stress-strain curve, at least not directly. In order to obtain such a stress-strain-curve, the nanoindentation experiment is combined with FE and the coefficients involved in the corresponding constitutive equations for stress and strain are obtained by means of the inverse method. The stress-strain curves from nanoindentation and tensile tests are compared for two mate-rials (aluminum and steel). Differences are explained in terms of the locality of the measurement. Finally, material properties at elevated temperature are of particular interest in order to characterize the materials even more completely. We describe the setup for hot stage nanoindentation tests in context with first results for selected materials.

Abstract: In this paper we will discuss the impact of residual stresses on the reliability of microelectronic components and the materials used therein. The following issues will be particularly emphasized: First, the tendency toward delamination and subsequent cracking along interfaces, such as between silicon dies, organic substrates, glues, and underfill material; second, the fatigue of electrolytically deposited copper vias within the substrate and FR4 board material; third, the accumulation of irreversibly accumulated plastic (creep) strain in lead containing as well as leadfree solders; the microstructural change observed during thermo-mechanical use within the bulk as well as at the interface of solder interconnects. We will present state-of-the-art numerical techniques that allow to quantify the development of stresses and strains within the aforementioned materials, mostly by finite element analysis, as well as the coupling between local stresses and diffusion processes, which is theoretically based on phase field models. Further emphasis is put on proper knowledge and determination of the inherent material parameters and how theoretical predictions can be linked to and validated by experimental observations and facts.