ABSTRACT of the Doctoral Thesis
Steadily increasing clock speeds and miniaturization in microelectronics are leading to increasing power densities. Accordingly, there is a demand for new, advanced materials in electronic package design that allow to engineer higher density systems. Certain metal matrix composites are promising candidate materials for electronic packaging applications due to the possibility of tailoring their properties. The latter, however, requires deep understanding and a thorough insight into the mechanisms of interaction between the constituents on the microlevel and of their effect on the overall behavior.
The present study aims to improve the understanding of heat conduction in composite materials, special attention is paid to the effects of imperfectly bonded constituents, i.e. the presence of interfacial thermal resistances.
An overview of selected analytical and numerical methods for describing the overall behavior of composite materials is provided. Subsequently, an introduction into hot pressed carbon-copper composites is given, which have high potential for electronic packaging applications.
Mori-Tanaka mean field approaches, among them newly developed methods, and a periodic microfield approach form the backbone of computational methods, which are employed in this work to estimate the effective conductivity of composites. These methods are discussed in detail in Chapter 3, where also the topic of heat conduction in homogeneous solids is addressed and the limits and assumptions underlying the employed micromechanical approaches are critically reviewed.
Single inclusion problems (i.e. solitary, imperfectly bonded inclusions embedded in an isotropic, unbounded matrix), are studied. For the case of ellipsoidal inclusion geometries an analytical method is developed which enables replacement of the original imperfectly bonded inclusion by a less conductive but perfectly bonded inclusion. The replacement formalism is extended to arbitrary inclusion shapes, the solution technique involving "dilute" unit cells. This numerical replacement procedure in combination with the Mori-Tanaka scheme forms a very versatile, "hybrid" micromechanical tool.
Results are presented primarily for carbon-copper composites. Different microgeometries are investigated and Mori-Tanaka predictions are compared with unit cell predictions, as well as with experimental results.