If several materials are combined within a microstructure, mechanical forces
occur if the volumes of the different materials change. Several effects
may enforce volume expansion, for instance chemical reactions, phase
interchanges and recrystallization, mass migration, and thermal expansion and
In this thesis, the mechanical stress due to thermal expansion is considered.
The mechanical stress
can be separated into a static and a thermal
stress component  as
represents the static stress component, which is
impressed and mostly fixed by the fabrication processes, for instance material
deposition, annealing, and packaging.
The thermal component of the stress
is a transient
quantity influenced by the ambient temperature and other
state variables of the system. The corresponding hydrostatic pressure
is then defined as the trace of the mechanical stress tensor
which represents an averaged value and can be used for significant comparisons,
as a figure of merit for optimization purposes, and to visualize the mechanical
stress in a microelectronic device structure.
The local force density which acts on the material can be described by the
mechanical stress tensor
, which can be derived from the mechanical
using the LAMÉ3.4 formalism to model
are the LAMÉ constants, which can be
expressed by YOUNG's modulus
and POISSON's ratio
For orthotropic materials the number of independent components for the stiffness and stress tensor is
reduced due to energetic considerations and symmetry in the
Hence, the number of independent components of the stiffness tensor (forth rank)
is reduced to nine and for the stress tensor (second rank) to six. Hence,
the mechanical problem can be expressed in terms of vectors and
matrices  according to the VOIGT notation.