Page 29 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

The Crystal Lattice System
ficients of continuum theory, acoustic dispersion, specific heat, thermal
expansion and heat conduction. In fact, going beyond our current goals, it
is possible to similarly treat dielectric, piezoelectric and elastooptic
effects. However, the predictions are of a qualitative nature in the major-
ity of cases, mainly because the interatomic potential of covalently
bonded atoms is so hard to come by. In fact, in a sense the potential is
reverse engineered, that is, using measurements of the crystal, we fit
parameters that improve the quality of the models to make them in a
sense “predictive”.

Chapter Goal Our goal for this chapter is to explain the observed crystal data with pref-
erably a single comprehensive model that accounts for all effects.

Chapter Our road map is thus as follows. We start by stating some of the relevant
Roadmap observable data for the three materials Si SiO and GaAs , without
,
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more than a cursory explanation of the phenomena.

Our next step is to get to grips with the concept of a crystal lattice and
crystal structure. Beyond this point, we are able to consider the forces
that hold together the static crystal. This gives us a method to describe
the way the crystal responds, with stress, to a strain caused by stretching
the lattice. Then we progress to vibrating crystal atoms, progressively
refining our method to add detail and show that phonons, or quantized
acoustic pseudo “particles”, are the natural result of a dynamic crystal
lattice.

Considering the phonons in the lattice then leads us to a description of
heat capacity. Moving away from basic assumptions, we consider the
anharmonic crystal and find a way to describe the thermal expansion. The
section following presents a cursory look at what happens when the regu-
lar crystal lattice is locally deformed through the introduction of foreign
atoms. Finally, we leave the infinitely-extended crystal model and briefly
consider the crystal surface. This is important, because most microsys-
tem devices are build on top of semiconductor wafers, and so are repeat-

28 Semiconductors for Micro and Nanosystem Technology