Page 147 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

The Electromagnetic System
in following the usage established by Albert Einstein (1879–1955), in his
seminal work on the photoelectric effect, that we now call the governing
electrodynamic equations the Maxwell equations. Einstein went on to
unify space-time electromagnetic theory in his work on relativity, result-
ing in a single expression for the Maxwell equations.

At interaction dimensions of the order of atomic spacings and smaller,
we have to also include the rules of quantum mechanics. We consider
both viewpoints.

Chapter Goal Our goal for this chapter is first to obtain a complete description of classi-
cal electrodynamics, and then to extend this model of radiation to a quan-
tum viewpoint.

Chapter Our road map is as follows: to state the Maxwell equations, quantify the
Roadmap concepts leading to electro-quasi-statics and magneto-quasi-statics, and
to their completely static counterparts. Next, we take a closer look at
light, which is that part of the electromagnetic spectrum that ranges from
the near infrared all the way through to the near ultraviolet, by treating
both its wave-like and particle-like characteristics. There will be practi-
cally no “optics” here, and the interaction between light and matter will
appear only later in the book.

4.1 Basic Equations of Electrodynamics

The Maxwell equations are remarkably structured. If it were not for the
absence of magnetic “charges” in nature, we would be able to exchange
the roles of the electric field E and the magnetic field H , as well as the
electric displacement D and the magnetic induction . We first write the
B
Maxwell equations in differential form; each equation must be satisfied
in every point of space:

144 Semiconductors for Micro and Nanosystem Technology