Page 157 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

The Electromagnetic System
4.1. What it tells us is that the magnetic induction field effectively dif-
fuses into a material.
Together, the four characteristic time constants can be used to decide on
which effects to effectively ignore. Thus, if β<<1 , we can certainly
ignore the wave-like effects and concentrate on diffusion-like formula-
tions, since the electromagnetic wave passes our system faster than it can
respond. Going one step further, and considering the case where

Electro- τ < τ < τ and β<<1 (4.31)
m em e
Quasi-Statics
we can formulate the electrical equations as if the magnetic phenomena
were instantaneous. For

Magneto- τ < τ < τ and β<<1 (4.32)
e em m
Quasi-Statics
we can assume that charge relaxation effects are instantaneous. Note that
quasi-statics by no means imply steady-state phenomena, which we treat
next, but merely address the extent of dynamic coupling between the
constituent charges, magnetic fields and the electromagnetic waves that
excite our system. In other words, for the dynamic equation the other
field appears effectively static because its time constant is small. The
resulting equation sets for the quasi-static approximations are summa-
rized in Table 4.1.

Table 4.1. The quasi-static equations of electrodynamics. Adapted from
[4.4].

Equations
Magneto- ∇× H = J ∂B
quasi-statics ∇× E = –
t ∂
(
∇• B = 0 B = µH = µ H + M)
0
∇• J = 0

154 Semiconductors for Micro and Nanosystem Technology