Page 156 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

Basic Equations of Electrodynamics
which is the typical time for electric-field dominated charge signals to
settle. The charge relaxation equation
∂
∇• σE = – ∇• εE or ∇• J = – q˙ (4.26)
t ∂
which can be obtained by manipulating the Maxwell equation set (see
also Table 4.1), is a diffusion equation governing the conservation of free
charge, and describes the way charge imbalance settles. Such processes
are dominated by τ . An electromagnetic wave traversing our system is
e
characterized by the time
λ
τ em = µ ε λ = --- = τ τ (4.27)
0 0
m e
c
which we have obtained by straightforward association. In addition, in
(4.24a) we have defined the factor

 τ em  2
Time-Rate β =  -------- (4.28)
τ 
Parameter
which characterizes the importance of the electromagnetic signal’s transit
time to times of interest in our system.

If we had based our normalization on the magnetic field instead on the
electric field, we would have obtained the parameter

Magnetic τ = µ σ λ 2 (4.29)
m 0 0
Diffusion
Time which is the typical time for magnetic field dominated signals to diffuse
through the system. This time dominates the magnetic diffusion equa-
tion:

1 ∂B
-------∇ 2 B = (4.30)
µσ t ∂
which in turn is obtained by a straightforward manipulation of the mag-
neto-quasi-static equations (neglecting material transport) given in Table

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