Page 149 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

The Electromagnetic System
Equation (4.2a) has a particularly simple interpretation. The line integral
•
° C ∫ E dl = U Ind is the induced electric potential, which is equal to
⁄
•
minus the rate of change of flux φ– ˙ = – ∂∂t( S ∫ B d S) that passes
through the surface enclosed by the loop, or
U = – φ ˙ (4.4)
Ind
The Ampere law (4.1b) describes how a magnetic field is generated in
response to both a charge current density and a time-varying electric
J
displacement D . By the same argument as before, the magnetic field
vector is perpendicular to the current density vector and the electric dis-
placement vector, and it will, in general, also not be spatially uniform.

The Gauss laws (4.1c) and (4.1d) confirm the experimental fact that only
charge monopoles, and no magnetic monopoles, are observed in nature.
In addition, the electrostatic law states that the electric displacement field
generated in a closed region of space is only due to the enclosed charges.
Inversely, if a region of space contains no charges, and hence the right-
hand side of (4.2c) is zero, we would measure no net electric displace-
ment: the divergence is of D zero.

Three constitutive equations are necessary to complete the set. They link
the various fields to each other and describe the influence of the material
on the propagation of the fields. The electric field E drives the charge
current , and is hampered in doing so by the conductivity σ of the
J
material:

J = σE (4.5)

In vacuum, Equation (4.5) of course falls away, and in semiconductors it
is a gross simplification of the actual nonlinear charge conduction mech-
anism taking place, which we discuss in more detail in Chapter 7. The
magnetic flux density B is driven by the magnetic field H , and is ham-
µ
pered thereby by the permeability of the material:
B = µH = µ µ H (4.6)
0 r

146 Semiconductors for Micro and Nanosystem Technology