Page 144 - Engineering Electromagnetics, 8th Edition

126 ENGINEERING ELECTROMAGNETICS

D5.6. A perfectly conducting plane is located in free space at x = 4, and
a uniform infinite line charge of 40 nC/m lies along the line x = 6, y = 3. Let
V = 0at the conducting plane. At P(7, −1, 5) find: (a) V ;(b) E.
Ans. 317 V; −45.3a x − 99.2a y V/m

5.6 SEMICONDUCTORS
If we now turn our attention to an intrinsic semiconductor material, such as pure
germanium or silicon, two types of current carriers are present, electrons and holes.
The electrons are those from the top of the filled valence band that have received
sufficient energy (usually thermal) to cross the relatively small forbidden band into
the conduction band. The forbidden-band energy gap in typical semiconductors is of
the order of one electronvolt. The vacancies left by these electrons represent unfilled
energy states in the valence band which may also move from atom to atom in the
crystal. The vacancy is called a hole, and many semiconductor properties may be
described by treating the hole as if it had a positive charge of e,a mobility, µ h , and
an effective mass comparable to that of the electron. Both carriers move in an electric
field, and they move in opposite directions; hence each contributes a component of
the total current which is in the same direction as that provided by the other. The
conductivity is therefore a function of both hole and electron concentrations and
mobilities,

σ =−ρ e µ e + ρ h µ h (19)

For pure, or intrinsic, silicon, the electron and hole mobilities are 0.12 and 0.025,
respectively, whereas for germanium, the mobilities are, respectively, 0.36 and 0.17.
These values are given in square meters per volt-second and range from 10 to 100
times as large as those for aluminum, copper, silver, and other metallic conductors. 6
These mobilities are given for a temperature of 300 K.
The electron and hole concentrations depend strongly on temperature. At 300 K
3
the electron and hole volume charge densities are both 0.0024 C/m in magnitude in
3
intrinsic silicon and 3.0 C/m in intrinsic germanium. These values lead to conductiv-
ities of 0.000 35 S/m in silicon and 1.6 S/m in germanium. As temperature increases,
the mobilities decrease, but the charge densities increase very rapidly. As a result, the
conductivity of silicon increases by a factor of 10 as the temperature increases from
300 to about 330 K and decreases by a factor of 10 as the temperature drops from 300
to about 275 K. Note that the conductivity of the intrinsic semiconductor increases
with temperature, whereas that of a metallic conductor decreases with temperature;
this is one of the characteristic differences between the metallic conductors and the
intrinsic semiconductors.

6 Mobility values for semiconductors are given in References 2, 3, and 5 listed at the end of this chapter.