Callister - An introduction - 8th edition

18.14 The Hall Effect • 747
Dependence of Hall
voltage on the Hall
coefficient, specimen
thickness, and current
and magnetic field
parameters shown in
Figure 18.20
voltage, termed the Hall voltage V H , will be established in the y direction. The magnitude
of V H will depend on I x , B z , and the specimen thickness d as follows:
V H R HI x B z
d
(18.18)
In this expression R H is termed the Hall coefficient, which is a constant for a
given material. For metals, wherein conduction is by electrons, R H is negative and
equal to
Hall coefficient for
metals
R H 1
ne
(18.19)
Thus, n may be determined, inasmuch as R H may be measured using Equation 18.18
and the magnitude of e, the charge on an electron, is known.
Furthermore, from Equation 18.8, the electron mobility is just
m e
m e s
ne
(18.20a)
For metals, electron
mobility in terms of
the Hall coefficient
and conductivity
or, using Equation 18.19,
m e R H s
(18.20b)
Thus, the magnitude of m e may also be determined if the conductivity s has also
been measured.
For semiconducting materials, the determination of majority carrier type and
computation of carrier concentration and mobility are more complicated and will
not be discussed here.
EXAMPLE PROBLEM 18.4
Hall Voltage Computation
The electrical conductivity and electron mobility for aluminum are 3.8 10 7
( # m ) 1 and 0.0012 m 2 /V# s , respectively. Calculate the Hall voltage for an
aluminum specimen that is 15 mm thick for a current of 25 A and a magnetic
field of 0.6 tesla (imposed in a direction perpendicular to the current).
Solution
The Hall voltage V H may be determined using Equation 18.18. However, it
first becomes necessary to compute the Hall coefficient (R H ) from Equation
18.20b as
R H m e
s
0.0012 m 2 /V# s
3.8 10 7 1# m2
1 3.16 1011 V# m/A # tesla