Direct Energy, 2018a

94 5.2 Physics of the Hall Eect
The electric eld intensity can be expressed as a function of the voltage
V AB measured across the width of the device, in the â y direction.
−→ E =
V AB
w ây (5.5)
q −→ E = −q −→ v × −→ B (5.6)
V AB
w = v xB z (5.7)
While the magnitude of the velocity of the charges v x is often not known,
the applied current, I x , in units amperes, is known. The current density
through a cross section of the device is the product of the charge concentration,
the strength of the charges, and the velocity of the charges.
current density =
I x
w·d thick
= q · v x · p (5.8)
Fromthe above expression, velocity can be expressed in terms of the current.
I x
v x =
(5.9)
w · d thick · q · p
Equations 5.7 and 5.9 can be combined.
V AB =
w · I x · B z
(5.10)
w · d thick · q · p
A magnetometer is a device that measures magnetic eld. To use a
Hall eect device as a magnetometer, start with a piece of semiconductor
of known dimensions and known charge concentration, and then apply a
current. If the voltage perpendicular to the current is measured, the magnetic
eld can be calculated. The measured voltage is proportional to the
strength of the external magnetic ux density.
B z = d thick · q · p · V AB
(5.11)
I x
Voltage is easily measured with a voltmeter, so no specialized tools are
needed. To reliably measure this voltage, it is often amplied.
Alternatively, if the strength of an external magnetic eld is known, the
Hall eect can be used to measure the concentrations of holes or electrons
in a piece of semiconductor. With some algebra, we can write the hole concentration
as a function of the dimensions of the semiconductor, the known
magnetic eld strength, the applied current, and the measured voltage.
p =
I x · B z
d thick · q · V AB
(5.12)