It is noticed that the resistance of the
sample changes when the magnetic field is turned on. The phenomenon,
called magnetoresistance, is due to the fact that the drift
velocity of all carriers is not same. With the magnetic field
on; the Hall voltage V is given as:
which compensates exactly the Lorentz force
for carriers with the average velocity; slower carriers will
be over compensated and faster one undercompensated, resulting
in trajectories that are not along the applied field. This
results in an effective decrease of the mean free path and
hence an increase in resistivity.
Here the above referred symbols are defines
as: v = drift velocity; E = applied electric field; t = thickness
of the crystal; H = Magnetic field
Description of the experimental setup
The set-up consists of the following:
It consists of 4 collinear, equally spaced
(2mm) and individually spring loaded probes mounted on a PCB
strip. Two outer probes for supplying the constant current
to the sample and two inner probes for measuring the voltage
developed across these probes. This eliminate the error due
to contact resistance which is particularly serious in semiconductors.
A platform is also provided for placing the sample and mounting
the Four Probes on it.
Ge Crystal (n-type) dimensions : 10 x 10 x 0.5 mm.
Magnetoresistance Set-up, Model
This unit consists of a digital millivoltmeter and
constant current power supply. The voltage and probe current
can be read on the same digital panel meter through a selector
(a) Digital Millivoltmeter
Intersil 3½ digit single chip
ICL 7107 been used. Since the use of internal reference
causes the degradation in performance internal heating
an external reference been used. Digital voltmeter is
much convenient to use, because the input voltage of
either polarity can be measured.
Range : 0-200mV (100mV
Accuracy : ±0.1% of reading ± 1 digit
Current Power Supply
power supply, specially designed for Hall Probe, provides
100% protection against crystal burn-out due to excessive
current. The supply is a highly regulated and practically
ripple free dc source.
Current : 0-20mA Resolution
Accuracy : ±0.2% of the reading ±1 digit
Load regulated : 0.03% for 0 to full load
Line regulation : 0.05% for 10% variatio
The Details of other subunits can be had
from their respective datasheets.