Transcript Slide 1

Hall Effect Experiment
Shunsuke Kato
Current vs Hall Voltage
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-4.9
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-0.109
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Hall Voltage (V)
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Current (A)
Temperature vs Resistivity
0.00E+00
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Resistivity (ohm/m)
•Apparatus
figure shows a schematic of the experiment.
The semiconductor crystal for this experiment is a
commercial gallium arsenide Hall generator (GaAs). The
crystal is mounted into a brass thermal conducting stand
and surrounded by a magnetic field from a wrapped cyoke. Temperature of the crystal is controlled by a dc
power supply. Liquid nitrogen is used to cool the crystal
to a desired temperature for the experiment. Another dc
power supply with a resistor produces a current in the
crystal. The Hall voltage created due to the magnetic field
and the current is recorded to a computer program.
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-2.00E-03
-4.00E-03
-6.00E-03
-8.00E-03
-1.00E-02
-1.20E-02
-1.40E-02
Temperature (K)
Temperature vs Hall Coefficient
0.00E+00
Hall Coefficient (m^3/C)
In 1879 Edwin H. Hall discovered that
when a current-carrying conductor
was placed at right angles to a
magnetic field, a potential difference
was produced across the strip
transverse to the current and
magnetic field directions. The
potential difference and the
production of this potential difference
are called the Hall voltage and the
Hall effect, respectively. The purpose
of this experiment is to demonstrate
the Hall effect and to measure the
Hall voltage and other parameters for
a semiconductor as functions of
temperature.
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-5.00E+10
-1.00E+11
-1.50E+11
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-3.00E+11
If a current flows along a conductor
in a magnetic field, the path is
deflected and a potential difference
(the Hall voltage) appears across
the conductor and transverse to the
magnetic field. This production of
the voltage was first discovered by
Edwin H. Hall in 1879. The physics
behind this phenomenon called the
Hall effect is the Lorentz force.
When an electron current moves in
a conducting plate, it experiences a
force acting normal to both
directions and is deflected. It is
possible to know to which direction
an electron current is deflected by
using the left hand rule.
Lorentz forece is described by
F =q (E + v x B), where q=charge,
E=electric field, v=velocity, and
B=magnetic field. The second term v x
B is transverse to the velocity and
magnetic filed and therefore, the Hall
voltage is produced across the
transverse dimension of the
conductor. When the Hall voltage is
measured, it can be used to derive the
Hall coefficient, the Hall angle, and the
Hall mobility by applying appropriate
formulas.
Temperature (K)
Temperature vs Hall Mobility
Hall Mobility (ｍ^2／Ｖ・S)
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-2.00E+07
-4.00E+07
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-8.00E+07
-1.00E+08
-1.20E+08
-1.40E+08
Temperature (K)
Temperature vs Hall Angle
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Hall Angle (theta)
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Temperature (K)
•Procedure
To cool the semiconductor crystal, liquid nitrogen is
poured to 3/4 full of the dewar where the GaAs crystal
is placed. The multimeters, magnet current supply, and
dc power supply are turned on. The apparatus is cooled
to 100 K before starting the data collection. When the
temperature is set, heater coil power supply is turned
on and crystal is heated as the computer program starts
the data collection. The program is run until it obtains
450-500 data points
From the negative value of the Hall
coefficient, it is turned out that the
supplied GaAs is an n-type
semiconductor. Statistical fluctuations
are attributed to the major source of
error as it was observed that the
fluctuations largely affected the data
and a certain amount of time was
required to stabilize the equipment for
valid data collections.