Title: Hall Effect Experiment
1Hall Effect Experiment Shunsuke Kato
ABSTRACT
DISCUSSION
METHODS
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.
- 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 c-yoke. 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.
INTRODUCTION
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.
CONCLUSION
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.
- 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
Lorentz forece is described by F q (E v x B),
where qcharge, Eelectric field, vvelocity, and
Bmagnetic 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.