Hall Effect Experiment Shunsuke Kato

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.

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.

•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.

•ProcedureTo 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.

-5 -4.9 -4.8 -4.7 -4.6 -4.5 -4.4 -4.3 -4.2 -4.1 -4

-0.116

-0.115

-0.114

-0.113

-0.112

-0.111

-0.11

-0.109

-0.108

-0.107Current vs Hall Voltage

Current (A)

Hal

l V

olt

age

(V)

80 90 100 110 120 130 140 150

-3.00E+11

-2.50E+11

-2.00E+11

-1.50E+11

-1.00E+11

-5.00E+10

0.00E+00

Temperature vs Hall Coefficient

Temperature (K)

Hall

Coeffi

cien

t (m

^3

/C)

80 90 100 110 120 130 140 150

-1.40E+08

-1.20E+08

-1.00E+08

-8.00E+07

-6.00E+07

-4.00E+07

-2.00E+07

0.00E+00

Temperature vs Hall Mobility

Temperature (K)

Hall

Mob

ility

(ｍ

^2

／Ｖ

・S

)

80 90 100 110 120 130 140 150

-5800

-5750

-5700

-5650

-5600

-5550

-5500

-5450

-5400

-5350

Temperature vs Hall Angle

Temperature (K)H

all

An

gle

(th

eta

)

90 95 100 105 110 115 120 125 130 135

-1.40E-02

-1.20E-02

-1.00E-02

-8.00E-03

-6.00E-03

-4.00E-03

-2.00E-03

0.00E+00

Temperature vs Resistivity

Temperature (K)

Resi

stiv

ity (

oh

m/m

)