MODERN PHYSICS (PHY 320) LAB

THE HALL EFFECT

OBJECT:

  1. To determine the Hall Coefficient of Copper metal.
    To deduce that the transfer of charge is by mobile negative charge carriers (electrons).
    To show that the Hall Voltage in a metal does not depend on temperature.

  2. To demonstrate the temperature dependence of electrical conductivity and the Hall Effect in semi-conductors.
    To demonstrate two different conduction mechanisms in doped semi-conductors (extrinsic and intrinsic).

APPARATUS:

BACKGROUND INFORMATION:

The basic theory for these operations is found in The Hall Effect, a lab procedure write-up provided by Northeastern State University, OK.  The basic equation for the Hall Effect predicts that the Hall Voltage UH is directly proportional to either the applied field B or the control current I (provided that the other parameter is held constant).   The Hall coefficient  RH and the sample thickness d are constants.

UH = RH ( I B/ d )


EXPERIMENT 1:    The Magnetic Field

Set up the magnet with only the transverse probe of the Gauss/Tesla meter placed at the center between the magnet pole pieces oriented with the magnetic flux perpendicular to the flat side of the probe.  Collect data for a graph of the Magnetic Field Strength B versus the Coil Current through the magnet windings.


EXPERIMENT 2:     Hall Effect in Copper

Cu Hall Effect.JPG (55459 bytes)

The Copper supporting plate 11803.00 is displayed in Figure 1.   The plate is fitted with an electrical heater and a thermocouple in order to show that the Hall voltage in a metal, unlike that in a semiconductor, does not depend on temperature.

The apparatus connections, exclusive of the heater, are now illustrated by the following circuit diagram:

wpe1.gif (7750 bytes)

Exercise 1

Without the heater connected, and without current in the magnet coils, slowly increase the copper current to 2 Amps.
Use knob 5 to cancel any offset voltage.

Select a magnetic field strength along the linear part of the graph of Experiment 1. (say near 4 KGauss)

Vary the control current  in 1 A steps up to 10A and determine the Hall voltage for each current.
Remember that for each current, the offset voltage must be rechecked.

Plot a graph of Hall Voltage versus Control Current.

Determine the Hall Coefficient for Copper.

Repeat the plotting on the same graph for other magnetic field values up to 8 KGauss.
Are the results consistent with the basic equation for the Hall Effect?


Exercise 2

Select the maximum magnetic field strength from Exercise 1. (say near 8 KGauss)

Keep the maximum magnetic current of 10A from Exercise 1. 

Connect a variac through a 6-8 V AC transformer to the heater (sockets 5).

Increase the heater voltage in small increments. Wait a minute to see if the temperature changes.  If it does, allow the temperature to stabilize and record the Hall and thermocouple voltages.

Caution:     As soon as the thermoelectric voltage reaches 5 to 6 mV (heating time approximately 2 minutes), the heating current should be turned off in order to avoid overheating the support plate.

Increase the heater voltage and repeat the measurements.  Try to take about ten measurements before you reach the maximum setting of the variac.

Plot a graph of Hall Voltage versus Temperature.

Do your results confirm that the Hall Voltage in copper does not depend on Temperature?


 


 


 

EXPERIMENT 3:     Hall Effect in p-germanium Crystal

Ge Hall Effect3.JPG (21077 bytes)

 

The Germanium supporting plate 11805.00 is displayed in Figure 1.   (Actually the n-Ge plate is shown, but a p-Ge plate will be used in the experiment.) The plate is fitted with an electrical heater and a thermocouple in order to show how the Hall voltage in a  semiconductor, varies with temperature.

The apparatus connections, exclusive of the heater, are now illustrated by the following circuit diagram:

wpe2.gif (8322 bytes)

 

Exercise 1

Without the heater connected, and without current in the magnet coils, slowly increase the crystal current to 10 mA.
Use knob 5 to cancel any offset voltage.

Select magnetic field strengths along the linear part of the graph of Experiment 1.  Measure  and record the the Hall voltage for Magnet coil currents of 4, 5, 6, 7, and 8 Amperes.

Vary the control current  from 10 to 35 mA in steps of 5 mV and repeat the measurements. 
Remember that for each current, the offset voltage must be reset for zero with magnet off.

Plot a graph of Hall Voltage versus Control Current for each selection of magnetic field strength.

All the plotting should be performed on the same graph. 
Are the results consistent with the basic equation for the Hall Effect?
Determine the value of the Germanium Hall Coefficient from each line plotted.


Exercise 2

Select the maximum magnetic field strength from Exercise 1. (say near 8 KGauss).  Keep the maximum magnetic current of 35 mA from Exercise 1. 

Connect a variac through a 6-8 V AC transformer to the heater (sockets 4).  Turn on the variac and increase the output to well over 50% maximum. As the temperature gradually changes, record simultaneous values of the Hall voltage, the thermocouple voltage and the crystal voltage.

Caution:    As soon as the thermoelectric voltage reaches 5 to 6 mV  (heating time about 2 minutes for the six volts AC), the heating current should be turned off in order to avoid overheating the support plate.

  • Plot a graph of Hall Voltage versus Temperature.   Determine from your graph the temperature at which the transition from extrinsic to intrinsic conduction occurs.

  • Plot a graph of Crystal Resistance versus Temperature.