The Hall Effect
Manual for Advanced Lab
University of Rochester
Department of Physics and Astronomy
A. David Pawlicki
G. Scott Smith
Table of Contents
I.
Introduction
a. What is the Hall Effect?
b. Important concepts
c. Objectives
II.
Lab set-up
a. Equipment overview
b. Liquid Nitrogen safety
c. Labview and Data Acquisition
III. Procedure
a. Simple experimental procedure
b. Incorporating Labview
IV. Suggested Exercises
a. Possible improvements
V.
Acknowledgements
VI. Appendices
a. Appendix A – Schematic of Experimental Setup
b. Appendix B – Hall Generator Housing Setup
c. Appendix C – LabView Block Diagram
d. Appendix D – Hall Generator Manual
e. Appendix E – Semiconductors, Conductivity and
Resisitivity
Introduction
The Hall Effect is a physical effect named after Edwin Hall, an American
physicist who discovered that when the path of electrons running through a
semiconductor was deflected by a magnetic field, a potential difference was induced
perpendicular to the direction of the current. In 1985 (over 100 years after Hall’s
discovery), a German physicist, Klaus von Klitzing was awarded a Nobel Prize for his
work with the quantized Hall Effect. The Hall Effect is the working mechanism in a
wide range of devices and applications including the gauss meter, ammeters, tachometers,
spectrum analyzers, paintball guns, and many more electronic devices.
The following diagram shows the basic theoretical description of the Hall Effect.
If a current I in a slab of conducting material runs in the x direction through an applied
magnetic field B, it will be deflected due to the magnetic force on the moving charges.
Depending on whether the charge is positive or negative, the charges will build up on
either face 3 or face 4 of the slab. This charge buildup causes an electrostatic potential
difference between faces 3 and 4, and is referred to as the Hall voltage, VH. The Hall
resistance is the ratio of VH / I, and is observed to increase as the applied magnetic field is
increased.
Measuring the Hall effect is useful in determining many things, including the type
of the semiconductor (p-type or n-type), the charge of the carriers, the concentration,
mobility, and band structure of the material.
Lab Setup
The setup is extremely vital to the success of the Hall Effect experiment. The
setup can actually be broken into two parts; the necessary equipment for looking at the
Hall Effect without a computer, and the equipment that funnels the data into the computer
system.
Figure 1
The most important aspect of the lab is the Hall apparatus which, to the naked
eye, appears simply as a cylinder of copper with wires sticking out of it. (Figure 1) On
top are resistive heaters, which are used to warm the apparatus. There are two important
devices inside the Hall apparatus. The first is a Type-T (Copper-constantan)
thermocouple, used to indirectly measure the temperature by measuring the voltage
created when a temperature gradient exists along the wire. A Type-T thermocouple is
suited for low temperatures and neither metal is magnetic, thus it is the ideal device for
this experiment. A section of the copper wire is placed in an ice bath during the
experiment so that the reference temperature of the thermocouple is 0°C. There is also a
gallium arsenide crystal (GaAs) Hall generator mounted within the brass conductor. This
generator is the semiconductor that the Hall voltage is measured across.
To power the apparatus, it is necessary to use three power supplies. One power
supply should control the heaters located on the Hall apparatus. With the current
resistive heaters (two 10-watt heaters) this power supply should be turned up to its
maximum voltage output, which still may not produce enough energy to sufficiently heat
the apparatus. A second power supply powers the electromagnet. This power should be
set at the beginning to a desired setting and then left untouched for the experiment. The
strength of the magnetic field is determined by the voltage (or current) supplied by this
power supply and can be measured with a gaussmeter. The third power source is
responsible for providing power to the Hall generator and should be set to 5V.
Because this experiment measures multiple independent variables, it is necessary
to use three multimeters. One should be used to measure the voltage through the
thermocouple, another to measure the Hall voltage, and the last measures to measure the
Hall resistance. These values are the critical data points necessary to observe the Hall
Effect.
One key element to this lab is liquid nitrogen, necessary to cool down the Hall
apparatus to extremely low temperatures. Liquid nitrogen can be dangerous, so it is
crucial to practice safe handling procedures and wear thick gloves while dispensing the
liquid nitrogen. DO NOT TOUCH THE LIQUID NITROGEN; IT WILL CAUSE
DAMAGE AND PAIN TO YOUR BODY! Always dispense liquid nitrogen from the
large tank into an intermediate container, which can then be poured into the bath for the
experiment. Also be aware that bending the dispensing hose after filling the liquid
nitrogen container may cause it to shatter into sharp ultra-cool pieces if the hose is made
of rubber or plastic, as it sometimes is.
Finally, to add ease and precision to the data collecting process, the experiment
can be analyzed the using LabView, a specialized computer program designed for data
acquisition and analysis. To do this it is essential to use a PCI DAQ card, and exterior
pin interface (Figure 2). Cables to connect the multimeters to the pin interface are also
needed so that the data can be transferred to the computer.
Figure 2
Procedure
1.
Before data collection can begin, the apparatus must first be cooled down to a
low temperature. As discussed above, this is done by placing the apparatus in
liquid nitrogen for an extended period of time. For the apparatus to be
sufficiently cooled for the experiment, letting it sit in the liquid nitrogen for at
least 45 minutes is recommended.
2. Prepare a bath of ice water in the stainless steel container and submerge an
exposed section of the copper wire of the thermocouple into the ice bath. Taping
this wire in place is recommended.
3. After the apparatus is sufficiently cooled (to a temperature of about 170K), it may
be necessary, depending on the power of the heaters, empty the liquid nitrogen
from the bath. Then cover the Hall apparatus with the vacuum tube (a shiny
silver-colored tube-shaped object), and move the setup so that it is in between the
two poles of the magnet. Rotate the apparatus so that it is perpendicular to the
magnetic field, such that the Hall voltage is at a maximum.
4. Turn on the power supply to the magnet and the heaters. Monitor the
temperature, Hall voltage, and Hall resistance, taking about 12 data points per
minute (1 every 5 seconds). Keep in mind a table will be necessary to compute
the thermocouple temperature from millivolts to degrees Kelvin. Continue taking
data until the thermocouple reaches a temperature of about 340 K
Clearly, this is an inefficient way of conducting an experiment, as manually recording
the data is time consuming and less precise. LabView can be used not only to collect the
data points, but also be used to help analyze the data. To use the LabView program, open
LabView and run the HallEffect.vi program. Presented onscreen should be a both a block
diagram of the experiment, representing all of the process done by the program to collect
the data, and a VI screen on which the data collection actually takes place. Make sure
that all of the multimeters are connected to the DAQ exterior pin interface (and
subsequently the pin interface to the DAQ card inside the computer). It is advisable to
have all the multimeters and power supplies turned on before starting the program, and
also to end the program before turning any apparatus off in order to limit the amount of
inaccurate or extraneous data points. Upon starting the program, the computer will ask
you to name the file that will be saved, containing all of the data points that the computer
takes. This data file will be generated in a line-by-line, comma-separated format so that
the data can be easily inputted into a graphing program or excel table.
Suggested Exercises
Information on these exercises can be found in the appendix.
1. Plot the Hall voltage, Hall angle, Hall mobility, and Hall coefficient as a
function of temperature.
2. Plot the carrier density and resistivity as a function of temperature.
3. Determine whether the GaAs crystal is a p-type or n-type semiconductor.
4. Determine the energy gap between bands of the semiconductor.
Final Note
This lab is not without flaws, and there is still room for many improvements to be
made if a group is given proper time. For starters, the heaters on the hall generator
module are too small for the experiment to be conducted properly. Ideally, the liquid
nitrogen should not have to be dispensed before turning the heaters on. The Labview
code can always be improved to give other interesting points of data.
Acknowledgements
Kishore Padmaraju
Professor John Howell
TA Steve Bloch
The old lab manual
Ohki, Thomas “The Hall Affect”
Appendix A – Schematic of Experimental
Setup
Appendix B – Hall Generator Housing
Setup
Appendix C – LabView Block Diagram
Appendix D – Hall Generator Manual
Appendix E – Semiconductors,
Conductivity, and Resistivity
Thermocouple Conversion Table