The Hall EffectManual for Advanced Lab

University of RochesterDepartment of Physics and Astronomy

A. David PawlickiG. Scott Smith

Table of Contents

I. Introductiona. What is the Hall Effect?b. Important conceptsc. Objectives

II. Lab set-upa. Equipment overviewb. Liquid Nitrogen safetyc. Labview and Data Acquisition

III. Procedurea. Simple experimental procedureb. Incorporating Labview

IV. Suggested Exercisesa. Possible improvements

V. Acknowledgements

VI. Appendicesa. Appendix A – Schematic of Experimental Setupb. Appendix B – Hall Generator Housing Setupc. Appendix C – LabView Block Diagramd. Appendix D – Hall Generator Manuale. 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

Procedure1. 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 ExperimentalSetup

Appendix B – Hall Generator HousingSetup

Appendix C – LabView Block Diagram

Appendix D – Hall Generator Manual

Appendix E – Semiconductors,Conductivity, and Resistivity

Thermocouple Conversion Table