PHY3901 PHY3905. Hall effect and semiconductors Laboratory protocol

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1 PHY3901 PHY3905 Hall effect and semiconductors Laboratory protocol

2 PHY3901 PHY3905 Hall effect and semiconductors Laboratory protocol Objectives Observe and qualitatively understand the phenomenon of transverse magnetoresistance. Understand the Hall effect and use it to determine fundamental electrical characteristics of a semiconductor sample: 1) the resistivity as a function of temperature; 2) the energy gap E g between the valence band and the conduction band; 3) the density of extrinsic charge carriers n ex ; 4) the impurity type; 5) the Hall mobility as a function of temperature and the importance of different scattering mechanisms which govern mobility. Equipment Identify and learn to properly handle and operate the following equipment: mechanical vacuum pump and accessories electromagnet and current source liquid nitrogen dewar and transfer line InSb semiconductor sample mounted inside a Janis Research cryostat current source to drive current through the sample F. W. Bell 6010 teslameter with temperature compensated probe Lakeshore 330 temperature controller with silicon diode probe and 25 Ω heating coil Multichannel voltmeter to measure V X, V R, V H 2 variables resistances R 1 and R 2 circuit wires and 100 Ω load resistor hardware and software for data acquisition via GPIB and serial ports Safety and precautions Please ensure that you keep in mind the following points throughout the experiment, for your own well-being and for the safety of the laboratory equipment: Do not ever disconnect the electromagnet from its current source or otherwise change the magnet current abruptly, as the large induced EMF would then constitute a serious electrical shock hazard. Beware of liquid nitrogen. It is not toxic but it can cause serious frost bites on skin due to its low temperature (77 K, or 196 C). Liquid nitrogen may also cause a pressure explosion if placed in a sealed enclosure, as it heats up and evaporates. Limit the current through the semiconductor sample to 2.5 ma at all times to avoid damaging the sample. You will need to calculate the corresponding maximum voltage V R. Be particularly gentle with the magnetic field probe. Do not ever bend it or force it into place. 2

3 1 Constructing the circuit The circuit should be made in accordance with figure 1. You will notice that it is quite impossible to connect your wires directly onto the sample. We facilitated your work and wired the sample to a labeled board with electrical inlets and outlets. You will also notice that the three voltmeters depicted on the figure seem to be absent in the available components. They ve been combined in a multichannel voltmeter to which wires have been attached and labeled to correspond with the voltages measured. All components are connected to a computer that will acquire the data during the experiment. Ask your teacher assistant for more details. 2 Methodology Steps to perform at the beginning of each experiment day Warm-up the different measurement components of your system (multichannel voltmeter, numerical thermometer, Gaussmeter) Calibrate the Gaussmeter with the help of the zero-field chamber Remove all air from the cryostat using a rotary pomp Start the computer and open the acquisition software Hall.vi Verify that all the components are able to communicate with the computer Apply voltage to the system making sure that V R does not get higher than a given limit Zero the Hall voltage using the variable resistances R 1 and R 2 The cryogenic procedure Certain experiments require the use of liquid nitrogen to be cooled down the sample. When the time comes for such cooling, your teacher assistant will provide you with the necessary explanations. Part I: Qualify the electric behavior of the sample We wish to know wether the sample behaves according to Ohm s law (V = RI) or not. Vary the tension inside the sample starting from a maximum value of V R and gradually go down to zero Acquire points using the software Hall.vi and save your data file under an appropriate name Part II: Magnetoresistance at room and liquid nitrogen temperatures We wish to observe how the resistivity of the sample varies with the strength of the magnetic field B Z passing through it at room and liquid nitrogen temperatures (ρ vs B Z ) At room temperature: 3

4 Position the cryostat in between the coils so that the induced magnetic field passes through the sample Insert the Gaussmeter s probe in between the coils At the highest accepted value of V R, gradually vary the magnetic field by varying the tension inside the coils and acquire the data with Hall.vi Save your data file using an appropriate name At liquid nitrogen temperature: The same steps are to be followed except that now the sample will have been cooled down to liquid nitrogen temperature following the cryogenic procedure. Part III: Electrical properties of sample in function of the temperature It is in this section that we use the Hall Effect to determine the electrical characteristics of our semiconductor sample (refer to the objectives at the beginning). We will look at the evolution of these characteristics as the sample s temperature climbs from the one of liquid nitrogen to the one of ambient air. For this part you will follow these steps: Cool the sample using liquid nitrogen Insert the sample and the Gaussmeter s probe in between the coils Make sure that no liquid nitrogen comes in contact with the sample Fix the rate of of increase at 4K per minute on the thermometer fixing the upper limit at 325K (starting temperature should be around 80K) You will use the Acquire Ramp function in Hall.vi, allowing the computer to take measurements on the system automatically The above steps should be repeated for the highest, two intermediate, and zero values of B Z 3 Theory related to semi-conductors and the Hall Effect An outline of the theory related to semi-conductors and the Hall Effect can be found annexed at the end of this document. 4

Last Revision: August,

A3-1 HALL EFFECT Last Revision: August, 21 2007 QUESTION TO BE INVESTIGATED How to individual charge carriers behave in an external magnetic field that is perpendicular to their motion? INTRODUCTION The