Instytut Fizyki Doświadczalnej Wydział Matematyki, Fizyki i Informatyki UNIWERSYTET GDAŃSKI

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1 Instytut Fizyki Doświadczalnej Wydział Matematyki, Fizyki i Informatyki UNIWERSYTET GDAŃSKI

2 I. Background theory. 1. Fundamentals of band theory. 2. Classification of solids using band theory. 3. Intrinsic and doped semiconductors. 4. Electrical and thermal conductivity of semiconductors. 5. The Hall effect and its applications. 6. The Hall constant, conductivity of materials, concentration and mobility of charge carriers. 7. Construction and use of Hall probes. II. Experimental tasks. 1. Refer to the setup shown in Picture 1 and the operating instructions in the Appendix. Place the measuring module (1) indicated by the laboratory supervisor between the poles of the electromagnet (3). 2. Before taking measurements, zero the teslameter using the knob on the right-hand side of the front panel (6) after removing the teslameter probe (5) from the electromagnet (3) (Picture 1). Picture 1. Experimental setup for studying the Hall effect: 1 measurement module with Hall effect sensor; 2 electromagnet and module power supply; 3 electromagnet; 4 universal multimeter; 5 teslameter probe; 6 teslameter. 3. Insert the magnetic field probe (5) into the measuring module (1) with the Hall effect sensor. Instytut Fizyki Doświadczalnej 1.

3 The magnetic field probe (5) is very delicate and should be gently inserted into the measuring unit (1) being very careful not to damage it! 4. Compensate for the Hall voltage U H using the knob on the right-hand side of the measuring module (1) with a current strength I = 0 A and magnetic field strength B=0 T. This step should be repeated before the next series of measurements. 5. Take measurements of the Hall voltage U H as a function of the control current I. Plot graphs of your results U H = f(i) and U = f(i). Include all appropriate measurement uncertainties. 6. Take measurements of the voltage U p across the probe as a function of magnetic field strength. Plot a graph of the relative change of electrical resistance (R(B)-R 0 )/R 0 = f(b), where R 0 probe resistivity with no magnetic field. Calculate the conductivity σ of the sample with the formula σ = l/(r 0 A), where l=20 mm, A=10 mm Measure the Hall voltage U H as a function of magnetic field strength B. Plot a graph of U H = f(b). Using linear regression to determine the value of the Hall constant R H, taking the sample thickness to be d = 1 mm. Calculate the concentration n and mobility μ of the charge carriers. 8. Measure the Hall voltage U H as a function of temperature U H = f(t). Plot a graph of U H = f(t). Indicate measurement uncertainties in your plot. Interpret your results. III. Apparatus. 1. Three modules with Hall effect sensors. 2. Module and electromagnet power supply. 3. Electromagnet. 4. Universal multimeter. 5. Teslameter probe. 6. Teslameter. IV. Literature. 1. Ch. Kittel Introduction to Solid State Physics, John Wiley & Sons, W. Ashcroft Solid State Physics, Saunders College, Philadelphia Solid State Physics. Pt. B, Electrical, Magnetic, and Optical Properties ed. by K. Lark-Horovitz and Vivian A. Johnson, London: Academic Press, New York J. Orear Physics, Vol.2., Macmillan Publishing Co., Inc., PHYWE Laboratory Experiments Physics, 2010, 6. A.P. Arya Fundamentals of Atomic Physics, Allyn & Bacon, Inc. Boston Instytut Fizyki Doświadczalnej 2.

4 Appendix Hints for making measurements Appx.. II. 5. Measure the Hall voltage using the digital multimeter (4) connected to the measurement module (1) as a function of sample control current in the range -30 ma to 30 ma in steps of 5 ma. To adjust the control current I, use the dial on the left-hand side of the measuring module (1). The current can be read off the display on the measuring module. Appx.. II. 6. With constant control current I = 30 ma, take measurements of the sample voltage U p with the digital multimeter (4) connected to the measuring module (lower output on the measuring module (1 in Picture 1) as a function of magnetic field strength B in the range 0 to 300 mt in steps of 20 mt. The magnetic field strength B is read off the teslameter display (6) and should be set by properly choosing the voltage and current on the power supply (2). Appx.. II. 7. With constant control current I = 30 ma, take measurements of the Hall voltage U H with the digital multimeter (4) connected to the measuring module (upper output on the measuring module (1 in Picture 1) as a function of magnetic field strength B in the range 0 to 300 mt in steps of 20 mt. The magnetic field strength B, is read off the teslameter display (6) and should be set by properly choosing the voltage and current on the power supply (2). Appx.. II. 8. With constant control current I = 30 ma and magnetic field strength B = 300 mt, take measurements of the Hall voltage U H with the digital multimeter (4) connected to the measuring module (1) as a function of temperature. Take a temperature range starting from room temperature, i.e., about 20 o C, to 140 o C in steps of 10 o C. After enabling the heating coil, the sample will be rapidly heated. Pay special attention not to exceed a temperature of 150 o C. Instytut Fizyki Doświadczalnej 3.

5 The temperature should be read from the display located on the measuring module (1) after setting the measuring module to temperature mode (with the Display button). Start the measurement when you turn on the sample heating coil, which is built into the measurement module (1), using its On/Off button on the rear of the measuring module. After reaching a temperature of 140 o C, turn off the sample heating coil. For measurements with the heating coil, take care for at least 5 minutes when handling the measuring module (1). Touching the measuring module plates during this time may cause serious burns. Instytut Fizyki Doświadczalnej 4.