Hall Effect

Instructions:

Fabricate two semiconductor Hall samples (one p-type and one n-type) and one copper sample. On each sample, measure resistivity and Hall voltages by following the instructions in the NIST manual and filling out the handy worksheet from the NIST manual.  You may want to perform the sequence of Hall voltage measurements for different values of current and magnetic field.

Fabrication of semiconductor samples:

Making a good metal-semiconductor contact is not trivial. The contact resistance may be high, or worse, the contact may act as a diode to some degree. Feel free to experiment with modifications to this procedure; it was developed largely through trial and error.

• Set the hot plate to the highest setting.
• Using a razor blade, slice off four small pieces of indium to serve as contacts. You may want to discard the top slice that was exposed to air.
• It seems to help to press Scotch tape onto the corners of the silicon where the indium will go, and then peel the tape off.
• Using the metal tweezers, press the pieces of indium onto the silicon so that they stick.
• Place the wafer on the hot plate; the indium should melt instantly.
• I have no idea what this does, but I can't make good contacts without it: Dip the metal tweezers into each molten indium dot and stir it around a little, gently scraping the silicon surface.
• Let the wafer sit on the hot plate for about three minutes.
• After the sample cools, attach wires using one of these techniques: sandwich the wire between the indium on the silicon and another piece of indium, and press with the metal tweezers; or use regular solder to attach the wires to the indium.

Fabrication of metallic thin films:

Hall voltages are proportional to the sheet resistance (R_S = r/d) of a sample. Whereas semiconductor resistivity is sufficiently high to permit measurements of sizeable Hall voltages (0.01-0.1 mV) on thick samples (~0.03 cm), the resistivity of metals is so low that similar voltages can only be measured on thin films. We use the evaporator to produce thin films of metal on a glass substrate.

• Raise the bell jar after opening the venting valve. Place your substrate above the boat and place the copper evaporation source in the boat. The best sample I've made so far came from using about 60 mg of copper.
• Lower the bell jar and close the venting valve.
• Turn on the water, which cools the evaporator.
• Turn on the mechanical pump.
• Open the valve between the mechanical pump and the bell jar.
• When the pressure in the bell jar drops below 20 mm of mercury, close the valve between the mechanical pump and the bell jar, and the open the valve between the mechanical pump and the back of the diffusion pump.
• When the pressure at the back of the diffusion pump drops below 20 mm of mercury, turn on the diffusion pump.
• Open the valve between the diffusion pump and the bell jar. THE DIFFUSION PUMP WILL BE DESTROYED UNLESS TWO CONDITIONS ARE SATISFIED: the pressure in the bell jar must be previously lowered below 20 mm of mercury, and the pressure behind the diffusion pump must be constantly maintained at a similar level by the mechanical pump.
• The ionization gauge, used to read very low pressures, may be turned on when the diffusion pump is evacuating the bell jar. THE IONIZATION GAUGE WILL BE DESTROYED UNLESS THE PRESSURE IN THE BELL JAR IS FAR BELOW 20 mm OF MERCURY.
• When the pressure has fallen below about 10^-5 torr, you may begin evaporation. Turn on the evaporation power. Turn the dial until the copper melts, then leave it at that setting (usually about 33) for two minutes. Then increase slowly to a higher setting, perhaps 48, and the copper should rapidly evaporate.
• To remove the sample: turn off the evaporation power, wait 15 minutes for the sample to cool, close the valve between the diffusion pump and the bell jar, turn off the ionization gauge, and open the vent valve. When the pressure in the bell jar reaches atmosphere, you can lift the bell jar.
• To make contacts to the thin film, you can press indium onto the thin film and sandwich a wire under another piece of indium.

Using the electromagnet:

Always turn the water on before the power supply. Always adjust the current slowly, and reduce it to zero before shutting off the power supply. Wait some time before turning off the water, but remember to turn it off before you leave for the day.

Lab report guidelines:

Your lab reports should address all of the following (and may, of course, include additional information and analysis):

• Explain the Hall effect in words.
• Briefly explain the difference between metals and semiconductors.
• Briefly explain the difference between p-type and n-type semiconductors.
• Using Figure 3, explain why V_24P would have a different sign for p-type and n-type carriers (assuming a perfectly square sample). For which carrier type is V_24P positive? For which type is it negative?
• Briefly define any terms that may be new to you (sheet resistance, bulk carrier density, sheet carrier density, etc.).
• Explain the purpose of making all the measurements on the worksheet.
• Derive Eq. (12) from Eq. (1). Specifically, where does the factor of 8 x 10^-8 come from?
• Thoroughly discuss your data. Do your measurements satisfy Eqs. (8) and (9)? If not, what does this imply?
• For each of your silicon samples, what resistivity, bulk carrier density, and carrier type are indicated by your data? Are the resistivity and carrier density values consistent with theory? (See www.solecon.com/sra/rho2ccal.htm.) Can you speculate as to the cause of any discrepancy?
• Do you observe a Hall voltage in your copper sample? Using the resistivity of copper (1.7 x 10^-6 W-cm) and your measured sheet resistance, what is the expected thickness of your copper film? Using this thickness and other parameters from your measurements, what is the expected Hall voltage? What do you conclude?
• Predict the carrier density for copper from its mass density (8.92 g/cm³) and atomic mass (63.5 g/mol). How does this compare with the carrier densities in your silicon samples?