1. The Hall Effect in N-Type and P-Type Semiconductors Trey Talley C’13 Department of Physics and Astronomy Sewanee: The University of the South, Sewanee, TN Introduction Many important conduction properties of doped semiconductors can be measured using the Hall Effect. The Hall Effect can be clearly observed in n- and p-type semiconductors when a current is flowing through the conductor with a magnetic field that is perpendicular to the direction of the current flow. The measurement of the Hall coefficient can be used to calculate the mobility and the carrier concentration within these semi- conductors. What is the Hall Effect? If a conducting material that carries a current down the x-axis is placed in a perpendicular magnetic field, a potential difference (Hall Voltage) is produced along the y-axis. The production of this voltage is known as the Hall effect, first observed by Edwin Hall in 1879. The Lorentz Force Why Study the Hall Effect? My Experiment Semiconductors Calculations Acknowledgements Figure 1: The Hall Effect in a material. Conduction is due to a single carrier type with charge q and mobility μ. When a magnetic field B is applied, then the carriers of charge q experience a Lorentz force: This force deflects the moving charge carriers in the material, and thus produces the Hall effect. The Lorentz Force can teach us valuable information about the movement of the charge carriers in materials. Figure 2: The Lorentz Fore causes the positive charges in this semiconductor to move to the far side of the material. We can learn about the charge transport properties of different materials through the behavior of the Hall Voltage. The concentration (carrier density), mobility, and sign of charge carriers can be determined. Most importantly, the conductivity of different materials can be determined. Doping: N-type and P-type Semiconductors Semiconductors are materials with electrical conductivity. They are the foundation of modern electronics: they are used in computers, telephones, radios, solar cells, LED’s, and diodes. Semiconductors can be doped with impurities to modify conductivity for constructing electronic devices. Intrinsic semiconductors are doped with impurity atoms, making them extrinsic semiconductors. The presence of these impurities affects the carrier concentration and the conductivity of the material. When a semiconductor is doped, it produces either N or P type semiconductors. Figure 4: This is the N-type silicon wafer that is doped with Phosphorus. The indium connections are at all four corners. First, I calculated the current density J by dividing the current by the area. Next, I calculated the electric field E by dividing volts per meter. After measuring the magnetic field B with a Hall probe, I was able to calculate the Hall coefficient R. Then I solved the last equation for n, the electron density. This is equal to the concentration of the charge carriers, which I found to be Thanks to Dr. Peterson, Rodger, Jim, and the P- Team C’13. My Experiment First, I used a diamond-tipped scriber to cut a 5 by 5 cm. wafer from the n-type and the p- type silicon. Next, I melted indium on all four corners, and scratched off the native oxide layer along the silicon-indium interface. Next, I melted 30 gauge wires to all four corners. The final product for the N- type sample is shown below. Measurements I took four tables of data. The first two tables are the van der Pauw resistivity data, and the second two tables are the Hall measurements that were taken while the wafer was in a magnetic field B of 1500 G. From the data that was taken, I was able to ultimately calculate the carrier concentration within the n- and p-type silicon wafers.