In this experiment there are 3 objectives to determine for a germanium sample; the sign of the charge carriers, charge carrier concentration and the mobility of the charge carriers. When a charge moves perpendicular to the field a magnetic force will act on it. This magnetic force transports charge carriers to a particular edge of the conductor which leaves a shortage of charge carriers on the other edge. This results in one side of the conductor being positive and the other being negative. This difference of the charge on either side creates an electric field. When the magnetic field is balanced with the electric force the charge carrier is in equilibrium. There is a potential difference which forms across the material and it is called the hall voltage. The way the current is flowing determines the polarity, and can be used to determine the sign of the charge carriers.
(1)
V_H=(B*i)/(n*e*t)
This equation can be used to calculate the hall voltage (VH). The density of the charge carriers is n which is measured in meters cubed. The magnitude of the charge of the electron is e. The magnetic field perpendicular to the sample is B. Current in the sample is i and the thickness of the sample which is directed by the magnetic field is t. Mobility differs in unique materials because the charge carriers are more mobile thus creating a greater or lesser flow in the current.
(2)
μ=i_x/V_x *L/(n*e*w*t)
This equation calculates the mobility of the charge carriers (μ)which is the ratio of drift velocity to the electric field which is described as parallel to the drift velocity. The length of the sample in the direction of the current flow is noted by L. The width of the sample in the direction of the hall voltage is shown as w, and the Vx is the voltage drop along the sample in the direction of L when carrying a certain current of ix. When the hall voltage and mobility are calculated they can be compared to the theoretical values to determine the percentage errors.