The Hall effect is used to measure electrical conductivity by applying a magnetic field and current to a material, then measuring the Hall voltage.
Measuring Electrical Conductivity Using the Hall Effect
The Hall effect is a valuable tool for understanding the electrical properties of materials, including electrical conductivity. In this article, we will explore how the Hall effect can be utilized to measure electrical conductivity in various materials.
Understanding the Hall Effect
When a current-carrying conductor is placed within a magnetic field oriented perpendicular to the direction of the current, a voltage difference, known as the Hall voltage, develops across the conductor. This phenomenon is called the Hall effect. The Hall voltage is directly proportional to the current, magnetic field strength, and material thickness, and inversely proportional to the charge carrier density and the charge of the carriers.
Hall Effect Measurements
To measure electrical conductivity using the Hall effect, a sample of the material is placed in a known magnetic field. A current is then passed through the sample, and the Hall voltage is measured across the sample. This allows us to calculate the Hall coefficient, which is the ratio of the Hall voltage to the product of the current and magnetic field. The Hall coefficient is related to the charge carrier concentration and the type of charge carrier (electrons or holes) in the material.
- Sample Preparation: The material sample must be shaped into a suitable geometry, typically a thin rectangular or square shape, with electrical contacts placed on opposite edges.
- Current Application: A constant current is applied to the sample while it is situated in a magnetic field perpendicular to the current flow.
- Hall Voltage Measurement: The Hall voltage is measured across the sample, and the magnetic field is varied to obtain multiple data points.
- Calculation of the Hall Coefficient: By plotting the Hall voltage against the magnetic field strength and determining the slope of the linear relationship, the Hall coefficient can be calculated.
Calculating Electrical Conductivity
Once the Hall coefficient is determined, the electrical conductivity can be calculated using the material’s resistivity. Resistivity is the inverse of conductivity and can be measured using a four-point probe or van der Pauw method. With the resistivity and Hall coefficient values, the charge carrier concentration and mobility can be calculated. Finally, the electrical conductivity is obtained by multiplying the charge carrier concentration, charge of the carriers, and mobility.
Applications of Hall Effect Conductivity Measurements
Hall effect measurements are widely used in semiconductor and material science research, as they provide valuable information about the electrical properties of materials. This technique can be employed to study the effects of doping, temperature, and pressure on electrical conductivity, as well as to characterize novel materials and investigate the properties of superconductors.
