Converters & Calculators
Hall Coefficient: Theory, Coefficient, And Applications
Introduction to the Hall Effect
The Hall effect occurs when a magnetic field is applied perpendicular to the electrical current flow in a conductor. This interaction results in a measurable voltage, known as the Hall voltage, across the material. The Hall coefficient is a fundamental parameter that characterises this phenomenon and provides information about the charge carriers in the material.
Calculation of the Hall Coefficient
The Hall coefficient (R_H) is calculated using the following formula:
R_H = E_H / (J * B)
where:
- E_H is the electrical Hall field,
- J is the current density,
- B is the magnetic field strength.
This coefficient is used to determine the type, concentration and mobility of charge carriers in a material.
Hall Coefficient in Bismuth Metal
Bismuth Metal exhibits a distinctive Hall coefficient owing to its low charge carrier concentration and high carrier mobility. These properties render bismuth suitable for investigating quantum effects in semimetals. The Hall effect in bismuth is particularly relevant for applications in thermoelectric devices and magnetic sensors.
Properties of the Hall Coefficient in Various Materials
|
Material |
Hall Coefficient (R_H) |
Type of Charge Carrier |
Charge Carrier Concentration |
Charge Carrier Mobility |
|
Copper |
5.96 × 10^-11 m³/C |
Electrons |
8.5 × 10^28 m^-3 |
43.1 cm²/Vs |
|
Silicon |
-4.15 × 10^-5 m³/C |
Holes |
1.5 × 10^20 m^-3 |
450 cm²/Vs |
|
-1.2 × 10^-4 m³/C |
Electrons and Holes |
1.0 × 10^19 m^-3 |
1 000 cm²/Vs |
Further information is available at Stanford Advanced Materials (SAM).
Applications of the Hall Coefficient
lIdentification of Charge Carriers
Determines whether a material conducts via electrons (n-type) or holes (p-type).
lMeasurement of Charge Carrier Concentration
Calculates the concentration of charge carriers in a material, which is crucial for semiconductor design.
lCharacterisation of Semiconductors
Serves to analyse the electrical properties of semiconductors, including doping.
lMagnetic Field Sensing
Forms the basis for Hall effect sensors used in magnetic field measurement and positioning systems.
lMagnetoresistance Studies
Contributes to investigations of magnetoresistance effects, particularly in spintronic applications.
lMaterials Research
Assists in the characterisation of new materials such as Graphene and topological insulators.
lThin Films and Nanomaterials
Is used to examine the behaviour of charge carriers in thin films and nanostructures.
lSuperconductors
Provides insights into charge carriers in superconducting materials.
Frequently Asked Questions
What is the Hall effect?
The Hall effect is the generation of a voltage difference across a conductor when a magnetic field is applied perpendicular to the current flow.
How is the Hall coefficient calculated?
It is calculated by dividing the electrical Hall field by the product of current density and magnetic field strength.
Why is bismuth metal significant for the study of the Hall effect?
Bismuth metal exhibits a low charge carrier concentration and high mobility. This renders it suitable for observing quantum effects and increases sensitivity in applications.
Can the Hall coefficient determine the type of charge carriers?
Yes, the sign of the Hall coefficient indicates whether the charge carriers are electrons or holes.
What are common applications of the Hall effect?
It is used in magnetic field sensors, automotive ignition systems and for determining material properties in semiconductors.
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