Hall effect
Introduction
The Hall effect is a fundamental principle in the field of semiconductor physics and electromagnetism, named after American physicist Edwin Hall. It describes the behavior of charge carriers, such as electrons, when they are subjected to both electric and magnetic fields. This phenomenon has been instrumental in the development of many electronic devices and has led to significant advancements in our understanding of material properties.
Discovery and Basic Principle
In 1879, Edwin Hall discovered the effect that now bears his name while working on his doctoral thesis at Johns Hopkins University. He observed that when a current-carrying conductor is placed in a magnetic field perpendicular to the direction of the current, a voltage difference, known as the Hall voltage, develops across the conductor. This voltage difference is perpendicular to both the current and the magnetic field.
The Hall effect is a direct result of Lorentz force acting on the charge carriers in the conductor. The Lorentz force, which is the sum of electric and magnetic forces on a point charge, causes the charge carriers to deflect to one side of the conductor, creating a voltage difference across it. This phenomenon can be mathematically described by the Hall effect equation:
V_H = I*B*d / (n*q*A)
where V_H is the Hall voltage, I is the current, B is the magnetic field strength, d is the thickness of the conductor, n is the charge carrier density, q is the charge of the carrier, and A is the cross-sectional area of the conductor.
Hall Coefficient and Carrier Type
The Hall coefficient (R_H) is a material property that can be determined from the Hall effect. It is defined as the ratio of the induced Hall voltage to the product of the current density and the applied magnetic field. The sign of the Hall coefficient indicates the nature of the charge carriers in the material. A positive Hall coefficient suggests that the dominant charge carriers are holes (positively charged), indicating a P-type semiconductor, while a negative Hall coefficient suggests that the dominant charge carriers are electrons (negatively charged), indicating an N-type semiconductor.
Applications of the Hall Effect
The Hall effect has numerous applications in various fields of science and technology. Some of the most significant applications include:
Magnetic Field Sensing
Hall effect sensors are devices that use the Hall effect to measure magnetic fields. These sensors are commonly used in many electronic devices, including speedometers, car ignition systems, and anti-lock braking systems. They are also used in industrial applications for current sensing and proximity detection.
Material Characterization
The Hall effect is used in the characterization of materials, particularly semiconductors. By measuring the Hall voltage, one can determine important properties of the material, such as the type and density of charge carriers and their mobility.
Quantum Hall Effect
The Quantum Hall effect, a quantum mechanical version of the Hall effect, has been used to define the standard for electrical resistance. This effect, observed at extremely low temperatures and high magnetic fields, has also provided insights into the quantum nature of matter and the behavior of electrons in low-dimensional systems.