Question

From the Hall Effect experiment, one can measure:

• A. Carrier concentration
• B. Nature of charge carriers
• C. Carrier concentration and Mobility of charge carriers
• D. Nature of charge carriers, concentration of charge carriers as well as their mobility

Hint:

Remember that in a Hall Effect setup, the magnetic field must be perpendicular to the current flow. The voltage that develops across the material (the Hall voltage) is directly proportional to the product of current and magnetic field, so by measuring the Hall voltage and knowing the other parameters, you can extract a lot of useful information about carrier properties.

Answer 1

The Correct Option is C

The Hall Effect experiment involves applying a magnetic field perpendicular to a current flowing through a conductor (or semiconductor). This results in a voltage, known as the Hall voltage, being generated perpendicular to both the current and the magnetic field. The Hall voltage ($V_H$) is related to the magnetic field ($B$), the current ($I$), the charge carrier density ($n$), and the thickness of the material ($t$) by the equation:
\(V_H = \frac{IB}{net}\)
Where $e$ is the charge of an electron.
From this experiment, two crucial parameters can be deduced:
Charge Carrier Concentration ($n$): By measuring the Hall voltage and knowing other parameters, the density of charge carriers (whether they are electrons or holes) can be determined.
Mobility ($\mu$): By measuring both the Hall voltage and the conductivity, the charge carrier mobility can be calculated. Mobility is related to how fast the charge carriers move in an electric field and is linked to their scattering rate in the material.
The Hall Effect can also tell you the sign of the charge carriers since the Hall voltage has opposite polarities for electrons and holes. Thus, the Hall experiment allows us to measure charge carrier concentration, mobility, and the type of charge carriers present (electrons or holes).