Module 5 part B4

Hall Effect Overview

The Hall effect is a fundamental phenomenon observed in conductors and semiconductors when an electric current passes through a material that also experiences a perpendicular magnetic field. In essence, when current is applied to a semiconductor sample, the charge carriers (typically electrons) experience a Lorentz force due to the magnetic field that redirects their motion. This results in a separation of charge within the material, leading to the generation of a Hall electric field across the sample. This phenomenon not only allows for the measurement of the Hall voltage but also plays a crucial role in identifying semiconductor types, as well as offering insights into their mobility and resistivity.

Experimentation in the Lab

Students will explore the Hall effect practically in the laboratory, where they will measure the Hall electric field and corresponding Hall voltage in semiconductor samples. Through these measurements, learners can gain deeper understanding of fundamental principles of solid-state physics and the behavior of charge carriers in magnetic fields.

Application of the Hall Effect

When implementing the Hall effect in experiments, the following components are essential:

  • Current Application: The current travels through the semiconductor from one electrode to another, establishing a primary flow direction.

  • Magnetic Field Orientation: A magnetic field is applied perpendicularly to the current flow, affecting the trajectory of charge carriers.

  • Lorentz Force: The motion of electrons is altered due to the Lorentz force exerted by the magnetic field, resulting in the accumulation of charge on one side of the semiconductor, creating a potential difference, or Hall voltage.

Calculating Resistivity and Hall Voltage

Example Calculation: Silicon Sample

To illustrate the Hall effect, consider a silicon sample doped with a phosphorus concentration of ( 10^{17} ) cm^-3 (resulting in donor electrons). To determine resistivity, we apply the formula related to conductivity:


[ \sigma = q \mu n ]Where:

  • ( \sigma ) = conductivity

  • ( q ) = charge of the electron (1.6 x 10^-19 coulombs)

  • ( \mu ) = mobility of the charge carriers

  • ( n ) = carrier concentration

The resistivity (( \rho )) can be deduced as the inverse of conductivity:


[ \rho = \frac{1}{\sigma}]

Hall Voltage Calculation

Next, to calculate the Hall voltage for a sample with a thickness of 100 microns, a current of 1 milliamp, and an applied magnetic field of 1 kilo Gauss, we use the Hall coefficient (R_H) given by:



[ R_H = -\frac{1}{q n_0}]After calculating ( R_H ), the Hall voltage (V_H) can be derived from:



[ V_H = R_H \frac{I d}{B}]Where:

  • ( I ) = current

  • ( d ) = thickness of the sample

  • ( B ) = magnetic field strength.

Important Note

To ensure accurate calculations, be mindful of units; for example, ensure that the thickness is expressed in centimeters when performing calculations related to the Hall effect.