Hall Effect:

• When magnetic field is applied perpendicular to a current-carrying conductor, then a voltage is developed in the material perpendicular to both magnetic field and current in the conductor.
• This effect is known as Hall Effect and the voltage developed is known as Hall voltage (VH).
• Hall Effect is useful to identify the nature of charge carriers in a material and hence to decide whether the material is n-type semiconductor or p-type semiconductor, also to calculate carrier concentration and mobility of carriers.

Importance of Hall Effect

• Hall Effect proved that band theory of solids is more accurate than free electron theory.
• Hall Effect proved that electrons are the majority carriers in all the metals and n-type semiconductors.
• In p-type semiconductors, holes are the majority carriers.

Measuring Mobility

• The first step in determining carrier mobility is to measure the Hall voltage (VH) by forcing both a magnetic field perpendicular to the sample (B) and a current through the sample (I). This combination creates a transverse current.
• The resulting potential (VH) is measured across the device.
• Accurate measurements of both the sample thickness (t) and its resistivity (r) are also required.
• The resistivity can be determined using either a four-point probe or the van der Pauw measurement technique.
• With just these five parameters (B, I, VH, t, and resistivity), the Hall mobility can be calculated:

• Both Hall voltages and the measured van der Pauw resistivity are typically quite small, so the right measurement and averaging techniques are critical for accurate mobility results.