Q14Engineering Physics

When a current-carrying conductor or semiconductor is placed in a strong, transverse magnetic field, the moving charge carriers experience a deflecting Lorentz force. This deflection causes charges to accumulate on one side of the material, generating a measurable transverse voltage known as the Hall Voltage. This entire phenomenon is the Hall Effect.

Definition of the Hall Coefficient

The transverse electric field ($E_H$) generated by this charge separation reaches an equilibrium when its electrostatic force exactly cancels the deflecting magnetic force. Through mathematical derivation based on the Lorentz force law ($F=qvB$), it is found that this resulting Hall electric field is directly proportional to both the applied current density ($J$) and the applied magnetic field strength ($B$).

The constant of proportionality connecting these three quantities is a unique intrinsic property of the specific material being tested, and is defined as the Hall Coefficient ($R_H$):

Furthermore, atomic theory shows that the Hall coefficient is strictly inversely proportional to the charge carrier density ($n$, the number of carriers per unit volume) and the fundamental charge of the carrier ($q$):

Applications and Significance

The Hall coefficient is one of the most powerful diagnostic tools in solid-state physics and semiconductor manufacturing. Its determination yields critical information:

• Determining the Type of Semiconductor (Sign of Charge Carriers): The most profound use of $R_H$ is its sign. If the charge carriers are negative electrons, they deflect one way. If the charge carriers are positive 'holes', they deflect the exact same physical way (because their velocity is opposite but their charge is also opposite, resulting in the same force vector). This creates a Hall voltage of opposite polarity. - A negative $R_H$ proves the material is an n-type semiconductor (electrons dominate). - A positive $R_H$ proves the material is a p-type semiconductor (holes dominate).
• Calculating Carrier Concentration ($n$): By simply measuring the Hall voltage in the lab to find $R_H$, engineers can directly calculate the exact number of charge carriers per cubic centimeter using the formula $n=\frac{1}{R_{H}q}$. This is essential for verifying the doping levels of silicon wafers during microchip fabrication.
• Calculating Carrier Mobility ($\mu$): If the electrical conductivity ($\sigma$) of the material is also measured, the drift mobility of the charge carriers can be instantly calculated using the relation $\mu =\sigma R_H$.