Module 6 : PHYSICS OF SEMICONDUCTOR DEVICES
Lecture 33 : Hall Effect
The origin of Hall voltage is Lorentz force that acts on charge carriers. The magnetic force acting on the charges $ q\vec v\times\vec B$ deflects the charge carriers in a direction perpendicular to the direction of the velocity. This leads to charge separation because of which an electric field $ \vec{\cal E}$ appears across the strip. The bending of the trajectory stops when the force due to the electric field balances that due to the magnetic field, i.e. $ \vec{\cal E}=-\vec v\times\vec B$. The forces being in the opposite directions, their magnitudes are equal, i.e $ {\cal E} = vB$.
  The current density $ J$ is given by $ J = nqv$, where $ n$ is the density of carriers. Thus we have, on equating the forces,
 
$\displaystyle n = \frac{JB}{q{\cal E}}$
   
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