"Hall EffectFigure shows the basic setup where an electric field is applied along the x- axis and a magnetic field is applied along the z-axis. Consider a p-type sample.The Lorentz force exerts an average downward force on the holes and thedownward-directed current causes a piling up of holes at the bottom side of thesample, which in turn gives rise to an electric field ? since there is no net current? along the y-direction in the steady state, the electric field along the y-axis (Hallfield) balances exactly the Lorentz force such that the carriers travel in a pathparallel to the applied field ? .( For n-type material, electrons also pile up at the? bottom surface, setting up a voltage of opposite polarity.)Lorentz force is given by ? = ? ? × ?? ? The carrier velocity v is related to the current density by? = ? ? ?? ? Here ? = ? ?? ? ? Since for each carrier the Lorentz force must be equal to the force exerted by theHall field, ? = ? ? = ? ? ?? ? ? ? As we have ? = we can write hall voltage as? ? * (?? ) ? ? ? ? ( ) ? ? (?? ) ? ? ? ? ( ) ( ) ? = ? * ?? = = ? ? = =? ? ? ? ? ( ) ? = ? ? ? ??? ? ? ? 1 1 Where hall coefficient is given by? = =? ? ? ? ? is charge density ,? = ? = ? ? ? ? ? ? Current and current density are related as ? = =? ? (? ? )? ? Than hall voltage becomes( ) ? ? ? ?? ? ? ? ? ? ? ? ? ? ? ? ? ? ? = = =? ( ) ? ? ? ? ? ? ? ? ? ?? ??? ?? ?? ?? ?? ??"