# Hall Effect in p-type semiconductors

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HALL EFFECT IN p-TYPE SEMICONDUCTOR

THEORY :- If a current carrying semiconductor specimen  is placed in a magnetic field , then an induced Electric field ( ) is generated , which will produced potential difference between two surfaces of semiconductor . This potential difference is known as “Hall Voltage” ( ) and is proportional to magnetic field ( ) and current ( )  =    Electric field = Electric force = Magnetic field = magnetic force = Unit vector along x,y and z direction = current flow in semiconductor specimen along x direction → Cross sectional area of surface perpendicular to direction of flow of current ASSUME : According to figure shown above :

(1) Current ( ) flow in Semiconductor towards X- direction ( ) so motion of holes will  in (+X) direction ( ) also

(2) Magnetic field ( ) is in z-direction ( ), represented as (3) Here we taken  p-type Semiconductor

(4) In p-type semiconductor holes are  majority carriers and electrons are minority carriers

Analysis :

If the holes are moving in a magnetic field then it acted by a magnetic force ( )

Vector = q(vector v× vector )      q represent charge on holes = e = v, represent drift velocity of holes in +x direction

= =  ( )

= = Vector = So magnitude of magnetic force vector on holes will be = ( this is the force acted on holes in -y direction )

Due to this magnetic force, holes start to  accumulate towards -y direction ( at surface 2) and electron start to accumulate towards +y direction ( at surface 1) to maintain the charge neutrality . so surface 2 get positive charge (due to +ve charge on holes ) and surface 1 get negative charge ( due to -ve charge on electron )

If this process of accumulation of electron and holes continue , charge density on surface 1 and surface 2 increases and due to positive ( at surface 2) and negative charge ( at surface 1) , an Electric field ( ) is developed between surface 2 and surface 1 of semiconductor specimen ,

So a potential difference between surface 1 and surface 2 is develop , this potential difference  is called Hall potential or Hall voltage ( )

Direction of electric field ( ) exist from surface 2 to surface 1 ( towards +y direction )

Electric field always start from positive charge and ends at negative charge

This electric field ( ) act an electric force ( ) on moving holes  and direction of this electric force will be in opposite direction of flow of holes i.e. towards electric field direction  (towards +y direction )

value of electric force vector will be

Vector = q( vector )                                                                         q= charge on holes  =+e

= = Magnitude of electric force is = At equilibrium electric force is equal to magnetic force =  ( )  = or we can simply write = vector = vector  vector SHARE
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