# 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

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