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