# HALL Effect in n-type Semiconductor

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HALL EFFECT IN n-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 ()

n-type Semiconductor specimen figure

=    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 electron will be in (-X)-direction ()

(2) Magnetic field () is in z-direction (), represented as

(3) Here we taken  n-type Semiconductor

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

Analysis :

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

Vector          = q(vector v× vector )            q represent charge on electron = -e

v represent drift velocity of electron in -x direction

= ( )

=     ()

=

=

Vector          =

So magnitude of magnetic force vector will be

=    ( this is the force acted on electron in -y direction )

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

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 1) and negative charge ( at surface 2) , an Electric field () is developed between surface 1 and surface 2 of semiconductor ,

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 1 to surface 2 ( towards -y direction )

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

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

value of electric force vector will be

Vector    = q( vector )                                                               q= charge on electron  =-e

=

=

Magnitude of electric force    is

=

At equilibrium electric force is equal to magnetic force

=

() =

=

or we can simply write

=                  eq (1)

CALCULATION OF HALL VOLTAGE ():

Hall voltage  is the potential difference between the surface 1 and surface 2

let the voltage on the surface 1 is  and voltage on the surface 2 is

so                >

from above figure

=                        eq (2)                    d= distance between surface 1 and surface 2

from eq(1) and eq(2)

=

=                       eq(3)

we know that conduction current density  is

=                           eq(4)                                                            = conductivity

we know that conductivity  is

=                         eq(5)                                                             = electron density

= mobility of electron

from eq(4) and eq(5)

=                       eq(6)

and drift velocity  of electron is

=                          eq(7)

from eq(6) and eq(7)

=

=                         eq (8)

from eq(3) and eq(8)

=                   eq(9)

we know     =                         eq(10)                                 i = current flowing in semiconductor

= area semiconductor surface =

from eq(9) and eq(10)

=

=

=                                                                                        = charge density =

=                                                                                      = = Hall coefficient

NOTE: Conclusion from Hall effect analysis on a semiconductor specimen

(1) For any semiconductor  specimen  and  is a constant , Hall Voltage  is proportional to magnetic field  and current flowing in the semiconductor specimen

(2) Current flow is due to electron only not due to Proton

(3) Hall gives idea of hole current or simply hole

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