- The directed motion of the charge carriers ( electrons + holes ) in the semiconductor done mainly by ( 1 ) Charge drift ( flow ) under the influence of electric field ( 2 ) Charge drift from high charge density to low charge density
No electric field
- When electric field is not applied to the semiconductor material at a temperature above 0 ^{o}K, the electrons as well as holes move randomly and collide with each other and other fixed ions within the crystal.
- The net velocity of the charge carriers in any direction is equal to zero therefore no current flows through the crystal.
Electric field applied
- When electric field applied to the semiconductor, the charge carriers moves in directed motion.
- This will result in net velocity of charge carriers is called as drift velocity in the direction of applied field.
- The electrons and holes move in the opposite direction but both produce current in the same direction due to their opposite charges.
- The drift velocity is directly proportional to the electric field E. The proportionally is called as mobility ( µ )
v α E
v = µ E ……. (
1 )
Where v = drift velocity ( meter / second )
E =
Electric field ( voltage / meter )
µ =
Mobility ( meter^{2} / voltage – second )
Current density due to charge carriers
( 1 ) Current density due to electron drift
J_{e} =
e µ_{e }n E
Where
µ_{e} = Electron Mobility
E = Electric field
n = Electrons
( 2 ) Current density due to hole drift
J_{h} =
e µ_{h }p E
Where
µ_{h}
= Hole Mobility
E=
Electric field
p = Holes
Total current density due to electrons and holes
carriers
J = J_{e} + J_{h}
= e µ_{e }n
E + e µ_{h }p E
= eE ( µ_{e
}n + µ_{h }p )
Drift Velocity
- It is defined as the average velocity attained by the charge particles due to applied electric field.
I = envA …… ( 2
)
Where
e =
Electron charge ( Coloumb )
v =
Electron drift velocity ( meter / second )
A = Cross
section area of conductor
n = Number
of free electrons per unit volume of conductor
( /meter^{3} )
from equation ( 1 ) and ( 2 )
I = enA ( µ E )
Where
E =
Electric field ( voltage / meter = V / L )
Therefore I = enAµ ( V / L )
V / I
= ( 1 / neµ ) L / a
R
= ( 1 / neµ ) L / a
Compare this equation with R = ρL / a
⸫ Resistivity ρ = ( 1 / neµ ) ohm – meter
Conductivity
σ = neµ ( 1 / ohm – meter )
Finally
Drift
velocity v α E v = µ E |
Current
density due to holes and electrons J
= eE ( µ_{e }n + µ_{h }p ) Where
µ_{e}
= Electron Mobility µ_{h}
= Hole Mobility n
= Number of electrons P
= Number of holes E
= Electric field per meter e
= Electric charge |
Drift Velocity v = I / enA Where e = Electron charge ( Coulomb ) v = Electron drift velocity ( meter
/ second ) A = Cross section area of conductor n = Number of free electrons per
unit volume of conductor ( /meter^{3} ) |
Resistivity
ρ = ( 1 / neµ ) ohm – meter Conductivity
σ = neµ ( 1 / ohm – meter ) |
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