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

# Effect of Electric Field on Semiconductor Material

## Semiconductor Material: 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.

## Semiconductor Material: Electric field Applied

- When electric field applied to the semiconductor, the charge carriers move 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.

## Drift Velocity Formula

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 Current

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 )

__Summary__

Drift velocity v α E v = µ E |

Current density due to holes and electrons J = eE ( µ Where µ µ 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 |

Resistivity ρ = ( 1 / neµ ) ohm – meter Conductivity σ = neµ ( 1 / ohm – meter ) |

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