## 05/04/2021

### Drift & Drift Velocity

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 oK, 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 ( meter2 / voltage – second )

### Current Density Due to Charge Carriers

( 1 ) Current density due to electron drift

Je = e µe n E

Where

µe = Electron Mobility

E = Electric field

n = Electrons

( 2 ) Current density due to hole drift

Jh = e µh p E

Where

µh = Hole Mobility

E= Electric field

p = Holes

Total current density due to electrons and holes carriers

J = Je + Jh

= e µe n E + e µh p E

= eE ( µe n + µh 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

( /meter3 )

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 ( µe n + µh p ) Where µe = Electron Mobility µh = 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 ( /meter3 ) Resistivity ρ = ( 1 / neµ ) ohm – meter Conductivity σ = neµ  ( 1 / ohm – meter )

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