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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