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

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.

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 ( 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 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

            ( /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 )

Finally


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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