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

 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

            ( /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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