# Drift Velocity

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Drift Velocity of charge carrier in semiconductors: Zig Zag Randomness of electron

We know that in absence of electric field in semiconductor electron moves randomly ( zig zag randomness) to maintain thermal equilibrium, as shown in above figure (a). the velocity with by they move is called random velocity( ) and it is in order of Average value of random velocity at each point in a semiconductor will always be zero ( vector addition of random velocity of all electron at a particular point will be cancel  out to each other )

Average value of random velocity < > = 0

After application of electric field E > , due to electric force all electron will aligned in a particular direction that is opposite to the direction of electric field and moves with a particular velocity .average value of this velocity is called drift velocity ( )  as shown in figure (b) below or Let m = mass of electron

a   = acceleration of electron = Electric force on electron = Effective mass of electron in semiconductor lattice

e= charge on electron

so Electric force acted on electron due to electric field can be given by = (1)

where e is the charge on electron

suppose that electron is moving with acceleration “a”, so force due to mass and its acceleration = (2)

at equilibrium + =   -( acceleration “a” can be expressed in terms of average distance ( ) traveled by electron and time( ) taken to cover this average distance

i.e. =  = -( )           (3)

integrating both side with respect to time (t)

∫( ) = ∫-( )  = -( ) + (4)

at = , and = ( random velocity )

after putting these above value in equation (4) we can get = so = -( ) + (5)

taking average on both side

< > = <-( ) > + <  = <t> = average value of time = average time of collision =τ

<m> = average value of mass of electron in semiconductor lattice =effective mass of electron =  = (-eτ/ )E              (6)

we know that drift velocity is = (7) = (-eτ/ where = mobility of electron

So from above calculation , it is clear that mobility depends on

(1) Effective mass ( ) of charge carrier

(2) Time of collision of charge carrier (τ)

(3) Type of material , on large doping time of collision (τ) of charge carrier will reduced