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
