Physics for Information Science: Unit II: Semiconductor Physics
Velocity - Electric Field Relations and Mobility of Charge Carriers
Semiconductor
We know that in conductors the mobility is due to average velocity acquired by the electrons whereas in semiconductor the velocity it is due to the following reasons, viz
VELOCITY
- ELECTRIC FIELD RELATIONS AND MOBILITY OF CHARGE CARRIERS
We
know that in conductors the mobility is due to average velocity acquired by the
electrons whereas in semiconductor the velocity it is due to the following
reasons, viz.
• The rapid random motion of both electrons and holes due to thermal energy.
• Additional velocity acquired by the
charge carriers due to external electric field.
(i.e)
vd ∞ E
Vd
= μe E
Where
μe is the mobility of the charge carriers.
In
a perfect crystal the drift velocity continuously increases, whereas in a
crystal with imperfections [such as missing atoms, vacancies, dislocations,
interstitial atoms, substitutional atoms etc,] charge carriers are scattered,
which in turn affects the drift velocity and hence the mobility of the charge
carriers.
The
two important causes for scattering in semiconductors are
(i)
Lattice vibrations (phonons)
(ii)
Ionised impurity atoms
If
μL is the mobility due to scattering by lattice vibrations and μI
is the mobility due to ionised impurities.
Then,
Actual mobility (μ) is given by
......(1)
As
mobility due to lattice vibrations, depends on temperature. We can write the
relation between mobility and temperature as
.....(2)
Similarly
the relation between mobility due to ionised impurities and temperature can be
written as
1/
μI ∞ T3/2
(or) 1/ μI = bT3/2
Where
'a' and 'b' proportional constants.
Substituting
eqns (2) and (3) in eqn (1) we can write the actual mobility as
Note:
On Calculating the mobilites of a imperfect crystal, it is better to take
relaxation time into consideration over the entire energy distribution.
Physics for Information Science: Unit II: Semiconductor Physics : Tag: : Semiconductor - Velocity - Electric Field Relations and Mobility of Charge Carriers
Physics for Information Science: Unit II: Semiconductor Physics
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Physics for Information Science
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