Physics for Information Science: Unit II: Semiconductor Physics
Einstein Relation [for Reference Purpose]
Semiconductor
Even though the drift and diffusion transport are independent phenomenon, they both can be directly related.
EINSTEIN
RELATION [For Reference Purpose]
Even
though the drift and diffusion transport are independent phenomenon, they both
can be directly related.
Einstein
showed that the mobility (μ) and the diffusion coefficient (D) can be related
as shown in Fig. 2.25.
This
graph shows that the diffusion always occurs from higher density region to
lower density region, in order to achieve uniform distribution.
Thus,
under thermal equilibrium, we can write
Drift
current = Diffusion current
Equating
equations (3) and (9), we can write
…….(1)
If
F=eE is the force required to restore the excess charge carriers to equilibrium
and to achieve uniform distribution of charge carriers, then, the force due to
the electrons (Δne) can be written as
F=Δ
ne eE…..(2)
From
Equations (1) and (2) We can write
…….(3)
The
force corresponding to pressure gradient is
………(4)
Eqns.
(3) and (4) we get
Diffusion
coefficient for electrons is
…….(5)
………(6)
Similarly
for holes we can write the diffusion coefficient as
……...(7)
……..(8)
Equations
(5) and (7) are called Einstein's relation which represents the relationship
between diffusion coefficient and mobility of charge carriers.
From
equations (6) and (8) we can write
……….(9)
Equation
(9) gives the relationship between diffusion coefficient in respect of their
mobilities.
Physics for Information Science: Unit II: Semiconductor Physics : Tag: : Semiconductor - Einstein Relation [for Reference Purpose]
Physics for Information Science: Unit II: Semiconductor Physics
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