In a pure semiconductor the number of free electrons is always equal to
number of holes. The thermal agitation continues to product new
hole-electron pairs while previous pairs disappear. This disappearing of
pairs is due to the process called recombination. The merging of a free
electron and hole is called recombination. The amount of time between
the creation and disappearance of a free electron and hole pair is
called its lifetime.
Thus a hole exists for τp seconds before it recombines while a free electron exists for τn seconds before it recombines.τp and τn are
called carrier lifetimes of hole and electron respectively. Carrier
lifetime is also called mean lifetime od the hole and electron. Carrier
lifetime range from nanosecond of hundreds of microseconds.
1.1 Diffusion of Length L
Due to the recombination, the concentration of charge carriers decrease
exponentially with the distance at the time of diffusion. The charge
carriers have mean life time denoted by τ for which they exist before recombination.
... τn = Mean life time of free electron
... τp = Mean life time of free hole
After recombination, these charge carriers vanish and concentration decreases exponentially with distance.
Note :
The average distance covered by an excess charge carrier while
diffusion during its life time is called diffusion length of that charge
carrier. It is denoted by L.
... Ln = Diffusion length of free electron
... Lp = Diffusion length of free hole
The diffusion length L is related to main life time τ through the diffusion constant D of the charge carrier. Mathematically this relationship is given by, τ
L = √(Dτ)
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