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 τ

_{p }seconds before it recombines while a free electron exists for τ_{n }seconds before it recombines.τ_{p }and τ_{n }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.

**.**τ

^{.}._{n }= Mean life time of free electron

**.**τ

^{.}._{p }= 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.

**.**L

^{.}._{n}

_{ }= Diffusion length of free electron

**.**L

^{.}._{p }= 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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