Carrier Lifetimes

        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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