Derive an expression for conductivity in case of srmiconductor
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Answer:
In a Semi-Conductor of length (ℓ) and area of Cross-Section. Let ne and nh be the no. of electrons and holes with drift velocities Ve and Vh respectively.
So, the total current in the semi-conductor will be the sum of current due to electrons as well as holes,
i.e. I = Ie + Ih (i)
As we know that
I = ne A Vd
\Ie = ne e A Ve
And Ih = nh e A Vh
I = ne e A Ve + nh e A Vh
I = eA[ne Ve + nh vh]
I/A = e[ne Ve + nh vh] (2)
As we know that
E = V/l (in magnitude)
Also, R = ρl/A
Or ρ = RA/l
Where ρ is resistivity and R is resistance
Or E/ρ = (V/l)/ ρ
Or E/ρ = (V/l)l/ RA
E/ρ = (V/RA)
E/ρ = I/A (3)
Put (3) in (2) we get,
E/ρ = e[ne Ve + nh vh]
I/ò ρ = e / E[ne Ve + nh vh]
σ = e [ne Ve/E + nh vh/E] (σ = Conductivity)
Here, mobility (m) = Drift vel./ Electric field
σ = e [ne me + nh mh]
This is the derivation and expression for the conductivity of a semiconductor.
I hope it will be helpful for you