Hello dear student

Let's derive the expression the expression for conductivity of semiconductor.

In a Semi-Conductor of length (L) and area of Cross-Section A.
Let n _e and n _h be the no. of electrons and holes with drift velocities V _e and V _h 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 = I _e + I _h (i)

As we know that

I = n _e A V _d

\I _e = n _e e A V _e

And I _h = n _h e A V _h

I = n _e e A V _e + n _h e A V _h

I = eA[n _e V _e + n _h v _h ]

I/A = e[n _e V _e + n _h v _h ] (2)

As we know that

E = V/l (in magnitude)

Also, R = l/A

Or = RA/l

Where is resistivity and R is resistance

Or E/ = (V/l)/

Or E/ = (V/l)l/ RA

E/ = (V/RA)

E/ = I/A (3)

Put (3) in (2) we get,

E/ = e[n _e V _e + n _h v _h ]

I/ = e / E[n _e V _e + n _h v _h ]

= e [n _e V _e /E + n _h v _h /E] ( = Conductivity)

Here, mobility (m) = Drift vel./ Electric field

= e [n _e m _e + n _h m _h ]



This is the derivation and expression for the conductivity of a semiconductor.


Hope that's helpful


Best of luck