# Minimum value of conductivity of a Semiconductor Sample

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Minimum value of conductivity of a Semiconductor:

In previous post Derivation of conductivity of Semiconductor we derived the expression of conductivity of a semiconductor , that is = (1)

where = charge on carrier =  electron concentration per unit volume = hole concentration per unit volume = mobility of electron = mobility of holes

From “Mass Action” law we know that  = / (2)

from equation (1) and (2) = ( +( / ) )                            (3)

on  differentiating equation (3) with respect to  = ( -( / ) )                 (4)

For maximum or minimum of conductivity ( )

put = from equation (4) ( -( / ) ) = after calculation we will get = √( / )

Again differentiate equation (4) with respect to to know occurrence of minimum or maximum at = √( / )  . / = / (5)

After putting the value of = √( / )  in equation (5) we will get / =   a positive quantity

that means at = √( / ) minimum  conductivity occurs

and minimum value of conductivity ( ) can be calculated by putting the  value of = √( / ) in equation (3) = √( )

Try to solve these Important Problems

Q1. Consider a piece of pure silicon 100 µm long with a cross-sectional area of 1 µm2. How much current would flow through this “resistor” at room temperature in response to an applied voltage of 1 volt?

Q2 (a) Show that the minimum conductivity of a semiconductor sample occurs when = √( / )

(b) What is the expression for the minimum conductivity?

(c) Is this value greatly different than the value of intrinsic conductivity ? given that = 1.45 x 1010 cm-3, = 1500 cm2 volt-1 sec-1 and , = 500 cm2 volt-1 sec-1

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