# 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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