Q12 of 71 Page 418

Estimate the proportion of boron impurity which will increase the conductivity of a pure silicon sample by a factor of 100. Assume that each boron atom creates a hole and the concentration of holes in pure silicon at the same temperature is 7 × 1015 holes per cubic meter. Density of silicon is 5 × 1028 atoms per cubic meter.


Given:


Since, the number conduction electron and holes are the same,


∴ Number of charge carriers initially


On adding the impurity to the pure silicon the conductivity becomes 100 times the initial , therefore the total charge carriers should become


(∵ σ is directly proportional to concentration of charge carriers)


Let be the holes after adding the impurity and will be the electrons


Now, the product of the total conduction electrons and holes remains nearly constant,


∴




Solving for by discriminant method,


We get



Rejecting the second value on the basis of the fact that the initial number of holes must be smaller than the number of holes after doping.


∴ the number of holes or boron atoms added



Ratio of number of silicon atom to boron atom



∴ boron must be added in proportion of 1 boron atom in 3.59× 1010 silicon atoms.


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