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The product of the hole concentration and the conduction electron concentration turns out to be independent of the amount of any impurity doped. The concentration of conduction electrons in germanium is 6×1019 per cubic metre. When some phosphorus impurity is doped into a germanium sample, the concentration of conduction electrons increases to 2×1023 per cubic metre. Find the concentration of the holes in the doped germanium.

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Solution

(Number of holes) (Number of conduction electrons) = Constant

At first,

Number of conduction electrons = 6×1019

Number of holes = 6×1019

After doping,

Number of conduction electrons = 2×1023

Number of holes = x

(6×1019) (6×1019)=(2×1023) x

6×6×1019+192×1023=x

x=18×1015=1.8×1016


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