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Question
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 metref conduction electrons increases to 2 × 1023 per cubic metre. Find the concentration of the holes in the doped germanium.. When some phosphorus impurity is doped into a germanium sample, the concentration o
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Solution
We know that for an intrinsic semiconductor, the concentration of electrons is equal to the concentration of holes.
The product of electron hole pair concentration always remains constant.
i.e. Number of holes × Number of conduction electrons = Constant
Initially, the number of conduction electron per cubic metre = 6 × 1019
We know,
Number of holes per cubic metre = Number of electrons per cubic metre
∴ Number of holes per cubic metre = 6 ×1019
After doping,
Number of conduction electrons per cubic metre = 2 × 1023
Now,
Let the number of holes per cubic metre be x.
As the product of electron hole pair concentration always remains constant,
\[(6 \times {10}^{19} )(6 \times {10}^{19} ) = (2 \times {10}^{23} )x\]
\[ \Rightarrow x = \frac{6 \times 6 \times {10}^{19 + 19}}{2 \times {10}^{23}} \]
\[ \Rightarrow x = 18 \times {10}^{15} = 1 . 8 \times {10}^{16}\]
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