Pure silicon crystal at 300 K has equal electron and hole concentration 2 × 1 0 16 per m 3 . Doping by indium increases hole concentration to 4 × 1 0 22 per m 3 . Electron concentration in doped silic

Question

Pure silicon crystal at 300 K has equal electron and hole concentration 2 × 1 0 16 per m 3 . Doping by indium increases hole concentration to 4 × 1 0 22 per m 3 . Electron concentration in doped silicon is

TestHub · Accepted Answer

According to the mass action law for semiconductors:

$n_{e} n_{h} = n_{i}^{2}$

Given $n_{i} = 2 \times 1 0^{16} / m^{3}$ and $n_{h} = 4 \times 1 0^{22} / m^{3}$ .

Substituting the values:

$n_{e} (4 \times 1 0^{22}) = (2 \times 1 0^{16})^{2}$

$n_{e} (4 \times 1 0^{22}) = 4 \times 1 0^{32}$

$n_{e} = \frac{4 \times 1 0 ^{32}}{4 \times 1 0 ^{22}}$

$n_{e} = 1 0^{10} / m^{3}$

Answer: $1 0^{10} / m^{3}$

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