What is the number density of donor atoms which must be added to a pure germanium semiconductor to make an $n$-type semiconductor of conductivity $6.4 \ \Omega^{-1} \ cm^{-1}$? The mobility of electrons in $n$-type germanium is $4 \times 10^3 \ cm^2 \ V^{-1} \ s^{-1}$. Neglect the contribution of holes to conductivity.

  • A
    $10^{16} \ m^{-3}$
  • B
    $10^{18} \ m^{-3}$
  • C
    $10^{20} \ m^{-3}$
  • D
    $10^{22} \ m^{-3}$

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The hole and the free electron concentrations in a pure silicon at room temperature are given by $1.4 \times 10^{16} \ m^{-3}$ each under equilibrium. When it is doped with indium and the hole concentration is $n_{h} = 4 \times 10^{22} \ m^{-3}$,the electron concentration is

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Reason: It is due to the law of mass action.

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The number of silicon atoms per $m^{3}$ is $5 \times 10^{28}$. This is doped simultaneously with $5 \times 10^{22}$ atoms per $m^{3}$ of Arsenic and $5 \times 10^{20}$ atoms per $m^{3}$ of Indium. Calculate the number of electrons and holes. Given that $n_{i} = 1.5 \times 10^{16} \; m^{-3}$. Is the material $n$-type or $p$-type?

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