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Question

A pure Si crystal is doped with 1 ppm of pentavalent impurity. If the Si atom density is \( 5 \times
10^{28} \, \text{m}^{-3} \), the number of donor atoms per cubic meter is:

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Explanation

**Charge carriers** in n-type majority electrons, minority holes, in p-type majority holes, minority electrons, minority concentration reduced due to recombination n_e n_h = n_i², doping increases majority, conductivity σ = e(n_e μ_e + n_h μ_h), increases with doping. Donor ionization energy small ~0.01 eV, electrons easily promoted to conduction band at room temperature. 1 ppm = 1 part per million = 10⁻⁶ . Number of donor atoms = 10⁻⁶ × 5 × 10²⁸ = 5 × 10²² m⁻³ . These contribute electrons, assuming full ionization at room temperature. Substituting values gives 5 × 10²² m⁻³, which matches expected behaviour for this semiconductor device configuration, confirming doping, depletion and rectifier principles.

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