Pure Si at 500 K has equal number of electron (ne) and hole

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Pure Si at 500 K has equal number of electron (n_e) and hole (n_h) concentrations of 1.5 × 10¹⁶ m^–3. Doping by indium increases n_h to 4.5 × 10²² m^–3. The doped semiconductor is of

1. n–type with electron concentration n_e = 5 × 10²² m^–3
2. p–type with electron concentration n_e = 2.5 ×10¹⁰ m^–3
3. n–type with electron concentration n_e = 2.5 × 10²³ m^–3
4. p–type having electron concentration n_e = 5 × 10⁹ m^–3

Correct Option: D

n₁² = n_en_h
(1.5 × 10¹⁶ )² = n_e (4.5 × 10²² )
⇒ n_e = 0.5 × 10¹⁰
or n_e = 5 × 10⁹
Given n_h = 4.5 × 10²²
⇒ n_h >> n_e
∴ Semiconductor is p-type and
n_e = 5 × 10⁹ m^–3.