Question

A pure \[\ce{Si}\] crystal having 5 × 10²⁸ atoms m⁻³ is dopped with 1 ppm concentration of antimony. If the concentration of holes in the doped crystal is found to be 4.5 × 10⁹ m⁻³, the concentration (in m⁻³) of intrinsic charge carriers in \[\ce{Si}\] crystal is about ______.

Options

• 1.2 × 10¹⁵

• 1.5 × 10¹⁶

• 3.0 × 10¹⁵

• 2.0 × 10¹⁶

Answer 1

A pure \[\ce{Si}\] crystal having 5 × 10²⁸ atoms m⁻³ is dopped with 1 ppm concentration of antimony. If the concentration of holes in the doped crystal is found to be 4.5 × 10⁹ m⁻³, the concentration (in m⁻³) of intrinsic charge carriers in \[\ce{Si}\] crystal is about 1.5 × 10¹⁶.

Explanation:

1 atom of \[\ce{Si}\] doped out of 10⁶ atom (1 ppm)

⇒ In 5 × 10²⁸ atoms, net doped = `(5 xx 10^28)/10^6`

= 5 × 10²² atoms

1 Antimony creates 1 excess electron

⇒ Number of excess electrons = n_e = 5 × 10²²

Also, n_i² = n_en_h

\[\ce{ni^2}\] = (5 × 10²²) (4.5 × 10⁹)

⇒ \[\ce{ni^2}\] = 1.5 × 10¹⁶