A silicon sample contains acceptor atoms at a concentration

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A silicon sample contains acceptor atoms at a concentration of N_a = 5 × 10¹⁵ cm^–3. Donor atoms are added forming and n-type compensated semiconductor such that the Fermi level is 0.215 eV below the conduction band edge. The concentration of donors atoms added are—

1. 1.2 × 10¹⁶ cm^–3
2. 4.6 × 10¹⁶ cm^–3
3. 3.9 × 10¹² cm^{– 3}
4. 2.4 × 10¹² cm^{– 3}

Correct Option: A

We know that, n₀ = N_d – N_a = N_c e ^{– {( E_C – E_F) / kT}
for S_i, N_c = 2.8 × 10¹⁹ cm–3}
given N_a = 5 × 10¹⁵ cm^–3
Now, N_d = N_a + N_c e ^{– {( E_C – E_F) / kT}
or N_d = 5 × 10¹⁵ + 2.8 × 10¹⁹ e ^{– (215eV / 26 x 10^-3eV)
{˙.˙ given that Fermi level is 0.215 eV below the or Nd = 1.19 × 10¹⁶ cm^–3 conduction band i.e. E_c – E_F = 0.215 eV}
Hence alternative (A) is the correct choice.}}