Question 12

# The number of silicon atoms per m 3 is 5 × 10 28 . This is doped simultaneously with 5 × 10 22 atoms per m 3 of Arsenic and 5 × 10 20 per m 3 atoms of Indium. Calculate the number of electrons and holes. Given that n i = 1.5 × 10 16 m −3 . Is the material n-type or p-type?

Number of silicon atoms, N = 5 × 10 28 atoms/m 3

Number of arsenic atoms, n As = 5 × 10 22 atoms/m 3

Number of indium atoms, n In = 5 × 10 20 atoms/m 3

Number of thermally-generated electrons, n i = 1.5 × 10 16 electrons/m 3

Number of electrons, n e = 5 × 10 22 − 1.5 × 10 16 ≈ 4.99 × 10 22

Number of holes = n h

In thermal equilibrium, the concentrations of electrons and holes in a semiconductor are related as: n e n h = n i2

Therefore, nh = n i2 / ne = (1.5x1016)2 / 4.99 x 1022 ≈ 4.51 x 109

Therefore, the number of electrons is approximately 4.99 × 10 22 and the number of holes is about 4.51 × 10 9 . Since the number of electrons is more than the number of holes, the material is an n-type semiconductor.