14.12 The number of silicon atoms per m3 is 5 × 1028. This is doped simultaneously with 5 × 1022 atoms per m3 of Arsenic and 5 × 1020 per m3 atoms of Indium. Calculate the number of electrons and holes. Given that ni = 1.5 × 1016 m-3. Is the material n-type or p-type?

Hint: \(n_{e}n_{h}=n^{2}_{i}\)
Step 1: Find the number of electrons.

Number of silicon atoms, N=5 ×1028 atoms/m3    Number of arsenic atoms, nAS=5×1022atoms/m3

Number of indium atoms nIn=5×1028 atom/m3 

 Number of thermally-generatd electrons, ni=1.5×1016 electron/m3

Number of elctrons,ne=5×1022-1.5×10164.99×1022
\(As~n_{e}.n_{h}=n^{2}_{i}\)
\(\Rightarrow~n_{h}=\frac{n^{2}_{i}}{n_{e}}=\frac{\left ( 1.5\times10^{16} \right )^{2}}{4.99\times10^{22}}\approx 4.51\times10^{9}\)

Step 2: Compare the number of electrons and holes.
Therefore, the number of electrons is approximately 4.99×1022 and the number of holes is about 4.51×109. Since the number of electrons is more than the number of holes the material is an n-type semiconductor.