Ncert Exercises & Solutions

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 n_i = 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 $\times 10^{28} a t o m s / m^{3}$ Number of arsenic atoms, $n_{A S} = 5 \times 10^{22} a t o m s / m^{3}$

Number of indium atoms $n_{I n} = 5 \times 10^{28} a t o m / m^{3}$

Number of thermally-generatd electrons, $n_{i} = 1.5 \times 10^{16} e l e c t r o n / m^{3}$

Number of elctrons, $n_{e} = 5 \times 10^{22} - 1.5 \times 10^{16} \approx 4.99 \times 10^{22}$
$As~n_{e}.n_{h}=n^{2}_{i}$
$\Rightarrow~n_{h}=\frac{n^{2}_{i}}{n_{e}}=\frac{\left ( 1.5\times10^{16} \right )^{2}}{4.99\times10^{22}}\approx 4.51\times10^{9}$

$_{}$ $_{}_{}$ Step 2: Compare the number of electrons and holes.
Therefore, the number of electrons is approximately $4.99 \times 10^{22}$ and the number of holes is about $4.51 \times 10^{9}$ . Since the number of electrons is more than the number of holes the material is an n-type semiconductor.

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