Question

The number of silicon atoms per ${m^3}$ is $5 \times {10^{28}}$ . This is doped simultaneously with $5 \times {10^{28}}$ atoms per ${m^3}$ of Arsenic and $5 \times {10^{28}}$ per ${m^3}$ atoms of Indium. Calculate the number of electrons and holes. Given that ${n_1} = 1.5 \times {10^{16}}{m^{ - 3}}$ . Is the material n-type or p-type?

Answer 1

Hint:In order to answer this question, as the number of atoms per ${m^3}$ of all three elements are given, so we can find the number of electrons. And then we can find the number of holes with the help of the found no. of electrons.

Complete step by step answer:
First we will find the number of electrons that will help in finding the number of holes.
The number of electron is given as:
${n_e} = 5 \times {10^{28}} - 5 \times {10^{20}}$
Now, we can find the number of holes with the help of the number of electrons.
Number of holes is given as:
${n_h} = \dfrac{{{n_i}^2}}{{{n_e}}}$
By substituting the values in the above equation we get:-
as given the value of ${n_i}$ , ${n_1} = 1.5 \times {10^{16}}{m^{ - 3}}$ .
$ \Rightarrow {n_h} = \dfrac{{{{(1.5 \times {{10}^{16}}{m^{ - 3}})}^2}}}{{5 \times {{10}^{28}} - 5 \times {{10}^{20}}}}$
$\therefore {n_h} = 4.54 \times {10^9}{m^{ - 3}}$

Since, the number of electrons is greater than the number of holes, it is n-type.

Note: Semiconductors are divided into two types: P Type and N Type. Positive charge is carried by the P type, whereas negative charge is carried by the N type. The charges are determined by the concentrations of holes and electrons. The positive charge is caused by a higher hole concentration in the P type semiconductor.