A pure Si crystal has 6 × 10²⁸ atoms m^-3. It is doped by 1 ppm concentration of pentavalent As. Then the number of electrons and holes are:

(Given that n_i = 1.5 × 10¹⁶ m^-3)

Concept:

Extrinsic semicodutor:

• ​Extrinsic semiconductors are semiconductors that are doped with specific impurities.
• The  modifies the electrical properties of the semiconductor and makes it more suitable for electronic devices such as diodes and transistors.
• Two types of extrinsic semiconductors: N-type and P-type
• ​The electron and hole concentration in a semiconductor is in thermal equilibrium. ni2 = ne × nh

​​Calculation:

Given,

ni = 1.5 × 1016 m^-3 

The number of atoms in a pure Si crystal =  6 × 1028 atoms m-3.

We know that 1 ppm = 10^-6 

Hence, the number of electrons, \(n_e=\frac{6× 10^{28}}{10^6}\)

n_e = 6 × 10²² m^-3

The electron and hole concentration in a semiconductor is in thermal equilibrium.

n_i² = n_e × n_h

\(\Rightarrow n_h=\frac{n_i^2}{n_e}\)

\(\Rightarrow n_h=\frac{(1.5\times 10^{16})^2}{6\times 10^{22}}=3.75\times 10^{9}~m^{-3}\)

Additional Information

 Intrinsic semiconductor:

• ​Semiconductors that are chemically pure, in other words, free from impurities are termed intrinsic semiconductors.
• The number of holes and electrons is therefore determined by the properties of the material itself instead of the impurities.
• In intrinsic semiconductors, the number of excited electrons is equal to the number of holes; n = p
• They are also termed undoped semiconductors or i-type semiconductors. Silicon and germanium are examples of the i-type semiconductor