The major factor affecting the value of resistivity when temperature changes in semiconductors is the number of free electrons per unit volume (n).

Explanation:

When it comes to semiconductors, the behavior of electrons is of crucial importance. In a semiconductor, the valence band is fully occupied with electrons, while the conduction band is partially filled or empty. These electrons in the conduction band are known as free electrons and are responsible for the conduction of electric current.

The resistivity of a material is a measure of how strongly it resists the flow of electric current. It is directly related to the number of free electrons available for conduction. When temperature changes, the number of free electrons can vary due to several factors such as thermal excitation and electron-hole pair generation.

When the temperature increases, the thermal energy of the material also increases. This thermal energy can cause some of the bound electrons in the valence band to gain enough energy to break free and move into the conduction band. As a result, the number of free electrons increases, and the resistivity decreases.

On the other hand, when the temperature decreases, the thermal energy decreases, and some of the free electrons can recombine with the holes (electron-hole pairs) in the valence band. This recombination process reduces the number of free electrons, leading to an increase in resistivity.

The relationship between resistivity and temperature in semiconductors can be described by the equation:

ρ = ρ0(1 + α(T - T0))

where ρ is the resistivity at temperature T, ρ0 is the resistivity at a reference temperature T0, and α is the temperature coefficient of resistivity. The temperature coefficient of resistivity, α, is a material-specific constant that determines how resistivity changes with temperature.

In conclusion, the major factor affecting the value of resistivity when temperature changes in semiconductors is the number of free electrons per unit volume (n). As the temperature increases, more electrons become free, leading to a decrease in resistivity, while a decrease in temperature reduces the number of free electrons, resulting in an increase in resistivity.