The thermal excitation of a carrier across bands - from the valence band to the conduction band- produces free carriers in the two bands. n_{i} is simply the intrinsic carrier concentration, which is the concentration of these carriers. Semiconductor material to which no impurities were added to change the concentrations of the carrier are called intrinsic material.
In the intrinsic semiconductors, when the valence electrons break the covalent bond and jump into the conduction band, there are two types of charge carriers that are generated. Those are free electrons and holes.
Intrinsic carrier concentration is the conduction band’s number of electrons per unit volume or the valence band’s number of holes per unit volume. Electron-carrier concentration is the number of electrons per unit volume in the conduction band and hole-carrier concentration is the number of holes per unit volume in the valence.
The number of electrons generated in the conduction band in an intrinsic semiconductor is equal to the number of holes generated in the valence band. Therefore, the electron-carrier concentration and the hole-carrier concentration are always equal.
So all Electrons and holes that partake in conduction are called Intrinsic carriers. These carriers concentration is dependent on both the temperature and band gap of the material, therefore affecting the conductivity of the material.
The larger the band gap the more difficult it becomes for a carrier to be thermally excited across the band gap, and consequently the intrinsic carrier concentration is lower in higher band gap materials. On the other hand, increasing the temperature makes it more possible that an electron can be excited into the conduction band, leading to the increase of the intrinsic carrier concentration.

Intrinsic carrier equations

This can be expressed as the following:
ni = n = p
Where:
n : electron carrier concentrationP : hole-carrier concentrationni : the intrinsic carrier concentration

Effect on Solar Cells

Intrinsic carrier concentration is directly related to solar cell efficiency and is studied to understand how maximize solar cell efficiency.
This lead to studying the precise value for the intrinsic carrier concentration in silicon due to its importance in solar cell modeling. At a temperature of 300 K the normal known value for the intrinsic carrier concentration of silicon, n_{i}, equals 9.65 x 10^{9} cm^{-3}.
Below is the formula for the intrinsic carrier concentration in silicon, expressed as a function of temperature:
ni(T)=5.29×10^{19}(T/300)^{2.54}exp(−6726/T)