Intrinsic semiconductors are highly pure materials with no impurities. At absolute zero, these semiconductors behave as perfect insulators because all the valence electrons are bound, and the conduction band is empty, disallowing electrical conduction. The Fermi level is a concept used to describe the probability of occupancy of energy levels by electrons at thermal equilibrium. In intrinsic semiconductors, the Fermi level is positioned at the midpoint of the energy gap at absolute zero. When the temperature of the semiconductor increases, thermal energy excites some electrons from the valence band to the conduction band, creating electron-hole pairs (EHPs). The creation of EHPs enables conduction because electrons can move freely in the conduction band and holes can act like positive charge carriers in the valence band.

The intrinsic carrier concentration, denoted as n_i, is the number of free electrons or holes in a pure semiconductor at thermal equilibrium. It is a temperature-dependent value and can be expressed by the formula:

Where B is a material constant, T is the temperature, E_g is the band gap energy, and k is the Boltzmann constant.

At any temperature above absolute zero, EHPs are generated at a rate g_i, and they recombine at a rate r_i. For the semiconductor to maintain thermal equilibrium, these rates must be equal. The recombination rate is proportional to the product of the electron (n₀) and hole (p₀) concentrations, described by:

where α_r is the recombination coefficient.

Intrinsic semiconductors can be altered to become extrinsic semiconductors by doping, which introduces impurities to change the material's electrical properties. Doping intrinsic semiconductors with pentavalent atoms creates N-type materials by adding free electrons. Conversely, trivalent dopants yield P-type materials with prevalent holes, shifting the Fermi level towards the valence band, thus modifying the semiconductor's conductive properties.