Excitation of Charge Carriers I

The Fermi-Dirac distribution function describes the probability of electrons occupying different states or levels of energy, when the material is at thermal equilibrium.  Thermal equilibrium means that no extra energy is included from electrical biasing, light absorption, or heat.

The Fermi level is the energy level where the probability of electrons occupying that level is 50%.  The Fermi level (E_F in the diagram below) is also known as the total chemical potential of an electron.  The Fermi level of a metal can be easily seen due to its single continuous electronic band, but for a semiconductor, the Fermi level lies in the forbidden band gap between the valence and conduction band where no electrons can occupy.  Hence, at a temperature of zero Kelvin, all electrons will occupy the valence band.  At higher temperatures, some electrons will occupy the conduction band.  There will be more electrons in the conduction band as temperature increases, so heat is one way to increase a semiconductor's conductivity.

Besides heat or thermal energy, there are another 2 ways to excite electrons from the valence band to the conduction band: using doping, and using light energy.

Pure semiconductor materials without impurities are called intrinsic, meaning that the density of each mobile carrier, the electrons and holes, are the same.  Doping means the inclusion of impurities in semiconductor materials intentionally, which increases the electrons or holes drastically.  For example, if we dope silicon with Phosphorus, a V-element in the periodic table, 4 of the valence electrons in phosphorus will be bonded to silicon, while the fifth valence electron will become a free electron that is easily excited to the conduction band.

Correspondingly, the bonded fixed phosphorus atom will become positively charged after losing its electron.  This is called n-doping, where electrons are the majority mobile charge carriers due to its higher density.  The minority mobile charge carriers are the holes.  In an electronic band diagram, Phophorus atoms are represented by extra donor states which lie in the forbidden band gap of silicon, close to the conduction band.  Hence, less energy is required to excite electrons from the donor state to the conduction band.  This usually happens at room temperatures.  The Fermi level will also be closer to the conduction band.



Reference:
2.3.1 Excitation of Charge Carriers I, Delft University of Technology, https://www.youtube.com/watch?v=LxRp0YGSWqw