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The Fermi-Dirac function is represented by an S-shaped curve indicating the probability of an energy state being occupied by an electron at a given temperature. The Fermi level is the energy level at which there is a fifty percent chance of finding an electron, and it is positioned between the lower-energy valence band and the higher-energy conduction band.
At absolute zero temperature, electrons fill all energy states up to the Fermi level, leaving upper states empty. As the temperature rises,...

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 contact of metal and semiconductor can lead to the formation of a junction with either Schottky or Ohmic behavior.
Schottky Barriers
Schottky barriers arise when a metal with a work function (Φm) contacts a semiconductor with a different work function (Φs). Initially, electrons transfer until the Fermi levels of the metal and semiconductor align at equilibrium. For instance, if Φm > Φs, the semiconductor Fermi level is higher than the metal's before contact. The...

The vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
Electron affinity in semiconductors refers to the energy gap between the minimum of its conduction band and the vacuum level and it is a critical parameter in determining how easily a semiconductor can accept additional electrons.
The work...

There is variation in the electrical conductivity of materials - metals, semiconductors, and insulators that are showcased with the help of the energy band diagrams.
Metals such as copper (Cu), zinc (Zn), or lead (Pb) have low resistivity and feature conduction bands that are either not fully occupied or overlap with the valence band, making a bandgap non-existent. This allows electrons in the highest energy levels of the valence band to easily transition to the conduction band upon gaining...

Schottky defects arise when some lattice points in a crystal, such as those in NaCl, remain unoccupied, creating lattice vacancies without disturbing the overall electrical neutrality of the crystal. This defect is common in ionic crystals where the positive and negative ions are similar in size, as seen in sodium chloride and cesium chloride. The presence of Schottky defects enables the crystal to conduct electricity to a small extent through an ionic mechanism. Electric fields cause nearby...