Fermi-Dirac integral

The Fermi-Dirac integral is a mathematical function used to describe the distribution of particles, like electrons, in materials at certain energies and temperatures. It accounts for the fact that electrons are indistinguishable and follow the Pauli exclusion principle, meaning no two can occupy the same state. This integral helps physicists understand how electrons fill energy levels in metals and semiconductors, especially under high-density conditions. It’s essential for predicting electrical, thermal, and quantum properties of materials, bridging quantum mechanics with practical applications in electronics and condensed matter physics.