1. What is the Condensed Electron Function?

The Fermi-Dirac distribution describes the probability that an energy state (E) is occupied by an electron in a system at thermal equilibrium. It's fundamental in condensed matter physics and semiconductor theory.

2. How Does the Calculator Work?

The calculator uses the Fermi-Dirac distribution formula:

Where:

• \( E \) — Energy of the state (eV)
• \( \mu \) — Chemical potential (eV)
• \( k_B \) — Boltzmann constant (8.617×10⁻⁵ eV/K)
• \( T \) — Absolute temperature (K)

Explanation: The function gives the probability (0 to 1) that a quantum state at energy E is occupied at temperature T.

3. Importance of Fermi-Dirac Distribution

Details: This distribution is crucial for understanding electrical conductivity, thermal properties, and quantum behavior of electrons in solids.

4. Using the Calculator

Tips: Enter energy and chemical potential in electron volts (eV), temperature in Kelvin (K). Temperature must be > 0K.

5. Frequently Asked Questions (FAQ)

Q1: What does f(E) = 0.5 mean?
A: At E = μ, the occupation probability is exactly 0.5, regardless of temperature.

Q2: How does temperature affect the distribution?
A: Higher temperatures "smear out" the distribution around the chemical potential.

Q3: What's the classical limit of this function?
A: At high T or low density, it approaches the Maxwell-Boltzmann distribution.

Q4: What is the chemical potential?
A: At T=0, it's the Fermi energy - the highest occupied state energy.

Q5: When is this distribution not applicable?
A: For systems not in thermal equilibrium or with strong interactions between particles.