Home▸Physics & Mechanics▸Fermi-Dirac Statistics: Why Electrons Refuse to Pile Into the Same State

🧊 Fermi-Dirac Statistics: Why Electrons Refuse to Pile Into the Same State

Explore Fermi-Dirac statistics, the quantum rule that governs how electrons and other fermions fill energy states, and see how it explains metals, white dwarfs, and semiconductors.

Physics & Mechanics3DModerate60 FPS

This simulation shows how the Fermi-Dirac occupation probability changes with energy and temperature, from a sharp step at absolute zero to a smoothed S-shaped curve at higher temperatures.

🔬 What It Demonstrates

This simulation shows how the Fermi-Dirac occupation probability changes with energy and temperature, from a sharp step at absolute zero to a smoothed S-shaped curve at higher temperatures.

🎮 How to Use

Adjust the temperature and Fermi energy sliders and watch how the occupation curve reshapes around the Fermi level in real time.

💡 Did You Know?

The Fermi energy of a typical metal corresponds to a temperature of tens of thousands of kelvin, which is why the electrons in a metal at room temperature are still overwhelmingly packed into their zero-temperature arrangement.

⚙ Under the hood

Explore Fermi-Dirac statistics, the quantum rule that governs how electrons and other fermions fill energy states, and see how it explains metals, white dwarfs, and semiconductors.

fermi-diracquantum-mechanicspauli-exclusionelectronssolid-state-physicsstatistical-mechanicswhite-dwarfssemiconductors

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install