Energia de Fermi (gás elétrons)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
Fermi Energy is a key concept in condensed matter physics, representing the highest energy level occupied by electrons in a system at absolute zero. This calculator estimates Fermi Energy using the formula EF = (ħ²/2m)(3π²n)^(2/3), where ħ is the reduced Planck constant, m is the electron mass, and n is the electron density. It's used to analyze conductors and electron behavior in solids.
To use the tool, input the electron density (n) in electrons per cubic meter. The formula assumes a non-interacting electron gas, a simplification for real materials. Results should be interpreted cautiously in systems with strong electron interactions or complex structures.
Fermi Energy helps explain electrical and thermal conductivity in metals. It's applied in superconductivity, semiconductor research, and topological materials. More advanced models, like band theory, are required for precise real-world material descriptions.
Frequently asked questions
What units should the electron density (n) be in?
Electron density (n) must be input in electrons per cubic meter (m⁻³) to match the formula's requirements.
How does temperature affect Fermi Energy?
Fermi Energy is calculated for absolute zero. At real temperatures, electron occupation varies thermally, but Fermi Energy remains a fundamental limit.
Is this calculator valid for all materials?
No. The formula assumes an ideal electron gas and is most accurate for simple metals. Complex materials require advanced models like band theory.
How to convert electron density from atoms/cm³ to m⁻³?
Multiply the value in atoms/cm³ by 1 × 10⁶ to get m⁻³ (1 m³ = 10⁶ cm³).