Fermi Level Calculator
Compute Fermi energy E_F for a 3D electron gas.
How to Use This Calculator
1
Enter electron density
Provide n in m⁻³ (e.g., ~10²⁹ for typical metals).
2
Set effective mass
Use m*/mₑ ≈ 1 unless material-specific values are known.
3
Calculate
E_F will be shown in electronvolts (eV).
Formula
E_F = ħ² (3π²n)^0.6666666666666666 / (2 m*)
Example: n = 8.5×10²⁸ m⁻³, m* = mₑ → E_F ≈ a few eV
About Fermi Level Calculator
Estimates the Fermi energy using a free-electron-like model. For semiconductors or complex band structures, specialized models are required.
Frequently Asked Questions
Is this valid for semiconductors?
Not directly. This model fits metals; semiconductors need different relations.
What is effective mass?
An empirical parameter capturing band-structure effects on electron inertia.