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Fermi–Dirac Occupation Calculator — result sheet
Estimate the equilibrium occupation probability of an energy state from its energy, Fermi level, and temperature.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: f(E) = 1/[exp((E−EF)/(kBT)) + 1], with kB = 8.617333262×10⁻⁵ eV/K.
The result is the Fermi–Dirac probability for a single state in thermal equilibrium. It is one half when the state energy equals the Fermi level and transitions become sharper as temperature falls.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- State energy — eV; minimum -1000; maximum 1000
- Fermi level — eV; minimum -1000; maximum 1000
- Absolute temperature — K; minimum 1.0E-6; maximum 1000000
Worked example
| Input | Value |
|---|---|
| State energy | 0.1 |
| Fermi level | 0 |
| Absolute temperature | 300 |
The state occupation probability is about 0.0205, or 2.05%.
Assumptions and limits
- Energy and Fermi level are referenced to the same zero and are expressed in electron-volts.
- The system is in thermal equilibrium and the single-state occupation model is used.
- Density of states, band structure, doping, carrier transport, and device behavior are not inferred.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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