Experiment 4
Fermi-Dirac Statistics and the Free Electron Model
Visualize the Fermi-Dirac distribution function and its temperature dependence in metals and semiconductors.
Simulation Controls
Key Equations
Fermi-Dirac Distribution:
f(E) = 1 / [exp((E-EF)/kBT) + 1]
Free Electron DOS (3D):
g(E) ∝ √E
Fermi-Dirac Function and DOS
Occupied Electron Distribution
Task: Temperature Effects
Observe the step function at T = 1 K. As you heat the gas to 5000 K, note the "smearing" of the distribution around EF. What fraction of electrons are actually excited?
Teaching Connection
Use the "water in a glass" analogy for EF. The surface ripples are like thermal excitations. This visualization helps students understand why only electrons near EF contribute to heat capacity.
Reflection Questions
- What is the value of f(E) exactly at E = EF for any temperature?
- In a semiconductor, where is EF located relative to the band gap?
- Why do electrons have kinetic energy even at absolute zero (T = 0 K)?