LatticeLab catalog

ESE 2180 · Carrier statistics

Fermi Level Visualizer

Doping sets the carrier ratio. Temperature smears occupancy. Together they pull EF — the energy where f(E) = ½ — toward a band edge or back to midgap.

Si-like · Eg = 1.12 eV · Ev = 0 · ħ-free teaching model

1 · Density of states N(E)

2 · Fermi–Dirac f(E)

3 · Carriers n(E), p(E)

The three plots share one energy axis. The orange dashed line is EF — identically f(EF) = ½. Shaded areas in plot 3 show shape (DOS × occupancy), not the absolute n0 on the dashboard.

Live calculation

Set point

ni(T)

Majority

Minority

n0 p0
ni2
EF
Ei (midgap)
EF − Ei = kT ln(n0/ni)

Cause → effect

Mass-action is the product constraint. Fermi–Dirac is the occupancy curve. EF is the one number that makes them agree with the doping you set.