Semiconductor Density of States & Fermi–Dirac Occupation (2D)

This 2D companion builds carrier density the way a solid-state physics course actually derives it: a parabolic-band density of states g(E) is integrated numerically against the real Fermi–Dirac occupation function f(E,T), and the result is checked live against the standard Boltzmann mass-action-law estimate. Four materials, three doping regimes, a dopant-concentration slider and a temperature slider all feed directly into both the plotted curves and the two independently computed carrier densities, so you can watch the numeric integral track — or deliberately depart from — the analytic approximation as doping pushes the Fermi level toward degeneracy.