Shockley–Queisser Photon Utilization Limit (2D)

Every solar cell is capped by a hard spectral ceiling long before any engineering losses come into play: a photon carrying more energy than the semiconductor's bandgap wastes the excess as heat, and a photon carrying less energy is not absorbed at all. This 2D cross-section simulator renders individual sunlight photons — sampled from a real Planck blackbody spectrum for the Sun's surface temperature — as they stream toward a semiconductor slab, colored by their fate: absorbed and converted, absorbed but partly thermalized, or transmitted and lost. A live particle-counting efficiency measurement runs alongside a closed-form numerical integration of the Shockley 1961 "ultimate efficiency" formula, so sweeping the bandgap slider shows both the simulated and theoretical curves converge on the same ~44% peak near 1.1 eV — the same spectral sweet spot silicon happens to sit at.