Bundle review table

Solar: the cap has an interior maximum

Supplied working report; original verdicts not validated.

Review status: Needs review. This is an archival source note, not a passed proof.

notes.md

# Solar: the cap has an interior maximum

**Claim tested.** "Single-junction solar efficiency is capped by the ratio of band gap to photon energy, producing an optimum gap rather than a monotonic improvement with absorption."

**Design.** Detailed-balance calculation on the ASTM G173 AM1.5G reference spectrum for gaps from 0.50 to 2.60 eV. The cell absorbs every photon above its gap, loses the excess as heat, and re-emits a 300 K blackbody spectrum with chemical potential qV. Short-circuit current, open-circuit voltage, fill factor and maximum power follow. No series resistance, no non-radiative recombination, absorptivity one above the gap and zero below.

**Result.** Efficiency peaks at 33.7% at a gap of 1.34 eV. It is 32.9% at 1.10 eV (silicon's neighbourhood) and 30.5% at 1.60 eV (perovskite's), so neither end of the practical range is the optimum. A secondary local maximum at 1.16 eV comes from water-absorption bands in the reference spectrum; the global maximum is still interior. At the optimum, 30% of the incident energy is lost to below-gap transmission, 23% to thermalisation, 13% to voltage and emission, and 34% is extracted.

**Reading.** The claim is a theorem, not an empirical finding: given the two loss channels, the optimum must be interior. The calculation confirms it and locates it. What measurements can add is how far real devices sit below the bound; nothing here shows that any fabricated cell reaches 33.7%.

**Limits.** Step-function absorptivity, radiative recombination only, one sun, 300 K, and a reference rather than an average outdoor spectrum.

Included code and results