Shockley-Queisser Limit Calculator (Bandgap Thermodynamic Efficiency)

Published by William Shockley and Hans-Walter Queisser in 1961, the limit calculates the maximum possible efficiency of a single-junction solar cell using detailed balance.

The theoretical ceiling peaks at approximately 33.7% for an optimal bandgap of ~1.34 eV under the AM 1.5G solar spectrum.

Two fundamental loss mechanisms govern the limit:

1. Transmission Loss: Photons with energy less than the bandgap (hν < Eg) pass straight through without absorption.

2. Thermalization Loss: Photons with energy greater than the bandgap (hν > Eg) absorb, but the excess energy is rapidly lost as heat (lattice phonons) as the electron relaxes to the band edge.

Silicon (1.12 eV) has a theoretical limit of ~29.4% (practical record: 26.8%).

GaAs (1.42 eV) has a limit of ~33.5% (practical record: 29.1%).

Exceeding this limit requires multijunction tandem stacks, hot-carrier harvesting, or optical solar concentrators.

• Bandgap selection: High bandgap reduces thermalization but increases transmission loss; optimal bandgap balances both.

• Assessing new photovoltaic absorber materials (perovskites, quantum dots, organic photovoltaics).
• Setting research targets for commercial solar cell architectures.

• Applies strictly to single p-n junction devices at 1-sun illumination without optical concentration.