Revealing the internal luminescence quantum efficiency of perovskite films via accurate quantification of photon recycling

The internal luminescence quantum efficiency ($Q_\mathrm{i}^\mathrm{lum}$) provides an excellent assessment of the optoelectronic quality of semiconductors. To determine $Q_\mathrm{i}^\mathrm{lum}$ of perovskite films from the experimentally accessible external luminescence quantum efficiency ($Q_\mathrm{e}^\mathrm{lum}$) it is essential to account for photon recycling, and this requires knowledge of the photon escape probability ($p_\mathrm{e}$). Here, we establish an analysis procedure based on a curve fitting model that accurately determines $p_\mathrm{e}$ of perovskite films from photoluminescence (PL) spectra measured with a confocal microscope and an integrating sphere setup. We show that scattering-induced outcoupling of initially-trapped PL explains commonly observed red-shifted and broadened PL spectral shapes and leads to $p_\mathrm{e}$ being more than 10% higher in absolute terms compared to earlier assumptions. Applying our model to CH$_3$NH$_3$PbI$_3$ films with exceptionally high $Q_\mathrm{e}^\mathrm{lum}$ up to 47.4% sets a real benchmark for $Q_\mathrm{i}^\mathrm{lum}$ at $78.0 \pm 0.5\%$, revealing there is beyond a factor of two more scope for reducing non-radiative recombination than previously thought.