This study aims at a quantitative understanding of the optical spectra taken from bound excitons weakly coupled to phonons in indirect semiconductors, which had been missing for decades. Insights on the properties of excitons bound at neutral acceptor impurities are obtained by analyzing the spectra reported for diamond with appropriate boron doping [Y. Kubo, Appl. Phys. Lett. 114, 132104 (2019)APPLAB0003-695110.1063/1.5089894]. We focus on the mirror symmetry holding between phonon-assisted absorption and luminescence simultaneously regarding energies, linewidths, and intensities. New analytic expressions are proposed to reproduce the spectra of phonon-assisted recombination lines. The detailed analysis reveals the contribution from excited bound-exciton states whose origin is discussed and modeled. Taking them into account improves simulation of the bound-exciton optical spectra in indirect band-gap semiconductors up to a quantitative level.
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