Bayesian Analysis of an Excitonic Absorption Spectrum in a Cu sub( 2)O Thin Film Sandwiched by Paired MgO Plates

We analyzed the absorption spectrum of a Cu sub( 2)O thin film sandwiched by paired MgO plates with the Metropolis algorithm of Bayesian estimation to estimate the energy shift of a yellow excitonic band gap. In the absorption spectrum, discrete excitonic resonant transitions with homogeneous and inhomogeneous widths are superimposed upon the tail parts of excitonic continuum and band-to-band absorption bands. On the basis of the Metropolis samplings with 2.5 million steps after sufficient burn-in steps, the spectral parameters of the excitonic resonant transitions can be estimated satisfactorily with a high degree of accuracy. In particular, we demonstrated that the yellow excitonic band gap in the Cu sub( 2)O thin film shifts to the lower energy side than that of Cu sub( 2)O bulk crystals. This result is consistent with the stress relaxation model for such Cu sub( 2)O thin films, which was reported in Eur. Phys. J. B 86, 194 (2013).