Calculation of up-conversion photoluminescence in Er3+ ions near noble-metal nanoparticles
In conventional silicon solar cells, photons with energies lower than the silicon band gap (1.12 eV) are not absorbed in the silicon layer. However, the near-infrared portion of the solar spectrum may still be able to contribute to photocurrent generation if use can be made of up-conversion processes that transform two or more infrared photons into a photon of sufficient energy to be absorbed in silicon. One possible material in which up-conversion processes occur are rare-earth ions such as Er3+. It has recently been shown that up-conversion in such ions could be enhanced by optical near-field coupling to metal nanoparticles in a highly controlled geometry. However, potential photovoltaic applications of the upconversion enhancement will certainly be characterized by different geometric arrangements, with random distances between ions and nanoparticles. Whether or not an overall enhancement of the up-conversion efficiency may be expected under such realistic conditions is an open question. In this work, we address an important aspect of this question, namely the particle-induced enhancement of the optical excitation rate in the rare-earth ions. Our model calculations show that the excitation rate in Er 3+ ions can be enhanced using spherical gold nanoparticles. The model includes random distances between ions and nanoparticles, as well as random polarizations of the exciting light. The enhancement of the rate of excitation of the fundamental transition results in increases of the up-conversion rate by up to 20% for an excitation wavelength of 1523 nm, provided that photoluminescence-quenching effects due to nonradiative relaxation in the metal can be neglected.