Multiphoton Near-Infrared Quantum Splitting of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:msup><mml:mi>Er</mml:mi><mml:mrow><mml:mn>3</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math>

Abstract

The efficiency of single-junction solar cells is limited to about 30% (the Shockley-Queisser limit). Spectral mismatch losses (transparency to low-energy photons, thermalization of high-energy photons) strongly contribute to lowering the maximum efficiency. To reduce thermalization losses, photon splitting is proposed and observed for a variety of lanthanide-doped materials. For ${\mathrm{Er}}^{3+}$, even a one-to-three photon-splitting process has been reported, yielding three IR photons at around 1530 nm following absorption of one blue-green photon. This is especially beneficial for narrow band gap solar cells, such as crystalline $\mathrm{Ge}$. Here, we report on photon splitting for ${\mathrm{Er}}^{3+}$ in ${\mathrm{YVO}}_{4}$. Following absorption in the ${}^{2}{\mathrm{H}}_{11/2}$ and ${}^{4}{\mathrm{S}}_{3/2}$ levels (520--550 nm), efficient cross-relaxation (CR) yields two excited ${\mathrm{Er}}^{3+}$ ions: one in the ${}^{4}{\mathrm{I}}_{9/2}$ state and one in the ${}^{4}{\mathrm{I}}_{13/2}$ state (CR1). A second CR step from the ${}^{4}{\mathrm{I}}_{9/2}$ state, leaving both ${\mathrm{Er}}^{3+}$ ions in the ${}^{4}{\mathrm{I}}_{13/2}$ excited state (CR2), is crucial in realizing efficient three IR photon splitting. It is demonstrated here that the second step has a low efficiency, as a result of competing fast multiphonon relaxation, ${}^{4}{\mathrm{I}}_{9/2}{\ensuremath{\rightarrow}}^{4}{\mathrm{I}}_{11/2}$, and a large energy mismatch, which makes the CR2 step thermally activated. Based on experiments and theory, a maximum quantum efficiency of 170% is calculated for IR emission, following blue-green excitation in ${\mathrm{YVO}}_{4}:{\mathrm{Er}}^{3+}$. An outlook is presented for three-photon splitting in low-phonon-energy hosts, where nonradiative multiphonon relaxation is suppressed. The anti-Stokes nature of the second CR step makes three-photon splitting unlikely and prevents the realization of IR quantum yields above 200%.

Topics & Concepts