Fig. 5: Comparing the photon-cutting potential of different host materials.

a Fitted Tm³⁺-to-Yb³⁺ cross-relaxation strength C_xr (see Eq. (2)) for the different host materials, plotted as a function of the maximum phonon energy of the host. b Corresponding intrinsic decay rates of the ¹G₄ level. c Calculated maximum quantum efficiency of YBO₃:Tm³⁺,Yb³⁺ as a function of Yb³⁺ concentration based on our phonon-assisted cross-relaxation model. We count only emission that can be absorbed by crystalline Si, i.e., visible emission from the Tm^{3+ 1}G₄ level (blue-shaded area) and near-infrared emission from Yb³⁺ (red-shaded area), and assume zero nonradiative decay from the Yb^{3+ 2}F_5/2 level. d Same, but for YAG:Tm³⁺,Yb³⁺. e Same, but for Y₂O₃:Tm³⁺,Yb³⁺. f Same, but for NaYF₄:Tm³⁺,Yb³⁺ and using our model for cooperative energy transfer. Of the four materials studied, only NaYF₄:Tm³⁺,Yb³⁺ is a photon-cutting phosphor that can produce two near-infrared photons (useful for crystalline Si) from a single blue photon absorption event