Quantitative mechanism of 1550 nm-excited up-conversion in the combustion-synthesized Ba–Na–Y–F:Er³⁺ phosphor: separating excited-state absorption, energy-transfer up-conversion, and cross-relaxation across the Er³⁺/Y³⁺ ratio

Er³⁺-doped barium–sodium–yttrium fluoride phosphors made by low-temperature combustion synthesis show green-favored up-conversion when Y³⁺-rich and red-favored up-conversion when Er³⁺-rich under 1550 nm excitation, but the mechanism behind this concentration law has only been argued qualitatively. The open problem is to determine quantitatively how excited-state absorption, energy-transfer up-conversion, and Er³⁺–Er³⁺ cross-relaxation jointly populate the green and red emitting levels as the Er³⁺/Y³⁺ ratio varies, what the operative cross-relaxation channels and rates are, and what the Y³⁺ ion physically does, yielding a quantitative mechanism assignment that accounts for the material's measured concentration- and power-dependent green-to-red emission behavior.

Background

Photon up-conversion (UC) in trivalent lanthanides converts two or more low-energy near-infrared photons into one visible photon through long-lived, sharply spaced 4f excited states. Erbium(III) is unusual in absorbing directly at 1550 nm — the telecommunications window — via the ground-state transition $^4$I$_{15/2}\to{}^4$I$_{13/2}$. The visible-emitting levels can then be reached by excited-state absorption (ESA), where the same ion sequentially absorbs further 1550 nm photons up its level ladder, or by energy-transfer up-conversion (ETU), where two neighboring Er$^{3+}$ ions both stored in $^4$I$_{13/2}$ exchange energy so that one is promoted toward the green-emitting levels ($^2$H$_{11/2}$, $^4$S$_{3/2}$) or red-emitting level ($^4$F$_{9/2}$) while the other relaxes. At higher Er$^{3+}$ content, cross relaxation — non-radiative ion–ion energy exchange between neighboring Er$^{3+}$ ions — redistributes population among these levels, typically feeding the red channel. Fluoride hosts are preferred because their low maximum phonon energy (roughly 350 cm$^{-1}$ for rare-earth fluorides) suppresses multiphonon relaxation, the non-radiative decay by lattice vibrations that would otherwise deplete the energy-storing levels. The standard diagnostics are the log-log slope $n$ of emission intensity versus excitation power density (the apparent photon order) and time-resolved rise/decay curves: a delayed rise of visible emission after a pulsed excitation is the hallmark of ETU feeding, while a prompt rise indicates direct ESA. This disentangling framework was established quantitatively decades ago in other Er$^{3+}$ systems: ESA and energy transfer were separated in Er$^{3+}$:LiYF$_4$ crystals (Rubin et al., 1986), ESA versus ETU mechanisms were modeled with rate equations in Er$^{3+}$-doped glasses (Zou and Izumitani, 1993), and their competition was resolved as a function of temperature in Er$^{3+}$ oxyfluoride glass ceramics (Sarakovskis et al., 2010). The present question concerns a specific powder phosphor, barium–natrium–yttrium fluoride doped with Er$^{3+}$, prepared by low-temperature combustion synthesis (LCS), a solution-combustion route yielding ultrafine fluoride powders; its infrared-to-visible UC was first reported by Lu et al. (2011). The source paper (Gong et al., 2018) used orthogonal design of the batch formula, X-ray diffraction and scanning electron microscopy for phase and morphology, and a matrix of Er$^{3+}$/Y$^{3+}$ concentrations, finding that Y$^{3+}$ enrichment favors green UC while Er$^{3+}$ enrichment favors red UC under 1550 nm excitation. The mechanistic interpretation reported for this concentration law — Y$^{3+}$ acting through host phonon energy and population dynamics, Er$^{3+}$ through cross relaxation — remained qualitative rather than a rate-level decomposition, leaving the exact ESA-versus-ETU contributions and the mechanism of 1550-nm-sensitive rare-earth-doped UC materials open.

Problem Statement

For the low-temperature-combustion-synthesized fluoride phosphor $\mathrm{Ba_xNa_yY_zF_{2x+y+3z+3m}:Er^{3+}_m}$ of Gong et al. (2018) under 1550 nm excitation, determine quantitatively the up-conversion mechanism across the Er$^{3+}$/Y$^{3+}$ composition series of samples reported in that paper through its orthogonal batch-formula design: (i) the relative contributions of excited-state absorption and energy-transfer up-conversion to populating the green-emitting levels ($^2$H$_{11/2}$, $^4$S$_{3/2}$) and the red-emitting level ($^4$F$_{9/2}$), as functions of excitation power density and dopant concentration; (ii) the operative Er$^{3+}$–Er$^{3+}$ cross-relaxation channels and their rates; and (iii) the physical origin of the Y$^{3+}$ dilution effect. These three parts are all required; the task is resolved only when they are delivered together as one account that reproduces the composition series' measured green-to-red emission ratio as a function of excitation power density and dopant concentration, and no proper subset of (i)–(iii), nor a qualitative trend-level narrative alone, resolves it. The goal is a quantitative mechanism assignment for this material that accounts for its measured concentration- and power-dependent green-to-red emission behavior, replacing the source's qualitative interpretation; the choice of supporting evidence (existing or newly acquired spectroscopic data) and of model formalism is not prescribed.

References

1. Xiaomeng Gong, Qiushuang Zhao, Xiaoyun Mi, Liping Lu, 'Effect of the ratio of Er3+ to Y3+ on up-conversion emission properties of BaxNayYzF2x+y+3z+3m:Er3+m under 1550 nm excitation', Applied Physics A 124 (2018), article 94. DOI: 10.1007/s00339-017-1513-1, https://doi.org/10.1007/s00339-017-1513-1
2. Liping Lu, Xiyan Zhang, Zhaohui Bai, Xiaochun Wang, 'Infrared-to-visible upconversion luminescence of Er3+ doped barium–natrium–yttrium–fluoride phosphor', Journal of Luminescence 131 (2011), 2372–2376. DOI: 10.1016/j.jlumin.2011.06.002, https://doi.org/10.1016/j.jlumin.2011.06.002
3. Feng Hu, Qian Wan, Liping Lu, Haiying Sun, Xiyan Zhang, Zhaohui Bai, Xiaoyun Mi, 'Enhanced up-conversion emission in Er3+-doped barium–natrium–yttrium–fluoride phosphors by alkali ion introduction under 1550 nm excitation', CrystEngComm 23 (2021), 5601–5608. DOI: 10.1039/d1ce00695a, https://doi.org/10.1039/d1ce00695a
4. Feng Hu, Liping Lu, Bohan Lei, Lin Ning, Haiying Sun, Xiyan Zhang, Zhaohui Bai, Xiaoyun Mi, 'Enhanced up-conversion emission of fluoride phosphor in the dual-fuel system under 1550 nm excitation', Optics & Laser Technology 159 (2023), 108983. DOI: 10.1016/j.optlastec.2022.108983, https://doi.org/10.1016/j.optlastec.2022.108983
5. Yangyang Zhang, Zhengce An, Liping Lu, Xiaoyun Mi, 'Controlling Er3+ multiphoton upconversion by synergistically regulating energy transfer and cross-relaxation for optical anti-counterfeiting', Physical Chemistry Chemical Physics 27 (2025), 20143–20153. DOI: 10.1039/d5cp02682b, https://doi.org/10.1039/d5cp02682b
6. J. Rubin, A. Brenier, R. Moncorgé, C. Pedrini, 'Excited-state absorption and energy transfer in Er3+ doped LiYF4', Journal of Luminescence 36 (1986), 39–47. DOI: 10.1016/0022-2313(86)90029-3, https://doi.org/10.1016/0022-2313(86)90029-3
7. Xuelu Zou, Teturo Izumitani, 'Spectroscopic properties and mechanisms of excited state absorption and energy transfer upconversion for Er3+-doped glasses', Journal of Non-Crystalline Solids 162 (1993), 68–80. DOI: 10.1016/0022-3093(93)90742-G, https://doi.org/10.1016/0022-3093(93)90742-G
8. A. Sarakovskis, J. Grube, G. Doke, M. Springis, 'Excited state absorption and energy-transfer mechanisms of up-conversion luminescence in Er3+-doped oxyfluoride glass ceramics at different temperatures', Journal of Luminescence 130 (2010), 805–811. DOI: 10.1016/j.jlumin.2009.11.037, https://doi.org/10.1016/j.jlumin.2009.11.037
9. Yufeng Chen, Jiwan Zhang, Yajiao Zhang, Li Wang, 'Synthesis of Er3+-doped hydrocalumite and its strong infrared emissions', Journal of the Iranian Chemical Society 17 (2020), 1933–1944. DOI: 10.1007/s13738-020-01898-y, https://doi.org/10.1007/s13738-020-01898-y
10. Xiaoyong Huang, 'Realizing efficient ultraviolet emission from Er3+-sensitized upconversion nanoparticles under 1550 nm excitation', Science Bulletin 64 (2019), 1295–1297. DOI: 10.1016/j.scib.2019.07.024, https://doi.org/10.1016/j.scib.2019.07.024