Lanthanide (Ln) ions could exhibit both efficient upconversion (UC) and downconversion (DC) emission properties 1 , where the UC process converts low-energy light, usually near infrared (NIR) or infrared, to higher energies, ultraviolet or visible, via multiple absorptions or energy transfers (ETs). In contrast, DC process is the conversion of higher-energy photons into lower-energy photons 2 . For the time being, DC of NIR luminescence (i.e., NIR quantum cutting (QC)), which down-converts one incident UV-blue photon into two NIR photons (approximately 1,000 nm), has attracted more attention for their application in silicon solar cells by modifying the incident light wavelength 3 .

As it is well known to us that the solar spectrum and the bandgap energy of silicon semiconductor do not match each other, thus photons with energy lower than the bandgap could not be absorbed, while for photons with energy larger than the bandgap, the excess energy is lost by thermalization of hot charge carriers 4 . Take these sources of energy loss into account for the solar spectrum; the maximum energy efficiency is 30% only for a crystalline Si solar cell with a bandgap of 1.12 eV 3 . Considering this, if the conversion of one UV or visible photon into two NIR photons with energies about 1.12 eV is realized through QC in a silicon solar cell, the energy loss related to thermalization of hot charge carriers can be reduced, and the solar cell efficiency will be enhanced greatly to satisfy the application requirement 5 .

To obtain high NIR QC efficiency, other Ln³⁺ ions are generally codoped with Yb³⁺ in the hosts, and it is commonly demonstrated in Ln³⁺-Yb³⁺ (Ln = Tb, Tm, Pr, Er, Nd, and Ho) couple-codoped materials 6 . Generally speaking, there are two mechanisms involved in the NIR QC in Ln³⁺-Yb³⁺ couple 5 : one is second-order cooperation of energy transfer (CET) based on one donor and two acceptor ions, and the other is first-order resonance energy transfer (ET). Nevertheless, CET process is not as efficient as resonance ET 7 8 9 , but high CET efficiency would be realized at high Yb³⁺ concentration. Thus, a NIR QC via resonant first-order ET process seems more favorable for luminescent materials, which requires an intermediate energy level of donor ion to resonantly excite acceptor ions by a two-step ET process. There are many reports about second-order CET 2 10 11 12 13 14 ; however, there are few reports about first- and second-order ETs occurring simultaneously in one research system.

On the other hand, to fulfill the requirements of NIR QC, host materials should have the energy of phonons as low as possible in order to reduce probabilities of multiphonon relaxations between spaced energy levels of Ln³⁺ ions. Cubic BaGdF₅, a tri-fluoride compound, has a wide bandgap and low phonon energy which is a suitable NIR QC matrix 15 . Meanwhile, Ho³⁺ ion has favorable metastable energy levels and considerable energy match between Yb³⁺ and Ho³⁺, so Ho³⁺/Yb³⁺ couple could be a good choice in NIR QC investigation. However, NIR QC reports in Ho³⁺/Yb³⁺-codoped materials are limited in NaYF₄ and glass ceramic 7 9 . In addition, considering NIR nanomaterials is convenient in the practical application of the coating for the solar cells. Herein, we prepared BaGdF₅: Ho³⁺, Yb³⁺ nanoparticles with different Yb³⁺ concentrations by a trisodium citrate (Cit³⁻)-assisted hydrothermal method, which is less finicky, low-cost, and effective for large-scale production. Furthermore, NIR QC via first- and second-order resonant ET processes and a back ET from Yb³⁺ to Ho³⁺ in BaGdF₅: Ho³⁺, Yb³⁺ nanoparticles is firstly investigated, and the corresponding quantum efficiencies (QE) are also calculated.

BaGd_{1 − 0.01 − x%}Yb _x%Ho_0.01 F₅ (0 ≤ x ≤ 20) samples were prepared by a hydrothermal process. Firstly, 1 mmol rare earth oxides Gd₂O₃, Yb₂O₃, and Ho₂O₃ were dissolved in dilute HNO₃ solution, and the residual HNO₃ was removed by heating and evaporation, resulting in the formation of clear solution of RE(NO₃)₃ (RE = Gd, Yb, Ho). Cit³⁻ aqueous solution was added into the Ba(NO₃)₂·2H₂O and RE(NO₃)₃ solution to form metal-Cit complex. After vigorous stirring for 30 min, aqueous solution containing 4 mmol NaBF₄ was poured into the above solution, and pH value of the mixture was adjusted to about 4.5 by adding diluted HCl or NH₃·H₂O. After additional agitation for 15 min, the as-obtained mixed solution was transferred into a 50-ml teflon autoclave, which was tightly sealed and maintained at 180°C for 24 h. As the autoclave was cooled to room temperature naturally, the resulting precipitates were separated via centrifugation, dried in oven at 80°C for 12 h.

The XRD patterns and representative SEM photograph of BaGd_{1 − 0.01 − x%}Yb _x%Ho_0.01 F₅ (0 ≤ x ≤ 20) nanoparticles are shown in Figure 1a, b, respectively. It is obvious that the locations and relative intensities of the diffraction peaks coincide well with the data reported in the JCPDS standard card (no. 24–0098). No additional peaks of other phases were found, indicating that the pure-phase BaGdF₅ is obtained. It can be seen from Figure 1b that the nanoparticles are relatively dispersed with uniform granular morphology and sizes which are about 40 nm.

Photoluminescence excitation (PLE) spectra monitoring at 540 nm and photoluminescence (PL) spectra in the visible region under 450-nm excitation of BaGdF₅: 1% Ho³⁺, x% Yb³⁺ (0 ≤ x ≤ 20) nanoparticles were investigated, as shown in Figure 2a,b, respectively. It is noticed from Figure 2a that the most intense excitation band of Ho³⁺ is at 450 nm, corresponding to the ⁵I₈ → ⁵ G₆, ⁵ F₁ transition of Ho³⁺ ions. Figure 2b shows the emission peaks of Ho³⁺ at about 483, 545, 651, and 747 nm which are attributed to the ⁵ F₃ → ⁵I₈, ⁵ F₄/⁵S₂ → ⁵I₈, ⁵ F₅ → ⁵I₈, and ⁵S₂ → ⁵I₇ transitions of Ho³⁺, respectively 16 17 . It is worthwhile pointing out that both the excitation and emission intensities decrease with increasing Yb³⁺ concentration, which may be due to the Ho³⁺ transferring its energy to the Yb³⁺, but it needs more evidence to testify this guess, which will be discussed as follows:

PLE spectra of BaGdF₅: 1% Ho³⁺, x% Yb³⁺ (0 ≤ x ≤ 20) nanoparticles are also recorded by monitoring the characteristic emission of Yb³⁺ at 980 nm (Figure 3a). The presence of Ho³⁺ excitation in the PLE spectra of BaGdF₅: 1% Ho³⁺, x% Yb³⁺ by monitoring the characteristic emission of Yb³⁺ gives an evidence to the energy transfer from Ho³⁺ to Yb³⁺. Furthermore, it is noteworthy that a broad emission band in the range of 950–1,100 nm, corresponding to the ² F_5/2 → ² F_7/2 transition of Yb³⁺ and ⁵S₂,⁵F₄ → ⁵I₆ transition of Ho³⁺ ions, has also been observed under the Ho³⁺ excitation at 450 nm (as shown in Figure 3b). This is another evidence of ET from Ho³⁺ to Yb³⁺. Simultaneously, the 1,180-nm emission due to ⁵I₆ → ⁵I₈ transition of Ho³⁺ is also detected. NIR emission intensity of Yb³⁺ intensifies rapidly with increasing Yb³⁺ concentration from 0 to 15 mol%. Whereas, 1,180-nm emission intensity of Ho³⁺ enhances with increasing Yb³⁺ concentration even when Yb³⁺ concentration is 20 mol%. That is to say, the NIR emission quenching concentration of Ho³⁺ is higher than that of Yb³⁺. The reasons for the above phenomenon will be discussed later.

For excitation at 450 nm, there are three possible ET processes from Ho³⁺ to Yb³⁺ responsible for the NIR emission of Yb³⁺ ions, in view of energy levels of Ho³⁺ xand Yb³⁺ ions (shown in Figure 4) 18 19 . (1) Ho³⁺: ⁵ F₃ → ⁵I₈ transition is located at approximately twice the energy of the Yb³⁺: ² F_5/2 → ² F_7/2 transition, which in theory can transfer its energy to Yb³⁺ ions through a CET mechanism: Ho³⁺(⁵ F₃) → 2Yb³⁺(² F_5/2) + hν; (2) Ho³⁺ ion could relax from its ⁵S₂, ⁵ F₄ to ⁵I₆ level and then transfer its energy to only one Yb³⁺ ion, which belongs to first-order resonance CR1 process (⁵S₂, ⁵ F₄(Ho) + ² F_7/2(Yb) → ⁵I₆(Ho) + ² F_7/2(Yb) + hν; and (3) similarly, CR2 process: ⁵ F₅(Ho) + ² F_7/2(Yb) → ⁵I₇(Ho) + ² F_7/2 (Yb) + hν.

According to the above mechanisms, the emission of Ho³⁺: ⁵I₆ → ⁵I₈ is mainly followed by the occurrence of CR1 process. Also, as it is well known to us that CET process is not efficient at lower Yb³⁺ content due to its intrinsic nature, but at a relatively high Yb³⁺ concentration of 15 mol%, the CET process could become efficient, and this efficiency (η _CET) can be estimated by Equation 1: 11

η ET = η x % Yb = 1 − ∫ I x % Yb d t ∫ I 0 % Yb d t

where I denotes the decay intensity, and x% Yb denotes the Yb³⁺ contents. To determine the η _CET for BaGdF₅: 1% Ho³⁺, x% Yb³⁺ (0 ≤ x ≤ 15) nanoparticles, a series of decay curves of Ho³⁺: ⁵ F₃ → ⁵I₈ emissions at 486 nm are determined, as shown in Figure 5a. All the decay curves demonstrate double-exponential feature (Table 1), so the decay times can be determined using a curve fitting technique based on the following equation:

I = A 1 exp − t τ 1 + A 2 exp − t τ 2

where I is phosphorescence intensity; A ₁ and A ₂, constants; t, time; and τ ₁ and τ ₂, decay constants deciding the rates for the rapid and the slow exponentially decay components, respectively. The average decay times (τ) can be calculated by the following formula:

< τ > = A 1 τ 1 2 + A 2 τ 2 2 / A 1 τ 1 + A 2 τ 2

Also, the corresponding lifetime values as well as η _CET are calculated, which are summarized in the inset of Figure 5a. Unexpectedly, η _CET is calculated to be as high as 92% in the BaGdF₅: 1% Ho³⁺, 15% Yb³⁺. In this case, the number of the remaining photons relaxed to the lower energy levels than ⁵ F₃ to give other emission is very small. Besides, double-exponential decay curves of Ho³⁺: ⁵ F₄, ⁵S₂ → ⁵I₈ emission at 545 nm as well as ⁵ F₅ → ⁵I₈ emission at 651 nm with logarithmic coordinates are plotted with various Yb³⁺ concentrations in Figure 5b, c, and the highest resonant ET efficiencies for CR1(η _CR1) and CR2(η _CR2) are calculated to be 71% and 69%, respectively, which are also efficient. All the above results just indicate that the Yb³⁺: ² F_5/2 → ² F_7/2 emission should demonstrate stronger intensity and higher quenching concentration than those of Ho³⁺: ⁵I₆ → ⁵I₈ emission.

However, the NIR emission spectra in Figure 3 show distinct results. Based on these experimental results and combining the energy levels of Yb³⁺ and Ho³⁺, we brought up a novelty back ET process from Yb³⁺ to Ho³⁺ (Yb³⁺(² F_5/2) + Ho³⁺(⁵I₈) → Yb³⁺(² F_7/2) + Ho³⁺(⁵I₆) + hν) which may be occurring in the NIR QC system, as shown in the Figure 5d, since the back ET phenomenon widely exists in UC for Yb³⁺, Ho³⁺-doped materials 20 21 . This ET not only increases the Ho³⁺: ⁵ F₅ → ⁵I₈ emission intensity but also reduces the Yb³⁺: ² F_5/2 → ² F_7/2 emission intensity, resulting in the spectral features in Figure 3.

The QE is known to be defined as the ratio of the number of photons emitted to the number of photons that are absorbed. It can be concluded from Figure 5d that the extra photons emitted come only by CET and CR1 process for every phonon absorbed when excited at 450 nm. Therefore, supposing that all the excited Yb³⁺ and the residual excited Ho³⁺ decay radiatively, a modified calculation equation for the total QE (η _QE) when excited at 450 nm can be theoretically expressed as follows according to 11 :

η QE = 1 + η CET + 1 − η CET η CR 1

where the last two terms stand for the extra QEs for CTE and CR1 processes, respectively. The total η _QE for BaGdF₅: 15% Yb³⁺, 1% Ho³⁺ is calculated to 192% by this formulation. This so high QE partly results from the Ho^{3+ 5}I₆ ⁵I₈ emission (1,180 nm), which is useless to enhance the efficiency of Si solar cells, since this emission does not match the spectral response of Si solar cells.

Unlike the common situation that two emitting photons are from the acceptor Yb³⁺ ions, both the donor (Ho³⁺) and the acceptor (Yb³⁺) could emit NIR photons under blue light excitation. The visible emissions decrease with the introduction of the Yb³⁺ ions, while the NIR emissions at 980 nm and 1,180 nm are greatly enhanced. The quenching concentration of Ho³⁺ is higher than that of Yb³⁺. The fluorescence decay lifetimes of ⁵ F₃ → ⁵I₈, ⁵ F₄, ⁵S₂ → ⁵I₈, and ⁵ F₅ → ⁵I₈ emissions of Ho³⁺ donors were recorded and calculated as a function of Yb³⁺ concentration. It could be concluded that NIR emissions are mainly through second- and first-order ET processes: Ho³⁺(⁵ F₃) → 2Yb³⁺(² F_5/2) + hν, Ho³⁺(⁵S₂) + Yb³⁺(² F_7/2) → Ho³⁺(⁵I₆) + Yb³⁺(² F_5/2) + hν by spectra and decay curve analysis. The corresponding QE are calculated to be 192% in BaGdF₅: 1% Ho³⁺, 15% Yb³⁺, so BaGdF₅: Ho³⁺, Yb³⁺ nanoparticles could open up an approach in designing ultra-efficient photonic devices, for the application in low bandgap solar cells and thermo-photovoltaic energy conversion, etc.

The authors declare that they have no competing interests.

LG participated in the design of the study, carried out the total experiments, and performed the result analysis, as well as drafted the manuscript. YhW participated in the design of the study, gave the theoretical and experimental guidance, and made the corrections of manuscript. JZ mainly helped in the experiments and measurements. YzW and PD gave the theoretical and experimental guidance and helped amend the manuscript. All authors read and approved the final manuscript.

LG, JZ, YzW, and PD are all Ph.D. candidates, and YhW is a Distinguished Young Scholar at the Department of Materials Science, School of Physical Science and Technology, Lanzhou University.