Near-infrared quantum cutting in Ho3+, Yb3+-codoped BaGdF5 nanoparticles via first- and second-order energy transfers

Infrared quantum cutting involving Yb3+ 950–1,000 nm (2 F5/2 → 2 F7/2) and Ho3+ 1,007 nm (5S2,5F4 → 5I6) as well as 1,180 nm (5I6 → 5I8) emissions is achieved in BaGdF5: Ho3+, Yb3+ nanoparticles which are synthesized by a facile hydrothermal route. The mechanisms through first- and second-order energy transfers were analyzed by the dependence of Yb3+ doping concentration on the visible and infrared emissions, decay lifetime curves of the 5 F5 → 5I8, 5S2/5F4 → 5I8, and 5 F3 → 5I8 of Ho3+, in which a back energy transfer from Yb3+ to Ho3+ is first proposed to interpret the spectral characteristics. A modified calculation equation for quantum efficiency of Yb3+-Ho3+ couple by exciting at 450 nm was presented according to the quantum cutting mechanism. Overall, the excellent luminescence properties of BaGdF5: Ho3+, Yb3+ near-infrared quantum cutting nanoparticles could explore an interesting approach to maximize the performance of solar cells.


Background
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 downconverts 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 Ln 3+ ions are generally codoped with Yb 3+ in the hosts, and it is commonly demonstrated in Ln 3+ -Yb 3+ (Ln = Tb, Tm, Pr, Er, Nd, and Ho) couple-codoped materials [6]. Generally speaking, there are two mechanisms involved in the NIR QC in Ln 3+ -Yb 3+ 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 Yb 3+ 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 Ln 3+ ions. Cubic BaGdF 5 , a tri-fluoride compound, has a wide bandgap and low phonon energy which is a suitable NIR QC matrix [15]. Meanwhile, Ho 3+ ion has favorable metastable energy levels and considerable energy match between Yb 3+ and Ho 3+ , so Ho 3+ /Yb 3+ couple could be a good choice in NIR QC investigation. However, NIR QC reports in Ho 3+ /Yb 3+ -codoped materials are limited in NaYF 4 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 BaGdF 5 : Ho 3+ , Yb 3+ nanoparticles with different Yb 3+ concentrations by a trisodium citrate (Cit 3− )-assisted hydrothermal method, which is less finicky, low-cost, and effective for large-scale production. Furthermore, NIR QC via first-and secondorder resonant ET processes and a back ET from Yb 3+ to Ho 3+ in BaGdF 5 : Ho 3+ , Yb 3+ nanoparticles is firstly investigated, and the corresponding quantum efficiencies (QE) are also calculated.

Methods
BaGd 1 − 0.01 − x% Yb x% Ho 0.01 F 5 (0 ≤ x ≤ 20) samples were prepared by a hydrothermal process. Firstly, 1 mmol rare earth oxides Gd 2 O 3 , Yb 2 O 3 , and Ho 2 O 3 were dissolved in dilute HNO 3 solution, and the residual HNO 3 was removed by heating and evaporation, resulting in the formation of clear solution of RE(NO 3 ) 3 (RE = Gd, Yb, Ho). Cit 3− aqueous solution was added into the Ba(NO 3 ) 2 ·2H 2 O and RE(NO 3 ) 3 solution to form metal-Cit complex. After vigorous stirring for 30 min, aqueous solution containing 4 mmol NaBF 4 was poured into the above solution, and pH value of the mixture was adjusted to about 4.5 by adding diluted HCl or NH 3 ·H 2 O. After additional agitation for 15 min, the asobtained 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.

Characterizaton
The XRD patterns were obtained on Rigaku D/max-2400 powder diffractometer (Rigaku Corporation, Tokyo, Japan) using Cu Kα radiation (1.5405 Å) at 40 kV and 60 mA. The size, shape, and structure of the as-prepared samples were characterized by SEM (S-4800). Emission and excitation measurements were performed using an Edinburgh Instruments' FLS920 fluorescence spectrometer (Livingston, UK), and a 0.3-m double excitation monochromator and two emission monochromators to record the emission spectra in the wavelength range of 200-850 nm (with a Hamamatsu R928 photomultiplier tube, Bridgewater, NJ, USA) or in the wavelength range of 850-1650 nm (with a liquid nitrogen-cooled Hamamatsu R5509-72 PMT). All spectra were measured at room temperature.

Results and discussion
The XRD patterns and representative SEM photograph of BaGd 1 − 0.01 − x% Yb x% Ho 0.01 F 5 (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 purephase BaGdF 5 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 BaGdF 5 : 1% Ho 3+ , x% Yb 3+ (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 Ho 3+ is at 450 nm, corresponding to the 5 I 8 → 5 G 6 , 5 F 1 transition of Ho 3+ ions. Figure 2b shows the emission peaks of Ho 3+ at about 483, 545, 651, and 747 nm which are attributed to the 5 F 3 → 5 I 8 , 5 F 4 / 5 S 2 → 5 I 8 , 5 F 5 → 5 I 8 , and 5 S 2 → 5 I 7 transitions of Ho 3+ , respectively [16,17]. It is worthwhile pointing out that both the excitation and emission intensities decrease with increasing Yb 3+ concentration, which may be due to the Ho 3+ transferring its energy to the Yb 3+ , but it needs more evidence to testify this guess, which will be discussed as follows: PLE spectra of BaGdF 5 : 1% Ho 3+ , x% Yb 3+ (0 ≤ x ≤ 20) nanoparticles are also recorded by monitoring the characteristic emission of Yb 3+ at 980 nm (Figure 3a). The presence of Ho 3+ excitation in the PLE spectra of BaGdF 5 : 1% Ho 3+ , x% Yb 3+ by monitoring the characteristic emission of Yb 3+ gives an evidence to the energy transfer from Ho 3+ to Yb 3+ . 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 Yb 3+ and 5 S 2 , 5 F 4 → 5 I 6 transition of Ho 3+ ions, has also been observed under the Ho 3+ excitation at 450 nm (as shown in Figure 3b). This is another evidence of ET from Ho 3+ to Yb 3+ . Simultaneously, the 1,180-nm emission due to 5 I 6 → 5 I 8 transition of Ho 3+ is also detected. NIR emission intensity of Yb 3+ intensifies rapidly with increasing Yb 3+ concentration from 0 to 15 mol%. Whereas, 1,180-nm emission intensity of Ho 3+ enhances with increasing Yb 3+ concentration even when Yb 3+ concentration is 20 mol%. That is to say, the NIR emission quenching concentration of Ho 3+ is higher than that of Yb 3+ . The reasons for the above phenomenon will be discussed later.
For excitation at 450 nm, there are three possible ET processes from Ho 3+ to Yb 3+ responsible for the NIR emission of Yb 3+ ions, in view of energy levels of Ho 3+ xand Yb 3+ ions (shown in Figure 4) [18,19].
According to the above mechanisms, the emission of Ho 3+ : 5 I 6 → 5 I 8 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 Yb 3+ content due to its intrinsic nature, but at a relatively high Yb 3+ concentration of 15 mol%, the CET process could become efficient, and this efficiency (η CET ) can be estimated by Equation 1: [11] where I denotes the decay intensity, and x% Yb denotes the Yb 3+ contents. To determine the η CET for BaGdF 5 : 1% Ho 3+ , x% Yb 3+ (0 ≤ x ≤ 15) nanoparticles, a series of  decay curves of Ho 3+ : 5 F 3 → 5 I 8 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: 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: 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 BaGdF 5 : 1% Ho 3+ , 15% Yb 3+ . In this case, the number of the remaining photons relaxed to the  lower energy levels than 5 F 3 to give other emission is very small. Besides, double-exponential decay curves of Ho 3+ : 5 F 4 , 5 S 2 → 5 I 8 emission at 545 nm as well as 5 F 5 → 5 I 8 emission at 651 nm with logarithmic coordinates are plotted with various Yb 3+ 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 Yb 3+ : 2 F 5/2 → 2 F 7/2 emission should demonstrate stronger intensity and higher quenching concentration than those of Ho 3+ : 5 I 6 → 5 I 8 emission.
However, the NIR emission spectra in Figure 3 show distinct results. Based on these experimental   Figure 5d, since the back ET phenomenon widely exists in UC for Yb 3+ , Ho 3+ -doped materials [20,21]. This ET not only increases the Ho 3+ : 5 F 5 → 5 I 8 emission intensity but also reduces the Yb 3+ : 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 Yb 3+ and the residual excited Ho 3+ 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]: where the last two terms stand for the extra QEs for CTE and CR1 processes, respectively. The total η QE for BaGdF 5 : 15% Yb 3+ , 1% Ho 3+ is calculated to 192% by this formulation. This so high QE partly results from the Ho 3+ 5 I 6 -5 I 8 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.