1. Introduction

Solar energy is very abundant. However there is a great disparity between its utilization and reserves, due to the fact that solar cells have high cost and low efficiency [1,2]. The largest question faced by solar cell photovoltaic equipment is that energy conversion must travel across the entire solar spectrum from ultraviolet, visible to near-infrared. Solar cells must possess high conversion efficiency throughout the entire solar spectrum. At near-infrared, opto-electricity conversion is limited by the energy band-gap Eg of crystalline and polycrystalline Si. That is, the small energy photons, which are lower than Eg, cannot be absorbed by semiconductor materials (transmission losses). However, for the larger energy photons, most of the photon energy is wasted in the conversion. The surplus energy (hν-Eg) is then converted to the kinetic energy of the electron–hole pair, which is sequentially converted to the heat energy of the matrix (thermalization losses). For single-junction crystalline and polycrystalline Si solar cells, Eg = 1.12eV. 70% of all energy losses are related to transmission loss and thermalization loss. This is known as spectral mismatch. Therefore a prospective method to enhance the solar cell efficiency by quantum cutting is to cut a high energy photon to multiple low energy photons to adapt the solar spectrum, in order to better match the solar cell [1–12].

Since the visible quantum cutting in Eu³⁺-Gd³⁺ material was reported by Prof. Wegh and Prof. Meijerink in Science in 1999 [3], the importance, application and significance of the quantum cutting phenomenon have been widely recognized [1–22]. In 2005, Vergeer and Meijerink first reported the second-order near-infrared quantum cutting used for developing solar cells [2]. Since 2007, near-infrared quantum cutting has become a hot research topic throughout the world, and many top journals have reported a series of interesting quantum cutting phenomena, such as quantum cutting in Yb_xY_1-xPO₄:Tb³⁺ [2], Ce³⁺Pr³⁺Yb³⁺:SrF₂ [9,11], and Er³⁺-Yb³⁺:Cs₃Y₂Br₉ [15] described by Meijerink, Vergeer, and Ende; Tb³⁺Yb³⁺:BaF₂ [12] and Yb²⁺Yb³⁺:CaAl₂O₄ [7] described by Qiu, Chen and Zhou; Ce³⁺Yb³⁺:borate glass [6] described by Chen and Wang; (Yb_xGd_1-x)Al₃(BO₃)₄:Tb and NaYF₄:Pr³⁺Yb³⁺ [5,14] described by Zhang and Huang; and Er³⁺:GdVO₄ [8] described by our group.

At present, the best development in solar cells should be silicon solar cells [1], which have been put into production in many countries around the world. New theories, materials, techniques, designs and products of solar cells have been developed at a very rapid pace. The development of germanium (Ge) solar cells as a new type of solar cells with a narrow band-gap width [1–8] has been especially fast, and has been used in the germanium, silicon-germanium and cascade three-junction solar cells [4,13]. The germanium solar cell has the characteristic advantages of its small band-gap width of germanium of 0.67eV:300K (5404cm⁻¹ = 1850.5nm) [1–8]. It can absorb almost all near-infrared solar spectra effectively. Therefore, its transmission loss is very small and can almost be neglected [11]. If solar spectra from ultraviolet to visible can be converted to near-infrared in about 1800 nm by quantum cutting, the absorption efficiency of the Ge solar cell would be greatly enhanced. Furthermore, the radiative photon numbers can be very greatly enhanced by multiphoton quantum cutting. The electron–hole pair numbers of the Ge solar cell would also be very greatly enhanced. It is also very possible that the opto-electricity conversion efficiency of the Ge solar cell would be very greatly enhanced, as it may have large acceleration effects for solar cell project research. Our present manuscript provides the first report of the multiphoton quantum cutting luminescence phenomena of Tm:YAG powder phosphor. It is found for the first time that Tm:YAG powder phosphor has strong four-photon near-infrared quantum cutting luminescence of 1788 nm ³F₄→³H₆ fluorescence of Tm³⁺ ion. It is also found that Tm:YAG powder phosphor has intense two-photon quantum cutting luminescence. In 2002, Trupke and Green theoretically derived that the largest energy efficiency limit of the downconversion quantum cutting solar cell is approximately 40% [22]. It is important to note that this work is based on two-photon quantum cutting, of which the largest quantum cutting efficiency is close to 200%. However, for four-photon quantum cutting, the largest quantum cutting efficiency may approach 400%. Therefore, it is entirely possible for the largest energy efficiency limit of the downconversion quantum cutting solar cell to exceed 40%, thus reaching a higher value for four-photon quantum cutting solar cell. It is valuable to aid in probing the third-generation solar cell proposed by Green [20].

2. Experimental samples and experimental devices

The samples used in our experiment are (A) (Y_0.800Tm_0.200)₃Al₅O₁₂ and (B) (Y_0.995Tm_0.005)₃Al₅O₁₂ powder phosphor. The Tm:YAG powder samples were prepared by a solid-state reaction. The starting materials were high-purity Y₂O₃ (99.99%), Al₂O₃ (99.99%), and Tm₂O₃ (99.99%). The raw powders were weighted according to the stoichiometric compositions. Then it was sintered at 1600°C for 2 h in a furnace in air.

The experimental equipment used was the Fluorescence Spectrometer FL3-2iHR, produced by the Horiba-JY Company(America, Japan, and France). The pumping light source is a Xe lamp. The visible detector used was an R2658p photomultiplier, which has a very high rate of sensitivity in the range of 250 to 1000 nm. The infrared detector used was a Solid State Indium Antimony detector DSS-IS020L, which has a high rate of sensitivity in the range of 1000 to 5000 nm. The monochromator is a high-precision monochromator with a resolution of 0.1nm. The direction of the excitation light is perpendicular to the direction of fluorescence reception. For all of the experimental results, two experimental curves within one figure can be compared directly already in fluorescence intensity.

3. X-ray diffraction spectra and absorption spectrum

Figure 1 shows the representative XRD patterns of the (Y_0.800Tm_0.200)₃Al₅O₁₂ powder phosphor. The X-ray diffraction (XRD) data for lattice parameter refinements were collected on a Philips (Holland) X’Pert PW-3040 diffractometer (45 kV × 40mA) with Cu Kα radiation (λ = 0.15406 nm) in the range of 2θ = 10–80^◦. It can be seen that all diffraction peaks can be well-assigned to the reported data of YAG(PDF#04-008-3458). Figure 2 shows the absorption spectrum of the (Y_0.800Tm_0.200)₃Al₅O₁₂ powder phosphor, which is measured by UV-3100 spectrophotometer (Shimadzu, Japan).

 

Fig. 1 XRD pattern of the (Y_0.800Tm_0.200)₃Al₅O₁₂ powder phosphor sample.

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Fig. 2 The absorption spectrum of the (Y_0.800Tm_0.200)₃Al₅O₁₂ powder phosphor sample.

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4. Experimental excitation spectra

First, the visible excitation spectra of (A) (Y_0.800Tm_0.200)₃Al₅O₁₂ and (B) (Y_0.995Tm_0.005)₃Al₅O₁₂ powder phosphor in the wavelength range of 300-710 nm, when the fluorescence received wavelength is positioned at 800 nm, are measured, as shown in Fig. 3. It is found that Tm:YAG powder phosphor has three group of excitation spectra signal peaks from ultraviolet to visible, the main peaks of which are positioned at 357.0, 459.0 and 680.0 nm, respectively. It is easy to recognize that these are the ³H₆→¹D₂, ³H₆→¹G₄, and ³H₆→³F₃ absorption transitions of Tm³⁺ ion [16,18]. In the figure, the small 415.5 nm peak is noise. The small 658.0 nm peak is the ³H₆→³F₂ absorption transitions of Tm³⁺ ion. B is the excitation spectrum signal of (B) (Y_0.995Tm_0.005)₃Al₅O₁₂ powder phosphor. A*10 is the amplified excitation spectrum signal of (A) (Y_0.800Tm_0.200)₃Al₅O₁₂ powder phosphor, which is amplified by 10 times. The 357.0 nm ³H₆→¹D₂, 459.0 nm ³H₆→¹G₄ and 680.0 nm ³H₆→³F₃ excitation spectra signal intensities of (B) (Y_0.995Tm_0.005)₃Al₅O₁₂ powder phosphor are larger than those of (A) (Y_0.800Tm_0.200)₃Al₅O₁₂ by 21.00, 72.50 and 122.88 times, respectively.

 

Fig. 3 The visible excitation spectra of (A) (Y_0.800Tm_0.200)₃Al₅O₁₂ and (B) (Y_0.995Tm_0.005)₃Al₅O₁₂ powder phosphor, when the fluorescence received wavelength is positioned at 800 nm.

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Sequentially, the excitation spectra of (A) (Y_0.800Tm_0.200)₃Al₅O₁₂ and (B) (Y_0.995Tm_0.005)₃Al₅O₁₂ powder phosphor in the wavelength range of 300-850 nm, when the fluorescence received wavelength is positioned at 1788 nm near-infrared wavelength, are measured, as shown in Fig. 4. It is found that Tm:YAG powder phosphor has four groups of excitation spectra signal peaks from 300 to 850 nm, the main peaks of which are positioned at 357.0, 460.5, 680.0 and 781.0 nm, respectively. It is easy to recognize that they are the ³H₆→¹D₂, ³H₆→¹G₄, ³H₆→³F₃, and ³H₆→³H₄ absorption transitions of the Tm³⁺ ion [16,18]. A is the excitation spectrum signal of (A) (Y_0.800Tm_0.200)₃Al₅O₁₂ powder phosphor, and B is the excitation spectrum signal of (B) (Y_0.995Tm_0.005)₃Al₅O₁₂ powder phosphor. The 357.0 nm ³H₆→¹D₂, 460.5 nm ³H₆→¹G₄ and 680.0 nm ³H₆→³F₃ excitation spectra signal intensities of (A) (Y_0.800Tm_0.200)₃Al₅O₁₂ powder phosphor are larger than those of (B) (Y_0.995Tm_0.005)₃Al₅O₁₂ by 15.87, 11.81 and 6.68 times, respectively. It entirely achieves the signal intensity reverse. Near-infrared fluorescence signal intensity is thus greatly enhanced.

 

Fig. 4 The excitation spectra of (A) (Y_0.800Tm_0.200)₃Al₅O₁₂ and (B) (Y_0.995Tm_0.005)₃Al₅O₁₂ powder phosphor, when the fluorescence received wavelength is positioned at 1788 nm near-infrared wavelength.

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5. Experimental luminescence spectra

First, the visible luminescence spectra of (A) (Y_0.800Tm_0.200)₃Al₅O₁₂ and (B) (Y_0.995Tm_0.005)₃Al₅O₁₂ powder phosphor are measured. The 357.0 nm ³H₆→¹D₂ excitation peak of Tm:YAG powder phosphor is selected as the excitation wavelength to measure the luminescence spectra of 418-700 and 700-1000 nm, as shown in Fig. 5. It is found that there is a strong luminescence peak at (454.5, 460.0 nm), a small peak at (485.0, 493.5 nm), a small peak at (660.5, 670.0 nm), and a middle-sized peak at (759.0, 785.0, 801.0 nm) for the Tm:YAG powder phosphor. It is easy to recognize that these are the luminescence transitions of ¹D₂→³F₄, ¹G₄→³H₆, ¹G₄→³F₄, and ³H₄→³H₆ [16,18]. In the figure, B is the luminescence spectrum signal of (B) (Y_0.995Tm_0.005)₃Al₅O₁₂ powder phosphor. A*10 is the amplified luminescence spectrum signal of (A) (Y_0.800Tm_0.200)₃Al₅O₁₂ powder phosphor, which is amplified by 10 times. The 454.5 nm ¹D₂→³F₄, 460.0 nm ¹D₂→³F₄, 485.0 nm ¹G₄→³H₆, 660.5 nm ¹G₄→³F₄, 785.0 nm ³H₄→³H₆, and 801.0 nm ³H₄→³H₆ luminescence spectra signal intensities of (B) (Y_0.995Tm_0.005)₃Al₅O₁₂ powder phosphor are larger than those of (A) (Y_0.800Tm_0.200)₃Al₅O₁₂ by 27.12, 39.25, 21.20, 29.92, 31.02 and 19.15 times, respectively.

 

Fig. 5 The luminescence spectra of (A) (Y_0.800Tm_0.200)₃Al₅O₁₂ and (B) (Y_0.995Tm_0.005)₃Al₅O₁₂ powder phosphor, when the 357.0 nm ³H₆→¹D₂ excitation peak is selected as the excitation wavelength.

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The 680.0nm ³H₆→³F₃ excitation peak of Tm:YAG powder phosphor is selected as the excitation wavelength to measure the luminescence spectra of 750-1000 nm, as shown in Fig. 6. It is found that there is a middle luminescence peak at (785.0, 798.0, 804.0 nm) of ³H₄→³H₆ fluorescence for the Tm:YAG powder phosphor. In Fig. 6, B is the luminescence spectrum signal of (B) (Y_0.995Tm_0.005)₃Al₅O₁₂ powder phosphor. A*10 is the amplified luminescence spectrum signal of (A) (Y_0.800Tm_0.200)₃Al₅O₁₂ powder phosphor, which is amplified by 10 times. The 785.0 nm ³H₄→³H₆, 798.0 nm³H₄→³H₆, and 804.0 nm³H₄→³H₆ luminescence spectra signal intensities of (B) (Y_0.995Tm_0.005)₃Al₅O₁₂ powder phosphor are larger than those of (A) (Y_0.800Tm_0.200)₃Al₅O₁₂ by 153.02, 143.10 and 125.00 times, respectively.

 

Fig. 6 The luminescence spectra of (A) (Y_0.800Tm_0.200)₃Al₅O₁₂ and (B) (Y_0.995Tm_0.005)₃Al₅O₁₂ powder phosphor, when the 680.0 nm ³H₆→³F₃ excitation peak is selected as the excitation wavelength.

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Then, the infrared luminescence spectra of (A) (Y_0.800Tm_0.200)₃Al₅O₁₂ and (B) (Y_0.995Tm_0.005)₃Al₅O₁₂ powder phosphor are measured. In the same manner, the 357.0 nm ³H₆→¹D₂ excitation peak of Tm:YAG powder phosphor is also selected as the excitation wavelength to measure the infrared luminescence spectra of 1200-2800 nm, as shown in Fig. 5. It is found that there is a group of strong (1788.0, 1908.0, 2018.0 nm) luminescence peaks for (A) (Y_0.800Tm_0.200)₃Al₅O₁₂ powder phosphor. It is easy to recognize that it is ³F₄→³H₆ luminescence transition [16,18]. In the figure, A and B are the luminescence spectrum signals of (A) (Y_0.800Tm_0.200)₃Al₅O₁₂ and (B) (Y_0.995Tm_0.005)₃Al₅O₁₂ powder phosphor respectively. The 1788.0 nm ³F₄→³H₆ and 2018.0 nm ³F₄→³H₆ luminescence spectra signal intensities of (A) (Y_0.800Tm_0.200)₃Al₅O₁₂ powder phosphor are larger than those of (B) (Y_0.995Tm_0.005)₃Al₅O₁₂ powder phosphor by 17.30 and 29.11 times, respectively. It entirely achieves the signal intensity reverse. The near-infrared luminescence signal intensity of (A) (Y_0.800Tm_0.200)₃Al₅O₁₂ powder phosphor is much larger than that of (B) (Y_0.995Tm_0.005)₃Al₅O₁₂ .

The 680.0 nm ³H₆→³F₃ excitation peak of Tm:YAG powder phosphor is also selected as the excitation wavelength to measure the luminescence spectra of 1200-2800 nm, as shown in Fig. 6. It is found that (B) (Y_0.995Tm_0.005)₃Al₅O₁₂ powder phosphor has three groups of small luminescence peaks positioned at 1478.0 nm, (1750.0, 2022.0 nm), and 2352.0 nm. It is easy to recognize that these are the ³H₄→³F₄, ³F₄→³H₆, and ³H₄→³H₅ luminescence transitions [16,18]. Meanwhile, it is found that the (A) (Y_0.800Tm_0.200)₃Al₅O₁₂ powder phosphor has only one group of strong ³F₄→³H₆ luminescence peaks positioned at (1788.0, 1898.0, 2018.0 nm). That is, when the concentration of Tm³⁺ ion of Tm:YAG is enhanced from 0.5 to 20%, the luminescence of the ³F₄ energy level is enhanced by 7.62 times, while the luminescence of the ³H₄ energy level is greatly reduced.

6. Experimental fluorescence lifetime measurement results

The fluorescence lifetime of the 460.0 and 800.0 nm visible fluorescence of (A) (Y_0.800Tm_0.200)₃Al₅O₁₂ and (B) (Y_0.995Tm_0.005)₃Al₅O₁₂ powder phosphor, as shown in Fig. 7, are measured by the Fluorescence Spectrometer FL3-2iHR, produced by the Horiba-JY Company. In the measurements, the pumping sources are the 360 nm NanoLED semiconductor quasi-laser and pulse Xe lamp. All fluorescence lifetime values of 460.0 and 800.0 nm fluorescences are fit from the measured fluorescence lifetime curves [2,5–12]. The fit method is tail fit. The original point is set after equipment response. It is found from the measurements that the fluorescence lifetime values of 460.0 and 800.0 nm of (A) (Y_0.800Tm_0.200)₃Al₅O₁₂ are τ_A(460nm) = 10.97μs and τ_A(800nm) = 115.2μs. It is also found that those of (B) (Y_0.995Tm_0.005)₃Al₅O₁₂ are τ_B(460nm) = 28.32μs and τ_B(800nm) = 459.8μs.

 

Fig. 7 The fluorescence lifetime of the 800.0 nm (left) and 460.0 nm (right) visible fluorescence of (A) (Y_0.800Tm_0.200)₃Al₅O₁₂ (red) and (B) (Y_0.995Tm_0.005)₃Al₅O₁₂ (blue) powder phosphor, when excited by 680.0 nm (left) and 368.0 nm (right) pulsed light respectively.

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According to well-known infrared quantum cutting literature, the theoretical energy transfer efficiency of the Tm³⁺ ion caused by cross-relaxation energy transfer is determined by Eq. (1) [2,5–12]:

Therefore it can be calculated that the theoretical energy transfer efficiencies of the 460.0 and 800.0 nm fluorescences are ${\eta }_{tr,20\%Tm}(460nm)=61.26\%$ and ${\eta }_{tr,20\%Tm}(800nm)=74.95\%$, respectively.

7. Analysis

It is well known that energy transfer theories have been developed by Forster, Dexter and Kushida [1,2,5–21]. These theories are based on several interaction models between the donor and acceptor, just like dipolar-dipolar interaction or wave function overlap exchange interaction. Their commonality lies in the fact that they both require resonance between the transitions of the donor and acceptor. That is to say, the cross-energy transfer can be strong only when the emission spectrum of the donor and the excitation spectrum of the acceptor overlap. The entire concept of quantum cutting is based on these theories [1,2,5–12,18–21]. The process and efficiency of quantum cutting of Tm:YAG are analyzed below by discussing the energy transfer processes.

The schematic diagram of energy level structure and quantum cutting process are shown in Fig. 8.

 

Fig. 8 The schematic diagram of energy level structure and quantum cutting process.

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The main quantum cutting downconversion processes originating from ³H₄ energy level are as follows:

When the ³H₄, ³F₃, and ³F₂ energy levels are excited, many populations of Tm³⁺ ion may be populated at the ³H₄ energy level, because of the rapid multiphonon non-radiative relaxation from ³F₃ and ³F₂ energy levels to ³H₄. It can be found that Tm³⁺ ion possesses a very effective {³H₄→³F₄, ³H₆→³F₄} CR1:ET^r31-ET^a01 cross-energy transfer process. Although its theoretical transition mismatch + 1195 cm⁻¹ is large, its reduced matrix elements U² (0.1275,0.1311,0.2113) and (0.5375,0.7261,0.2382) of Tm³⁺ ion are extremely large [16,18], therefore the cross energy transfer rate of {³H₄→³F₄, ³H₆→³F₄} CR1:ET^r31-ET^a01 is also very large. For high-concentration Tm³⁺-doped YAG powder phosphor, the population of ³H₄ energy level may directly transfers to the first excited state ³F₄ energy level mainly through the {³H₄→³F₄, ³H₆→³F₄} CR1:ET^r31-ET^a01 cross-energy transfer process. It results in the very effective two-photon near-infrared quantum cutting of the ³F₄→³H₆ fluorescence.

Therefore the two-photon near-infrared quantum cutting efficiency of 1788.0 nm ³F₄→³H₆ fluorescence when the ³F₃ energy level is excited by 680.0nm light can be expressed as follows:

It is easy to calculate that ${\eta }_{CR,20\%Tm}{(}^3{H}_4)={\eta }_{CR,20\%Tm}(680nm)=174.95\%$.

The main quantum-cutting downconversion processes originating from ¹D₂ energy level are as follows:

When the ¹D₂ energy level is excited, many population of Tm³⁺ ion may populated at the ¹D₂ energy level because ¹D₂ energy level is a metastable energy state. It can be found that the Tm³⁺ ion possesses an effective {¹D₂→¹G₄, ³H₆→³F₄} CR9:ET^r76-ET^a01 cross-energy transfer process. Although its theoretical transition mismatch + 1051 cm⁻¹ is large, the reduced matrix elements U² (0.1874,0.1799,0.0022) and (0.5375,0.7261,0.2382) of the Tm³⁺ ion are very large as well [16,18], therefore the cross-energy transfer rate of {¹D₂→¹G₄, ³H₆→³F₄} CR9:ET^r76-ET^a01 is also large.

The Tm³⁺ ion also possesses a very effective {¹D₂→³F₂, ³H₆→³H₄} CR10:ET^r75-ET^a03 cross-energy transfer process. Its theoretical transition mismatch + 377 cm⁻¹ is small, and the reduced matrix elements U² (0.0643,0.3065,0) and (0.2357,0.1081,0.5916) of the Tm³⁺ ion are very large [16,18], therefore the cross-energy transfer rate of {¹D₂→³F₂, ³H₆→³H₄} CR10:ET^r75-ET^a03 is very large.

The Tm³⁺ ion also possesses an effective {¹D₂→³F₃, ³H₆→³H₄} CR11:ET^r74-ET^a03 cross-energy transfer process. Its theoretical transition mismatch + 991 cm⁻¹ is moderate, and the reduced matrix elements U² (0.1633,0.0687,0) and (0.2357,0.1081,0.5916) of Tm³⁺ ion are large [16,18], therefore the cross-energy transfer rate of {¹D₂→³F₃, ³H₆→³H₄} CR11:ET^r74-ET^a03 is large.

The Tm³⁺ ion also possesses an effective {¹D₂→³H₄, ³H₆→³F₃} CR12:ET^r73-ET^a04 cross-energy transfer process. Its theoretical transition mismatch + 991 cm⁻¹ is moderate, and its reduced matrix elements U² (0.1248,0.0096,0.2280) and (0,0.3164,0.8413) of Tm³⁺ ion are large [16,18], therefore the cross-energy transfer rate of {¹D₂→³H₄, ³H₆→³F₃} CR12:ET^r73-ET^a04 is large.

The Tm³⁺ ion also possesses an effective {¹D₂→³H₄, ³H₆→³F₂} CR13:ET^r73-ET^a05 cross-energy transfer process. Its theoretical transition mismatch + 377 cm⁻¹ is small, but the reduced matrix elements U² (0.1248,0.0096,0.2280) and (0,0,0.2550) of Tm³⁺ ion are moderate [16,18], therefore the cross-energy transfer rate of {¹D₂→³H₄, ³H₆→³F₂} CR13:ET^r73-ET^a05 is large.

The Tm³⁺ ion also possesses a very weak {¹D₂→³H₅, ³H₆→¹G₄} CR14:ET^r72-ET^a06 cross-energy transfer process. Its theoretical transition mismatch −1427 cm⁻¹ is very large, and its reduced matrix elements U² (0,0.0011,0.0193) and (0.0483,0.0748,0.0125) of Tm³⁺ ion are small [16,18], therefore the cross-energy transfer rate of {¹D₂→³H₅, ³H₆→¹G₄} CR14:ET^r72-ET^a06 is very small.

The Tm³⁺ ion also possesses a weak {¹D₂→³F₄, ³H₆→¹G₄} CR15:ET^r71-ET^a06 cross-energy transfer process. Its theoretical transition mismatch + 1051 cm⁻¹ is very large, its reduced matrix elements U² (0.5680,0.0928,0.0230) and (0.0483,0.0748,0.0125) of Tm³⁺ ion are moderate [16,18], therefore the cross energy transfer rate of {¹D₂→³F₄, ³H₆→¹G₄} CR15:ET^r71-ET^a06 is small.

In conclusion, for high-concentration Tm³⁺-doped YAG powder phosphor, the population of the ¹D₂ energy level may directly transfer to the lower energy level mainly through the {¹D₂→³F₂, ³H₆→³H₄} CR10:ET^r75-ET^a03 cross-energy transfer process, i.e. one population of the ¹D₂ energy level may very effectively lead to two populations of the ³H₄ energy level through {¹D₂→³F₂, ³H₆→³H₄} CR10:ET^r75-ET^a03 cross-energy transfer process. Then it may also very effectively lead to four populations of the ³F₄ energy level through CR1:ET^r31-ET^a01{³H₄→³F₄, ³H₆→³F₄} cross-energy transfer process consequently. It results in the effective four-photon near-infrared quantum cutting of the ³F₄→³H₆ fluorescence of Tm³⁺ ion.

Therefore the four-photon near-infrared quantum cutting efficiencies of the 1788.0 nm ³F₄→³H₆ fluorescence when the ¹D₂ energy level is excited by 357.0 nm can be expressed as follows:

It is then easy to calculate that ${\eta }_{CR,20\%Tm}{(}^1{D}_2)={\eta }_{CR,20\%Tm}(357nm)=282.12\%$.

It can be found from Fig. 2, Fig. 3 and Fig. 4 that compared to the absorption spectrum of Fig. 2 and visible excitation spectrum of Fig. 3, the action of 357.0nm peak in infrared excitation spectrum of Fig. 4 is very effective. It illustrates that the excitation of ¹D₂ energy level can result in very strong 1788.0nm ³F₄→ ³H₆ luminescence, which is a very effective quantum cutting.

It is obviously that the (Y_0.800Tm_0.200)₃Al₅O₁₂ powder phosphor has very higher quantum cutting efficiency. The reason for high quantum cutting efficiency is partly due to the cross-energy transfer processes in (Y_0.800Tm_0.200)₃Al₅O₁₂ powder phosphor is first-order energy transfer mechanisms, which generally have a much higher probability (typically a factor of 10³) to occur than second-order mechanisms, emphasized by Meijerink [11].

Because emission wavelength of the ³F₄→³H₆ fluorescence of Tm³⁺ ion of (Y_1-xTm_x)₃Al₅O₁₂ powder phosphor is 1788 nm, it is resonant entirely with the band-gap width Eg of germanium of 1850.5 nm, 5404 cm⁻¹ (0.67 eV:300 K). The resonant energy transfer from Tm³⁺ ion to germanium would be very effective. It is very valuable to enhance the efficiency of Ge solar cell by the multiphoton near-infrared quantum cutting of (Y_1-xTm_x)₃Al₅O₁₂ powder phosphor.

The further work is to look for suitable sensitizer to enhance the absorption efficiency both in the strong absorption intensity and broad absorption wavelength range.

8. Conclusion

In the present manuscript, the x-ray diffraction spectra, visible to near-infrared excitation and emission spectra, and fluorescence lifetimes have been measured. It is found that (A) (Y_0.800Tm_0.200)₃Al₅O₁₂ powder phosphor possesses intense two-photon quantum cutting luminescence resulting from the CR1:ET^r31-ET^a01{³H₄→³F₄, ³H₆→³F₄} cross-energy transfer. It is found that its theoretical up-limit of the two-photon near-infrared quantum cutting efficiency is approximately 174.95%. Moreover, it is found for the first time that (A) (Y_0.800Tm_0.200)₃Al₅O₁₂ powder phosphor has strong four-photon near-infrared quantum cutting luminescence of 1788 nm ³F₄→³H₆ fluorescence of Tm³⁺ ion, which results both from the {¹D₂→³F₂, ³H₆→³H₄} and {³H₄→³F₄, ³H₆→³F₄} cross-energy transfers. It is found also that the theoretical up-limit of the four-photon near-infrared quantum cutting efficiency is approximately 282.12%. To the knowledge of the authors, this is the first time that the near-infrared quantum cutting efficiency exceeding 200% has been reported.