1. Introduction

The mismatch between the solar spectrum and the band gap energy of silicon semiconductor limits the energy efficiency of crystalline silicon based solar cells, which occupy a majority of the market share in the field of solar cells. Photons with energy lower than the band gap cannot be absorbed, while for photons with energy larger than the band gap, the excess energy is lost by thermalization of hot charge carriers [1]. To achieve a higher energy efficiency, tandem solar cells consisted of multiple semiconductor layers have been developed and each semiconductor layer has a characteristic band gap converting a different part of the solar spectrum [2]. However, the complicated fabrication and high cost limit their practical use. Another feasible method allowing the solar cells to capture more energy from the solar spectrum is by spectral modification through near-infrared quantum cutting [3,4]. Cutting a ultraviolet or blue photon into two near-infrared photons, which can be well absorbed by solar cells, can reduce the energy loss related to thermalization of hot charge carriers and then boost the efficiency of solar cells. Because of this potential application in solar cells near-infrared quantum cutting has attracted a lot of recent research attention [5–14].

Effective spectral modification can be obtained by combination of different rare earth ions thanks to the unique and rich energy levels of lanthanide rare earth ions covering a wide spectral range from ultraviolet to infrared. Near-infrared quantum cutting was first achieved in YPO₄:Tb³⁺,Yb³⁺ [5] where a visible photon was converted into two near infrared photons through cooperative energy transfer from Tb³⁺ to Yb³⁺. Yb³⁺ ion possesses only two manifolds: the ²F_7/2 ground state and the ²F_5/2 excited state, which are separated by about 10000cm⁻¹ in the energy level scheme. Photons emitted by Yb³⁺ ions is around 1000nm, just above the band gap of crystalline silicon, where the silicon solar cells show an excellent spectral response. Similar phenomena have also been observed in RE³⁺/Yb³⁺ (RE = Bi, Tm, and Ce) codoped phosphors and glasses [10–12]. Nevertheless, due to the second order nature of the transfer process, such a cooperative energy transfer is not as efficient as resonance energy transfer, and a high transfer efficiency will only be possible at relatively heavy Yb³⁺ doping where Yb³⁺ emission is largely depressed by concentration quenching [13]. Therefore resonance energy transfer between rare earth ions is more favorable in order to get a higher quantum efficiency. However, until now, there have been few reports of near-infrared quantum cutting through resonance energy transfer [13,14].

Ho³⁺/Yb³⁺ codoped NaYF₄, a host with phonon energy about 400cm⁻¹ [15], is well-known as a high-efficiency upconversion phosphor due to efficient energy transfer from Yb³⁺ to Ho³⁺. Figure 1 presents a schematic diagram of the energy levels of Ho³⁺ and Yb³⁺ that are of interest. Close inspection shows that the energy gap of ⁵G₄ and ⁵F₅, ⁵F₅ and ⁵I₇ are resonant with the energy for the transition from ²F_5/2 to ²F_7/2 on Yb³⁺. As a result, resonance energy transfer by cross relaxation can be expected to realize quantum cutting. In this paper we investigate the spectroscopic properties of Ho³⁺ single doped and Ho³⁺/Yb³⁺ codoped NaYF₄, and demonstrate the existence of near infrared quantum cutting as well as the quantum cutting mechanism for the first time.

 

Fig. 1 Energy levels diagram of Ho³⁺ and Yb³⁺ showing possible mechanisms for a near-infrared quantum cutting. One ultraviolet photon absorbed by Ho³⁺ is converted into two Yb³⁺ near infrared photons through two-step sequential cross relaxations. Solid, dotted, curly arrows represent optical transition, cross relaxation, and multiphonon relaxation, respectively.

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2. Experiments

The powder samples of NaYF₄ doped with Ho³⁺(0.5mol%) and Yb³⁺(0,5,10,20mol%) were synthesized by hydrothermal method. All the chemicals are of analytical grade reagents and used without further purification. The RE(NO₃)₃ standard solutions(Y/Ho/Yb, 2 mmol in total) with desired stoichiometric ratio were added into 35ml aqueous solution containing 16 mmol NaF by dropwise under magnetic stirring. Then the resulting suspension was transferred into a 50 ml Teflon bottle held in a stainless steel autoclave, sealed, and maintained at 180°C for 24h. After cooling to room temperature, the precipitates were separated by filtration, washed with ethanol for several times and then dried in air. The crystalline phases of the synthesized samples were characterized by XRD(MAC Science Co. Ltd. MXP18AHF), using nickel-filtered Cu Kα radiation in the$2\theta$range from 10° to 70°. Luminescent spectra were measured with a Jobin Yvon Fluorolog-3 system equipped with a 450W Xe-lamp as excitation source and a 50W flash lamp for time resolved measurements, where the visible and infrared emission were detected with a Hamamatsu R928 photomultiplier tube and a liquid nitrogen-cooled DSS-IGA020L InGaAs detector, respectively. To compare the emission intensities of samples with different Yb³⁺ doping, the emission spectra were recorded at identical experimental conditions. All the measurements were carried out at room temperature.

3. Results and discussion

The XRD patterns for NaYF₄ samples with 0.5mol% Ho³⁺ and different Yb³⁺ doping concentrations are shown in Fig. 2 . The little change of the lanthanide ions in their atomic radii facilitates the substitution for Ho³⁺ and Yb³⁺ within the NaYF₄ matrix. Compared with standard data(JCPDS No.16-0334), all the samples exhibit the peaks of pure hexagonal phase. No second phase is detected in the XRD pattern, revealing the successful doping of Ho³⁺ and Yb³⁺ ions in NaYF₄. Additionally, the fairly narrow full width at half maximum and intense diffraction peaks indicate the well crystallization of the sample. However, due to the preferential growth effect in the hydrothermal process [16], the relative intensities of the peaks are a little different from those in standard data.

 

Fig. 2 XRD patterns of the NaYF₄:Ho³⁺,Yb³⁺ samples with different Yb³⁺ doping concentration compared with NaYF₄ standard data JCPDS No.16-0334.

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In Fig. 3 the emission spectra for NaYF₄ doped with Ho³⁺(0.5mol%) and Yb³⁺ (0,5,10,20mol%) are shown for Ho^{3+ 5}G₅’ excitation at 359nm. For the Ho³⁺ single-doped sample, excitation into the Ho^{3+ 5}G₅’ level yields the Ho³⁺ characteristic emission from the ⁵G₄, ⁵G₅, ⁵F₃, ⁵S₂, ⁵F₅ level. The intensities of the ⁵G₄, ⁵G₅ and ⁵F₃ emission are rather weak compared to the strong emission originating from the ⁵S₂→⁵I₈ transition(about two orders of magnitude weaker in integrated intensity). The energy gap between the ⁵G₄, ⁵G₅ and ⁵F₃ level to the next lower level is about 2000cm⁻¹, 1500cm⁻¹ and 2000cm⁻¹, respectively. The energy gap law [17] predicts that radiative decay and multiphonon relaxation can compete only when the gap is five times the phonon energy. Based on the present observations and the energy gap law, we can assert that multiphonon relaxation dominates over radiative decay for the ⁵G₄, ⁵G₅ and ⁵F₃ level. Apart from visible emission from Ho³⁺, infrared emission band around 1200nm, corresponding to the ⁵I₆→⁵I₈ transition, as well as intense Yb^{3+ 2}F_5/2 emission around 1000nm are also observed. The appearance of Yb³⁺ infrared emission in Ho³⁺/Yb³⁺ codoped sample results from energy transfer from Ho³⁺ to Yb³⁺. Furthermore, visible emissions from Ho³⁺ are significantly weakened in their intensities with the increase of Yb³⁺ concentration, while the most intense Yb³⁺ emission at 1000nm is obtained for 5mol% Yb³⁺ doping as a result of concentration quenching. In addition, Ho³⁺ emissions in the visible range can hardly been observed in the sample with 20mol% Yb³⁺ doping, suggesting an efficient energy transfer from Ho³⁺ to Yb³⁺.

 

Fig. 3 Visible to near infrared emission spectra of NaYF₄: Ho³⁺,Yb³⁺ with various Yb³⁺ doping upon 359nm excitation.

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Further information of energy transfer from Ho³⁺ to Yb³⁺ can be obtained from the excitation spectra for Ho³⁺ emission at 540nm corresponding to the ⁵S₂→⁵I₈ transition, as shown in Fig. 4 . The excitation spectra for all the samples with various Yb³⁺ concentrations are normalized to the ⁵G₆/⁵F₁ level. A series of bands appear in the excitation spectra as excitation into these energy levels is followed by multiphonon relaxation to the ⁵S₂ level. An obvious decrease in the excitation intensities for the bands corresponding to the transition to the ⁵G₄ level as well as the upper levels (from 325nm to 400nm, denoted as Part A) compared with the bands below the ⁵G₄ level (from 400nm to 500nm, denoted as Part B) is observed as Yb³⁺ concentration increases, whereas the excitation bands inside Part A and Part B undergo almost no change in their relative intensities. This decrease is ascribed to the cross relaxation from Ho³⁺(⁵G₄→⁵F₅) to Yb³⁺(²F_7/2→²F_5/2), since it depopulates the population of the ⁵S₂ level only when excitation is not lower than the ⁵G₄ level. If no such cross relaxation occurs, however, the relative intensities of the excitation spectra should remain unchanged. Assuming that excitation into levels between ⁵G₂ and ⁵F₃ is followed by multiphonon relaxation to the ⁵S₂ level except for the cross relaxation from Ho^{3+ 5}G₄ to Yb³⁺, the efficiency of the cross relaxation can be expressed as

 

Fig. 4 Excitation spectra of Ho³⁺ emission at 540nm in NaYF₄:Ho³⁺,Yb³⁺ with various Yb³⁺ doping. All the spectra are normalized to the ⁵G₆/⁵F₁ level.

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The cross relaxation depopulates the ⁵G₄ level but simultaneously populates the ⁵F₅ level. Thus an increase of the ⁵F₅ emission intensity is expected in NaYF₄:Ho³⁺,Yb³⁺ compared with that in NaYF₄:Ho³⁺. On the contrary, the ⁵F₅ emission intensity drops with increasing Yb³⁺ concentration according to Fig. 3. Figure 5 presents the decay curves of Ho^{3+ 5}S₂ emission at 540nm as well as ⁵F₅ emission at 650nm. It is noted that both the Ho³⁺ emissions in all the samples show a nearly exponential decay and the lifetime, fitted by a single exponential, decreases rapidly with the increase of Yb³⁺ concentration as can be seen in the insets of Fig. 4. Since the Ho³⁺ concentration was maintained constant in all the samples, the decline of the lifetime should not be attributed to the concentration quenching of Ho³⁺ but to extra decay pathway introduced by Yb³⁺ doping: resonance energy transfer from Ho³⁺ to Yb³⁺ by cross relaxation from Ho³⁺(⁵S₂→⁵I₆) to Yb³⁺(²F_7/2→²F_5/2) and Ho³⁺(⁵F₅→⁵I₇) to Yb³⁺(²F_7/2→²F_5/2), which accelerates the depopulation of ⁵F₄(⁵S₂) and ⁵F₅ level, respectively, and leads to a shorter lifetime and weaker intensity for both emission. The presence of the former cross relaxation can also be confirmed by the pronounced increase of ⁵I₆ emission in Ho³⁺/Yb³⁺ codoped sample. The ⁵I₆ emission around 1200nm, however, is beyond the spectral response of Si solar cells. From the decay curves the energy transfer efficiency can be determined using the following equation [5]:

 

Fig. 5 Decay curves of (a) Ho^{3+ 5}S₂ emission at 540nm and (b) ⁵F₅ emission at 650nm under 359nm excitation in NaYF₄:Ho³⁺,Yb³⁺ with different Yb³⁺ concentration. Insets show the lifetime(τ) of ⁵S₂ and ⁵F₅ level, respectively.

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In the above discussions near-infrared quantum cutting involved two-step sequential cross relaxation: Ho³⁺(⁵G₄→⁵F₅) to Yb³⁺(²F_7/2→²F_5/2) followed by Ho³⁺(⁵F₅→⁵I₇) to Yb³⁺ (²F_7/2→²F_5/2), has been clearly demonstrated as exhibited in Fig. 1. A measurement of excitation spectra of Yb³⁺ emission in the Ho³⁺/Yb³⁺ codoped sample can provide a direct test of the performance of quantum cutting in comparison with excitation spectra of Ho³⁺ 1190nm emission in Ho³⁺ single doped sample as shown in Fig. 6 . The infrared excitation spectra were run with a wider monochromator slit width and thus it has a lower spectral resolution compared with the visible excitation spectra. The excitation spectra are normalized to the ⁵G₆/⁵F₁ level as well. If quantum cutting occurs in the ⁵G₄ level, the relative intensity of the excitation bands related to the transition to this level as well as the levels above should increase in the excitation spectra of Yb³⁺ emission; meanwhile, the excitation bands below the ⁵G₄ level should remain the same, since in the quantum cutting process two near-infrared photons are generated, rather than one in a trivial one-step energy transfer from the ⁵S₂ level [18]. In Fig. 6 an expected increase of excitation intensity at ⁵G₄ level together with the levels above is clearly observed, verifying the occurrence of near infrared quantum cutting. Supposing there is no nonradiatvie energy loss by defects and impurities, the quantum efficiency can be estimated, to a good approximation, according to the formula below:

 

Fig. 6 Excitation spectra of Yb³⁺ 1013nm emission in NaYF₄:0.5% Ho³⁺,20% Yb³⁺ and Ho³⁺ 1190nm emission in NaYF₄:0.5% Ho³⁺. Both the spectra are normalized to the ⁵G₆/⁵F₁ level.

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4. Conclusions

In summary, an efficient near-infrared quantum cutting through two sequential resonant energy transfer from Ho³⁺ to Yb³⁺ has been demonstrated in Ho³⁺/Yb³⁺ codoped NaYF₄. A maximum quantum efficiency of 155.2% can be determined from excitation spectra and decay curves. The high quantum efficiency and the intense Yb³⁺ near-infrared emission indicate the potential application in realizing a high energy efficiency of crystalline silicon based solar cells.