Energy Transfer Dynamics and Quantum Yield Derivation of the Tm3+

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Energy Transfer Dynamics and Quantum Yield Derivation of the Tm3+ Concentration Dependent ThreePhoton Near-Infrared Quantum Cutting in La2BaZnO5 Ting Yu, Qinyuan Zhang, Huihong Lin, Dechao Yu, and Shi Ye J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b07729 • Publication Date (Web): 28 Oct 2015 Downloaded from http://pubs.acs.org on October 30, 2015

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The Journal of Physical Chemistry

Energy Transfer Dynamics and Quantum Yield Derivation of the Tm3+ Concentration Dependent Three-Photon Near-Infrared Quantum Cutting in La2BaZnO5

Ting Yu, Huihong Lin, Dechao Yu, Shi Ye, Qinyuan Zhang a) State Key Laboratory of Luminescent Materials and Devices, and Institute of Optical Communication Materials, South China University of Technology, Guangzhou 510641, P. R. China ABSTRACT Near-infrared (NIR) quantum cutting (QC) from the Tm3+: 1G4 state essentially occurs via a three-step cascade radiation (case 1) and two-step cross-relaxations (case 2) by varying the Tm3+ content (x) from 0.0005 to 0.05 in La2-xTmxBaZnO5. In case 1, with the Tm3+ content x < 0.005, the energy of the 1G4 excited state is down-converted to three NIR photons emitted at approximately 1200, 1480 and 1800 nm, with 3H4 and 3F4 acting as intermediate levels, while in case 2, with the Tm3+ content x ≥ 0.005, the energy will be triply cut into approximately 1800 nm photon emissions. The three-photon NIR QC phenomena are investigated in terms of the static and dynamic photoluminescence. Based on the dependence of cross-relaxation and concentration quenching on Tm3+ density, a rate-equation model was built to describe the energy transfer (ET) dynamics of Tm3+. The calculation of internal quantum yield (QY) was developed by considering nonradiative processes, and the maximum QY for photon emission at 1800 nm was 198% in La1.99Tm0.01BaZnO5. These phenomena provide insight into the triple cutting mechanisms of Tm3+-doped materials, thereby improving the potential applications of this quantum tripling in Ge photovoltaic devices (band gap approximately 0.67 eV), and laser devices.

a)

Electronic mail: [email protected] 1

ACS Paragon Plus Environment


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1. INTRODUCTION Quantum cutting (QC) with quantum yield (QY) more than unity has the potential to promote the development of efficient luminescent materials emitting photons in the visible and near-infrared (NIR) spectral ranges.1,2 A vacuum ultraviolet-excited visible QC system, such as the Gd3+-Eu3+ couple with approximately 190% red emission efficiency, can be potentially applied in mercury-free fluorescent lamps and plasma displays.3 In addition, the development of NIR QC in recent years promises to greatly enhance the efficiency of solar cells.4-7 Theoretically, an ideal QC layer with emission at 1000 nm can increase the efficiency of Si solar cells up to approximately 40%,8,9 which is much greater than its approximately 15% practical efficiency and even exceeds the Shockley-Queisser efficiency limit of approximately 30%. In addition to the extensive studies on RE3+/Yb3+ (RE = Tb, Pr, Tm, Er, and Nd) co-doping as a promising QC layer for Si solar cells,4,5,10-15 the multi-photon NIR luminescence of RE3+ (RE = Dy, Ho, Tm, and Er) single doping system is spectroscopically demonstrated through energy transfer (ET) mechanisms of multi-step cascade radiation or/and cross-relaxation (CR), thereby enhancing the photo-response of Ge solar cells.16-24 In addition to the ET dynamics, QY is well known to be one of the most important factors for luminescent materials, especially for QC materials.2 However, for the NIR QC system, its emission covers a rather broad region from ultraviolet (approximately 300 nm) to infrared (approximately 1800 nm).6 Due to the photo-response limitation of various detectors (such as the R928 photomultiplier with 185-900 nm spectral response, the R5509-72 photomultiplier with optimal spectral response at 700-1700 nm, and InGaAs PIN photodiodes with 900-2100 nm spectral response, etc.),25 the practical QY cannot be measured directly via 2


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the integrating sphere setup.26,27 Therefore, the theoretical calculation of QY has been systematically developed to determine the efficiency of the NIR QC materials.19,28 The calculation procedures make absolute sense, based on the convincing demonstration of QC; however, such calculations ignore the nonradiative processes, such as the significant concentration quenching (CQ) at higher dopant content. Accordingly, the resultant QY is the maximum value for the NIR QC system, which is much larger than the actual QY even roughly measured.19,28-30 Consequently, more suitable calculation models should be further developed to essentially optimize the internal QY for the NIR QC system. In this study, we experimentally demonstrated the Tm3+-concentration dependent three-photon NIR QC in La2-xTmxBaZnO5 (x = 0.0005-0.075) phosphors. La2BaZnO5 was chosen as an ideal host because its shorter RE-RE (La-La) distance of approximately 3.4 Å (even less than that of β-NaYF4, approximately 3.5 Å, YVO4 approximately 3.9 Å and YAG approximately 3.7 Å) enables efficient CR at higher Tm3+ concentration.31 La2BaZnO5 host lattice has a lower ħωmax (maximum phonon energy) of approximately 600 cm-1 (ħωmax of β-NaYF4 approximately 450 cm-1, YVO4 approximately 900 cm-1 and YAG approximately 700 cm-1) to benefit the efficient NIR emission of Tm3+.21,32 Besides, Jaffrès et al. enlighteningly discussed that, originating from blue-excited 1G4 state of Tm3+, several nearly-resonant cross-relaxation ET just proceed to achieve the efficient NIR emission at about 1800 nm in theory.32 Furthermore, we primarily investigated the ET dynamics as a function of the Tm3+ concentration in La2BaZnO5 in spectroscopic experiments. Based on the rate equation and consideration of nonradiative processes, a proper model to calculate the internal QY was developed for the three-photon NIR-QC in La2-xTmxBaZnO5. 3



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2. EXPERIMENTAL DETAILS A series of polycrystalline La2-xTmxBaZnO5 (x = 0.0005, 0.0025, 0.005, 0.01, 0.025, 0.035, 0.05, 0.06, and 0.075) powder samples were prepared via solid-state reactions. Appropriate amounts of starting materials of La2O3, BaCO3, ZnO and Tm2O3 (all 99.99%) were homogenously mixed, and then completely ground, followed by sintering at 1200 °C in air atmosphere for 12 h. After cooling down to room temperature, the as-obtained powder samples were reground and then heated a second time at 1200 °C for 12 h, thereby ensuring high phase purity and good crystallization. The structure of all the samples was identified using a Philips Model PW1830 X-ray diffractometer (XRD) with a Cu Kα radiation source operated at 40 kV and 40 mA. The diffraction pattern was similar for each sample, corresponding to pure phase La2BaZnO5 (JCPDS Card No. 80-1882).21 Steady photoluminescence spectra were measured using an Edinburgh FLS920 spectrofluorimeter equipped with a continuous wave 450-W xenon lamp excitation source, a Hamamatsu R928 photomultiplier tube (PMT) for photon detection in 470-850 nm and a liquid-nitrogen cooled R5509-72 NIR PMT for 800-1650 nm. Moreover, dynamic fluorescence spectra in the form of decay curves were recorded using the FLS920 system equipped with microsecond μF900 xenon lamp excitation sources. The mid-infrared (MIR) luminescence spectra were obtained using a thermoelectrically cooled G5852 InGaAs PIN photodiode, and an optical parametric oscillator (OPO) system (Opotek HE 355 II) pumped by the third harmonic of a Nd: YAG laser (pulse width 10 ns; repetition rate 20 Hz) employed as excitation source. The MIR decay curves were recorded using a digital oscilloscope (HP54503a) and an 800 nm Ti: Sapphire laser used as an excitation source with a 4


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mechanical chopper to modulate the excitation laser beam. To perform spectroscopic comparison of different samples, the same species of luminescence was measured under identical conditions. All experiments are performed at room temperature.

3. RESULTS AND DISCUSSION 3.1. Spectroscopic analysis of three-photon NIR QC in La2-xTmxBaZnO5. The broad emission band in 750-850 nm (Figure 1(a); upon 465 nm excitation) comprise a sharp peak at 784 nm and a broad shoulder at 800 nm, which notably originates from the 1G4 → 3H5 (energy gap approximately 12740 cm-1) and, 3H4 → 3H6 (energy gap approximately 12500 cm-1) of Tm3+, respectively.21,32 Decay curves of 651, 784 and 798 nm for the sample doped with lower x = 0.0005 Tm3+ are depicted in Figure 1(b), where the 651 and 798 nm decay curves were well fitted to a monoexponential function with lifetime of approximately 244 and 588 μs, respectively, and the 784 nm curve was fitted by a nonexponential decay with a calculated lifetime of 315 μs (decay components τ1 approximately 246 μs, τ2 approximately 697 μs). These results suggest that emission at 800 nm is purely from the 3H4 state, but that at approximately 784 nm primarily from the 1G4 state of Tm3+. Whereas for the higher x = 0.025 (Figure 1(c)), the decay curves of 651 and 798 nm obviously become nonexponential with rather short calculated lifetimes of 61 and 187 μs, respectively, and that of 784 nm has a lifetime of 130 μs, which is caused by the extra decay paths from the excited 1G4 and 3H4 states of Tm3+. Moreover, the 750-850 nm emission bands of all the samples were normalized by their integral intensities, as shown in Figure 1(a). It is of interest, the ratio of the emission intensity of 784 nm to that of 800 nm, I784nm/I800nm, was found to dramatically decrease by 5



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increasing Tm3+ content, which spectroscopically reveals that CR between 1G4 and 3H4 additionally occurs from the 1G4 excited state at higher Tm3+ concentration. Figure 2 shows the NIR emission spectra in 1050-1650 nm of La2-xTmxBaZnO5 under excitation of 465 nm. Note that the 3F4 → 3H6 transition at approximately 1620 nm is just due to the sharp decrease of spectral response of R5509-72 NIR PMT beyond 1600 nm.19,20 Here, by means of a thermoelectrically cooled G5852 InGaAs PIN photodiode (incremental spectral response in 1500–2100 nm), the entire emission bands of Tm3+ around 1800 nm are easily recorded for La2-xTmxBaZnO5 pumped by a 465 nm laser. The NIR emission of 1200, 1480 and 1800 nm exhibit the following intensity versus Tm3+ concentration (the inset of Figure 2): (i) the 1G4 → 3H4 at approximately 1200 nm reaches its maximum at 0.005 Tm3+; (ii) the 3H4 → 3F4 at approximately 1480 nm achieves its maximum at 0.01 Tm3+; (iii) distinct from (i) and (ii), the intensity of 3F4 → 3H6 at approximately 1800 nm monotonically increases till 0.025 Tm3+. For issue (i), no CQ occurs, and the energy of 1G4 excited state is sequentially downconverted to three NIR photons with 3H4 and 3F4 intermediate levels (case 1, three-step cascade radiation).19 However, for issues (ii) and (iii), the different quenching thresholds of 3

H4 (0.01) and 3F4 (0.025) to that of 1G4 (0.005) reveal that the efficient ET between Tm3+

occurs, such as the multi-channel CR, to finally improve three NIR photon emission at approximately 1800 nm (case 2).

3.2. Energy transfer mechanisms of three-photon NIR QC in La2-xTmxBaZnO5. Theoretically, the large energy differences of 1G4 → 3F2 (approximately 6000 cm-1), 3H4 → 3

H5 (approximately 4400 cm-1) and 3F4 → 3H6 (approximately 5800 cm-1) of Tm3+ require the 6


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absorption of at least 10, 8 and 10 phonons by La2BaZnO5, respectively, which indicates that multiphonon-assisted nonradiative relaxation would be impossible. According to Judd-Ofelt theory, the luminescence branching ratios of 1G4 → 3H4, 3H4 → 3F4 and 3F4 → 3H6 of Tm3+ are typically reported be approximately 0.10, 0.09, and 1.00, respectively,33 which suggests that the energy in the excited 1G4, 3H4 and 3F4 can be efficiently depopulated via NIR radiative transitions. In practice, as x < 0.005, once 1G4 is excited by a blue photon at approximately 470 nm, the energy can be sequentially de-excited to 3H4 and 3F4 states by 1200, 1480 and 1800 nm photons emitting as schematically depicted in Figure 3(a), finally achieving the three-step three-photon NIR QC. In the experiment, the luminescence of Tm3+ is rather sensitive to its concentration due to the richness of the electronic energy levels. For example, the optimal concentration of Tm3+ in upconversion is typically approximately 1% in NaYF4.34 For the 1G4 state with Tm3+ content exceeding the CQ threshold (here, Tm3+ content x ≥ 0.005), multi-channel CR between Tm3+ can efficiently occur, such as the possible CR of 1G4 → 3H4 + 3H6 → 3H5 (A1), 1G4 → 3F2 + 3

H6 → 3F4 (A2), 1G4 → 3H5 + 3H6 → 3H4 (A3), and 1G4 → 3F4 + 3H6 → 3F2 (A4). In principle,

an efficient CR is determined by the energy mismatch and the reduced matrix elements U2 of these electronic transitions. The energy mismatch of the above-mentioned four probable approaches are +175 cm-1 (A1), +400 cm-1 (A2), -30 cm-1 (A3) and +195 cm-1 (A4).32 Moreover, relative to other three processes, the 1G4 → 3H4 + 3H6 → 3H5 (A1) CR has rather large U2 reduced matrix elements (0.1645, 0.0052, 0.4114) and (0.1074, 0.2314, 0.6385) of Tm3+, while for 1G4 → 3F4 + 3H6 → 3F2 (A4) CR, the U2 reduced matrix elements (0.0020, 0.0182, 0.0693) and (0, 0, 0.2550) of Tm3+ are small.35,36 Furthermore, under excitation at 465 7



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nm [Figure 1(a) and Figure 2], no emission is detected from the 3F2 and 3H5 states, revealing that the 3F2 and 3H5 excited states are not stable enough, thereby enabling the multi-phonon relaxation to occur efficiently. As a consequence, the 1G4 → 3H4 + 3H6 → 3H5 (A1) CR would be the dominant relaxation path from the excited 1G4 state, as shown in Figure 3(b), which, at x ≥ 0.005 in La2-xTmxBaZnO5, finally decreases the emission from 1G4 state but enhances the emission from 3H4 and 3F4 state (NIR emission spectra in Figure 2). Here, Case-1, i.e., the sequential three-photon NIR-QC, becomes Case-2, i.e., the three-photon NIR-QC, with the accelerated 1480 and 1800 nm photon emission. However, once the Tm3+ content exceeds the CQ threshold of 3H4 state, e.g., x ≥ 0.01 in La2-xTmxBaZnO5, the CR of 3H4 → 3F4 + 3H6 → 3F4 (CR2) becomes rather efficient.21 Energy in the populated 3H4 state would be de-excited into the 3F4 state, thereby greatly decreasing the NIR emission at 1480 nm from the 3H4 state, but increasing the emission at 1800 nm from the 3F4 state (NIR emission spectra in Figure 2). In this case, all the energy in the excited 1G4 state would primarily be downconverted into three 1800 nm photon emissions (another style of Case-2), as presented in Figure 3(b). Furthermore, as the Tm3+ concentration x increases beyond 0.025, the NIR emission band at approximately 1800 nm quickly reduces, typically due to significant CQ caused by non-negligible energy migration among the Tm3+ sub-lattice due to the presence of impurities and defects in La2-xTmxBaZnO5 phosphors.

3.3. Energy transfer models based on dynamics in La2-xTmxBaZnO5. To better understand the processes, including spontaneous radiative transitions, CR and CQ, which determine the population dynamics of Tm3+ levels, a series of models are established in terms 8


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of the rate equation of this system. The experimental results are generalized using the model portrayed in Figure 4, and the set of rate equations required to describe the model are listed below:37

dn5 = σΦn0 − (A50 + A51 + A52 + A53 + Q5 )n5 − C1n5 dt dn3 = C1n5 + A53 n5 − (A30 + A 31 + Q3 ) n 3 − C2n3 dt dn1 = C1n5 + (A51 + A52 )n5 + 2C2n3 + A 31 n3 − (A10 + Q1 ) n1 dt

(2)

Ai = ∑ βij Aij ,(i > j )

(4)

(1)

(3)

where ni is the population of level i, σΦ represents the pumping rate, σ is the absorption cross section, and Φ is the excitation photon flux. The Aij’s are the spontaneous emission rates from the ith level to the jth level, which are determined via multiplying the branching ratio βij by the total radiative relaxation rate Ai. The Ck (k = 1, 2) and Qi (i = 1, 3, 5) represent the ET rate of CR and that of CQ, respectively. Here, the rate equations that are for the population of different levels will be solved under the following assumptions. First, the efficient population of intermediate energy levels (3H5, 3F2,3) are neglected because the energy difference between 3H5 (3F2,3) and the next 3F4 (3H4) lower level is rather small (approximately 2000 cm-1) relative to the maximum phonon energy approximately 600 cm-1 of La2BaZnO5 host. Accordingly, the rapid multiphonon relaxation dominates over the transitions between them. This assumption is consistent with the nonluminous feature of the 3H5 and 3F2,3 states under excitation of 465 nm (Figure 2). Second, upconversion phenomenon is not taken into consideration because all experiments were performed using low excitation density. Third, a low excitation density allows for neglecting any depletion of the 3H6 ground state. Thus, the ground-state population (n0) in 3H6 can be reasonably 9



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considered to be equal to the Tm3+ population (nTm). In practice, a limited number of fitting parameters and several spectroscopic parameter values are required to solve these rate equations. The critical radius is defined in terms of the competition between the donor-acceptor transfer rate and the decay rate of an isolated ion,38 and a critical radius of approximately 10 Å occurs for the CR process.39-41 Here, for the lowest Tm3+ content doped sample, La1.9995Tm0.0005BaZnO5, the Tm3+-Tm3+ distance can be determined to be 6800 Å, far larger than the 10 Å critical radius. Therefore, ET between Tm3+ ions could be ignored in La1.9995Tm0.0005BaZnO5,42 and every excited Tm3+ ion can be regarded as an isolated luminescent center, i.e., the fluorescence lifetimes of La1.9995Tm0.0005BaZnO5 can be taken as the intrinsic lifetimes. Correspondingly, the intrinsic radiation rate, equal to the reciprocal of intrinsic lifetime, can be estimated, A5 =

s-1 and A1 =

1

τ 1r

1

τ 5r

= 4098 s-1, A3 =

1

τ 3r

= 1699

= 233 s-1.

Experimentally the branching ratios (β50,51,52,53) of 1G4 energy level can be calculated by recording the 1G4 entire emission spectrum in 470-1300 nm of La1.9995Tm0.0005BaZnO5. Due to the spectral responses of the different detectors, the 1G4 entire emission spectra can be feasibly obtained by integrally normalizing the overlapped 750-850 nm emission bands after correcting for the instrumental response. For the 3H4 energy level, the branching ratios β30 and β31 can be easily calculated by comparing the emission integral intensities of the 3H4 → 3H6 and 3H4 → 3F4 in La1.9995Tm0.0005BaZnO5 excited at 690 nm. Here, due to the lack of observation of other electronic transition emissions, their branch ratio values could be regarded to be approximately zero. Correspondingly, the best set of parameter values 10


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calculated are: β50 = 0.348, β51 = 0.195, β52 = 0.329, β53 = 0.128, β30 = 0.871 and β31 = 0.129; this set well agrees with the Judd-Ofelt analysis of some Tm3+-doping, such as Tm3+-doped BaF2-Ga2O3-GeO2-La2O3 glass: β50 = 0.396, β51 = 0.141, β52 = 0.324, β53 = 0.116, β30 = 0.921 and β31 = 0.066.43 All the values of radiative transition rate are listed in Table 1. According to the above-mentioned Case-2 of two-step CR and Ref 30, the phenomenological rate constants (Ci) for CR are proportional to the microparameter and should increase linearly with ionic density, as given by

Ck = cmk ⋅ nTm

(5)

where k is either CR process 1 or 2, cmk is a coefficient constant for CR associated with the kth process, and nTm is the density of Tm3+ ions in the lattice. However, CQ is shown to be significant when the Tm3+ concentration exceeds 0.025, where energy of all excited states is trapped by the quenching centers after energy migration among Tm3+ sub-lattices. In principle, energy migration is a multi-step process involving resonant ET from one ion to another ion of the same species in a random walk manner. The CQ rate (Qi) for each excited state followed by energy migration is proportional to the square of ionic density44,45,46 2 Qi = qi ⋅ nTm

(6)

where i corresponds to the energy state, qi is a coefficient constant for CQ associated with the ion density for the energy state ni, and nTm is the ion density in the lattice. Decay curves of the 1G4 and 3H4 energy levels as a function of the Tm3+ content are shown in Figures 5(a) and 5(b), respectively. The decay rate becomes faster as the Tm3+ density increases. In practice, all the monoexponential decay curves can be well fitted to a first-order exponential function of I = A0 exp( −t / τ 0 ) , and the nonexponential one is well 11



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fitted to a second-order exponential function of I = A1 exp( −t / τ 1 ) + A2 exp( −t / τ 2 ) , where I is luminescence intensity; A0, A1 and A2 are constants, repectively; t is time; τ0 is lifetime for the single-exponential decay curve, τ1 and τ2 are fast and slow lifetime of exponential components for the nonexponential decay, respectively. Furthermore, the lifetime of the nonexponential decay curve is determined by the expression τ ave =

A1τ 12 + A2τ 22 . A1τ 1 + A2τ 2

For 1G4 and 3H4 energy levels, the decay rate consists of several competitive processes: radiative relaxation rate (Aij), nonradiative relaxation rate by multiphonon assistance and CR (Ck), and CQ rate (Qi). The radiative relaxation rate (Aij) is independent of the Tm3+ ionic density.37 The multiphonon assisted nonradiative relaxation rate is expected to be small and can be neglected with the large energy difference in this study. The CR rate (Ck) and the CQ rate (Qi) have a linear and a quadratic dependence on the Tm3+ ion density, respectively. Thus, the relaxation rates of the 1G4 and 3H4 levels can be expressed as45,46

1

−

1

τ ix τ ir where

1

τ ix

2 = Qi + Ci = qi nTm + cmk nTm

is the reciprocal of lifetime of the Tm3+ content x, and

(7)

1

τ ir

is the reciprocal of

intrinsic lifetime for energy level i. Here, i = 5 and k = 1, which corresponds to the case of the 1

G4 energy level; i = 3 and k = 2 corresponds to that of the 3H4 energy level. Next, the

parameters of q5 = 2.426×10-38 cm6·s-1, cm1 = 2.783×10-17 cm3·s-1 and q3 = 1.350×10-38 cm6·s-1, cm2 = 5.479×10-18 cm3·s-1 can be readily obtained through the nonlinear least-squares fitting method for the relaxation rate versus the Tm3+ density, as shown in Figures 5(c) and 5(d), respectively. The 3F4 energy level, the first excited state, cannot be quenched by CR between other 12


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energy levels, but the decay curves of the 3F4 energy level also change from single-exponent to non-exponent character, as shown in Figure 6(a). The relaxation rate becomes progressively faster in high Tm3+ concentration doped samples. For various Tm3+ content, the intrinsic radiative relaxation rate (A10) remains approximately constant, and the relaxation rate only increases due to the CQ rate (Q1). Thereby, the relaxation rate of 3F4 levels can be given as45,46

Q1 =

1

τ 1x

−

1

τ 1r

2 = q1 ⋅ nTm

(8)

Accordingly, the value of parameter q1 can be fit via a least squares criterion, and the best fit value is obtained for q1 = 9.322×10-40 cm6·s-1, as shown in Figure 6(b). All the parameters are listed in Table 2. It should be noted that both the rates of CR and CQ grows with Tm3+ concentration increase. At lower Tm3+ dopant concentration, the CR processes increase to dominate over the CQ, thereby leading to the enhancement of NIR emission intensity from lower energy-levels, as comparatively shown in Figures 1(a) and 2. Whereas, as Tm3+ dopant concentration increases too high, nearly all the emission intensities decrease largely due to the dominant CQ processes caused by the increase of defects and/or impurities. To confirm the model, the rate equations are solved under steady-state conditions, dni/dt = 0, with i = 1, 3, 5. The dependence of Tm3+ density on the population ratio can actually be compared with the experimental results because the population ratio between two emitting levels is proportional to the corresponding ratio of their emission integrated intensities. The ratio of n3/n5 between 3H4 and 1G4 population and the ratio of n1/n5 between 3F4 and 1G4 population can be deduced from the steady-state equations. Equation (2) is then expressed as

13



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n3 A53 + C1 A53 + cm1nTm = = 2 n5 A3 + C2 + Q3 A3 + cm 2nTm + q3nTm

(9)

that is, after reaching the stationary regime, the population ratio of the 3H4 and 1G4 energy levels depends on the Tm3+ density. Using the values of parameters, A53 = 648 s-1, A3 = 1699 s-1, cm1 = 2.783×10-17 cm3·s-1, cm2 = 5.479×10-18 cm3·s-1 and q3 = 1.350×10-38 cm6·s-1, a curve as a function of the Tm3+ density is obtained, as shown in Figure 7(a). Note that the experimental results of the n(3H4)/n(1G4) ratio is I(3H4 → 3F4)/I(1G4 → 3H4) under excitation at 465 nm. Both the simulated curve and the experimental data first increase and then decrease with the increase of the Tm3+ density. The increase of the n(3H4)/n(1G4) ratio at higher Tm3+ density is because the rate of 1G4 → 3H4 + 3H6 → 3H5 CR (C1) is greater than the sum of that of 3H4 → 3F4 + 3H6 → 3F4 (C2) and that of the CQ rate (Q3). However, as the Tm3+ content further increases, the relaxation rate of the 3H4 energy level exceeds C1 due to the rather efficient 3H4 → 3F4 + 3H6 → 3F4, resulting in the ratio decrease. The deviation between the simulated curve and the experimental results might be due to the experimental uncertainties in the case of weak photoluminescence. Using the same approach to solve Equations (1), (2) and (3), the ratio of n(3F4)/n(1G4) can be presented as

n1 A51 + A52 + C1 ( A31 + 2C2 )( A53 + C1 ) = + n5 A10 + Q1 ( A3 + C2 + Q3 )( A10 + Q1 )

(10)

where the direct comparison of the emission integral intensities between the 3F4 and 1G4 excited states is possible only after instrumental response correction and normalization through the overlapped emission bands at approximately 800 nm (availably measured by both R928 and R5509-72 PMTs) and 1480 nm (effectively detected by both R5509-72 PMT and 14


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G5852 InGaAs PIN photodiode). Thus, it is also reasonable to compare the emission intensity of 3F4 → 3H6 with the population of the 3F4 excited state (n1), which, combining Equations (1) and (10), could be derived as ⎡ A + A52 + C1 ( A31 + 2C 2 )( A53 + C1 ) ⎤ n1 = n5 ⎢ 51 + ⎥ ( A + Q A 10 1 3 + C 2 + Q 3 )( A10 + Q1 ) ⎦ ⎣

(11)

Utilizing some parameters from Tables 1 and 2 in Equation (11), both the population of n1 and the emission integral intensity of 3F4 → 3H6 are normalized, as shown in Figure 7(b). The simulated curve is well consistent with the experimental curve versus Tm3+ density, which first increases and then decreases with the maximum value occurring at certain content. These curves increase because a sequential two-step CR process rapidly populates the 3F4 energy level, while the curves decrease due to the more efficient CQ rates from 3F4 excited state than radiative rates. Deviation between the simulated curve and the experimental curve is present in the heavily Tm3+-doped samples, which indicates that the actual concentration is more substantial than the model expected. Generally, through the rate-equation modeling, the simulated results are demonstrated to be in good accord with the experimental results. All of these results obviously reveal that the effects of CR and CQ are significant to the three-photon NIR-QC of Tm3+ as the Tm3+ ion density increases in La2-xTmxBaZnO5.

3.4. Internal quantum yield calculation in La2-xTmxBaZnO5. La2-xTmxBaZnO5 can represent the system of the Tm3+ quantum tripler.21 The higher Tm3+ ionic density in La2BaZnO5 promotes the occurrence of a quantum tripler via a sequential two-step CR between Tm3+.21 However, in a heavily Tm3+-doped system, the influence of CQ cannot be 15



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neglected. Thus the internal QY of the quantum tripling system is quite complicated. Generally, the QY of each level is not a constant value, but depends on several factors like the vibrational frequency of host lattice, energy difference between two neighboring energy levels, etc. Figures 1(a) and 2 indicate that there exist radiative transitions only from 1G4, 3H4 and 3F4 levels of Tm3+. It means that, due to the relatively small band gaps of 3F2,3 → 3H4 and 3H5 → 3

F4, both the QY of 3F2,3 and 3H5 states could be zero, thereby noluminescence detected in

experiments. Most importantly, there is another dimension to the QY of emitting levels, which is efficiently caused by energy migration to quenching centers like defects and impurities, especially in the samples with higher dopant concentration. According to the mechanisms of CR and CQ, the internal QY can be expressed as19,30

ηQY = ηVIS + ηNIR = η1G (1 − ηCR1 ) + η 3 H [η1G (1 − ηCR1 ) β53 + ηCR1 ](1 − ηCR 2 ) 4

4

(12)

4

+ η 3F {η1G (1 − ηCR1 )( β51 + β52 ) + η 3H [η1G (1 − ηCR1 )β53 + ηCR1 ](1 − ηCR 2 )β31 + ηCR1 + 2ηCR 2 } 4

4

where η1G , η 3 H 4

4

4

and η 3 F

4

4

is the radiative QY of 1G4, 3H4 and 3F4 energy level,

respectively. ηCR1 and ηCR 2 are the CR efficiency values of 1G4 → 3H4 + 3H6 → 3H5 (CR1) and 3H4 → 3F4 + 3H6 → 3F4 (CR2), respectively. βij is the luminescence branch ratio from energy levels i to j. The radiative QY is defined as the ratio of the intrinsic radiative rate to the total relaxation rate (comprised of the radiative transition rate and the CQ rate), which can be given by30

ηG = 1

4

τ −G1 1

(13)

4

Q5 + τ 1−G1

4

ηH = 3

4

τ −H1 3

(14)

4

Q3 + τ 3−H1

4

16


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ηF = 3

4

τ −F1 3

4

Q1 + τ 3−F1

(15)

4

where τ 1−G1 , τ 3−H1 4

4

and τ 3−F1 are the intrinsic radiative rates of 1G4, 3H4 and 3F4, and equal to 4

A5, A3 and A1, respectively. Q5, Q3 and Q1 are CQ rates of 1G4, 3H4 and 3F4, respectively. As the quantum tripling at higher Tm3+ concentration occurs through CR processes, the CR efficiency can be further expressed as30

ηCR1 =

C1 C1 + τ 1−G1

(16)

C2 C2 + τ 3−H1

(17)

4

ηCR 2 =

4

where C1 and C2 are the CR rates of the 1G4 and 3H4 states, respectively, versus the Tm3+ concentration. Table 3 summarizes the internal QY of various samples: i) ηQY is greater than 100% for the lowest doped Tm3+ sample due to a sequential three-step NIR quantum splitting from the excited Tm3+: 1G4 state;19 ii) with the increase of the Tm3+ content, the internal QY increases from 124% to 198% due to the increase of the CR rate C1 and C2; iii) as the Tm3+ content exceeds 0.01, the internal QY reduces to 47% for the La1.925Tm0.075BaZnO5 sample, which is due to the more efficient CQ rates than the CR rates. However, if we do not take CQ into consideration, the internal QY always increases with Tm3+ concentration (Table 3). These results clarify the apparent conflict with the spectroscopic experiments obtained in heavily doped samples.

4. CONCLUSIONS In summary, two different three-photon NIR-QC mechanisms were proposed via analysis of 17



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the VIS-NIR-MIR spectra and the decay curves in Tm3+-doped La2BaZnO5 system. The predominance of CR and CQ as a function of Tm3+ density is quantified on the basis of the rate-equation model, which provides good agreement with the experimental results. Following the parameters determined by the modeling results in La2-xTmxBaZnO5, we further performed the calculation of internal QY versus Tm3+ concentration that more than unit. Without considering CQ, the internal QE dependence on the Tm3+ density is contrary to the experimental result. If we take into account the effect of quenching processes among Tm3+ ions, then the internal QE is much closer to the real efficiency. These competing processes drastically limit the efficiency of Tm3+ quantum tripler; however, the insights obtained will contribute to the development of optimized quantum cutting materials. Noted that, to the application in area of solar-voltaic or even in imaging, the different sample preparation, such as in the form of thin film, nanocrystals, or as a colloidal solution, would be crucial, where the optical properties and luminescence efficiencies have some changes relevant to some factors like refractive index, particle morphology, optical transparency and size distribution, etc.

18


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ACKNOWLEDGEMENTS T. Y. and H. L. contributed equally to this work. Financial support from the National Science Foundation of China (Grant nos. 51125005 and 51472088) is gratefully acknowledged. We gratefully acknowledge Prof. A Meijerink and Dr. FT Rabouw (Utrecht University) for mid-infrared spectra measurements and Prof. C Liu and Dr. ZY Zhao (Wuhan University of Technology) for decay lifetime measurements.

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(45) de Sousa, D. F.; Nunes, L. A. O. Microscopic and Macroscopic Parameters of Energy Transfer between Tm3+ Ions in Fluoroindogallate Glasses. Phys. Rev. B 2002, 66, 024207. (46) M J V Bell; W G Quirino; S L Qliveira; D F de Sousa and L A O Nunes. Cooperative Luminescence in Yb3+-doped Phosphate Glasses. J. Phys.: Condens. Matter 2003, 15, 4877-4887.

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Graphical TOC Entry

Tm3+ concentration dependent three-photon near-infrared quantum cutting in La2BaZnO5 has been demonstrated for ultra-efficient optical converters.

26


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Figure captions:

Figure 1. (a) Emission spectra of La2-xTmxBaZnO5 samples under excitation of 465 nm, where the fluorescence integral intensity in 750-850 nm are normalized. Decay curves of (b) La1.9995Tm0.0005BaZnO5 and (c) La1.975Tm0.025BaZnO5 obtained at 651, 784 and 798 nm.

Figure 2. NIR emission spectra of La2-xTmxBaZnO5 samples upon excitation at 465 nm. Inset: the integrated emission intensities as a function of Tm3+ concentration.

Figure 3. Two different mechanisms of the multi-photons process: (a) a sequential three-step three-photon NIR quantum splitting (Case-1); and (b) a possible CR mechanism that results in the emission of three photons (Case-2) for each absorbed photon in the Tm3+: 1G4 state.

Figure 4. Schematic energy level diagram of Tm3+ illustrating the fluorescence and ET processes. Solid arrows represent excitation and radiation transitions, dashed arrows represent CR processes and CQ, and broken lines represent non-radiative relaxation.

Figure 5. Fluorescent decay curves of (a) 1G4 (λex = 465 nm, λem = 651 nm) and (b) 3H4 (λex = 690 nm, λem = 798 nm) energy levels versus Tm3+ content, and the orange solid curves are the fitted curves. Relaxation rate of (c) 1G4 and (d) 3H4 energy levels as a function of Tm3+ density; solid spheres are the experimental results of the La2-xTmxBaZnO5 samples, and the red curve is the fitting outcome.

27



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Figure 6. (a) Decay curves of the 3F4 (λex = 800 nm, λem = 1800 nm) energy level for various Tm3+ content, and the navy solid curves are the fitted curves. (b) Relaxation rate of the 3F4 energy levels as a function of Tm3+ density; solid spheres are the experimental results of the La2-xTmxBaZnO5 samples, and the red curve is the fitting outcome.

Figure 7. (a) Experimental emission intensity ratio compared to the simulated population ratio, and (b) normalized experimental emission intensity (3F4-3H6) compared to the simulated population as a function of the Tm3+ content.

28


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Table captions:

Table 1. The values of radiative transition rate Aij.

Table 2. The microparameter constants of CR, cm1 and cm2, and CQ, q1, q3 and q5.

Table 3. The internal QY of different Tm3+-doped samples.

29



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Figures

Figure 1

30


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Figure 2

31



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Figure 3

32


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Figure 4

33



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Figure 5

34


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Figure 6

35



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Figure 7

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Table 1 Parameter

Value (s-1)

A50

1719

G4 → 3F4

A51

981

1

G4 → 3H5

A52

750

1

G4 → 3H4

A53

648

3

H4 → 3H6

A30

1481

Transition 1

G4 → 3H6

1

3

H4 → 3F4

A31

218

3

F4 → 3H6

A10

233

37



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Table 2 ET process

Parameter

Value

1

G4 → 3H4 + 3H6 → 3H5 (CR1)

cm1

2.783×10-17 cm3·s-1

3

H4 → 3F4 + 3H6 → 3F4 (CR2)

cm2

5.479×10-18 cm3·s-1

1

G4 → 1G4 → ··· → quenching

q5

2.426×10-38 cm6·s-1

3

H4 → 3H4 → ··· → quenching

q3

1.350×10-38 cm6·s-1

3

F4 → 3F4 → ··· → quenching

q1

9.322×10-40 cm6·s-1

38


Page 39 of 39

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Table 3 Tm3+ Content (x%)

0.05

0.25

0.5

1.0

2.5

3.5

5.0

6.0

7.5

ηQY (%)

124

158

183

198

159

124

84

66

47

ηQY (%)-without CQ

124

160

188

221

258

268

277

280

284

39


Energy Transfer Dynamics and Quantum Yield Derivation of the Tm3+

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