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Comprehensive Rate Equation Analysis of Upconversion Luminescence Enhancement Due to BaCl Nanocrystals in Neodymium Doped Fluorozirconate-based Glass Ceramics 2

Ulrich Skrzypczak, Charlotte Pfau, Gerhard Seifert, and Stefan Schweizer J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp5021033 • Publication Date (Web): 28 May 2014 Downloaded from http://pubs.acs.org on June 2, 2014

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The Journal of Physical Chemistry

Comprehensive Rate Equation Analysis of Upconversion Luminescence Enhancement Due to BaCl2 Nanocrystals in Neodymium Doped Fluorozirconate-based Glass Ceramics

U. Skrzypczak1,*, C. Pfau1, G. Seifert1,2, S. Schweizer3,4 1

Centre for Innovation Competence SiLi-nano®, Martin Luther University of HalleWittenberg, Karl-Freiherr-von-Fritsch-Str. 3, 06120 Halle (Saale), Germany

2

Fraunhofer Center for Silicon Photovoltaics CSP, Otto-Eißfeldt-Str. 12, 06120 Halle (Saale), Germany 3

Department of Electrical Engineering, South Westphalia University of Applied Sciences, Lübecker Ring 2, 59494 Soest, Germany

4

Frauhofer Application Center for Inorganic Phosphors, Branch Lab of Fraunhofer Institute for Mechanics of Materials IWM, Walter-Hülse-Str. 1, 06120 Halle (Saale), Germany

*Corresponding author: [email protected]

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Abstract

In neodymium-doped fluorozirconate-based glasses, a huge increase of up to a factor of 20 of the Nd3+ photoemission is possible by the introduction of BaCl2 nanocrystals. A rate equation system was developed to describe the excitation and relaxation dynamics of neodymium ions in such composite matrix to quantify the enhancement mechanism due to the embedded nanocrystals. The model is extended to include the previously unknown quantitative nanocrystal influences in an effective-medium model, considering the change in the phonon spectrum

in

particular.

Having

verified

the

coefficients

with

time-dependent

photoluminescence experiments, it is used to predict the intensity dependence of steady-state upconversion. The good agreement to experimental data indicates that the rate equations enable the quantitative simulation of photon upconversion in glass and glass-ceramics under a variety of excitation scenarios. In addition, the strong reduction of the phonon emission probability in the BaCl2 nanocrystals is confirmed as the key reason for (upconversion) emission enhancement in the fluorozirconate-based glass ceramics.

Keywords: Rare-Earths, Glasses, Glass ceramics, Optical Spectroscopy, Rate equations


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1. Introduction Photonic glasses doped with rare-earth (RE) ions such as erbium, neodymium or europium have gathered widespread interest concerning their applicability as active mediums in conventional1,2 or upconversion3,4 laser systems, as phosphors of ionizing radiation,5-7 frequency converters in light emitting diodes8 and 3D-displays.9 In any of the aforementioned technologies, special attention is paid to the reduction of excitation losses to either the glass matrix, parasitic processes detrimental to the particular optical transitions of interest, or any impurities from the glass preparation. In particular, losses to the glass matrix in the form of multiphonon-relaxation (MPR) cause a strong dependency on the host material, because the maximum phonon frequency available in a matrix defines the order of the phononic process, and thus governs the probability of MPR. Among favorable optical matrices the ZBLAN family10 of fluorozirconate glasses has proven to be particularly useful due to its broad optical transparency, good RE solubility and in particular due to its low maximum phonon energies of around 580 cm-1.11,12

As previously shown,13,14 hexagonal BaCl2 nanocrystals can be uniformly grown within ZBLAN-based glasses by the exchange of some of the fluoride by chloride and a thermal treatment procedure following glass production. Contrary to their bulk counterpart, these nanometer sized crystals15 are stable within the glass matrix. When the optically active ions are embedded in the nanocrystals, their even lower phonon energies with a maximum12,16 of 220 cm-1 lead to a drastic increase of luminescence14 and upconversion intensities.13,17 The general idea of frequency conversion with RE ions in nanometric particles is not new, and possibilities for controlling their dynamics have recently been reviewed.18



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Rate equation analysis of RE ions in general and neodymium in particular has been intensely investigated by Pollnau et al. for different host materials.19,20 Similar analyses in literature often focus on neodymium lasing, with some exceptions,21 as usually there is no significant emission from higher levels as to their prevalently quick depletion by MPR. On the other hand, the RE specific mechanisms leading to upconversion were extensively investigated by Auzel.22 A comprehensive rate equation treatment of a composite material system as the presented glass ceramics has, to the best of our knowledge, not been reported in the literature so far.

The target of this work is a spectrally-resolved rate equation description of all optical transitions of neodymium inside ZBLAN-based glasses and glass ceramics, since a detailed understanding of the physical mechanisms behind the efficiency enhancement is the basis for further material optimization. Based on both theoretically and experimentally derived coefficients, experimental spectra and luminescence decays are described and verified in dependence of dopant-concentration, excitation power and nanocrystal influence to establish a quantitative description of the excitation dynamics. From this description, the rates of the major processes can be extracted, the mechanisms of luminescence enhancement by the nanocrystals can be confirmed, and quantitative simulations to predict the ‘best’ material composition for a special upconversion situation become possible.

2. Methods 2.1 Sample preparation The glasses and glass-nanocrystal composites are based on the ZBLAN composition.10 Substituting a part of the fluorine for chlorine ions yields the base material for the composite, namely

(53-x)ZrF4-10BaF2-10BaCl2-(20-x)NaCl-3.5LaF3-3AlF3-0.5InF3-xKCl-xNdF3. 4 ACS Paragon Plus Environment

A

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sample series at two different doping levels, x = 1 mol% and x = 5 mol%, was prepared. In the following, abbreviations for the samples will be used as introduced in Table 1.

Table 1. Sample abbreviations Sample type ZBLAN-based FCZ glass, as-made ZBLAN-based FCZ glass, heat-treated at 260 °C

Nd3+ doping level 1 mol% 5 mol% FCZ1 FCZ5 FCZ1-c FCZ5-c

The chemicals were melted in a glassy carbon crucible at 745 °C under an inert gas (argon) atmosphere. Poured into a brass mold at 200 °C temperature, the melt was then left to cool down to room temperature. The formation of differently sized BaCl2 nanocrystals inside the glass was induced by a subsequent annealing step of 20 minutes. The choice of the annealing temperature in the range between 240 °C and 260 °C determines the average size of the resulting nanocrystals.13,14 Higher annealing temperatures changed the visual appearance of the FCZ samples from transparent to milky white. The nanocrystal volume fraction and average size were determined previously to be around 20% and 20 nm, respectively.15

2.2 Spectroscopic measurements Linear absorption measurements were accomplished with a PerkinElmer Lambda900 photospectrometer. Pulsed emission spectra and photoluminescence decays were obtained with a femtosecond laser source (Light Conversion Pharos) equipped with an optical parametric amplifier (Light Conversion Orpheus). Excitation frequencies within the visible and near-infrared spectral region were used, with pulse lengths of around 180 fs and at repetition rates of 100 Hz or less. The latter was achieved by controlling the regenerative amplifier’s pulse picker with a frequency division system. This ensured that the equilibrium state of the neodymium ions is safely reached prior to the next excitation pulse. To exclude 5 ACS Paragon Plus Environment


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nonlinear optical effects like instantaneous multiphoton absorption, second harmonic generation and absorption saturation, 23 the laser intensity was always kept as low as possible. Besides pulsed excitation at various wavelengths, continuous-wave pumping was accomplished near 800 nm with a diode laser (Axcel Photonics M9-808-0100). Photoluminescence was then detected at room temperature with photomultiplier tubes (Hamamatsu R943 and H10330A), attached to a spectral monochromator (Acton SP2500). Photoluminescence decays were recorded with a photon counter (PicoQuant NanoHarp 250).

2.3 Rate equation model The energy level scheme of neodymium was mapped to 15 excited states up to 25,000 cm-1, labeled simply by their order number j, and the ground state (see Figure 1); population density on the levels is denoted as Nj. Processes involving higher lying levels were not considered, because these are located above the glass absorption edge and therefore overlapped by the much stronger matrix absorption. Levels at energy positions separated by less than or approximately equal to kBT were treated as one effective level: any population exchange between the levels of such a group can be treated as instantaneous since the relevant phonon transition rates are expected in the nano- to picosecond timescale (considering the energy gap laws for the analyzed samples (see Section 2.3.1).

In general, population enters the system via either pulsed or continuous laser excitation transferring ions from ground state to an excited state (ground state absorption, GSA). Subsequently, spontaneous emission is possible from each populated to any lower lying level. For all levels, apart from the metastable level N4, the main relaxation channel will be the emission of one or more phonons (multi-phonon-relaxation, MPR) and the resulting decay to the next lower lying level. Thermal population of the next higher lying level by the absorption 6 ACS Paragon Plus Environment

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of phonons is also possible but at significantly smaller rates. Apart from that, the prerequisite for spectral upconversion, i.e. population of any levels lying higher than the initially excited one can only be achieved by two main processes: The first process, called energy transfer upconversion (ETU), is the energy transfer between two excited ions, donor and acceptor, exciting the acceptor to a higher, and the donor simultaneously to a suitable lower level. The highest levels are reached, when the donor is de-excited back to the ground level (ETU4 in Figure 1). The second upconverting mechanism is the absorption of pump light by an already excited ion, called excited-state-absorption (ESA). For a typical situation like that sketched in Figure 1, phonon relaxation is necessary before the second excitation step, i.e. a persisting pump light is required. Contrary to these mechanisms, another ion-ion process, the crossrelaxation (CR), does not increase the net excitation in the higher levels, but depletes them, as it transfers energy from an excited ion to an ion in the ground state, leaving both in a low energy state. An overview of the processes and the participating levels is given in Figure 1; details on the physics and the model description of these processes will be discussed in the following sections.



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Figure 1. Significant processes considered during the analysis for the cw pumping scheme: ground state absorption (GSA) near 800 nm, excited state absorption (ESA) of the pump radiation, energy transfer (ETU) upconversion and cross-relaxation (CR). Not shown are processes involving phonons between any adjacent levels, as well as radiative decays from each level to any lower lying level. Also, stimulated emission (STE) at the pumping wavelength is not shown here for brevity.

2.3.1 Spontaneous processes The Einstein coefficients used here to describe the spontaneous emission (SPE) are based on the results of a Judd-Ofelt analysis24-26 published previously.27,28 For the case of glass ceramics, this was accomplished using an effective-refractive index medium.

Table 2. Energy level (group) assignment with approximate spectral positions


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j 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

level 4 I9/2 4 I11/2 4 I13/2 4 I15/2 4 F3/2 4 F5/2+2H9/2 4 F7/2+4S3/2 4 F9/2 2 H11/2 4 G5/2+2G7/2 2 K13/2+4G7/2 4 G9/2 2 K15/2+2G9/2+2(D,P)3/2 4 G11/2 2 P1/2 2 D5/2

λ / nm k / cm-1 ground state 5,315 1,900 2,560 3,900 1,695 5,900 865 11,500 795 12,500 740 13,500 680 14,700 625 15,900 580 17,300 520 19,200 510 19,600 475 21,100 455 21,900 430 23,100 425 23,400

The energy levels are abbreviated for clarity in the following text. Their assignment is summarized in Table 2, with energy positions consistent to literature values.29-33 As already mentioned, thermal coupling (quasi-instantaneous population redistribution) was assumed whenever the spectral separation of two or more (considerably broadened) levels was in the order of kBT. The strong broadening of the spectral features in this amorphous host is clearly seen in the absorption spectrum shown in Figure 2.

Figure 2. Absorption cross-section spectrum of glass sample FCZ1. The numbers j mark the absorption transitions N0 to Nj. The levels 1 to 3 are not shown here. 9 ACS Paragon Plus Environment


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Decay rates of the individual levels of thermally coupled level groups were Boltzmannweighted. Together with the branching ratios β, all radiative transitions from any level to any lower-lying level were accounted for with a coefficient matrix such that the population of each level j has loss and gain terms of the form

, = −, + , ,

(1)

where ASPE,j is the total radiative decay rate of level j, the product ASPE,j·βi,j the rate of population increase coming from higher lying levels i, with i > j (implicit summation over all i). 2.3.2 Stimulated processes Stimulated processes include ground state absorption (GSA), excited state absorption (ESA) and stimulated emission (STE). For modeling GSA, the two excitation schemes need to be considered independently. For pulsed excitation, the generation rate of population on the target level follows the temporal shape of the pump laser pulse:21,34

= + / .

(2)

Here, = /ℎ , I is the optical intensity and ν the laser frequency. The pulse duration τ was determined precisely from SHG-FROG (Second-Harmonic Generation-FrequencyResolved Optical Gating35) measurements to be τ = (178.3 ± 0.9) fs. The GSA cross- sections for each excitation wavelengths, σGSA, were determined from absorption spectroscopy (see Figure 2). In case of continuous pumping, the coefficient for GSA is the same, but without the time dependence. In all excitation schemes, the optical intensity I was treated in a spatially resolved manner in simplified cylindrical coordinates, &'

!, " = exp − ( − * " )

(3)

to account for the nonlinear pump power dependence of several processes throughout the Gaussian laser profile inside the sample. In equation (3), w0 is the Gaussian beam waist and is 10 ACS Paragon Plus Environment

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either 1 mm or 50 µm for pulsed or cw excitation, respectively. In the following, the resulting r-z-discretization of the resulting population densities Nj(r,z,t) is implicitly presumed. In the pulsed, weak pumping regime, the absorption coefficient α in Eq.(3) equals σGSA·N0(t = 0), because ESA does not play a role. In the cw pumping case, α must be replaced by σGSA·N0 + σESA·N4. With an approximate matrix density of 4.3 g/cm3,36 the total RE ion density N0(t = 0) was estimated to be 1.8·1026 m-3 for the FCZ1 and FCZ1-c, and 8.8·1026 m-3 for the FCZ5 and FCZ5-c samples and was assumed to be maintained over the nanocrystal growth procedure as no clustering-related concentration quenching was found.

ESA can be modeled in analogy to GSA. Which ESA processes need to be considered, depends on the question, what higher lying level(s) can be populated with the pump photons by transitions from the level(s) initially populated via GSA. For 800 nm pumping, one process gives a non-vanishing spectral overlap integral, namely N4 to N15 (see Figure 1). The metastable level N4 is also the only long-living level being able to accumulate enough population for probable ESA. Shorter pumping wavelengths have no matching absorption overlap. The corresponding absorption cross-section was then calculated with -

+ = ,+, . / 0 1 .

(4)

Here, g(ν0) is the lineshape function of N4 at the ESA frequency and j = 15 and i = 4 are the participating levels. The refractive index n is either the one for plain ZBLAN or for the effective-n medium,27 depending on the sample type. The obtained ESA cross-sections are 0.016 pm2 for the glass and 0.018 pm2 for the glass-ceramic samples. These relatively low cross-sections, afflicted with the standard Judd-Ofelt uncertainty of 10-20%, are comparable to literature values for neodymium in another host material.37 The ESA process enters the rate equations of the involved levels exactly as in the GSA case. To account for energy conservation, however, the relative amount of optical intensity entering ESA with respect to 11 ACS Paragon Plus Environment


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GSA was estimated from the spectral overlap integral of each transition and weighted accordingly with a factor η for ESA and (1-η) for GSA, respectively. This yielded η = 2% for the FCZ5 glass and 11% for the FCZ5-c glass ceramic. The higher η for the latter is expected, as the additional Stark splitting increases line widths in these samples. Nonetheless, the overlap integrals already show that the probability for ESA at the pumping wavelength is way below the one for GSA.

Stimulated emission at the pump wavelength is accounted for in again a similar way. The respective cross-sections have been determined from Einstein coefficient relations; for the respective transition from N5 to N0 values of 3.7 pm2 were found for the untreated and 3.3 pm2 for the samples with nanocrystals. Both values are in agreement with literature values for FZ glasses.29,38

2.3.3 Non-radiative processes involving phonons For the glass matrix, the MPR rate dispersion, i.e. the dependence of the phonon emission probability on the energy gap to the next lower lying level, is known in the form of energy gap laws.39,40 Recently, a similar analysis derived an effective energy gap law for the glass matrix and the glass-ceramic matrix from the temperature dependence of photoluminescence data amongst others.41 The energy gap laws enable calculating the population decrease rate from Nj in the form –WPE,j(∆Ej) Nj(t), where ∆Ej is the energy gap between level Nj and Nj-1. The same term with the opposite sign enters the equation of the next lower lying level, j-1, to account for particle or energy conservation, respectively.


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The inverse process to phonon emission, that is the absorption of phonons, also depends strongly on the energy gap (to the next higher lying level). The rate constant WPA is related to the phonon emission rate WPE by42,43

23, = 4+5/67 8 2, ,

(5)

yielding WPA ≈ 0.01 WPE for typical energy gaps of 1000 cm-1. This is enough to transfer a significant amount of population to higher states, which is particularly relevant for the metastable level N4. In summary, transitions involving phonons in either way contribute to the population change of level j in the form of

3/, = −2, + 2,9: 9: + 23, : − 23,9: .

(6)

2.3.4 Non-radiative processes involving ion-ion interactions For neodymium, several ion-ion interactions are possible provided that sufficiently small ion-ion distances (given by the ion density) are present. Two process classes are possible that lead either to up- (ETU) or to down-conversion (CR) of excitation frequency. As spectral overlap between acceptor and donor transition again determines the significance of the overall process, the spectral overlap integrals have been determined for all combinations of transitions. Non-vanishing values were found for seven ETU and one CR processes as outlined in Figure 1. As three out of four ETU processes (denoted ETU2 to ETU4) end in nearby states, they have been merged symbolically to one arrow in the figure.

Table 3. ETU processes and the corresponding rate constants Symbol ETU1 ETU2a ETU2b ETU3a

Process 2·N4 → N3 + N9 N2 + N10 N2 + N11 N1 + N12

k / cm- AETU in 10-24 s-1m3 FCZ5 FCZ5-c 5,600 39.2 40.5 7,500 53.2 48.5 7,700 15.1 18.1 9,900 46.1 44.4 1



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ETU3b ETU4a ETU4b

N1 + N13 N0 + N14 N0 + N15

10,300 16.3 12,100 59.8 12,300 1.3

22.1 55.7 1.6

Table 3 lists these processes together with their rate coefficients which have been determined by calculating the total ETU constant with the formula given by Ref. (44), and then distributed over the single processes by their relative weights with the overlap integrals. The ETU processes enter the rate equations for the level N4 from which they originate as

;

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