Review—Temperature Dependence of Luminescence Intensity and Decay Time in Mn⁴⁺-Activated Fluoride and Oxyfluoride Phosphors

In principle, the phonon-assisted activation model can be applied to the luminescence phenomena caused by the dipole forbidden transitions, especially for the intra-3d-orbital transitions in ions, such as Mn⁴⁺, Cr³⁺, and Mn²⁺. Figure 2 shows the Tanabe−Sugano energy-level diagram for the 3d³ configuration of Mn⁴⁺. The intra-3d³-shell transitions in Mn⁴⁺ are caused by the parity-forbidden transitions. Therefore, the luminescence intensity due to such parity-forbidden transitions, ² E_g → ⁴ T_2g , should be very weaker than the usual parity-allowed transitions. However, one can measure relatively sharp, strong, and efficient emission peaks caused by an activation due to the local vibration modes of the Mn⁴⁺-related octahedral complexes.

The temperature dependence of the PL intensity can now be written as

$$\begin{eqnarray}\begin{array}{lll}{I}_{{\rm{PL}}}\left(T\right) & = & {I}_{{\rm{ZPL}}}+{I}_{{\rm{S}}}\left(T\right)+{I}_{a \mbox{-} S}\left(T\right)\\ & = & {I}_{{\rm{ZPL}}}\,+\,c\displaystyle \displaystyle \sum _{j}{\left|\left\langle i\right|{M}_{j}\left|f\right\rangle \right|}^{2}{\left({E}_{{\rm{ZPL}}}\mp h{\nu }_{j}\right)}^{4}\left({n}_{j}+\displaystyle \frac{1}{2}\pm \displaystyle \frac{1}{2}\right)\end{array}\end{eqnarray} \tag{ 5 }$$

where c is a proportionality constant, ∣〈i∣M_j ∣f〉∣ is an optical transition operator (i = initial state; f = final state; M_j = momentum matrix element), E_ZPL is the ZPL emission energy, and ν_j is the lattice or local vibrational frequency in a octahedral complex (j = vibration mode). The upper and lower signs in Eq. 5 correspond to the Stokes and anti-Stokes processes, respectively, and n_j is the Bose–Einstein occupation number given by

$$\begin{eqnarray}&&{n}_{j}\,=\,\displaystyle \frac{1}{\exp \left(h{\nu }_{j}/{k}_{{\rm{B}}}T\right)-1}\end{eqnarray} \tag{ 6 }$$

The Stokes and anti-Stokes emission components I_S and I_a−S can be given by ^13,14

$$\begin{eqnarray}&&{I}_{{\rm{S}}}\left(T\right)=c\displaystyle \displaystyle \sum _{j}{\left|\left\langle i\right|{M}_{j}\left|f\right\rangle \right|}^{2}{\left({E}_{{\rm{ZPL}}}-h{\nu }_{j}\right)}^{4}\left(1+{n}_{j}+\alpha T\right)\end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray}&&{I}_{a \mbox{-} S}\left(T\right)=c\displaystyle \displaystyle \sum _{j}{\left|\left\langle i\right|{M}_{j}\left|f\right\rangle \right|}^{2}{\left({E}_{{\rm{ZPL}}}+h{\nu }_{j}\right)}^{4}\left({n}_{j}+\alpha T\right)\end{eqnarray} \tag{ 8 }$$

Not only the optical phonons but also the acoustic phonons may act an important part in the phonon-assisted luminescence activation process. Therefore, we added an acoustic phonon term, αT, to Eqs. 7 and 8. This term is understood to be proportional to T. ¹⁵ Assuming αT = 0, for simplicity, the anti-Stokes to Stokes ratio can be given from Eqs. 7 and 8 by ^13,14

$$\begin{eqnarray}&&\displaystyle \frac{{I}_{{\rm{a}}-{\rm{S}}}\left(T\right)}{{I}_{{\rm{S}}}\left(T\right)}=\displaystyle \displaystyle \sum _{j}{\left(\displaystyle \frac{{E}_{0}+h{\nu }_{j}}{{E}_{0}-h{\nu }_{j}}\right)}^{4}\exp \left(-\displaystyle \frac{h{\nu }_{j}}{{k}_{{\rm{B}}}T}\right)\end{eqnarray} \tag{ 9 }$$

Expressions 5, 7, and 8 promise that the total luminescence intensity I_PL(T) is written as (Ref. 14)

$$\begin{eqnarray}\begin{array}{lll}{I}_{{\rm{PL}}}\left(T\right) & = & {I}_{{\rm{ZPL}}}+c\displaystyle \displaystyle \sum _{j}{\left|\left\langle i\right|{M}_{j}\left|f\right\rangle \right|}^{2}{\left({E}_{{\rm{ZPL}}}\right)}^{4}\left(1+2{n}_{j}+2\alpha T\right)\\ & = & {I}_{{\rm{ZPL}}}+c\displaystyle \displaystyle \sum _{j}{\left|\left\langle i\right|{M}_{j}\left|f\right\rangle \right|}^{2}{\left({E}_{{\rm{ZPL}}}\right)}^{4}\\ & & \,\times \,\left[1+\displaystyle \frac{2}{\exp \left(h{\nu }_{j}/{k}_{{\rm{B}}}T\right)-1}+2\alpha T\right]\end{array}\end{eqnarray} \tag{ 10 }$$

with an assumption of E_ZPL ± hν_j ∼ E_ZPL. Simplification of Eq. 10 gives

$$\begin{eqnarray}&&{I}_{{\rm{PL}}}\left(T\right)={I}_{0}\left[1+\displaystyle \frac{2}{\exp \left(h{\nu }_{{\rm{s}}}/{k}_{{\rm{B}}}T\right)-1}+2\alpha T\right]\end{eqnarray} \tag{ 11 }$$

where ν_s is the appropriately weighted average frequency of the various lattice vibrations in the Mn⁴⁺-activated phosphors. In Eq. 11, we included the I_ZPL term into the Stokes component one. This is because the intensity of the I_ZPL term is usually much smaller than that of the Stokes component one (I_S) and, moreover, both terms exhibit no strong temperature dependence below ∼400 K (see, e.g., Fig. 7 below).

Combining Eqs. 4 and 11, we finally obtain an expression for the temperature dependence of the Mn⁴⁺ emission intensity in the various host materials, like fluorides, oxides, and oxyfluorides, by

$$\begin{eqnarray}&&{I}_{{\rm{PL}}}\left(T\right)={I}_{0}\left[1+\displaystyle \frac{2}{\exp \left(h{\nu }_{{\rm{s}}}/{k}_{{\rm{B}}}T\right)}+2\alpha T\right]\displaystyle \frac{1}{1+\displaystyle {\sum }_{i}{a}_{i}\exp \left(-\tfrac{{E}_{{\rm{q}}i}}{{k}_{{\rm{B}}}T}\right)}\end{eqnarray} \tag{ 12 }$$

It should be noted that the first two terms in the square bracket of the right-hand side of Eq. 12 can be expressed by the well-known hyperbolic cotangent function in the manner

$$\begin{eqnarray}\begin{array}{lll}{I}_{\mathrm{PL},0}(T) & = & {I}_{0}\left[1+\displaystyle \frac{2}{\exp \left(h{\nu }_{{\rm{s}}}/{k}_{{\rm{B}}}T\right)}\right]={I}_{0}\left[\displaystyle \frac{\exp \left(h{\nu }_{{\rm{s}}}/{k}_{{\rm{B}}}T\right)+1}{\exp \left(h{\nu }_{{\rm{s}}}/{k}_{{\rm{B}}}T\right)-1}\right]\\ & = & {I}_{0}\,\coth \left(h{\nu }_{{\rm{s}}}/2{k}_{{\rm{B}}}T\right)\end{array}\end{eqnarray} \tag{ 13 }$$

Figure 3 shows the specral features of the emission and excitation transitions in K₂SiF₆: Mn⁴⁺ at T = 20 K. The experimental data are taken from Ref. 16 The vertical bars on the PL excitation (PLE) spectrum show the analysis results using the Franck−Condon principle with the CC model given by the following expression: ^14,17

$$\begin{eqnarray}&&{I}_{{\rm{PLE}}}\left(E\right)=\displaystyle \displaystyle \sum _{n}{I}_{n}^{{\rm{ex}}}\left(n\right)\exp \left[-\displaystyle \frac{{\left(E-{E}_{{\rm{ZPL}}}-nh{\nu }_{p,\mathrm{ex}}\right)}^{2}}{2{\sigma }_{{\rm{ex}}}^{{\rm{2}}}}\right]\end{eqnarray} \tag{ 14 }$$

with

$$\begin{eqnarray}&&{I}_{n}^{{\rm{ex}}}\left(n\right)={I}_{0}^{{\rm{ex}}}\exp \left(-S\right)\displaystyle \frac{{S}^{n}}{n!}\end{eqnarray} \tag{ 15 }$$

Here, E_ZPL is the ZPL transition energy in the PLE process, σ_ex is the broadening energy of each Gaussian component, ${I}_{0}^{{\rm{ex}}}$ represents the ZPL excitation intensity, S is the mean local vibration number (Huang−Rhys factor) defined by the Poisson statistics (Eq. 15)and hν_p,ex is the lattice vibration energy involved in the excitation transition process.

The vertical bars in the PLE spectrum are obtained by fitting the experimental data with assuming the two excitation transition bands, ⁴ A_2g → ⁴ T_2g and ⁴ A_2g → ⁴ T_1g,a. The fit-determined parameters are E(⁴ T_2g )_ZPL = 2.676 eV (S = 2) and E(⁴ T_1g,a)_ZPL = 3.20 eV (S = 6) with hν_p,ex = 65 meV. The value of hν_p,ex = 65 meV corresponds to that of the ν₂ vibration mode. Table I summarizes the lattice phonon energies (ν₁ − ν₆) for the molecule in the fluoride crystal. ^17,18

The ZPL emission energy E(² E_g )_ZPL (² E_g → ⁴ A_2g ) can be easily determined from a weak, but clear peak in the PL spectrum at ∼1.998 eV. Because the PL spectrum in Fig. 3a was measured at cryogenic temperature (T = 20 K), no strong anti-Stokes emission peaks can be observed in its spectrum. The dominant PL peaks are caused by the activation due to the ν₃, ν₄, and ν₆ local vibration modes (Table I). One can also find the PL peaks due to the lattice acoustic modes (TA = transverse acoustic; LA = longitudinal acoustic) observed in the region near the ZPL emission peak.

Figure 4 shows the temperature dependence of the PL spectra of the Rb₂GeF₆:Mn⁴⁺ phosphor measured between T = 20 and 500 K in 40 K increments. ¹⁹ A gradual increase in the anti-Stokes emission intensity (λ < 622 nm) with increasing T has been observed at T up to ∼420 K. Contrarily, no strong change in the Stokes emission intensity can be seen from 20 up 420 K. Above 420 K, both the Stokes and anti-Stokes emission intensities show a decrease with increasing T, which is caused by the thermal quenching.

Let us show in Figs. 5 and 6 the theoretical I_PL vs T curves, together with those for the Stokes (I_S) and anti-Stokes (I_a−S) intensities, calculated using Eq. 11 (Eqs. 7 and 8) with hν_s = 40 meV and α as a parameter varying from 0 to 8 × 10⁻⁴ K⁻¹ (Fig. 5) and with α = 4 × 10⁻⁴ K⁻¹ and hν_s as a parameter varying from 20 to 60 meV (Fig. 6). It is understood that the I_a−S component depends very sensitively on hν_s and α.

Figure 7 shows the integrated PL intensities of the Stokes (I_S) and anti-Stokes emission components (I_a−S) as a function of T, together with that of the ZPL emission intensity (I_ZPL), for the Rb₂GeF₆:Mn⁴⁺ phosphor (see also Fig. 4). The I_ZPL values were obtained by integrating PL spectra at wavelengths between λ = 620−625 nm. As expected, no strong temperature dependence was observed on the I_ZPL intensity below ∼450 K. The gradual decreases in the I_S, I_a−S, and I_ZPL vs T plots at T ≥ 450 K come from the thermal quenching (see E_q in Eq. 4).

The solid and dashed lines in Fig. 7 (I_S, I_a−S) represent the theoretical curves of the Stokes and anti-Stokes emission intensities calculated using Eq. 7 (I_S) and 8 (I_a−S) with and without considering the acoustic phonon contribution, respectively. The thermal quenching parameters used in these calculations are as follows: a₁ = 3.5 × 10¹¹ and E_q1 = 1.1 eV (i = 1 only). An excellent agreement can be achieved between the experimental data and theoretical calculations. An anomalous increase in the integrated luminescence intensity with increasing T up to ∼450 K can be understood to be due to the breakdown of the parity and spin forbidden transitions by the effects of the optical/acoustic phonon vibrations (Eq. 11).

Figure 8 shows the I_PL(T) data for some Mn⁴⁺-activated fluoride phosphors of type I₂−IV−F₆ host: K₂GeF₆:Mn⁴⁺, ^20,21 K₂TiF₆:Mn⁴⁺, ⁸ Na₂SiF₆:Mn⁴⁺, ^22,23 KNaSiF₆:Mn⁴⁺, ^24,25 and (NH₄)₂SiF₆:Mn⁴⁺. ²⁶ The solid lines show the theoretical I_PL vs T curves calculated using Eq. 12. The fit-determined parameters are summarized in Table II. One can see that all these phosphors show an increase in the integrated PL intensity (I_PL) with increasing T. As in Fig. 7, such an increase in I_PL with increasing T can be well explained by gaining the optical transition probability with the lattice vibrations of the "gerade" modes (ν₃, ν₄, and ν₆; see also Fig. 4) The I_PL value observed at T ∼ 420 K for the K₂GeF₆:Mn⁴⁺ phosphor is about 1.8 times larger than that at T → 0 K. The (NH₄)₂SiF₆:Mn⁴⁺ phosphor also shows an increase in I_PL with increasing T, but its degree of increase is smaller than that observed in the K₂GeF₆:Mn⁴⁺ phosphor [I_PL(T ∼ 190 K)/I_PL(T → 0 K) ∼ 1.2].

The thermal quenching becomes remarkable at T above ∼200 K for (NH₄)₂SiF₆:Mn⁴⁺. The corresponding quenching energy determined here is E_q1 ∼ 0.50 eV for (NH₄)₂SiF₆:Mn⁴⁺ (Table II). This is in accord with the fact that the host material of lower melting point (T_melt) has the smaller quenching energy of E_q1 [T_melt ∼ 160 °C (∼433 K) and E_q1 ∼ 0.50 eV for (NH₄)₂SiF₆:Mn⁴⁺]. The smaller quenching energy of the lower melting-point host material may be correlated to a collapse of its rigid lattice network system at high lattice temperatures.

The I_PL vs T plots for some Mn⁴⁺-activated fluoride phosphors of type II−IV−F₆ host, BaTiF₆:Mn⁴⁺, ²⁷ BaSiF₆:Mn⁴⁺, ²⁸ and BaSnF₆:Mn⁴⁺, ²⁹ are shown in Fig. 9. The theoretical I_PL(T) data using Eq. 12 are shown by the solid lines. The fit-determined parameters are listed in Table II. As in Fig. 8, the peculiar I_PL vs T plots can be well explained by considering the theoretical model of Eq. 12. The largest increase of I_PL with increasing T observed in Fig. 9 is I_PL(T ∼ 380 K)/I_PL(T → 0 K) ∼ 1.6 (BaTiF₆:Mn⁴⁺).

The host materials of K₂SnF₆·H₂O:Mn⁴⁺ and ZnGeF₆·6H₂O:Mn⁴⁺ phosphors are of types I₂−IV−F₆ and II−IV−F₆, respectively. Let us show in Fig. 10 the I_PL vs T data for the K₂SnF₆·H₂O:Mn⁴⁺ (Refs. 30 and 31) and ZnGeF₆·6H₂O:Mn⁴⁺ phosphors, ³² together with their theoretical I_PL(T) curves calculated using Eq. 12. A very weak increase in I_PL with increasing T can be observed in the K₂SnF₆·H₂O:Mn⁴⁺ phosphor at T ∼ 100 − 280 K, which reflects a large value of hν_s = 110 meV required in Eqs. 11–13 (see Table II). An anomalous increase of I_PL(T) in the ZnGeF₆·6H₂O:Mn⁴⁺ phosphor is also observed with a value of I_PL(T ∼ 220 K)/I_PL(T → 0 K) ∼ 1.4 (Fig. 10). An occurrence of the thermal quenching at relatively low temperatures below 300 K has been observed in the ZnGeF₆·6H₂O:Mn⁴⁺ phosphor and also in similar hydrate phosphors like ZnSiF₆·6H₂O:Mn⁴⁺, ³³ ZnSnF₆·6H₂O:Mn⁴⁺, ³⁴ and ZnTiF₆·6H₂O:Mn⁴⁺. ³⁵ As in the case of (NH₄)₂SiF₆:Mn⁴⁺ (Fig. 8), a family of Zn−IV−F₆·6H₂O host materials has a relatively low melting/decomposition temperature, e.g., T_melt/decom ∼ 120 °C for ZnSiF₆·6H₂O.

Figure 11 shows the I_PL vs T plots for some Mn⁴⁺-activated oxyfluoride phosphors: CsMoO₂F₃:Mn⁴⁺, ¹¹ Cs₂WO₂F₄:Mn⁴⁺, ³⁶ and K₃HF₂WO₂F₄:Mn⁴⁺. ³⁷ The solid lines show the theoretical I_PL vs T data calculated using Eq. 12. The fit-determined parameters are listed in Table II. An extremely large increase in I_PL(T) can be observed in the CsMoO₂F₃:Mn⁴⁺ phosphor above T ∼ 20 K, peaking at 430 K with I_PL(T ∼ 430 K)/I_PL(T → 0 K) ∼ 8. Such an anomalous increase in I_PL(T) can be successfully explained by Eq. 12. A weak increase of I_PL with increasing T has also been observed in the K₃HF₂WO₂F₄:Mn⁴⁺ phosphor (Fig. 11).

The extremely large increase in I_PL(T) in the CsMoO₂F₃:Mn⁴⁺ phosphor may come from its complex crystal structure and, therefore, its complex phonon dispersion curve nature. Note that phonons, representing lattice vibrations at a frequency of ω_q, have an energy ħω_q, where ħ is the reduced Planck's constant, and have a momentum ħq . In the primitive cell, if there are N different types of atoms either of differing mass or ordering in space, 3 N vibration modes will result. Three of these branches, namely the acoustic branches, will disappear at the zone center (Γ). The remaining 3 N − 3 branches will be optical branches. As mentioned in " Phonon-assisted activation process ," the Mn⁴⁺ luminescence is caused by the party and spin forbidden transitions (² E_g → ⁴ A_2g ), but gained by the effects of the optical/acoustic phonon vibrations. The anomalously large increase in I_PL(T) with increasing T may thus come from a more complex crystal structure (or, in other words, from more complex phonon dispersion relations) of some oxyfluoride phosphors like CsMoO₂F₃:Mn⁴⁺ and Cs₂WO₂F₄:Mn⁴⁺. In fact, no such remarkable increase in I_PL(T) has been observed in phosphors of more simple crystal structures like I₂−IV−F₆:Mn⁴⁺ in Figs. 7 and 8. Further study needs to make clear this problem.

It should be noted that Cr³⁺ and V²⁺ ions have the same electronic configuration, 3d³, as Mn⁴⁺. Therefore, the proposed analysis model can be used to interpret the temperature-dependent luminescence intensities of not only the Mn⁴⁺-activated phosphors, but also of other 3d³-activated ones (Cr³⁺, V²⁺), regardless of fluoride, oxyfluoride, or other host materials like oxides. ²³