J. Phys. Chem. B 2000, 104, 11045-11057
11045
The Role of Laser Heating in the Intrinsic Optical Bistability of Yb3+-Doped Bromide Lattices Daniel R. Gamelin,† Stefan R. Lu1 thi,‡ and Hans U. Gu1 del* Department of Chemistry and Biochemistry, UniVersity of Bern, Freiestrasse 3, CH-3000 Bern 9, Switzerland ReceiVed: May 31, 2000; In Final Form: August 17, 2000
Materials displaying intrinsic optical bistability (IOB), i.e., allowing the coexistence of two stable steadystate excitation rates for a single given excitation power, are of interest for potential technological applications related to optical data switching and manipulation. The properties of the unusual IOB previously observed in Yb3+-doped Cs3Lu2Br9 and CsCdBr3 host materials are studied here using absorption and luminescence spectroscopies. The IOB phenomenon is concluded to derive ultimately from laser heating effects. When combined with a strongly increasing and nonlinear dependence of the material’s absorbance on internal temperature, laser heating leads to a positive-feedback absorption amplification process showing a hysteresis in both power- and temperature-sweep experiments. A simple model describing this effect in terms of rates of sample heating and cooling in the irradiated volume reproduces the power, temperature, concentration, and excitation-energy dependence of the Yb3+ IOB using only the experimental absorption data as input. The temperature dependence of the absorption cross section is correlated with thermal changes in the monomeric YbBr63- geometry, which becomes more asymmetric as the temperature is elevated. The IOB observed in Yb3+-doped Cs3Lu2Br9 and CsCdBr3 host lattices is therefore a property of the monomeric Yb3+ ion in these materials, and not a dimer property as was previously believed. These results also emphasize the more general conclusion that laser heating may contribute significantly to the shape or slope of an excitation power dependence curve, and may even be the dominant aspect of that curve when absorption cross sections are strongly dependent on temperature.
Introduction Intrinsic, or mirrorless, optical bistability (IOB) is a subject of great technological interest as the telecommunications industry strives to maximize the efficiency of telephone, Internet, and other data transmission over fiber optical cables. A key operation commonly performed electronically is that of data switching, and the need to convert optical signals to electronic signals and back again for this operation involves unnecessary losses in time and energy. Optical switching could potentially be faster and require less energy than conventional electronic switching, and development of methods to do this, either intrinsically or using an external optical cavity, is the subject of intense research worldwide. IOB has been observed in several semiconductors.1-4 In most cases, it appears that band gap renormalization caused by the formation of electron-hole plasma upon high-power irradiation is responsible for the IOB effect in these semiconductors.5 The photophysical properties of Yb3+-doped halide lattices have recently come under renewed scrutiny since the initial reports that IOB could be generated by Yb3+-doped bromide host materials under certain conditions.6-8 IOB in an ionic crystalline material was first observed in 10% Yb3+:Cs3Y2Br96,7 and has subsequently been observed in 1% Yb3+:CsCdBr38 and in variations of the former material (10% Yb3+:Cs3Lu2Br9 and Cs3Yb2Br9).9 A great deal of theoretical work has been undertaken to understand the experimentally observed IOB behavior and to predict new physical scenarios which would be conducive for IOB. † Permanent address: Department of Chemistry, University of Washington, Seattle, WA 98195-1700. E-mail:
[email protected]. ‡ Present address: Department of Chemistry, The University of Queensland, Brisbane, Queensland 4072 Australia.
The electronic structure of Yb3+ has been studied extensively in many host environments. Yb3+ has a 4f13 electronic configuration which gives rise to two spin-orbit split terms, 2F7/2 and 2F , as shown in Figure 1a. Each term is additionally split by 5/2 the crystal field. The spin-orbit splitting energy, 7/2ξ, is about 10000 cm-1, while the crystal-field splittings are an order of magnitude smaller. States derived from the higher energy 2F5/2 term thus lie in the near-infrared (NIR) spectral region, and isolated Yb3+ monomers absorb and emit in the NIR. Condensed materials containing Yb3+ commonly show visible (VIS) cooperative luminescence at twice the energy of the 2F5/2 levels.10,11 This luminescence involves simultaneous deactivation of two Yb3+ ions in their 2F5/2 excited states, and is illustrated schematically in Figure 1b using a dimer notation. The VIS cooperative luminescence intensity is governed by interionic multipolar and/or exchange interaction strengths, which are both strongly dependent upon interionic separation R.10-13 Relative integrated luminescence intensities have been reported for several Yb3+ materials and are consistently on the order of 10-6-10-8 VIS:1 NIR.14-18 IOB in Yb3+-doped Cs3Y2Br9, Cs3Lu2Br9, and CsCdBr3 was observed while monitoring both the NIR and VIS luminescence signals following low-temperature NIR excitation into the Yb3+ 2 2F 7/2 f F5/2 absorption feature (Figure 1a). More specifically, previous studies6-9 have only reported IOB with 2F7/2(0) f 2F (2′) excitation. These studies all show generally similar 5/2 behavior, defined by the observation of luminescence hystereses with variable power at constant temperature, and conversely with variable temperature at constant power. In 10% Yb3+: Cs3Lu2Br9 and Cs3Yb2Br9, the switching of the NIR and VIS luminescence signals show opposite polarities,7 while in 1%
10.1021/jp001988m CCC: $19.00 © 2000 American Chemical Society Published on Web 11/04/2000
11046 J. Phys. Chem. B, Vol. 104, No. 47, 2000
Figure 1. Energy-level diagrams for (a) isolated Yb3+ monomers in a trigonally distorted octahedral crystal field and (b) Yb3+ dimers neglecting crystal-field splittings. The down arrows in (b) indicate the possible VIS (dashed) and NIR (solid) luminescence transitions.
Figure 2. Power-sweep hystereses observed in 10% Yb3+:Cs3Y2Br9, plotted as integrated VIS cooperative emission intensity versus NIR excitation power density at various fixed external (cryostat) temperatures. From ref 7.
Yb3+:CsCdBr3 the NIR and VIS switching polarities are the same.8 The properties of the variable-power hystereses are sensitive to changes in cryostat temperature, growing narrower and occurring at lower power as the cryostat temperature is elevated. This trend is independent of the experimental method of probing the hystereses. Representative data from ref 7 are reproduced in Figure 2. Similarly, the properties of the variabletemperature fixed-power hystereses are sensitive to the laser power, growing narrower and occurring at higher temperatures as the excitation power is reduced. Plotting the hysteresis data in a Temperature versus Power bistability phase diagram for 10% Yb3+:Cs3Y2Br9 showed that the variable-power and variable-temperature hysteresis experiments define the same phase space.7 In all cases, IOB is restricted to low temperatures ( Text(solid)), and are defined as the internal temperature on the lower branch Tint,lower (O), and the internal temperature on the upper branch Tint,upper (+). (b) Model for Calculation of IOB from Absorption Spectra. The above section draws a phenomenological correlation between the IOB and the variable-temperature absorption properties of the Yb3+ materials in this study and shows that laser heating can change the absorption spectrum in the same way as does elevation of the external temperature. In this section we treat the laser heating process more quantitatively by considering the rates of heat deposit and removal at the irradiated sample during the course of the IOB experiment. In the simplest case, the rate of heat deposit is given by eq 1, where P is the laser power, A(Tint) is the sample absorbance per unit volume at the laser energy, and R describes the efficiency of converting absorbed photons into heat and is assumed to be temperature independent within the relevant temperature range.
RH ) RA(Tint)P
(1)
A(Tint) is a function of the internal temperature of the sample and is proportional to the sample’s absorption cross section σ(Tint), and the concentration of ground-state ions N0 (assumed constant, vide infra), as described by eq 2.
A(Tint) ∝ N0σ(Tint)
(2)
The temperature dependence of A(Tint) has been determined experimentally for various excitation energies in Yb3+-doped Cs3Lu2Br9 and CsCdBr3, and representative curves are shown in the data of Figure 8. In these experiments, Tint was varied by changing Text with no laser heating the sample. Under these conditions, Tint ) Text. As seen in Figure 8, A(Tint) at excitation energies relevant to IOB increases significantly with increasing temperature up to about 60 K and then levels off and starts to decrease. According to eq 1, the heat deposited in the sample for a given laser power P has the same functional dependence on Tint as A(Tint). On the other hand, for a given Text, the internal temperature Tint increases with increasing laser power P. In the temperature range up to about 80 K this therefore leads to selfamplification of the laser heating.
Yb3+-Doped Bromide Lattices
J. Phys. Chem. B, Vol. 104, No. 47, 2000 11053
Figure 13. Dependence of A(Tint) on Tint for 1% Yb3+:CsCdBr3, measured at Text ) 10 K for an excitation energy of 10608 cm-1 (strong full line, taken from Figure 8a). The weaker straight lines plot the function ∆T/ηP for different ηP values in arbitrary units. The shaded area is the bistable region. In a power hysteresis measurement, the switching occurs at the values of ηP indicated by open circles.
To model the dependence of A(Tint) on laser power for a given Text, we also consider the rate of cooling of the sample RC by the cryogenic bath. RC is given by eq 3, where ∆T ) Tint Text.
RC ) β∆T
(3)
The parameter β is assumed temperature independent in the relevant temperature range. Under steady-state excitation conditions RH ) RC, and defining η ) R/β this yields eq 4.
A(Tint) -
∆T )0 ηP
(4)
Figure 13 plots in a strong full line A(Tint) as a function of Tint, determined experimentally for 10608 cm-1 excitation of 1% Yb3+:CsCdBr3, as in Figure 8a. The weaker straight lines in Figure 13 plot ∆T/ηP as a function of Tint for different values of ηP in arbitrary units. The points at which A(Tint) and ∆T/ηP cross are solutions of eq 4. Outside the shaded region, i.e., for ηP < 130 and ηP > 250, there is only one solution to eq 4 (short dashed lines as examples). These are the normal regions. In the shaded region between these two limits (e.g., ηP ) 180, long dashed line) there are three solutions, two of which are stable as described by eq 5.
∆T d A(Tint) 0 dTint ηP
unstable
[
[
]
]
(5)
This shaded region is therefore bistable, with two possible A(Tint) values and hence two possible internal temperatures for a given laser power and constant Text. The two A(Tint) values correspond to the two transmitted intensity values in the bistable region of Figure 3c, while the two internal temperatures correspond to Tint,upper and Tint,lower in Figure 11. Figure 13 is useful for illustrating the origin of the hystereses in the power sweep experiments (e.g., those shown in Figure 3): Upon increasing the excitation power from ηP ) 0, the
Figure 14. Power hystereses for 1% Yb3+:CsCdBr3 calculated (a) at various values of Text for ∆ ) +4 cm-1 (10608 cm-1) excitation, and (b) at various values of ∆ for Text ) 10 K. These hystereses are calculated from the absorption data of Figure 6 as described by eq 4 and Figure 13, without the use of any variable parameters beyond ηP. The curves are plotted as relative transmitted laser power PTr versus relative incident laser power, ηP, where PTr ) P × 10-A(Tint). Each curve is displaced vertically for clarity, and would otherwise intersect the (0,0) origin. ∆ is the detuning energy of the excitation source to higher energy of the low-temperature absorption maximum.
sample’s internal temperature gradually increases, and the sample’s absorbance follows the function A(Tint) continuously until a critical power is reached above which there is no continuous solution (open circle at ηP ) 250). The smallest increase above that critical power forces Tint and A(Tint) to jump to new, significantly larger values. This jump is the switch to the upper branch observed experimentally in Figure 3. In returning to ηP ) 0 from this new high-power solution, the system does not follow the same path but instead follows A(Tint) continuously on the upper branch until another critical power is reached, below which no continuous solution exists (open circle at ηP ) 130). Any small reduction in power below this critical value forces Tint and A(Tint) to drop to new, significantly lower values. This process results in a hysteresis in the power dependence of any observable associated with the sample absorbance, including laser transmission and luminescence processes. The experimental properties of the Yb3+ IOB in Yb3+-doped Cs3Lu2Br9 and CsCdBr3 can now be calculated from their variable-temperature absorption spectra. Using the experimental absorbance data shown in Figure 8a,b (obtained directly from Figure 6a,b), the dependence of A(Tint) on P for a fixed value of Text can be obtained by finding solutions to eq 4 at each value of P, and these solutions thus provide the power dependence of A(Tint). Changing Text results in a different set of solutions, and the temperature dependence of the power dependence can thus be calculated from the same variabletemperature absorption data set. The results for 1% Yb3+: CsCdBr3 calculated at 10608 cm-1 for various values of Text are presented in Figure 14a. The y axis is represented not as A(Tint) but rather as relative transmitted laser power, where PTr ) P × 10-A(Tint), to mimic the experimental data presentation in Figure 3c. The individual curves are vertically offset for clarity of presentation. Very similar hystereses are calculated from the absorbance data of 1% Yb3+:Cs3Lu2Br9 in Figure 8b. No hystereses are predicted for Yb3+ excitation in any of the other host materials of Figure 5. The energy resolution of the
11054 J. Phys. Chem. B, Vol. 104, No. 47, 2000 absorption data used for the calculations is lower than that obtained with laser excitation (see Figure 10), and this effectively means that the calculated behavior based on the absorption data involves an average over a small range of laser excitation energies. Nevertheless, the calculated hystereses provide a remarkably good reproduction of the key experimental aspects of the power hystereses observed in both 1% Yb3+: CsCdBr3 and Yb3+-doped Cs3Lu2Br9. Specifically, the power hysteresis at a given excitation energy is predicted to shift to lower power, to narrow in width, and to decrease in height as the temperature is increased, until eventually only a broad S-shaped feature remains. As mentioned above, this trend is independent of the experimental method of probing the hystereses. Changing the excitation energy in this model affects the calculated hystereses since it changes the variable-temperature absorption function A(Tint), as shown in Figure 8. The excitation energy dependence of the hystereses in 1% Yb3+: CsCdBr3 calculated from the variable-temperature absorption data of this material is shown in Figure 14b. As seen in Figure 14b, increasing the detuning interval (∆) above the low-temperature maximum by very small amounts at a given temperature causes the power required for observation of the hysteresis to increase rapidly, with concomitant increases in hysteresis width and height. Thus, larger hystereses are obtained with greater ∆ values, but the rapid increase in the power required to switch from the lower to the upper branch with increasing ∆ also rapidly pushes the hysteresis out of the experimentally accessible power range. This behavior exactly reproduces the experimental trend reported in Figure 2 of ref 8 for 1% Yb3+:CsCdBr3 and confirmed in our studies. From Figures 6 and 8, positive detuning leads to smaller values of A(Tint) at small Tint, and the power required to initiate the amplification event increases concomitantly. Finally, increases in dopant concentration have been reported to narrow the hystereses and shift them to lower incident excitation powers (see also Figure 4).9 This dependence of IOB on concentration is easily understood from Figure 13. The y axis in Figure 13 represents a volumetric absorbance property. Increasing the concentration increases A(Tint) correspondingly, as described by eq 2. In this model, when A(Tint) increases at a fixed Text the values of ηP in Figure 13 required to access the bistable region decrease and the widths and heights of the hystereses also decrease. In this regard, increasing the concentration is identical to decreasing the applied laser power by the appropriate scalar amount, as was concluded experimentally from the data in Figure 4. One property of the IOB in these materials which we have not modeled is that of the luminescence switching polarities. This model indicates that the 2F7/2 f 2F5/2 excitation rate increases upon switching from the low- to the high-power hysteresis branch, a fact that is confirmed by the data in Figure 3c. If all other factors remain equal, this increase should result in increased NIR and VIS luminescence intensities. Experimentally, the VIS luminescence does always gain intensity upon switching to the high-power hysteresis branch. With 2F7/2(0) f 2F (2′) excitation, the polarity of the NIR switch is the same 5/2 as that of the VIS switch in Yb3+-doped CsCdBr3, but it is opposite that of the VIS switch in Yb3+-doped Cs3Lu2Br9. This difference between hosts was previously attributed to differences in energy migration rates, with fast migration leading to opposite NIR and VIS luminescence switching polarities due to a depletion of the monomer excited-state population upon switching within the dimer units.8 In this study, we have demonstrated
Gamelin et al.
Figure 15. Comparison of experimental and calculated bistability phase diagrams for 2F5/2(2′) excitation in Yb3+-doped Cs3Lu2Br9 and CsCdBr3. The experimental data for 10% Yb3+: Cs3Lu2Br9 are taken from Figure 4 (10591 cm-1 excitation), and the experimental data for 1% Yb3+: CsCdBr3 are adapted from ref 8 (10604 cm-1 excitation). For both calculated phase diagrams, eq 6 is used to calculate power hystereses at a variety of Text values from the variable-temperature absorption data of Figure 6 without any variable parameters beyond ηP, and the switching-up and switching-down powers of these hystereses are then assembled to generate a calculated phase diagram in analogy to the assembly of the experimental phase diagram shown in Figure 4. The calculated hystereses were obtained using the 10592 and 10607 cm-1 absorption data of 1% Yb3+:Cs3Lu2Br9 and 1% Yb3+:CsCdBr3, respectively, shown in Figure 6. The solid (open) triangles indicate switchingup (down) powers of a hysteresis. The vertical lines represent the hysteresis widths.
that the factors which determine the hysteresis properties are independent of the presence or absence of dimers and that such a synergistic depletion process could only account for less than ca. 0.001% of the total NIR switching intensity. We choose instead to attribute the luminescence polarity differences to experimental artifacts, and emphasize one specific factor which might contribute: Figure 11 shows that the internal sample temperature increases quite substantially on switching from the lower to the upper branch of the hysteresis with 2F7/2(0) f 2F (2′) excitation in Yb3+-doped Cs Lu Br . It is not uncom5/2 3 2 9 mon for luminescence quantum yields to decrease with increasing temperature due to increased excitation trapping rates associated with thermally enhanced energy migration rates. Since energy migration is much more efficient in 10-100% Yb3+:Cs3Lu2Br9 than in 1% Yb3+:CsCdBr3, such trapping effects should be more prominent in the former, and may plausibly lead to a reduction in the total luminescence of Yb3+doped Cs3Lu2Br9 upon increasing the excitation rate. In support of this notion, we note that the ca. 10% reduction in integrated NIR luminescence intensity observed experimentally upon switching from the lower to the upper branch (Figure 3b and discussion thereof), combined with the small absolute magnitude of the VIS luminescence relative to the NIR luminescence (10-6 - 10-8 VIS:1 NIR14-18), implies that the total luminescence quantum yield of 10% Yb3+:Cs3Lu2Br9 also decreases by approximately 10% upon switching from the lower to the upper branch of the hysteresis, despite the fact that the excitation rate has increased considerably upon switching (Figure 3c). The thermal model can also be used to calculate phase diagrams for each of the materials shown in Figure 5. For 10% Yb3+:Cs3Lu2Br9 and 1% Yb3+:CsCdBr3, the calculated bistability phase diagrams are shown in Figure 15 and are in very
Yb3+-Doped Bromide Lattices
Figure 16. Comparison of (a) true Photon Avalanche (three electronic states) and (b) Yb3+ thermal avalanche (two electronic states) excitation mechanisms. GSA and ESA indicate ground- and excited-state absorption, and CR indicates nonradiative cross-relaxation. The GSA and GSA(cold) arrows are dashed to indicate weak absorption, while the ESA and GSA(warm) arrows are solid to indicate strong absorption. The down arrow in (b) indicates luminescence, while the curly arrows indicate Yb3+ phonon emission processes.
good agreement with the experimental results. The trends in the experimental phase diagrams of step height and slope, and the quantitative temperature region, in which the hystereses occur, are predicted remarkably well from the absorption data. The fact that these results are derived from a model with no free parameters is commanding evidence for the conclusion that IOB in Yb3+:Cs3Lu2Br9 and Yb3+:CsCdBr3 is due to the effect of temperature on the absorbance of these materials. This same thermal mechanism was previously credited with the generation of IOB in GeSe2 semiconductors, which show a positive nonlinear dependence of the absorbance on temperature between 300 and 500 K.4 From the generality of the effect, any material with an appropriate variable-temperature absorption behavior is a candidate for the observation of IOB. Appropriate absorption behavior is a necessary but not sufficient condition, however, as it only relates to the rate of laser heating (eq 1). The proportionality constant R in eq 1, as well as the equally important cooling proportionality constant β in eq 3, must also be appropriately balanced in order for this effect to occur in an experimentally accessible power range. Although the function A(Tint) can be determined experimentally, as shown in Figure 8, the constants R and β are not readily obtained experimentally. Thus, a material having the appropriate variable-temperature absorption behavior may still not lead to IOB within the accessible experimental power range because of either inefficient laser heating or efficient cooling by the bath. Nevertheless, this absorption behavior in principle allows rapid screening of potential materials for this use, and defines the temperature range and excitation energies for which IOB will be observed if R and β are suitable. (c) The Yb3+ Thermal Avalanche Analogy. In this section, we discuss a thermal analogy to the photon avalanche kinetic model, relate it to the steady-state model described in section (b), and use it to understand the excitation dynamics observed in these Yb3+ materials. Figure 16a depicts the three-level photon avalanche excitation mechanism schematically. Two important properties of true photon avalanches must be considered: (a) avalanche excitation relies on population of an intermediate level by runaway cross relaxation (CR) and (b)
J. Phys. Chem. B, Vol. 104, No. 47, 2000 11055 the excited-state absorption cross section responsible for promoting ions from this intermediate reservoir to the upper excited state must greatly exceed the ground-state absorption cross section at the excitation wavelength (i.e., σ1 . σ0, where Pσ0 ∝ GSA and Pσ1 ∝ ESA in Figure 16a). Both properties must exist in order for the excitation avalanche to be observed. As Yb3+ has only one metastable excited state, these Yb3+doped materials cannot fulfill either of these two requirements in the normal sense. The data in Figure 10 reveal how the Yb3+-doped materials may meet the avalanche requirements: The observation in Figures 10b,c of an excitation energy region in which a material is almost transparent at low excitation powers but highly absorbing at high excitation powers is a classic signature of a photon avalanche process.11,28 Rather than using an intermediate electronic level, however, these materials “store” excitation energy in the form of heat, or lattice phonons. Warm ions thus serve as the population of the intermediate level N1, while cold ions serve as the ground-state population N0. The thermal avalanche mechanism is depicted in Figure 16b. Phonons emitted in both the ground and excited states of an absorbing ion contribute to heating of the lattice and lead to an increased absorbance at the laser excitation energy. The excitation avalanche thus involves runaway sample heating at high excitation powers, rather than runaway cross relaxation. In the photon avalanche model, the critical ESA pump rate constant ESAcrit, required to cross the avalanche threshold, can be expressed analytically in terms of other system rate constants as in eq 6,28 where k1 is the decay rate constant of level 1 in Figure 16a, k21 is the sum of rate constants for feeding of level 1 by the level 2 population, including cross relaxation contributions, and τ2 is the lifetime of level 2.
ESAcrit )
k1 τ2k21 - 1
(6)
In the Yb3+ Thermal Avalanche analogy, k21 represents the rate constant associated with all phonon emission processes resulting from electronic excitation (i.e., following both the absorption and emission steps shown in Figure 16b), and τ2 describes the total lifetime of the electronically excited 2F5/2 state. When applied to Figure 16b, the denominator of eq 6 thus translates as a branching ratio which governs the quantum efficiency of heat production upon electronic excitation, akin to the constant R in eq 1. k1 can be identified with the sample cooling process described by eq 3, from which it is seen to be linearly proportional to the difference ∆T ) Tint - Text. As shown experimentally in Figure 11, increasing Text reduces ∆T. This would reduce k1 in eq 6 and drive ESAcrit to lower applied powers, as observed experimentally in Figures 2 and 4. The sensitivity of the Yb3+ hysteresis threshold to the exact energy of excitation results from the fact that the absorption maximum shifts in energy slightly with increasing temperature. A judicious choice of excitation energy allows optimization of the GSAwarm/GSAcold (or σ1/σ0) ratio and sharpens the nonlinearity, analogous to the behavior observed in photon avalanches.11 Slight detuning to lower excitation energies changes the shape of the power dependence from very sharp with a bistable region to broad and S-shaped with no bistable region (see Figure 2 of ref 8 and Figure 12a). Phenomenologically, this response is now more closely comparable to those observed in classic photon avalanche systems. The time dependencies under these latter conditions are clearly analogous to those observed in true photon avalanches.
11056 J. Phys. Chem. B, Vol. 104, No. 47, 2000
Gamelin et al.
If the lifetime of level 1 in Figure 16a is significantly longer than that of level 2, as is generally the case, the population dynamics of level 2 follow those of level 1, and the dynamics of level 1 are described by eq 7.33
(
)
Pσ1N1 dN1 ) Pσ0N0 - k1N1 1 dt ESAcritN0
(7)
Eq 7 defines three general dynamic scenarios for three different excitation power ranges. When the excitation power is very low, the second term simply collapses to the linear decay term k1N1, and the system behaves with normal 2-level dynamics. When the critical pump threshold ESAcrit is reached, the avalanche feeding mechanism is competitive with the linear decay rate k1N1. At this threshold, the time to reach steady state during a square wave laser pulse can be extremely long, and is described by eq 8.28
N1(t) ) N1(∞) tanh(t/tc)
(8)
where
tc ≈
1 ESAcrit
x
σ1 σ0
r Since σ1 . σ0, this time can be much longer than those predicted from any of the system’s linear decay rate constants. Increasing the excitation power from this threshold, the time required to reach steady state shortens and eventually is too small to be observed. Experimental results obtained for 50% Yb3+:Cs3Lu2Br9 are shown in Figure 12b. Square-wave excitation at 36 mW, below the critical power, shows monoexponential rises for both NIR and visible luminescence signals. Square wave excitation at 82 mW, slightly above the critical power, shows a dramatically long induction period of several milliseconds before steady state is achieved, during which the visible luminescence gains intensity and the NIR luminescence loses intensity on the same time scale. This delay before reaching steady state is over an order of magnitude longer than the natural Yb3+ 2F5/2 decay time in this crystal. The duration of this induction period is dependent upon the power used: Increasing the excitation power shortens the induction period, while decreasing the excitation power to approach the critical power threshold of ca. 60 mW lengthens the induction period, as predicted by eq 7. Note that these data correspond to detuned excitation, where the effective curvature of Figure 13 would be close to linear, not strongly nonlinear as shown. Under hysteresis conditions, only the two limits of very small and very large deviations from the normal two-level dynamics of eq 7 can be probed experimentally, and the dramatic steady-state induction periods are not observed.34 (d) Origin of the Temperature Dependence of the Absorption Intensities and Energies. The data in Figures 5-9 show that certain crystal-field electronic origins in Yb3+:Cs3Lu2Br9 and Yb3+:CsCdBr3 display large increases in intensity with increasing temperature. The observation that this behavior is essentially independent of Yb3+-doping level in Cs3Lu2Br9 allows the conclusion that it is a property of monomeric Yb3+ ions occupying the trigonally distorted dopant sites of this host lattice, and by analogy also those of CsCdBr3. This behavior must relate to thermally activated changes in the wave functions of the ground and/or excited states of these electronic transitions (Figure 1a). Within each term, the energy differences between the various electronic states are due to crystal-field interactions of the Yb3+ f electrons with the surrounding bromide ligands,
and are thus largely due to the orbital parts of the spin-orbit wave functions describing these f electrons. Similarly, the differences in intensity must be due to different orbital contributions to the one-electron promotions involved. These differences likely relate to differences in Yb3+-Br- covalency, which is responsible for contributing Br- f Yb3+ ligand-to-metal chargetransfer absorption character to the weak, formally laporte´forbidden f-f transitions. The first intense LMCT absorption band of YbBr63- has an energy of ca. 29000 cm-1. A structural change is observed in Cs3Yb2Br9 between 10 and 300 K involving anisotropic expansion of the lattice constants with increasing temperature.26 More detailed studies on the isostructural Cs3Ho2Br9 lattice over the same temperature range show that this distortion is already active between 1.5 and 25 K and continues smoothly up to room temperature.35 At elevated temperatures, the sample also shows large anisotropic thermal ellipsoids of the bromide atoms. Microscopically, the thermally induced distortion is characterized by elongation of the dimer units along their trigonal (M-M) axes with increasing temperatures, and concomitant contraction of the three terminal M-Br bonds at the expense of the three bridging M-Br bonds. Although these distortions are very small, the odd-parity Yb3+ crystal field thus increases with increasing temperature. We therefore attribute the thermally induced crystal-field absorption intensity in Cs3Yb2Br9 and related materials to this thermally induced increase in the asymmetry of the monomeric Yb3+ crystal field, which should affect absorption intensities by inducing greater interaction between the crystal-field and chargetransfer electronic configurations. The proposed correlation between geometry and absorption intensity in these materials is currently under further investigation. While the temperature dependence of the MBr63- structure in CsCdBr3 is not known in such detail, the geometry of this site is also defined by a similarly large trigonal distortion, and the variable-temperature absorption data suggest a similar geometric distortion in this lattice with increasing temperature. The Cs3Lu2Cl9 lattice is isostructural with Cs3Lu2Br9, but is significantly more rigid and its first Cl- f Yb3+ charge-transfer transitions lie at substantially higher energies (ca. 38000 cm-1). As a consequence, the temperature dependencies of the 2F 2 3+ 7/2 f F5/2 excitations of 10% Yb :Cs3Lu2Cl9 (Figure 5), although positive in sign, are an order of magnitude smaller than those observed in the bromide. This change in absorption is apparently insufficient for the observation of IOB in 10% Yb3+:Cs3Lu2Cl9. Additionally, the higher phonon energies of the chloride lattice may hinder the observation of IOB by providing greater heat dissipation rates (eq 3). Conclusions On the basis of the new experimental results and analysis presented in this paper, we have come to the conclusion that the unusual IOB phenomenon observed in Yb3+-doped Cs3Lu2Br9 and CsCdBr3 ultimately derives from the effect of laser excitation power on the internal temperature of the sample. When combined with a strongly increasing and nonlinear sample absorbance with increasing internal temperature, laser heating in these materials leads to an unusual positive-feedback absorption amplification process showing a hysteresis in both power and temperature sweep experiments. The temperature dependence of the absorption cross section is correlated with thermal changes in the YbBr63- geometry. A simple model describing this effect reproduces the power, temperature, concentration, and excitation-energy dependence of the Yb3+ IOB using only the experimental absorption data as input. The IOB observed
Yb3+-Doped Bromide Lattices in Yb3+-doped Cs3Lu2Br9 and CsCdBr3 host lattices is therefore attributable to laser-induced thermal changes of the monomeric Yb3+ absorption cross sections and is not a dimer property, as was previously believed. This result suggests that a wider range of materials might show IOB than was previously considered, and that such materials could be pre-screened by measurement of their variable-temperature absorption characteristics. Such laser heating effects are generally not accounted for in power dependence analyses, since in most cases absorption cross sections of electronic origins only decrease slowly with heating, which may result in only a small flattening of the observed power dependence. The power dependencies of Yb3+doped Cs3Lu2Br9 and CsCdBr3 described here show that the contribution of laser heating to the shape of a power dependence curve may be significant, or even the dominant aspect of that power dependence, when absorption cross sections increase with increasing temperature. Acknowledgment. The authors thank the Swiss National Science Foundation for financial support, and Naomi Furer for expert assistance with the crystal growth. References and Notes (1) Neuendorf, R.; Quinten, M.; Kreibig, U. J. Chem. Phys. 1996, 104, 6348. (2) Bohnert, K.; Kalt, H.; Klingshirn, C. Appl. Phys. Lett. 1983, 43, 1088. (3) Rossman, H.; Henneberger, F.; Voigt, H. Phys. Status Solidi 1983, B115, K 63. (4) Hajto´, J.; Ja´nossy, I. Philos. Mag. B 1983, 47, 347. (5) Schmidt, H. E.; Haug, H.; Koch, S. W. Appl. Phys. Lett. 1984, 44, 787. (6) Hehlen, M. P.; Gu¨del, H. U.; Shu, Q.; Rai, J.; Rand, S. C. Phys. ReV. Lett. 1994, 73, 1103. (7) Hehlen, M. P.; Gu¨del, H. U.; Shu, Q.; Rand, S. C. J. Chem. Phys. 1996, 104, 1232. (8) Hehlen, M. P.; Kuditcher, A.; Rand, S. C.; Lu¨thi, S. R. Phys. ReV. Lett. 1999, 82, 3050. (9) Lu¨thi, S. R.; Hehlen, M. P.; Riedener, T.; Gu¨del, H. U. J. Lumin. 1998, 76&77, 447.
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