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Continuous function decay analysis of a multisite impurity activated solid
15 November 1998
Optics Communications 156 Ž1998. 409–418
Full length article
Continuous function decay analysis of a multisite impurity activated solid Marek Grinberg
a,1
, D.L. Russell b, Keith Holliday Cz. Koepke c
b,)
, K. Wisniewski c ,
a
b
Institute of Experimental Physics, UniÕersity of Gdansk, ˜ Wita Stwosza 57, 80-952 Gdansk, ˜ Poland Optical Materials Research Centre, Department of Physics and Applied Physics, UniÕersity of Strathclyde, ColÕille Building, North Portland Street, Glasgow G1 1XN, UK c Institute of Physics, N. Copernicus UniÕersity, 87-100 Torun, ˜ Poland Received 30 April 1998; revised 17 August 1998; accepted 18 August 1998
Abstract The technique of continuous function decay analysis, previously used in studies of molecular dynamics, is applied to a solid that is optically activated through impurity doping. Chromium ions occupy several different sites in gahnite glass ceramics, each of which has different luminescence lifetime characteristics but overlapping absorption and emission spectra. Continuous function decay analysis maps the decay patterns of the decaying species, producing histograms of the relative strengths of decay at Žin this case. 125 logarithmically spaced lifetimes. The results for chromium ions in gahnite glass ceramics are related to the interaction between the impurity ions and the solid state environment and correlate well with previous studies of this material that have used standard techniques. Continuous function decay analysis is thus shown to be an effective method for understanding the optical behaviour of multisite materials. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Continuous function decay analysis; Impurity doping; Multisite material
1. Introduction This paper presents the application of a technique previously used in studies of molecular dynamics to study the decay of a multisite optically activated solid. When materials contain optically active species that occupy more than one site it is often difficult to determine site occupancies and dynamics due to the overlap of absorption and luminescence spectra. Time resolved spectroscopy can occasionally help to resolve some of the site dependent structure but when the number of centres increases beyond
) 1
Corresponding author. E-mail: [email protected] E-mail: [email protected]
two or when one of the sites consists of a continuous distribution of environment parameters Žcrystal field parameters for a solid. a new method is required. Here the technique of continuous decay analysis is presented. This allows simple luminescence decays to be broken down into a large number of contributions at different lifetimes. In the case presented here, decay curves of chromium ions in gahnite glass ceramics are decomposed into histograms showing the contributions of 125 logarithmically spaced lifetimes to the overall decay. These decays are shown to correspond very well to the known properties of the material and, such is the aptitude of the technique, new conclusions can also be drawn. Gahnite glasses are composed of a mixture of oxide compounds, principally SiO 2 and Al 2 O 3 but with concen-
0030-4018r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 Ž 9 8 . 0 0 4 6 3 - 5
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trations of up to 10% of ZnO, Li 2 O, TiO 2 , ZrO 2 and As 2 O 3. Heat treatment produces gahnite glass ceramics, which include various crystal phases. The duration of the heat treatment determines the degree and type of crystallisation as evidenced by the effects on the luminescence spectra of Cr 3q ions included in the structure as impurities w1x. Long term heat treatment results in the majority of the Cr 3q ions being incorporated in crystallites of ZnAl 2 O4 with sizes of around 30 nm. This is confirmed by the similarity of Cr 3q luminescence spectra of such ceramics to the bulk spinel crystal w2,3x. Shorter periods of heat treatment produce some crystallites of ZnAl 2 O4 but also other crystalline phases w1x. Cr 3q impurity ions in both crystalline phases luminesce via vibronically structured 2 E ™4A 2 transitions. The luminescence spectrum of the untreated Cr 3q-doped glass is much broader and smoother, characteristic of 4 T2 ™4A 2 emission. The gahnite glass ceramic used in this study has intermediate crystallinity as can be seen from luminescence spectra excited at different wavelengths ŽFig. 1.. When excited in the middle of the 4A 2 ™4 T2 absorption band the sample luminescence shows the characteristic structure of Cr 3q in spinel hosts Ž686–725 nm. as well as features associated with the other crystalline phase Ž; 690–750 nm., thought to be virgilite w1,4x. As the excitation energy is reduced, the contribution of the crystalline phases to the luminescence spectrum reduces and a broad, smooth spectrum becomes dominant. This corresponds to Cr 3q ions decaying via the 4 T2 ™4A 2 transition which must occupy a third phase of the sample, corresponding to the pure gahnite glass. The multisite nature of the ceramic can immediately be identified by considering Fig. 1a, in particular by considering the 4A 2 ™4 T2 absorption band at wavelengths longer than about 470 nm. The absorption spectrum of the ceramic appears to be composed of components from the crystalline phases, represented by the R-line excitation spectrum, and the glassy phase, represented by the absorption spectrum of the glass. The 4A 2 ™4 T2 absorption band of the Cr 3q ions in the glassy phase is shifted to lower energy relative to those in the crystalline phases. That the shift is large can be immediately seen by inspecting the samples; the glass is green whereas the ceramic is red. The R-line at 686 nm and the sharp sideband structure are barely apparent when the system is excited at wavelengths longer than about 590 nm because the glassy phase has much stronger absorption at these wavelengths. The luminescence lifetime of Cr 3q ions in spinel crystals is around 30 ms at low temperatures w3x whereas the other crystalline phase has been shown to decay more rapidly using time-resolved measurements w1,5x. The 4 T2 ™4A 2 transition always has a shorter lifetime than 2 E ™ 4 A 2 transitions and so three quite different lifetimes can be expected to dominate the behaviour of this sample Žin fact, it will be shown that a fourth centre also contributes.. Different combinations of lifetimes will dominate depend-
Fig. 1. Ža. Absorption, excitation and luminescence spectra of the Cr 3q-doped gahnite materials measured at 10 K. Absorption spectra are shown as dashed lines for the glass wgx and the glass ceramic wg–cx. Above the absorption spectra, the excitation spectra for the same samples are indicated by solid lines. The Fano anti-resonance between the 4 T2 and 2 E states is indicated by FA for the glass. It is not resonant with the R line of the emission from the Cr 3q ions in the spinel phase of the glass ceramic as can be seen in the luminescence spectrum excited at 488 nm, also drawn using a solid line above. Two other emission spectra are shown, excited at 540 nm and 590 nm as indicated. Žb. The three luminescence spectra of the glass ceramic, as shown in Ža., on a larger scale. The R and N1 lines are indicated. All spectra were excited by a dye laser providing constant excitation power. The luminescence was dispersed by a 0.5 m monochromator, detected by a germanium detector and corrected for instrumental response.
ing on the combination of excitation energy, detection wavelength and sample temperature but the decay would rarely be expected to be a single exponential. This paper is mainly concerned with the analysis of luminescence kinetics, the purpose being to show that the
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technique of continuous decay analysis can be applied to solids. This technique is used to estimate the number of different contributions to the luminescence decay and to relate them to various chromium sites or other emission centres. 2. Luminescence decay analysis In studying radiative processes in Cr 3q impurity ions it is necessary to consider the effect of breaking the spinselection rule. Depending on the strength of the local crystal field, the first excited state of the Cr 3q ion is either 2 E Žstrong field. or 4 T2 Žweak field.. Since the ground state is always 4A 2 , the doublet 2 E is a metastable state in strong field sites with the spin-forbidden 2 E ™4A 2 transition yielding narrow R-line luminescence mainly due to the spin–orbit interaction which mixes the 2 E and 4 T2 states w6–10x. It has been found that this mixing is related to the energy separation between the doublet and quartet states, and to the electron–lattice coupling of the 4 T2 state w11x. Since both quantities depend on the crystal field strength and nearest neighbour arrangement, there is a site to site variation and this yields a distribution of the radiative lifetime. Ions in weak field sites decay via the much stronger 4 T2 ™4A 2 spin-allowed transition leading to considerably shorter radiative lifetimes. Several factors influence luminescence decay. For parity forbidden electric dipole radiative transitions, local crystal field symmetry is important but, in many cases, non-radiative processes compete with radiative relaxation. Donor–acceptor energy transfer, multiphonon processes and internal conversion transitions are all examples of such non-radiative processes and all prevent the total luminescence decay from having a single exponential form. The luminescence detected is a superposition of the emission from all the emitting centres. Independent of the processes that influence the relaxation, the intensity of the luminescence from each individual site, i, excited at time t s 0, is given by Ii Ž t . s
Pi Ž t .
t i ,rad
Ž1.
where t i,rad is the radiative lifetime of the centre and Pi Ž t . is the probability of finding the ith centre in the excited state at time t. This is a solution of the master equation w12x: d Pi Pi s Ý wi k Ž k ™ i . Pk y Ý wk i Ž i ™ k . pi y dt t i ,rad k/ i k
Ž2. In Eq. Ž2., wi k Ž k ™ i . and w k i Ž i ™ k . denote the nonradiative transfer rates describing intercentre excitation exchange. In the second sum the rate for k s i, wii Ž i ™ i . corresponds to the intracentre non-radiative internal conversion rate w13,14x.
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For an ensemble of centres that all have the same radiative decay rate, it can be shown that the distribution of measured luminescence lifetimes is related to the distribution of the efficiency of non-radiative processes. This is also valid when donor–acceptor non-radiative transfer perturbs the luminescence. The effective Žaveraged. luminescence decay has been modelled w15–18x and found to be related to the overlap between absorption and emission. Luminescence decay for an individual centre is still exponential however w19x. Fig. 1a shows that there is some overlap between the absorption and emission of the Cr 3qdoped glass ceramic, indicating that energy transfer between sites might be possible. However, the overlap is small so that the rate of energy transfer is expected to be low and in the analysis that follows the rates wi k Ž k ™ i . and wk i Ž i ™ k . are set to zero Žexcept for k s i, wii Ž i ™ i . which corresponds to the intracentre non-radiative decay rate.. For each centre, the probability Pi Ž t ., depends exponentially on time; Ni yt r t i ,eff Pi Ž t . s e Ž3. N0 Here Ni is the number of initially excited centres characterised by the decay time t i,rad and N0 is the total number of such centres, respectively. The ratio of Ni to N0 will vary with excitation wavelength. The effective decay rate is given by; 1 1 1 s q Ž4. t i ,eff t i ,rad t i ,nr where t i,rad and t i,nr s 1rwi i Ž i ™ i . are the radiative and non-radiative decay constants respectively Žas intercentre transfer is set to zero in this case.. The conclusion is that, in solids, variation in luminescent decay between centres is related to both non-radiative decay rates as well as the oscillator strengths for radiative transitions. This is important in the analysis of materials with internal disorder such as gallogermanates, garnets and glasses. The starting point for luminescence decay analysis, in all cases, is the assumption of a single-exponential luminescence decay for each individual site, and this results in the following relationship for the time dependence of the total luminescence; IŽt. s Ý i
A i Ž t i ,eff .
t i ,rad
eyt r t i ,eff
Ž5.
The main challenges are to recover the distribution of the decay constants, A i Žt i,eff ., and then to relate them to specific physical phenomena. The coefficients, A i Žt i,eff ., will vary with excitation and detection wavelength as they represent the number of ions of any given lifetime that are contributing to the total luminescence. To recover the distribution of decay constants from the experimentally measured luminescence decays, the nonlinear least squares analysis w20,21x has been used in this
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work, whereby the x 2 function of the luminescence decay profile was minimised. This function is defined as I Ž t k . y I ex Ž t k .
x 2s Ý
2
Ž6.
sk
k
where I Ž t k . is the theoretical decay function given by Eq. Ž6., I ex Ž t k . is the experimental emission decay and s k is the weighting of the experimental point, k. In glasses and internally disordered crystals a continuous distribution of the local crystal field is expected and so the summation ŽEq. Ž5.. represents a continuous distribution of the decay constant, AŽt . w22x. In order to represent the decay contributions over a wide variation in lifetime, it is common practice w22,23x to use a logarithmic scale for the decay constant. When only the radiative processes are taken into account, teff s trad s t , and; AŽt .
eyt r t s d Ž ln t . A Ž t . eyt r t t so that the following expression;
Ž7.
I Ž t . s Ý A i eyt r t i
Ž8.
I Ž t . s dt
H
H
i
can replace Eq. Ž5. under the assumption that the constant difference t i y t iy1 is replaced by a constant difference of lnŽt i . y lnŽt iy1 .. The coefficients A i enumerate the contributions of those sites that have a decay constant of t i . In the more general case, when the radiative process is not the only process to deexcite the centres, the quantities recovered are not the distribution of the decay constants, A i . When the logarithmic scale is used for teff the following analogue of Eq. Ž9. is obtained; t i ,eff yt r t i ,eff I Ž t . s Ý Ai e Ž9. t i ,rad i so that the recovered quantity, A i,rec , is actually; t i ,eff A i ,rec s A i t i ,rad
ing from Eq. Ž12. will be expected to describe the shift of the distribution to shorter times as temperature increases. Returning to Eq. Ž6., the final consideration is the choice of the weighting factors, s k . They have been chosen to reflect the actual errors associated with individual experimental points. The weightings chosen are therefore;
s k s I ex Ž t k . y I ex Ž t ky1 .
Ž 13. 2
FORTRAN procedures, which minimise s using the Levenberg–Marquardt method w24x were used to find solutions. The 10 000 data points per decay curve of the original experimental data were initially reduced to one thousand by adjacent value averaging. The first 200 points were not averaged so that the number of points at short times was greater. This is numerically convenient when using logarithmic spacings for histogram contributions. The lifetime distribution could then be approximated by a maximum of 200 t i values. The results presented below correspond to 125 different values for t i . As the experimental curve is fit using 125 parameters it is important to discuss how reasonable the fits are, in particular whether the results of the fits are unambiguous. In order to determine the reliability of the process, computer generated artificial multiexponential decays were produced and the fitting procedure applied to them. An example of a fit using this method is presented in Fig. 2. Here the solid curve represents an invented distribution of the decay constants with a signal to noise ratio of 0.1% and the histogram shows the lifetimes subsequently recovered using the technique outlined above. It was found that the method reproduces the shape of continuous lifetime distributions quite well. Single value exponential decays are also represented by a continuous distribution, albeit centred on the single lifetime value and with an integrated
Ž 10.
It is important to discuss the relationship between the distribution, A i , and the probability of finding the system in the excited state, Pi , which is a solution of master Eq. Ž2.. Effectively, A i corresponds to the probability that the excited system will emit a photon. Assuming that all processes are local and take place in the individual centre; t i ,eff A i s Pi Ž 11. t i ,rad so that, combining Eqs. Ž10. and Ž11., the recovered distribution coefficients can be written; A i ,rec s Pi
t i ,eff
ž / t i ,rad
2
Ž 12.
Since the nonradiative transition rate and consequently the effective decay time, t i,eff , is a function of temperature, the recovered decay time distribution must also depend on temperature. In particular, the coefficients result-
Fig. 2. A test case for the continuous decay analysis technique. The solid curve represents a computer generated input decay distribution Žwith a 0.1% noise component. and the histogram corresponds to the recovered distribution.
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area proportional to the size of the input Žactual. sharp distribution. A proper choice of the range of the decay constants is extremely important for the quality of the fits. If the predicted decay range is adequate it is possible to unambiguously distinguish various different decay distributions whose peaks differ by no less than 1r5 of the decay range. Experimental signal to noise ratios vary with time after excitation during the signal decay but the weighting procedure outlined above is chosen to take account of this. At almost all times the experimental signal to noise ratio is less than 1% and at such levels the analysis can be taken to be unambiguous.
3. Luminescence decay measurements and fitting to the experimental data The luminescence was excited by a small nitrogen pumped dye laser and detected using a photomultiplier after emission dispersion by a monochromator. The data was accumulated by a digital oscilloscope and the whole apparatus was controlled by a computer. Initially 10 000 points were taken over the decay of the luminescence, the points being separated by 0.1–10 ms depending on the decay rate. Typical decay curves are shown in Fig. 3. The results of the lifetime decay analyses for various combinations of excitation photon energies and detection wavelengths are illustrated in Fig. 4. The emission lifetime contributions are monitored at 686 nm Žresonant with the R line emission., 694 nm Žresonant with the R line sideband structure., 708 nm Žat the wavelength dominated by
Fig. 3. Typical experimental luminescence decays detected at 686 nm and excited by laser radiation at the wavelengths indicated. As for the calculations, the first 200 data points are not adjacent point averaged so that noise appears to be greater for the first 2 ms of the decay of the upper three traces Žand for a shorter period not clearly visible in the lower two traces.. Smooth lines represent fits obtained using the technique outlined in this paper.
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the virgilite phase luminescence w1x. and 800 nm Žin the region where contributions from the crystalline phases are expected to be very small.. For high photon energy excitation Ž485 nm, 515 nm and 550 nm. and high photon energy detection Ž686 nm. there are three different decay distributions with mean constants of about 20 ms, 1 ms and 0.08 ms. For the same detection conditions but exciting at lower photon energies Ž600 nm and 645 nm. the longest decay time distribution is not present and the other two distributions drift to shorter lifetimes Ž0.3 ms and 0.02 ms.. The differences in the luminescence decay distributions can be directly related to the differences in the emission spectra excited at different wavelengths. For instance, in Fig. 1, it is seen that the R line and sharp line sideband disappears from the spectrum when the excitation wavelength is changed from 540 nm to 590 nm whilst Fig. 4 shows that the longest lifetime contribution disappears from the distribution between 550 nm and 600 nm. The three main lifetime distribution contributions observed in Fig. 4a can be simply related to the three phases into which Cr 3q ions are incorporated as discussed in the introduction. The longest lifetime corresponds to the spinel crystalline phase with a lifetime of about 20 ms, the intermediate lifetime corresponds to the virgilite crystalline phase with a lifetime around 1 ms and the shortest lifetime, significantly below 1 ms, corresponds to the glassy phase emission. A fourth contribution at around 2 ms appears when monitoring emission at 694 nm ŽFig. 4b. and this is thought to be related to the N1 line Žsee Fig. 1.. The N1 line is observed in many gahnite ceramic samples and has been ascribed to a distorted spinel site w3x. When detecting emission at 708 nm ŽFig. 4c., the spinel and distorted spinel phases make only small contributions to the decay. At high excitation energies the virgilite phase decay is dominant but, as for higher detection photon energies, the glassy phase becomes the major contributor when the excitation wavelength increases beyond 600 nm. When detecting emission beyond the limit of the vibronic structure, around 750 nm, only the fast decay corresponding to the glassy phase remains. Examples of this are shown in Fig. 4d for detection at 800 nm with excitation at high and low photon energy. It is instructive to examine a plot of the lifetime data for one of these distributions on a logarithmic scale ŽFig. 5.. The best fit is not a straight line and so is not a single exponential decay but rather a distribution. Thus the distribution recovered in Fig. 4d appears to provide a good representation of the broadening of the lifetime distribution. In Fig. 6 the recovered luminescence decay time distributions for the emission excited at 485 nm and 645 nm and monitored at different wavelengths are shown. Again, the distributions are dominated by four separate decays corresponding to the four different Cr 3q sites as discussed above. The absence of the longest decay when exciting at 645 nm is immediately noticeable. When exciting at 485
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Fig. 4. Histograms representing the recovered lifetime decay coefficients, A i , for luminescence detection at 686 nm ŽŽa., resonant with main R line emission., 694 nm ŽŽb., resonant with the R line sideband structure., 708 nm ŽŽc., in the region dominated by the virgilite phase luminescence. and 800 nm ŽŽd., in the region dominated by the broadband luminescence. and excited at the wavelengths indicated.
nm, this long component makes a decreasing contribution as the detection wavelength is increased. Conversely, for both excitation wavelengths, the fastest decay increases in relative strength with increasing detection wavelength whilst gradually drifting to shorter lifetime. The distorted spinel phase with a lifetime of around 2 ms is most prevalent in the spectrum excited at 485 nm and detected at 689 nm, exactly resonant with the N1 line indicated in Fig. 1, adding weight to the assignment. An understanding of the luminescence decay distributions follows directly from the discussion, above, of the multisite nature of the material. The four sites are summarised as follows. Ž1. The spinel phase that decays with an invariant lifetime of about 20 ms. The 4A 2 ™4 T2 absorption band of
this phase is at high energy, between about 460–620 nm Žsee Fig. 1.. Excitation in this band at low temperature results in R line luminescence at 686 nm and structured vibronically assisted emission to about 750 nm. The behaviour of this centre is very similar to that of Cr 3q ions in single crystals of ZnAl 2 O4 w3x though the lifetime we observe is slightly lower. Ž2. The distorted spinel phase that gives rise to the N1 line of the luminescence spectrum and which decays with a lifetime of about 2 ms. Again, this lifetime is somewhat lower than that measured previously. It should be noted that a number of different N lines, all corresponding to differently distorted sites have been reported in single crystal spinels w25x. It is likely that the lifetime contributions observed here are due to more than one of these
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similar to the spinel and so is not shown. As the 2 E state is lower in energy than the 4 T2 state in the spinel and virgilite phases then R line emission Žwith structured vibronic sidebands. is observed. For the spinel phase, only one set of sites is observed leading to a relatively narrow absorption band and luminescence with a single lifetime. The virgilite phase is represented by several slightly different potential wells shifted by the effects of disorder within the ceramic. The energies of the 4 T2 states are at slightly lower energy than in the spinel phase thus increasing the wavefunction mixing between 2 E and 4 T2 states due to spin–orbit coupling and reducing the luminescence lifetime w7,9x. The 4 T2 states of these differently distorted
Fig. 5. Experimental luminescence decays detected at 800 nm and excited by laser radiation at the wavelengths indicated. Smooth lines obtained represent fits using the technique outlined in this paper.
distorted sites though it is difficult to identify unambiguously other N lines due to the complexity of the luminescence spectrum of this multiphase material. Ž3. The second crystalline phase, thought to be virgilite but not conclusively ascribed, that decays with a lifetime of between 0.3 and 1 ms. Such ions can be excited at all wavelengths used in this investigation and luminesce at wavelengths similar to the spinel phase. The structure close to 708 nm seems to be dominated by the virgilite phase as can be seen from the dominance of the 1 ms decay contribution in Fig. 4c and from previous experiments that have measured time resolved luminescence spectra w1x. The broad absorption spectrum and shift in lifetime as a function of excitation and emission wavelength suggests that this phase is considerably disordered, perhaps due to substitutional disorder as is observed in gallogermanate crystals w11x. Ž4. The glassy phase that decays with a lifetime of between 0.01 and 0.08 ms. The excitation band of this phase is again across the full range of excitation wavelengths used here and can be expected to be well into the infrared according to the absorption spectra shown in Fig. 1. The emission band is similarly broad and dominates the emission spectrum at wavelengths beyond about 750 nm. The contributions of each of the four sites at any given combination of excitation and detection energies is thus a reflection of the relative strength of emission of the different phases for these experimental conditions. The configuration coordinate diagrams shown in Fig. 7 further illustrate how selection takes place during the excitation and emission processes. Sets of curves are shown for Cr 3q ions in the spinel phase, in the virgilite phase and in the glassy phase. The distorted spinel would appear very
Fig. 6. Histograms representing the recovered lifetime decay coefficients, A i , for excitation at 485 nm ŽŽa., resonant with 4 A 2 ™4 T2 absorption for all phases. and 800 nm ŽŽb., beyond the 4 T2 ™4A 2 excitation band for R line emission. and detected at the wavelengths indicated.
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Fig. 7. Schematic sets of configuration coordinate diagrams indicating the effect of the variation in crystal field from site to site for Ža. the spinel phase Žand distorted spinel phase., Žb. the virgilite phase and Žc. the glassy phase.
sites are shifted to different energies thus causing variation in the amount of wavefunction mixing, leading to a variation in the luminescence lifetime as different sites are selectively excited or detected. Low energy excitation or detection implies lower energy 4 T2 states and this implies shorter lifetimes. This is observed. The lifetime decreases as either the excitation or detection wavelength decreases. The diagrams shown imply that the site-to-site variation is only in crystal field strength so that the potential wells are shifted vertically up and down in configuration coordinate space. However, it is entirely possible that, as in the case of gallogermanates w11x and CaYAlO4 w26x, variation in electron–phonon coupling also contributes to the lifetime variation. The data recovered using this technique cannot distinguish clearly between the two. Similar shifts in the lifetime distribution peak are observed for the glassy phase but to a greater extent. A different explanation of this effect than for the virgilite phase must be invoked as mixing of the 2 E state into the 4 T2 state does not greatly effect the luminescence lifetime when the 4 T2 state is the lower in energy. For the glassy phase, the decrease in emission lifetime with decreasing excitation energy can be explained in terms of non-radiative internal conversion processes. It has been shown for gallogermanates that nonradiative processes are considerably more effective for weaker field sites within a distribution w27x. Thus, considering Eq. Ž4., the effective decay time is shorter when the weaker field sites are preferentially excited or detected. A final speculative comment on the low temperature data is in relation to the somewhat lower lifetime of the Cr 3q ions present in the spinel nanocrystals Ž; 20 ms. relative to that reported in bulk samples Ž31 ms w3x.. It is known that long term heat treatment of gahnite glasses produces crystallites with sizes of around 30 nm. The size of the nanocrystals in the present sample are likely to be somewhat smaller due to a reduced heat treatment period. Studies of Mn2q impurities in ZnS nanocrystals revealed a
significant reduction in luminescence lifetime compared to that measured in bulk material w28x. Though these results have proved controversial and have been refuted by some w29x, it is possible that the measured luminescence lifetime in our samples is influenced by the small size of the crystallites in which the chromium impurities are housed. Further evidence that the technique presented here is able to quantitatively describe the decay of multisite materials can be seen in Fig. 8 in which the decay distributions for excitation at 550 nm and detection at 686 nm, resonant with the R line, are compared for different temperatures. The same three components are observed but relative contributions differ with temperature. With increasing temperature, the longest component becomes weaker whilst the shortest component becomes stronger. This is due to the decreased intensity of the R line luminescence from the spinel phase and the increased intensity of luminescence at higher energies in the ‘glassy’ phase. Both of these effects are due to the blue shift of luminescence bands with temperature due to the thermal occupation of higher vibronic states. Thus there is less spinel phase luminescence at 686 nm and more from the glassy phase. There is a shift in the distribution maxima toward shorter time with increasing temperature. The shift of the shortest component, related to the glassy phase Cr 3q ions, can be explained in terms of increasing internal conversion rates though it is unclear why this effect is seen only for temperatures smaller than 100 K. For the longer components, this effect is due to increasing occupation of the higher vibronic states of the first excited electronic manifold Žwhich, due to the spin–orbit interaction, is a superposition of the 2 E and 4 T2 states w7,9x, as mentioned above.. The thermally occupied higher states are energetically closer to the 4 T2 level and consequently have more quartet character than the zero-phonon level resulting in faster
Fig. 8. Histograms representing the lifetime decay coefficients, A i , for luminescence detection at 686 nm, resonant with the Cr 3q R line emission from the spinel phase of the gahnite glass ceramic, excited at 550 nm at different temperatures as indicated.
M. Grinberg et al.r Optics Communications 156 (1998) 409–418
decay of the luminescence than when only the ground vibronic state is occupied. When monitoring emission at 739 nm, only luminescence from the medium and weak field sites is observed. Fig. 9 compares the decay constant distributions measured at 10 K and room temperature, excited at various wavelengths. In all cases decays at 10 ms and 800 ms are observed, corresponding to the glassy and virgilite phases of the ceramic. For all excitation energies, in going from 10 K to room temperature, there is a significant increase in the relative magnitude of the short lifetime contribution and a decrease in the lifetime of the longer contribution. The relative changes in the distribution concern the decay
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distribution of the luminescence and are best seen for excitation at 485 nm and 515 nm. Here the situation is the same as in the case of luminescence monitored at 686 nm, the increase in the shorter component of the decay is related to the shift of the respective emission band to higher energy. When the luminescence is excited with longer wavelength an additional effect is observed, the appearance of a much shorter decay ŽF 1 ms. at room temperature. This is related to the broad distribution of crystal fields experienced by the chromium ions in the glassy phase. The weakest field sites have an increased probability of decaying non-radiatively through internal conversion w13,14x. Since the rate at which this process takes place increases strongly with temperature, the effective decay constant is expected to decrease with temperature as observed. Since this effect mainly concerns the sites characterised by the weakest crystal field Žand therefore the longest wavelength absorption peak., shorter decays are observed when exciting at 550 nm, 600 nm and especially at 645 nm. Taking into account Eq. Ž12. which describes the relationship between the recovered quantity and the actual distribution of the decay constants, that is, the probability that the ith site is excited, it can be seen that the actual change in luminescence decay for an individual site is even more dramatic than can be observed by comparing Fig. 9a and 9b. 4. Conclusions
Fig. 9. Comparison of histograms representing the lifetime decay coefficients, A i , at 10 K and room temperature. Emission was detected at 739 nm, beyond the range of spinel phase emission, and excited at various wavelengths as indicated.
At first thought, it may seem absurdly hopeful to fit the luminescence decay of a disordered multisite material using what are effectively 125 exponentials but the behaviour of Cr 3q impurities in the gahnite glass ceramic have been shown to be well modelled by the technique of continuous function decay analysis presented here. It has revealed detailed characteristics of the luminescent centres in the materials. Four different groups of sites, detailed above, have been clearly identified and their behaviour has been directly related to previous experiments on Cr 3qdoped gahnite ceramics, gahnite glasses and spinel crystals. The only remaining question is whether the widths of the distribution have real meaning. It would seem likely that the longest lifetime contribution, relating to Cr 3q ions in the spinel phase, should be a single exponential and therefore not correctly described by a distribution Žthough nanocrystals of different sizes could conceivably influence the decay times of impurity ions contained within.. The ‘glassy’ phase, on the other hand, is likely to have a genuine spread of lifetimes as evidenced by the shift in its peak with excitation wavelength and the non-exponential decays presented in Fig. 5. The approach we have used to recover the distribution of luminescence decay times can be applied for any arbitrary non-exponential luminescence decay Žwhere, as is almost always the case, each emitting chromophore decays
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exponentially.. The advantage of this method is that no luminescence decay model or physical model of the material are required a priori. This method of analysis also has a great advantage over time resolved spectroscopy in that different sites can be identified even when they emit via broad bands which overlap the same spectral region. It is also worth briefly mentioning the validity of our method when nonexponential luminescence decay is related to nonradiative donor acceptor energy transfer. When back transfer Žfrom acceptor to donor. can be excluded, the emission of any particular donor is single exponential with a decay constant given by Eq. Ž3.. In such a case the decay time distribution is related to the distribution of the acceptors around the donor site. Acknowledgements This paper is supported in part by KBN Research Grant number 2P03B003 13. References w1x V. Poncon, J. Kalisky, G. Boulon, R. Reisfeld, Chem. Phys. Lett. 133 Ž1987. 363. w2x G.H. Beall, D.A. Duke, J. Mater. Sci. 4 Ž1969. 340. w3x D.L. Wood, G.F. Imbusch, R.M. Macfarlane, P. Kisliuk, D.M. Larkin, J. Chem. Phys. 48 Ž1968. 5255. w4x C. Koepke, K. Wisniewski, M. Grinberg, D.L. Russell, K. Holliday, Proc. SPIE 3176 Ž1997. 42. w5x V. Poncon, M. Bouderbala, G. Boulon, A.-M. Lejus, R. Reisfeld, A. Buch, M. Ish-Shalom, Chem. Phys. Lett. 130 Ž1986. 444. w6x S. Sugano, Y. Tanabe, H. Kamimura, Multiplets of Transition Metal Ions in Crystals, Academic Press, New York, 1970.
w7x w8x w9x w10x w11x w12x w13x w14x w15x w16x w17x w18x w19x w20x w21x w22x w23x w24x
w25x w26x w27x w28x w29x
M. Grinberg, T. Orlikowski, J. Lumin. 53 Ž1992. 447. B. Struve, G. Huber, Appl. Phys. B. 36 Ž1985. 195. M. Grinberg, J. Lumin. 54 Ž1993. 369. D. Galanciak, P. Perlin, M. Grinberg, A. Suchocki, J. Lumin. 60 Ž1994. 223. M. Grinberg, P.I. Macfarlane, B. Henderson, K. Holliday, Phys. Rev. B. 52 Ž1995. 3917. C. Bojarski, G. Zurkowska, Z. Naturforsch. A 42 Ž1987. 1451. M. Grinberg, A. Mandelis, K. Fieldsted, Phys. Rev. B 48 Ž1993. 5955. M. Grinberg, A. Mandelis, Phys. Rev. B 49 Ž1994. 12496. Th. Forster, Z. Naturforsh. A 4 Ž1949. 321. ¨ Th. Forster, Ann. Phys. 2 Ž1948. 55. ¨ D.L. Dexter, J. Chem. Phys. 21 Ž1953. 836. M. Inokuti, F. Hirayama, J. Chem. Phys. 43 Ž1965. 1978. J. Kaminski, A. Kawski, Z. Naturforsch. A 32 Ž1977. 140. ˜ J.N. Demas, Excited State Lifetime Measurements, Academic Press, New York, 1983. M. Grinberg, K. Wisniewski, Cz. Koepke, D. Russell, K. Holliday, Spectrochimica Acta, in press. L.B. McGrown, S.L. Hemmingsen, J.M. Shaver, L. Geng, Appl. Spectr. 49 Ž1995. 60. J.C. Brochon, A.K. Liversey, J. Pouget, B. Valeur, Chem. Phys. Lett. 174 Ž1990. 517. W.H. Press, B.P. Flannery, S.A. Tenkolsky, W.T. Vetterling, Numerical Recipes, The Art of Scientific Computing, Cambridge Univ. Press, 1986. W. Mikenda, A. Preisinger, J. Lumin. 26 Ž1981. 53. M. Yamaga, P.I. Macfarlane, K. Holliday, B. Henderson, N. Kodama, Y. Inoue, J. Phys.: Cond. Matter 8 Ž1996. 3487. M. Grinberg, W. Jaskolski, P.I. Macfarlane, K. Holliday, J. Phys.: Cond. Matter 9 Ž1997. 2815. R.N. Bhargava, D. Gallagher, X. Hong, A. Nurmikko, Phys. Rev. Lett. 72 Ž1994. 416. M.A. Chamarro, V. Voliotis, R. Grousson, P. Lavallard, T. Gacoin, G. Counio, J.P. Boilot, R. Cases, J. Cryst. Growth 159 Ž1996. 853.
Optics Communications 156 Ž1998. 409–418
Full length article
Continuous function decay analysis of a multisite impurity activated solid Marek Grinberg
a,1
, D.L. Russell b, Keith Holliday Cz. Koepke c
b,)
, K. Wisniewski c ,
a
b
Institute of Experimental Physics, UniÕersity of Gdansk, ˜ Wita Stwosza 57, 80-952 Gdansk, ˜ Poland Optical Materials Research Centre, Department of Physics and Applied Physics, UniÕersity of Strathclyde, ColÕille Building, North Portland Street, Glasgow G1 1XN, UK c Institute of Physics, N. Copernicus UniÕersity, 87-100 Torun, ˜ Poland Received 30 April 1998; revised 17 August 1998; accepted 18 August 1998
Abstract The technique of continuous function decay analysis, previously used in studies of molecular dynamics, is applied to a solid that is optically activated through impurity doping. Chromium ions occupy several different sites in gahnite glass ceramics, each of which has different luminescence lifetime characteristics but overlapping absorption and emission spectra. Continuous function decay analysis maps the decay patterns of the decaying species, producing histograms of the relative strengths of decay at Žin this case. 125 logarithmically spaced lifetimes. The results for chromium ions in gahnite glass ceramics are related to the interaction between the impurity ions and the solid state environment and correlate well with previous studies of this material that have used standard techniques. Continuous function decay analysis is thus shown to be an effective method for understanding the optical behaviour of multisite materials. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Continuous function decay analysis; Impurity doping; Multisite material
1. Introduction This paper presents the application of a technique previously used in studies of molecular dynamics to study the decay of a multisite optically activated solid. When materials contain optically active species that occupy more than one site it is often difficult to determine site occupancies and dynamics due to the overlap of absorption and luminescence spectra. Time resolved spectroscopy can occasionally help to resolve some of the site dependent structure but when the number of centres increases beyond
) 1
Corresponding author. E-mail: [email protected] E-mail: [email protected]
two or when one of the sites consists of a continuous distribution of environment parameters Žcrystal field parameters for a solid. a new method is required. Here the technique of continuous decay analysis is presented. This allows simple luminescence decays to be broken down into a large number of contributions at different lifetimes. In the case presented here, decay curves of chromium ions in gahnite glass ceramics are decomposed into histograms showing the contributions of 125 logarithmically spaced lifetimes to the overall decay. These decays are shown to correspond very well to the known properties of the material and, such is the aptitude of the technique, new conclusions can also be drawn. Gahnite glasses are composed of a mixture of oxide compounds, principally SiO 2 and Al 2 O 3 but with concen-
0030-4018r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 Ž 9 8 . 0 0 4 6 3 - 5
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trations of up to 10% of ZnO, Li 2 O, TiO 2 , ZrO 2 and As 2 O 3. Heat treatment produces gahnite glass ceramics, which include various crystal phases. The duration of the heat treatment determines the degree and type of crystallisation as evidenced by the effects on the luminescence spectra of Cr 3q ions included in the structure as impurities w1x. Long term heat treatment results in the majority of the Cr 3q ions being incorporated in crystallites of ZnAl 2 O4 with sizes of around 30 nm. This is confirmed by the similarity of Cr 3q luminescence spectra of such ceramics to the bulk spinel crystal w2,3x. Shorter periods of heat treatment produce some crystallites of ZnAl 2 O4 but also other crystalline phases w1x. Cr 3q impurity ions in both crystalline phases luminesce via vibronically structured 2 E ™4A 2 transitions. The luminescence spectrum of the untreated Cr 3q-doped glass is much broader and smoother, characteristic of 4 T2 ™4A 2 emission. The gahnite glass ceramic used in this study has intermediate crystallinity as can be seen from luminescence spectra excited at different wavelengths ŽFig. 1.. When excited in the middle of the 4A 2 ™4 T2 absorption band the sample luminescence shows the characteristic structure of Cr 3q in spinel hosts Ž686–725 nm. as well as features associated with the other crystalline phase Ž; 690–750 nm., thought to be virgilite w1,4x. As the excitation energy is reduced, the contribution of the crystalline phases to the luminescence spectrum reduces and a broad, smooth spectrum becomes dominant. This corresponds to Cr 3q ions decaying via the 4 T2 ™4A 2 transition which must occupy a third phase of the sample, corresponding to the pure gahnite glass. The multisite nature of the ceramic can immediately be identified by considering Fig. 1a, in particular by considering the 4A 2 ™4 T2 absorption band at wavelengths longer than about 470 nm. The absorption spectrum of the ceramic appears to be composed of components from the crystalline phases, represented by the R-line excitation spectrum, and the glassy phase, represented by the absorption spectrum of the glass. The 4A 2 ™4 T2 absorption band of the Cr 3q ions in the glassy phase is shifted to lower energy relative to those in the crystalline phases. That the shift is large can be immediately seen by inspecting the samples; the glass is green whereas the ceramic is red. The R-line at 686 nm and the sharp sideband structure are barely apparent when the system is excited at wavelengths longer than about 590 nm because the glassy phase has much stronger absorption at these wavelengths. The luminescence lifetime of Cr 3q ions in spinel crystals is around 30 ms at low temperatures w3x whereas the other crystalline phase has been shown to decay more rapidly using time-resolved measurements w1,5x. The 4 T2 ™4A 2 transition always has a shorter lifetime than 2 E ™ 4 A 2 transitions and so three quite different lifetimes can be expected to dominate the behaviour of this sample Žin fact, it will be shown that a fourth centre also contributes.. Different combinations of lifetimes will dominate depend-
Fig. 1. Ža. Absorption, excitation and luminescence spectra of the Cr 3q-doped gahnite materials measured at 10 K. Absorption spectra are shown as dashed lines for the glass wgx and the glass ceramic wg–cx. Above the absorption spectra, the excitation spectra for the same samples are indicated by solid lines. The Fano anti-resonance between the 4 T2 and 2 E states is indicated by FA for the glass. It is not resonant with the R line of the emission from the Cr 3q ions in the spinel phase of the glass ceramic as can be seen in the luminescence spectrum excited at 488 nm, also drawn using a solid line above. Two other emission spectra are shown, excited at 540 nm and 590 nm as indicated. Žb. The three luminescence spectra of the glass ceramic, as shown in Ža., on a larger scale. The R and N1 lines are indicated. All spectra were excited by a dye laser providing constant excitation power. The luminescence was dispersed by a 0.5 m monochromator, detected by a germanium detector and corrected for instrumental response.
ing on the combination of excitation energy, detection wavelength and sample temperature but the decay would rarely be expected to be a single exponential. This paper is mainly concerned with the analysis of luminescence kinetics, the purpose being to show that the
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technique of continuous decay analysis can be applied to solids. This technique is used to estimate the number of different contributions to the luminescence decay and to relate them to various chromium sites or other emission centres. 2. Luminescence decay analysis In studying radiative processes in Cr 3q impurity ions it is necessary to consider the effect of breaking the spinselection rule. Depending on the strength of the local crystal field, the first excited state of the Cr 3q ion is either 2 E Žstrong field. or 4 T2 Žweak field.. Since the ground state is always 4A 2 , the doublet 2 E is a metastable state in strong field sites with the spin-forbidden 2 E ™4A 2 transition yielding narrow R-line luminescence mainly due to the spin–orbit interaction which mixes the 2 E and 4 T2 states w6–10x. It has been found that this mixing is related to the energy separation between the doublet and quartet states, and to the electron–lattice coupling of the 4 T2 state w11x. Since both quantities depend on the crystal field strength and nearest neighbour arrangement, there is a site to site variation and this yields a distribution of the radiative lifetime. Ions in weak field sites decay via the much stronger 4 T2 ™4A 2 spin-allowed transition leading to considerably shorter radiative lifetimes. Several factors influence luminescence decay. For parity forbidden electric dipole radiative transitions, local crystal field symmetry is important but, in many cases, non-radiative processes compete with radiative relaxation. Donor–acceptor energy transfer, multiphonon processes and internal conversion transitions are all examples of such non-radiative processes and all prevent the total luminescence decay from having a single exponential form. The luminescence detected is a superposition of the emission from all the emitting centres. Independent of the processes that influence the relaxation, the intensity of the luminescence from each individual site, i, excited at time t s 0, is given by Ii Ž t . s
Pi Ž t .
t i ,rad
Ž1.
where t i,rad is the radiative lifetime of the centre and Pi Ž t . is the probability of finding the ith centre in the excited state at time t. This is a solution of the master equation w12x: d Pi Pi s Ý wi k Ž k ™ i . Pk y Ý wk i Ž i ™ k . pi y dt t i ,rad k/ i k
Ž2. In Eq. Ž2., wi k Ž k ™ i . and w k i Ž i ™ k . denote the nonradiative transfer rates describing intercentre excitation exchange. In the second sum the rate for k s i, wii Ž i ™ i . corresponds to the intracentre non-radiative internal conversion rate w13,14x.
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For an ensemble of centres that all have the same radiative decay rate, it can be shown that the distribution of measured luminescence lifetimes is related to the distribution of the efficiency of non-radiative processes. This is also valid when donor–acceptor non-radiative transfer perturbs the luminescence. The effective Žaveraged. luminescence decay has been modelled w15–18x and found to be related to the overlap between absorption and emission. Luminescence decay for an individual centre is still exponential however w19x. Fig. 1a shows that there is some overlap between the absorption and emission of the Cr 3qdoped glass ceramic, indicating that energy transfer between sites might be possible. However, the overlap is small so that the rate of energy transfer is expected to be low and in the analysis that follows the rates wi k Ž k ™ i . and wk i Ž i ™ k . are set to zero Žexcept for k s i, wii Ž i ™ i . which corresponds to the intracentre non-radiative decay rate.. For each centre, the probability Pi Ž t ., depends exponentially on time; Ni yt r t i ,eff Pi Ž t . s e Ž3. N0 Here Ni is the number of initially excited centres characterised by the decay time t i,rad and N0 is the total number of such centres, respectively. The ratio of Ni to N0 will vary with excitation wavelength. The effective decay rate is given by; 1 1 1 s q Ž4. t i ,eff t i ,rad t i ,nr where t i,rad and t i,nr s 1rwi i Ž i ™ i . are the radiative and non-radiative decay constants respectively Žas intercentre transfer is set to zero in this case.. The conclusion is that, in solids, variation in luminescent decay between centres is related to both non-radiative decay rates as well as the oscillator strengths for radiative transitions. This is important in the analysis of materials with internal disorder such as gallogermanates, garnets and glasses. The starting point for luminescence decay analysis, in all cases, is the assumption of a single-exponential luminescence decay for each individual site, and this results in the following relationship for the time dependence of the total luminescence; IŽt. s Ý i
A i Ž t i ,eff .
t i ,rad
eyt r t i ,eff
Ž5.
The main challenges are to recover the distribution of the decay constants, A i Žt i,eff ., and then to relate them to specific physical phenomena. The coefficients, A i Žt i,eff ., will vary with excitation and detection wavelength as they represent the number of ions of any given lifetime that are contributing to the total luminescence. To recover the distribution of decay constants from the experimentally measured luminescence decays, the nonlinear least squares analysis w20,21x has been used in this
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work, whereby the x 2 function of the luminescence decay profile was minimised. This function is defined as I Ž t k . y I ex Ž t k .
x 2s Ý
2
Ž6.
sk
k
where I Ž t k . is the theoretical decay function given by Eq. Ž6., I ex Ž t k . is the experimental emission decay and s k is the weighting of the experimental point, k. In glasses and internally disordered crystals a continuous distribution of the local crystal field is expected and so the summation ŽEq. Ž5.. represents a continuous distribution of the decay constant, AŽt . w22x. In order to represent the decay contributions over a wide variation in lifetime, it is common practice w22,23x to use a logarithmic scale for the decay constant. When only the radiative processes are taken into account, teff s trad s t , and; AŽt .
eyt r t s d Ž ln t . A Ž t . eyt r t t so that the following expression;
Ž7.
I Ž t . s Ý A i eyt r t i
Ž8.
I Ž t . s dt
H
H
i
can replace Eq. Ž5. under the assumption that the constant difference t i y t iy1 is replaced by a constant difference of lnŽt i . y lnŽt iy1 .. The coefficients A i enumerate the contributions of those sites that have a decay constant of t i . In the more general case, when the radiative process is not the only process to deexcite the centres, the quantities recovered are not the distribution of the decay constants, A i . When the logarithmic scale is used for teff the following analogue of Eq. Ž9. is obtained; t i ,eff yt r t i ,eff I Ž t . s Ý Ai e Ž9. t i ,rad i so that the recovered quantity, A i,rec , is actually; t i ,eff A i ,rec s A i t i ,rad
ing from Eq. Ž12. will be expected to describe the shift of the distribution to shorter times as temperature increases. Returning to Eq. Ž6., the final consideration is the choice of the weighting factors, s k . They have been chosen to reflect the actual errors associated with individual experimental points. The weightings chosen are therefore;
s k s I ex Ž t k . y I ex Ž t ky1 .
Ž 13. 2
FORTRAN procedures, which minimise s using the Levenberg–Marquardt method w24x were used to find solutions. The 10 000 data points per decay curve of the original experimental data were initially reduced to one thousand by adjacent value averaging. The first 200 points were not averaged so that the number of points at short times was greater. This is numerically convenient when using logarithmic spacings for histogram contributions. The lifetime distribution could then be approximated by a maximum of 200 t i values. The results presented below correspond to 125 different values for t i . As the experimental curve is fit using 125 parameters it is important to discuss how reasonable the fits are, in particular whether the results of the fits are unambiguous. In order to determine the reliability of the process, computer generated artificial multiexponential decays were produced and the fitting procedure applied to them. An example of a fit using this method is presented in Fig. 2. Here the solid curve represents an invented distribution of the decay constants with a signal to noise ratio of 0.1% and the histogram shows the lifetimes subsequently recovered using the technique outlined above. It was found that the method reproduces the shape of continuous lifetime distributions quite well. Single value exponential decays are also represented by a continuous distribution, albeit centred on the single lifetime value and with an integrated
Ž 10.
It is important to discuss the relationship between the distribution, A i , and the probability of finding the system in the excited state, Pi , which is a solution of master Eq. Ž2.. Effectively, A i corresponds to the probability that the excited system will emit a photon. Assuming that all processes are local and take place in the individual centre; t i ,eff A i s Pi Ž 11. t i ,rad so that, combining Eqs. Ž10. and Ž11., the recovered distribution coefficients can be written; A i ,rec s Pi
t i ,eff
ž / t i ,rad
2
Ž 12.
Since the nonradiative transition rate and consequently the effective decay time, t i,eff , is a function of temperature, the recovered decay time distribution must also depend on temperature. In particular, the coefficients result-
Fig. 2. A test case for the continuous decay analysis technique. The solid curve represents a computer generated input decay distribution Žwith a 0.1% noise component. and the histogram corresponds to the recovered distribution.
M. Grinberg et al.r Optics Communications 156 (1998) 409–418
area proportional to the size of the input Žactual. sharp distribution. A proper choice of the range of the decay constants is extremely important for the quality of the fits. If the predicted decay range is adequate it is possible to unambiguously distinguish various different decay distributions whose peaks differ by no less than 1r5 of the decay range. Experimental signal to noise ratios vary with time after excitation during the signal decay but the weighting procedure outlined above is chosen to take account of this. At almost all times the experimental signal to noise ratio is less than 1% and at such levels the analysis can be taken to be unambiguous.
3. Luminescence decay measurements and fitting to the experimental data The luminescence was excited by a small nitrogen pumped dye laser and detected using a photomultiplier after emission dispersion by a monochromator. The data was accumulated by a digital oscilloscope and the whole apparatus was controlled by a computer. Initially 10 000 points were taken over the decay of the luminescence, the points being separated by 0.1–10 ms depending on the decay rate. Typical decay curves are shown in Fig. 3. The results of the lifetime decay analyses for various combinations of excitation photon energies and detection wavelengths are illustrated in Fig. 4. The emission lifetime contributions are monitored at 686 nm Žresonant with the R line emission., 694 nm Žresonant with the R line sideband structure., 708 nm Žat the wavelength dominated by
Fig. 3. Typical experimental luminescence decays detected at 686 nm and excited by laser radiation at the wavelengths indicated. As for the calculations, the first 200 data points are not adjacent point averaged so that noise appears to be greater for the first 2 ms of the decay of the upper three traces Žand for a shorter period not clearly visible in the lower two traces.. Smooth lines represent fits obtained using the technique outlined in this paper.
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the virgilite phase luminescence w1x. and 800 nm Žin the region where contributions from the crystalline phases are expected to be very small.. For high photon energy excitation Ž485 nm, 515 nm and 550 nm. and high photon energy detection Ž686 nm. there are three different decay distributions with mean constants of about 20 ms, 1 ms and 0.08 ms. For the same detection conditions but exciting at lower photon energies Ž600 nm and 645 nm. the longest decay time distribution is not present and the other two distributions drift to shorter lifetimes Ž0.3 ms and 0.02 ms.. The differences in the luminescence decay distributions can be directly related to the differences in the emission spectra excited at different wavelengths. For instance, in Fig. 1, it is seen that the R line and sharp line sideband disappears from the spectrum when the excitation wavelength is changed from 540 nm to 590 nm whilst Fig. 4 shows that the longest lifetime contribution disappears from the distribution between 550 nm and 600 nm. The three main lifetime distribution contributions observed in Fig. 4a can be simply related to the three phases into which Cr 3q ions are incorporated as discussed in the introduction. The longest lifetime corresponds to the spinel crystalline phase with a lifetime of about 20 ms, the intermediate lifetime corresponds to the virgilite crystalline phase with a lifetime around 1 ms and the shortest lifetime, significantly below 1 ms, corresponds to the glassy phase emission. A fourth contribution at around 2 ms appears when monitoring emission at 694 nm ŽFig. 4b. and this is thought to be related to the N1 line Žsee Fig. 1.. The N1 line is observed in many gahnite ceramic samples and has been ascribed to a distorted spinel site w3x. When detecting emission at 708 nm ŽFig. 4c., the spinel and distorted spinel phases make only small contributions to the decay. At high excitation energies the virgilite phase decay is dominant but, as for higher detection photon energies, the glassy phase becomes the major contributor when the excitation wavelength increases beyond 600 nm. When detecting emission beyond the limit of the vibronic structure, around 750 nm, only the fast decay corresponding to the glassy phase remains. Examples of this are shown in Fig. 4d for detection at 800 nm with excitation at high and low photon energy. It is instructive to examine a plot of the lifetime data for one of these distributions on a logarithmic scale ŽFig. 5.. The best fit is not a straight line and so is not a single exponential decay but rather a distribution. Thus the distribution recovered in Fig. 4d appears to provide a good representation of the broadening of the lifetime distribution. In Fig. 6 the recovered luminescence decay time distributions for the emission excited at 485 nm and 645 nm and monitored at different wavelengths are shown. Again, the distributions are dominated by four separate decays corresponding to the four different Cr 3q sites as discussed above. The absence of the longest decay when exciting at 645 nm is immediately noticeable. When exciting at 485
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Fig. 4. Histograms representing the recovered lifetime decay coefficients, A i , for luminescence detection at 686 nm ŽŽa., resonant with main R line emission., 694 nm ŽŽb., resonant with the R line sideband structure., 708 nm ŽŽc., in the region dominated by the virgilite phase luminescence. and 800 nm ŽŽd., in the region dominated by the broadband luminescence. and excited at the wavelengths indicated.
nm, this long component makes a decreasing contribution as the detection wavelength is increased. Conversely, for both excitation wavelengths, the fastest decay increases in relative strength with increasing detection wavelength whilst gradually drifting to shorter lifetime. The distorted spinel phase with a lifetime of around 2 ms is most prevalent in the spectrum excited at 485 nm and detected at 689 nm, exactly resonant with the N1 line indicated in Fig. 1, adding weight to the assignment. An understanding of the luminescence decay distributions follows directly from the discussion, above, of the multisite nature of the material. The four sites are summarised as follows. Ž1. The spinel phase that decays with an invariant lifetime of about 20 ms. The 4A 2 ™4 T2 absorption band of
this phase is at high energy, between about 460–620 nm Žsee Fig. 1.. Excitation in this band at low temperature results in R line luminescence at 686 nm and structured vibronically assisted emission to about 750 nm. The behaviour of this centre is very similar to that of Cr 3q ions in single crystals of ZnAl 2 O4 w3x though the lifetime we observe is slightly lower. Ž2. The distorted spinel phase that gives rise to the N1 line of the luminescence spectrum and which decays with a lifetime of about 2 ms. Again, this lifetime is somewhat lower than that measured previously. It should be noted that a number of different N lines, all corresponding to differently distorted sites have been reported in single crystal spinels w25x. It is likely that the lifetime contributions observed here are due to more than one of these
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similar to the spinel and so is not shown. As the 2 E state is lower in energy than the 4 T2 state in the spinel and virgilite phases then R line emission Žwith structured vibronic sidebands. is observed. For the spinel phase, only one set of sites is observed leading to a relatively narrow absorption band and luminescence with a single lifetime. The virgilite phase is represented by several slightly different potential wells shifted by the effects of disorder within the ceramic. The energies of the 4 T2 states are at slightly lower energy than in the spinel phase thus increasing the wavefunction mixing between 2 E and 4 T2 states due to spin–orbit coupling and reducing the luminescence lifetime w7,9x. The 4 T2 states of these differently distorted
Fig. 5. Experimental luminescence decays detected at 800 nm and excited by laser radiation at the wavelengths indicated. Smooth lines obtained represent fits using the technique outlined in this paper.
distorted sites though it is difficult to identify unambiguously other N lines due to the complexity of the luminescence spectrum of this multiphase material. Ž3. The second crystalline phase, thought to be virgilite but not conclusively ascribed, that decays with a lifetime of between 0.3 and 1 ms. Such ions can be excited at all wavelengths used in this investigation and luminesce at wavelengths similar to the spinel phase. The structure close to 708 nm seems to be dominated by the virgilite phase as can be seen from the dominance of the 1 ms decay contribution in Fig. 4c and from previous experiments that have measured time resolved luminescence spectra w1x. The broad absorption spectrum and shift in lifetime as a function of excitation and emission wavelength suggests that this phase is considerably disordered, perhaps due to substitutional disorder as is observed in gallogermanate crystals w11x. Ž4. The glassy phase that decays with a lifetime of between 0.01 and 0.08 ms. The excitation band of this phase is again across the full range of excitation wavelengths used here and can be expected to be well into the infrared according to the absorption spectra shown in Fig. 1. The emission band is similarly broad and dominates the emission spectrum at wavelengths beyond about 750 nm. The contributions of each of the four sites at any given combination of excitation and detection energies is thus a reflection of the relative strength of emission of the different phases for these experimental conditions. The configuration coordinate diagrams shown in Fig. 7 further illustrate how selection takes place during the excitation and emission processes. Sets of curves are shown for Cr 3q ions in the spinel phase, in the virgilite phase and in the glassy phase. The distorted spinel would appear very
Fig. 6. Histograms representing the recovered lifetime decay coefficients, A i , for excitation at 485 nm ŽŽa., resonant with 4 A 2 ™4 T2 absorption for all phases. and 800 nm ŽŽb., beyond the 4 T2 ™4A 2 excitation band for R line emission. and detected at the wavelengths indicated.
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Fig. 7. Schematic sets of configuration coordinate diagrams indicating the effect of the variation in crystal field from site to site for Ža. the spinel phase Žand distorted spinel phase., Žb. the virgilite phase and Žc. the glassy phase.
sites are shifted to different energies thus causing variation in the amount of wavefunction mixing, leading to a variation in the luminescence lifetime as different sites are selectively excited or detected. Low energy excitation or detection implies lower energy 4 T2 states and this implies shorter lifetimes. This is observed. The lifetime decreases as either the excitation or detection wavelength decreases. The diagrams shown imply that the site-to-site variation is only in crystal field strength so that the potential wells are shifted vertically up and down in configuration coordinate space. However, it is entirely possible that, as in the case of gallogermanates w11x and CaYAlO4 w26x, variation in electron–phonon coupling also contributes to the lifetime variation. The data recovered using this technique cannot distinguish clearly between the two. Similar shifts in the lifetime distribution peak are observed for the glassy phase but to a greater extent. A different explanation of this effect than for the virgilite phase must be invoked as mixing of the 2 E state into the 4 T2 state does not greatly effect the luminescence lifetime when the 4 T2 state is the lower in energy. For the glassy phase, the decrease in emission lifetime with decreasing excitation energy can be explained in terms of non-radiative internal conversion processes. It has been shown for gallogermanates that nonradiative processes are considerably more effective for weaker field sites within a distribution w27x. Thus, considering Eq. Ž4., the effective decay time is shorter when the weaker field sites are preferentially excited or detected. A final speculative comment on the low temperature data is in relation to the somewhat lower lifetime of the Cr 3q ions present in the spinel nanocrystals Ž; 20 ms. relative to that reported in bulk samples Ž31 ms w3x.. It is known that long term heat treatment of gahnite glasses produces crystallites with sizes of around 30 nm. The size of the nanocrystals in the present sample are likely to be somewhat smaller due to a reduced heat treatment period. Studies of Mn2q impurities in ZnS nanocrystals revealed a
significant reduction in luminescence lifetime compared to that measured in bulk material w28x. Though these results have proved controversial and have been refuted by some w29x, it is possible that the measured luminescence lifetime in our samples is influenced by the small size of the crystallites in which the chromium impurities are housed. Further evidence that the technique presented here is able to quantitatively describe the decay of multisite materials can be seen in Fig. 8 in which the decay distributions for excitation at 550 nm and detection at 686 nm, resonant with the R line, are compared for different temperatures. The same three components are observed but relative contributions differ with temperature. With increasing temperature, the longest component becomes weaker whilst the shortest component becomes stronger. This is due to the decreased intensity of the R line luminescence from the spinel phase and the increased intensity of luminescence at higher energies in the ‘glassy’ phase. Both of these effects are due to the blue shift of luminescence bands with temperature due to the thermal occupation of higher vibronic states. Thus there is less spinel phase luminescence at 686 nm and more from the glassy phase. There is a shift in the distribution maxima toward shorter time with increasing temperature. The shift of the shortest component, related to the glassy phase Cr 3q ions, can be explained in terms of increasing internal conversion rates though it is unclear why this effect is seen only for temperatures smaller than 100 K. For the longer components, this effect is due to increasing occupation of the higher vibronic states of the first excited electronic manifold Žwhich, due to the spin–orbit interaction, is a superposition of the 2 E and 4 T2 states w7,9x, as mentioned above.. The thermally occupied higher states are energetically closer to the 4 T2 level and consequently have more quartet character than the zero-phonon level resulting in faster
Fig. 8. Histograms representing the lifetime decay coefficients, A i , for luminescence detection at 686 nm, resonant with the Cr 3q R line emission from the spinel phase of the gahnite glass ceramic, excited at 550 nm at different temperatures as indicated.
M. Grinberg et al.r Optics Communications 156 (1998) 409–418
decay of the luminescence than when only the ground vibronic state is occupied. When monitoring emission at 739 nm, only luminescence from the medium and weak field sites is observed. Fig. 9 compares the decay constant distributions measured at 10 K and room temperature, excited at various wavelengths. In all cases decays at 10 ms and 800 ms are observed, corresponding to the glassy and virgilite phases of the ceramic. For all excitation energies, in going from 10 K to room temperature, there is a significant increase in the relative magnitude of the short lifetime contribution and a decrease in the lifetime of the longer contribution. The relative changes in the distribution concern the decay
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distribution of the luminescence and are best seen for excitation at 485 nm and 515 nm. Here the situation is the same as in the case of luminescence monitored at 686 nm, the increase in the shorter component of the decay is related to the shift of the respective emission band to higher energy. When the luminescence is excited with longer wavelength an additional effect is observed, the appearance of a much shorter decay ŽF 1 ms. at room temperature. This is related to the broad distribution of crystal fields experienced by the chromium ions in the glassy phase. The weakest field sites have an increased probability of decaying non-radiatively through internal conversion w13,14x. Since the rate at which this process takes place increases strongly with temperature, the effective decay constant is expected to decrease with temperature as observed. Since this effect mainly concerns the sites characterised by the weakest crystal field Žand therefore the longest wavelength absorption peak., shorter decays are observed when exciting at 550 nm, 600 nm and especially at 645 nm. Taking into account Eq. Ž12. which describes the relationship between the recovered quantity and the actual distribution of the decay constants, that is, the probability that the ith site is excited, it can be seen that the actual change in luminescence decay for an individual site is even more dramatic than can be observed by comparing Fig. 9a and 9b. 4. Conclusions
Fig. 9. Comparison of histograms representing the lifetime decay coefficients, A i , at 10 K and room temperature. Emission was detected at 739 nm, beyond the range of spinel phase emission, and excited at various wavelengths as indicated.
At first thought, it may seem absurdly hopeful to fit the luminescence decay of a disordered multisite material using what are effectively 125 exponentials but the behaviour of Cr 3q impurities in the gahnite glass ceramic have been shown to be well modelled by the technique of continuous function decay analysis presented here. It has revealed detailed characteristics of the luminescent centres in the materials. Four different groups of sites, detailed above, have been clearly identified and their behaviour has been directly related to previous experiments on Cr 3qdoped gahnite ceramics, gahnite glasses and spinel crystals. The only remaining question is whether the widths of the distribution have real meaning. It would seem likely that the longest lifetime contribution, relating to Cr 3q ions in the spinel phase, should be a single exponential and therefore not correctly described by a distribution Žthough nanocrystals of different sizes could conceivably influence the decay times of impurity ions contained within.. The ‘glassy’ phase, on the other hand, is likely to have a genuine spread of lifetimes as evidenced by the shift in its peak with excitation wavelength and the non-exponential decays presented in Fig. 5. The approach we have used to recover the distribution of luminescence decay times can be applied for any arbitrary non-exponential luminescence decay Žwhere, as is almost always the case, each emitting chromophore decays
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exponentially.. The advantage of this method is that no luminescence decay model or physical model of the material are required a priori. This method of analysis also has a great advantage over time resolved spectroscopy in that different sites can be identified even when they emit via broad bands which overlap the same spectral region. It is also worth briefly mentioning the validity of our method when nonexponential luminescence decay is related to nonradiative donor acceptor energy transfer. When back transfer Žfrom acceptor to donor. can be excluded, the emission of any particular donor is single exponential with a decay constant given by Eq. Ž3.. In such a case the decay time distribution is related to the distribution of the acceptors around the donor site. Acknowledgements This paper is supported in part by KBN Research Grant number 2P03B003 13. References w1x V. Poncon, J. Kalisky, G. Boulon, R. Reisfeld, Chem. Phys. Lett. 133 Ž1987. 363. w2x G.H. Beall, D.A. Duke, J. Mater. Sci. 4 Ž1969. 340. w3x D.L. Wood, G.F. Imbusch, R.M. Macfarlane, P. Kisliuk, D.M. Larkin, J. Chem. Phys. 48 Ž1968. 5255. w4x C. Koepke, K. Wisniewski, M. Grinberg, D.L. Russell, K. Holliday, Proc. SPIE 3176 Ž1997. 42. w5x V. Poncon, M. Bouderbala, G. Boulon, A.-M. Lejus, R. Reisfeld, A. Buch, M. Ish-Shalom, Chem. Phys. Lett. 130 Ž1986. 444. w6x S. Sugano, Y. Tanabe, H. Kamimura, Multiplets of Transition Metal Ions in Crystals, Academic Press, New York, 1970.
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