^{1}, D. Paparo

^{2}, F. Miletto Granozio

^{2}, U. Scotti di Uccio

^{1,2}and L. Marrucci

^{1,2,a)}

### Abstract

The blue-green photoluminescence emitted by pure and electron-doped strontium titanate under intense pulsed near-ultraviolet excitation is studied experimentally as a function of excitation intensity and temperature. Both emission spectra and time-resolved decays of the emission are measured and analyzed in the framework of simple phenomenological models. We find an interesting blue-to-green transition occurring for increasing temperatures in pure samples, which is absent in doped materials. The luminescence yield and decay rate measured as a function of temperature can be modeled well as standard activated behaviors. The leading electron-hole recombination process taking place in the initial decay is established to be second order, or bimolecular, in contrast to recent reports favoring a third-order interpretation as an Auger process. The temporal decay of the luminescence can be described well by a model based on two interacting populations of excitations, respectively identified with interacting defect-trapped (possibly forming excitons) and mobile charges. Finally, from the measured doping and sample dependence of the luminescence yield, we conclude that the radiative centers responsible for the luminescence are probably intrinsic structural defects other than bulk oxygen vacancies.

I. INTRODUCTION

II. EXPERIMENTS

III. MEASUREMENT RESULTS: SPECTRA

IV. MEASUREMENT RESULTS: TEMPORAL DECAYS

V. MODELING THE TEMPORAL DECAY

VI. DISCUSSION AND CONCLUSIONS

### Key Topics

- Photoluminescence
- 56.0
- Luminescence
- 27.0
- Doping
- 19.0
- Electrons
- 13.0
- Crystal defects
- 9.0

## Figures

PL spectra from [(a) and (b)] I-STO and [(c) and (d)] N-STO samples at various temperatures and at an excitation fluence of [(a) and (c)] or [(b) and (d)] . Labels GL, BL, and VL (green, blue, and violet luminescence) in (a) mark the peaks of the three separate luminescence bands that can be singled out in our spectra. A blue-to-green spectral transition (a redshift of the peak) of the PL is seen in the I-STO spectra, while it is absent in the N-STO-doped samples. The lines in (b) are best-fit curves based on our theory. The lines in the other panels are guides to the eye.

PL spectra from [(a) and (b)] I-STO and [(c) and (d)] N-STO samples at various temperatures and at an excitation fluence of [(a) and (c)] or [(b) and (d)] . Labels GL, BL, and VL (green, blue, and violet luminescence) in (a) mark the peaks of the three separate luminescence bands that can be singled out in our spectra. A blue-to-green spectral transition (a redshift of the peak) of the PL is seen in the I-STO spectra, while it is absent in the N-STO-doped samples. The lines in (b) are best-fit curves based on our theory. The lines in the other panels are guides to the eye.

Temperature behavior of the amplitudes of the three spectral bands GL (triangles), BL (circles), and VL (squares), as seen in the (a) I-STO and (b) N-STO PL. The excitation fluence was . Solid lines are best fits based on Eq. (2); the resulting activation energies are reported in the legend. The case of high excitation fluence gives similar results, except for a slightly smaller activation energy of the VL component (≈0.2 eV instead of ≈0.3 eV).

Temperature behavior of the amplitudes of the three spectral bands GL (triangles), BL (circles), and VL (squares), as seen in the (a) I-STO and (b) N-STO PL. The excitation fluence was . Solid lines are best fits based on Eq. (2); the resulting activation energies are reported in the legend. The case of high excitation fluence gives similar results, except for a slightly smaller activation energy of the VL component (≈0.2 eV instead of ≈0.3 eV).

Histogram of the (a) PL yield and (b) PL-tail exponential decay time for different samples at room temperature. Samples 1–5 are I-STO (blue online), sample 6 is O-STO (red online), and samples 7–8 are N-STO (green online).

Histogram of the (a) PL yield and (b) PL-tail exponential decay time for different samples at room temperature. Samples 1–5 are I-STO (blue online), sample 6 is O-STO (red online), and samples 7–8 are N-STO (green online).

Time decay of the PL signal of an I-STO sample following its excitation by a UV picosecond pulse for different excitation fluences at room temperature. Data are shown as gray dots (blue online). The solid lines are the result of a global best fit based on our models [including a final convolution with the measured instrumental response time ]. The black line is based on the C2PUBv1 bimolecular model, and the gray line (red online) is based on the 1PUT trimolecular model. Data and curves referring to different fluence values are vertically shifted for clarity.

Time decay of the PL signal of an I-STO sample following its excitation by a UV picosecond pulse for different excitation fluences at room temperature. Data are shown as gray dots (blue online). The solid lines are the result of a global best fit based on our models [including a final convolution with the measured instrumental response time ]. The black line is based on the C2PUBv1 bimolecular model, and the gray line (red online) is based on the 1PUT trimolecular model. Data and curves referring to different fluence values are vertically shifted for clarity.

Time decays of the PL signal of an I-STO sample at room temperature for different excitation fluences, shown here in semilogarithmic scale to highlight the exponential PL tail. Data are shown as dots, while the solid lines are the result of a global best fit based on the C2PUBv1 model. The wiggles seen in the tail for both data and model predictions are due to the detection-system response function , which is shown in the inset (inset axis labels and units are the same as those for the main panel).

Time decays of the PL signal of an I-STO sample at room temperature for different excitation fluences, shown here in semilogarithmic scale to highlight the exponential PL tail. Data are shown as dots, while the solid lines are the result of a global best fit based on the C2PUBv1 model. The wiggles seen in the tail for both data and model predictions are due to the detection-system response function , which is shown in the inset (inset axis labels and units are the same as those for the main panel).

Experimental decay rates as a function of excitation fluence and temperature for the an I-STO sample. The decay rate is here defined as the inverse of the decay time . The upper axis gives our estimate of the density of photoinduced e-h pairs after excitation. The lines are linear best fits of the fluence dependence.

Experimental decay rates as a function of excitation fluence and temperature for the an I-STO sample. The decay rate is here defined as the inverse of the decay time . The upper axis gives our estimate of the density of photoinduced e-h pairs after excitation. The lines are linear best fits of the fluence dependence.

Characteristic PL decay times (squares) and (circles), the latter at the reference fluence of , vs temperature for (a) an I-STO sample and (b) a N-STO sample. The lines are best fits based on the activated behavior given by Eq. (2). The resulting activation energies are given in the legend.

Characteristic PL decay times (squares) and (circles), the latter at the reference fluence of , vs temperature for (a) an I-STO sample and (b) a N-STO sample. The lines are best fits based on the activated behavior given by Eq. (2). The resulting activation energies are given in the legend.

PL yield, computed from the time integral of the decay signal, as a function of temperature for I-STO and N-STO samples. Solid lines are best fits based on the activated behavior given by Eq. (2). The resulting activation energies are given in the legend.

PL yield, computed from the time integral of the decay signal, as a function of temperature for I-STO and N-STO samples. Solid lines are best fits based on the activated behavior given by Eq. (2). The resulting activation energies are given in the legend.

Inverse decay times vs excitation fluence for the four PL decay curves reported in Fig. 1 of Ref. 31. The times have been estimated graphically from the initial decay slope in the semilogarithmic chart. The line (red online) is a linear best fit. The good linearity of the decay rates vs fluence confirms a bimolecular behavior for the initial fast decay.

Inverse decay times vs excitation fluence for the four PL decay curves reported in Fig. 1 of Ref. 31. The times have been estimated graphically from the initial decay slope in the semilogarithmic chart. The line (red online) is a linear best fit. The good linearity of the decay rates vs fluence confirms a bimolecular behavior for the initial fast decay.

Inverse decay rates vs fluence as measured for an I-STO sample (squares) and as predicted by different models (lines) after a global best fit on the measured decays. Besides ours, the data of Yasuda *et al.* (already given in Fig. 9) are also plotted (circles). The two sets of data do not merge into a single smooth behavior because of the much slower response of our apparatus as compared to that used by Yasuda *et al.* in Ref. 31. The predictions of the C2PUBv1 model (black lines), after a global fit on our data only, explain both our data (solid line, obtained after a convolution with our instrumental response function) and the data of Yasuda *et al.* (dot-dash line, obtained from the C2PUBv1 model assuming an instantaneous instrumental response). Dashed and dotted curves correspond to the predictions of the 1PUT model (gray line, red online) and of the 2PUT model (light gray line, orange online) after convolution with our response function (dashed lines) or for an instantaneous response (dotted lines). The gray solid line (cyano online) is a linear best fit to our data.

Inverse decay rates vs fluence as measured for an I-STO sample (squares) and as predicted by different models (lines) after a global best fit on the measured decays. Besides ours, the data of Yasuda *et al.* (already given in Fig. 9) are also plotted (circles). The two sets of data do not merge into a single smooth behavior because of the much slower response of our apparatus as compared to that used by Yasuda *et al.* in Ref. 31. The predictions of the C2PUBv1 model (black lines), after a global fit on our data only, explain both our data (solid line, obtained after a convolution with our instrumental response function) and the data of Yasuda *et al.* (dot-dash line, obtained from the C2PUBv1 model assuming an instantaneous instrumental response). Dashed and dotted curves correspond to the predictions of the 1PUT model (gray line, red online) and of the 2PUT model (light gray line, orange online) after convolution with our response function (dashed lines) or for an instantaneous response (dotted lines). The gray solid line (cyano online) is a linear best fit to our data.

Schematic picture of the main electronic processes that may be postulated for interpreting the rate equations of our decay models C2PUB v1 and v2: (a) pump photon (UV) absorption and e-h pair generation, (b) nonradiative direct e-h recombination, and (c) radiative cross recombination between a free electron and a trapped hole, with blue photon (BL) emission and nonradiative thermal untrapping of holes, (d) radiative crossed recombination between a free electron and a trapped exciton, and (e) radiative spontaneous annihilation of a trapped exciton. The constants , , and are the dynamical rates of each process.

Schematic picture of the main electronic processes that may be postulated for interpreting the rate equations of our decay models C2PUB v1 and v2: (a) pump photon (UV) absorption and e-h pair generation, (b) nonradiative direct e-h recombination, and (c) radiative cross recombination between a free electron and a trapped hole, with blue photon (BL) emission and nonradiative thermal untrapping of holes, (d) radiative crossed recombination between a free electron and a trapped exciton, and (e) radiative spontaneous annihilation of a trapped exciton. The constants , , and are the dynamical rates of each process.

## Tables

Different PL decay models tested in this work. The two best-fit values of reported in the last two columns are averaged over different samples and repeated measurements after normalizing to the minimum value obtained among all models for each given sample/measurement (in order to weigh all samples equally). The first (no amplitude) is computed for decays normalized to their maximum, so that the behavior of the decay amplitude with excitation fluence does not enter the fit, and the model testing is focused on the decay rates. The second (with amplitude) is instead computed, taking also the decay amplitudes into account. The reported differences are statistically highly significant (the formal likelihood ratio between the best model and the others is of thousands of orders of magnitude).

Different PL decay models tested in this work. The two best-fit values of reported in the last two columns are averaged over different samples and repeated measurements after normalizing to the minimum value obtained among all models for each given sample/measurement (in order to weigh all samples equally). The first (no amplitude) is computed for decays normalized to their maximum, so that the behavior of the decay amplitude with excitation fluence does not enter the fit, and the model testing is focused on the decay rates. The second (with amplitude) is instead computed, taking also the decay amplitudes into account. The reported differences are statistically highly significant (the formal likelihood ratio between the best model and the others is of thousands of orders of magnitude).

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