Silicon nanocluster sensitization of erbium ions under low-energy optical excitation

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I. INTRODUCTION
The discovery of the sensitizing action of silicon nanocluster (Si-nc) on erbium ions (Er 3þ ) offered a new material platform where silicon based optical amplifiers and laser sources could be developed. 1Complementary metal oxide semiconductor (CMOS) process compatibility combined with convenient light emission in the third telecom window (1.5 lm) has been considered as a particular advantage of this material. 2In spite of promising initial reports of optical gain 3 and efficient electrical excitation, 4 the demonstration of a laser action seems still to be quite challenging.][11] Although, the transfer mechanism between Si-nc and Er 3þ has been thoroughly studied, 7,11,12 there is no clear consensus in literature on the more appropriate model to describe this interaction.Most of the studies have been performed with optical excitation in the high energy spectral region (blue, UV) where the absorption cross section of Si-nc is dominating that of the Er 3þ ions. 13,14[17][18]

II. EXPERIMENTAL DETAILS
We report on a photoluminescence (PL) study of silicon rich oxide thin films co-doped with Er 3þ ions (SRO:Er 3þ ), under low-energy optical excitation.The general features of the PL dynamics are studied by time resolved photoluminescence (TR PL) measurements, performed both in the visible and in the infrared.
Samples are produced by reactive magnetron cosputtering.Detailed description of fabrication details can be found in Ref. 19.The sample details are summarized in Table I.Photoluminescence measurements were done using, as an excitation source, the optical pulses (6 ns pulse length, 10 Hz repetition rate) of an optical parametric oscillator (OPO) pumped with the third harmonic of a Nd:YAG laser.The excitation photon flux (10 24 ph cm À2 s À1 ) was maintained constant over the whole used spectral range.Continuous wave (CW) PL measurements were performed using the 476 nm line of an Argon laser (3 Â 10 20 ph cm À2 s À1 ).Detection consisted of a spectrograph (Chromex) coupled to a streak camera (Hamamatsu, visible) or of a monochromator (Chromex) coupled to an InGaAs photomultiplier (Hamamatsu, infrared) with overall time resolution of 2 ns (visible) and 40 ns (infrared), respectively.All measurements were performed at room temperature.All spectra were corrected for the spectral response of the instruments.
These samples have been previously systematically characterized under a short wavelength excitations (355 nm, 476 nm), pulsed and continuous. 7Based on these results, a model describing the energy interaction between Si-nc and Er 3þ in this (high energy) regime was proposed.

III. RESULTS AND DISCUSSION
When optically exciting this material (with energy not matching any of the possible internal transitions of Er 3þ ions, see Fig. 1), the pump photons are absorbed by the silicon nanoclusters and the energy is subsequently transferred to the Er 3þ ions.Recently, it has been demonstrated that this energy transfer occurs on a very short temporal scale. 6,10,12s a consequence of the energy transfer, the exciton population in Si-nc is decreased, leading to a quenching of the visible PL (originating from Si-nc) in the Er 3þ doped sample. 10n our samples, we monitor the visible PL dynamic (at 750 nm) in the first 400 ns after the laser pulse arrival, by using a 50 ns time gate (Fig. 2) in order to filter out any initial fast contribution that might not be due to radiative interband exciton recombination in Si-nc.We observe that although there is a clear difference in the emission dynamic for the two samples (A and B, see Table I) with a "blue" pump (470 nm), the dynamics becomes equal moving towards the "red" (640 nm) (Fig. 2).
It is important to underline that the difference in the emission dynamic of the two samples under "blue" pump condition does not necessary imply that the energy transfer from Si-nc to Er 3þ is still occurring on the timescale of observation (%100 ns).In fact, it was demonstrated recently that the energy transfer could be a very fast process, 6,10,12 taking place typically on the timescale shorter than 100 ns (Ref.6) (<36 ns in our samples). 10On the other hand, the exciton recombination dynamics in Si-nc depends heavily on the exciton population itself, due to effects such as Auger recombination 20 and inter-nanocluster transport. 21,22This is well illustrated in the Fig. 2 if we consider the emission dynamic of the same sample under two different excitation conditions ("blue" and "red").Although, approximately, the same excitation photon fluxes were used (see Experimental Details), the wavelength dependence of the absorption crosssection 13 of the Si-nc leads to different exciton populations and different fast (<ls) emission dynamics.
The difference in emission dynamics we observe between different samples (A and B) under the same ("blue" pump) excitation condition is an indicator of a different exciton population in the two samples.This difference is not related to a change in the absorption cross-section (as we are using the same pump conditions), but to the Er 3þ ions presence. 13,14As already mentioned previously, Er 3þ ions are introduced in our samples during the deposition phase, 19 minimizing, therefore, the occurrence of erbium related defect states. 23Hence, we associate the difference in emission dynamics (exciton population) with the energy transfer mechanism present in erbium co-doped sample. 24owever, if we consider the different samples (A and B) under the same "red" pump condition (Fig. 2) the emission dynamics (exciton populations) we observe are practically the same.As it is rather unlikely that non-radiative recombination due to Er 3þ related defect states show such a strong dependence on excitation wavelength in this range of energies, 23,25 we attribute this distinct behavior to a change in the energy transfer process.
In order to investigate further this phenomenon, we monitor the initial PL dynamics of the 4 I 13/2 -4 I 15/2 transition of Er 3þ ions (at 1535 nm, transition from the first excited to fundamental state, see Fig. 1) while changing the excitation wavelength in the spectral range (540 nm-680 nm) around the value of the "red" pump previously used (640 nm). 26n the literature, the dynamics of the scale, 5.5 ms in our sample) (see Fig. 3). 6,7The later is due to the radiative 4 I 13/2 -4 I 15/2 transition and, in the absence of detrimental effects such as cooperative up-conversion, it is independent on the excitation photon flux. 27On the other hand, the initial microseconds rise dynamic is considered to be due to the internal relaxation from high energy states of Er 3þ to the 4 I 13/2 state. 7,11,28The higher energy states of Er 3þ are indirectly populated by the energy transfer process.
Although the first tens of ns are hidden by a very fast PL decay contribution (Fig. 3, inset), it is evident that the ls PL rise does not start from a zero level.This implies that a fraction of the Er 3þ ions have been excited through the energy transfer process directly to the first excited state. 7,11,28he very fast PL decay contribution (Fig. 3, inset), in our samples, has been experimentally related to the presence of the silicon nanoclusters (silicon excess) in the silicon dioxide matrix 7,10,29 in accordance with what reported in Ref. 30.However, based on similar experimental findings, an alternative interpretation involving Er 3þ 4 I 13/2 -4 I 15/2 radiative transition and Er 3þ related traps has been proposed. 6,23Considering that the contribution of this component to the total PL is practically negligible and that the elucidation of its exact origin falls out of the scope of this work, it will not be investigated further.
In order to quantify the relative contributions of the direct and higher state energy transfer contributions to the total PL, we fit the experimental data with the equation (see Appendix for more details) where I Background (background level) and t 0 (laser pulse arrival time) are fit parameters, t 1 ¼ 4.2 ls and t 2 ¼ 5.5 ms have been independently measured. 10The other fit parameters are A Slow and A All (A Fast being A All -A Slow ).Their graphical interpretation is presented in Fig. 3.A Slow weights the electronic contribution to the first excited state coming from the internal relaxation from higher energy states while A Fast represents the direct contribution to the first excited state.A All is simply the sum of the two, or in other words, the total contribution to the first excited state.More insight on the underlying physics could be gained by the plot of the ratio A Fast /A All (see Fig. 4 and inset of Fig. 4), which yields an estimate of the "fast" direct contribution (given by A Fast ) to the total excited Er 3þ population, as a function of the excitation wavelength. 31e observe a non-monotonic dependence of the A Fast / A All ratio upon excitation wavelength (see Fig. 4).For excitation wavelength shorter than 600 nm, a saturation region where the ratio is almost independent of the excitation photon wavelength is found.On the contrary, for longer excitation wavelengths, the ratio is increasing, and reaches a value of one for 680 nm excitation independently of the photon flux (within the limits imposed by our experimental setup).The antiresonant feature at 650 nm is related with the direct resonant excitation of Er 3þ ions to 4 F 9/2 energy state (see Fig. 1).Indeed, in this case we observe an increase of the "slow" contribution (given by A Slow ), leading to a decrease of the ratio A Fast /A All .Note that resonant features at shorter wavelengths are not observed, since the energy transfer to high Er 3þ states becomes more efficient than the direct excitation.
A ratio of one corresponds to a complete absence of the contribution from higher lying states to the Er 3þ 4 I 13/2 state.In other words, energy transfer from Si-nc to higher excited states of Er 3þ is not allowed any more at the excitation FIG. 3. Initial PL dynamics of the 4 I 13/2 -4 I 15/2 transition of Er 3þ ions under 560 nm pulsed excitation (black spheres).The best fit by Eq. (1) (red line) of the experimental data is also shown.The meaning of the fit parameter A All is illustrated as well.Inset: Zoom on the first ls of the initial PL dynamics.Graphical interpretation of the fit parameters A Slow and A Fast is shown.

FIG. 4. Variation of the A Fast /A
All ratio (black spheres) with the excitation wavelength.The black dashed line represents the value at which no contribution from higher excited state of Er 3þ ions is present.The red solid line is only a guideline for the eyes.Inset: Initial PL dynamics of the 4 I 13/2 -4 I 15/2 transition of Er 3þ ions under 560 nm (thin black bottom curve), 640 nm (thin red middle curve), and 680 nm (thin blue upper curve) pulsed excitation.The best fits by Eq. ( 1) (thick lines of corresponding color) of the experimental data are also shown.The data and fit curves have been normalized and offset by 0.2 for clarity.energy of 1.82 eV, where the excess energy with the respect to the second excited state of Er 3þ is approximately 0.55 eV.It is worth noticing that transition to this state is rather smooth, taking place for the excitation energies in the range between 2.1 and 1.8 eV (see Fig. 4).Moreover, a part from the change in its initial dynamics (Fig. 2), visible PL coming from the Si-nc is still observable.
These observations could be associated with the intraband model for the energy transfer. 10,11In this model, intraband electronic transitions are responsible for the energy transfer to Er 3þ and, in particular, they require a minimum excess energy corresponding to a bandgap value of silicon nanoclusters. 10,11However, it comes as a surprise the relatively small amount of the measured excess energy values needed for the transfer to occur towards the 4 I 11/2 state (0.8-0.55 eV).These values are lower than the expected bandgap energy of silicon nanoclusters in our samples (%1.6 eV) 32 and even lower than the bulk crystalline silicon bandgap (%1.1 eV), indicating a participation of a subbandgap state in the energy transfer process. 10ub-bandgap states have been theoretically predicted in amorphous Si-nc with low hydrogen content. 33In addition, a modest spread in energy has been suggested to occur for weakly localized states due to limited effects of quantum confinement. 33t should be mentioned, that recently, it has been postulated, as well, the possible existence of deep trap states related with presence of Er 3þ ions in the bulk silicon. 25n alternative explanation to our experimental observations would be that we have two different types of sensitizers present in our samples.As the absorption cross-section of the silicon nanoclusters is decreasing with wavelength, the effective cross-section of Er 3þ ions sensitization through the Si-nc may reach a lower value, where the contribution from another sensitizer type could become significant.
The influence of Er related matrix defects on Er 3þ photoluminescence has been demonstrated recently, but in very different energy range. 23On the other hand, the silicon excess related "luminescence center" erbium sensitization has been well established in a wide range of excitation energies. 15,29However, an even distribution in the energy of these defect states is expected, 15,28,29 with wavelength dependence of effective cross-section for erbium sensitization mirroring one of the silicon nanoclusters. 15Moreover, the energy transfer to higher energy states of Er 3þ ions would be still possible for this sensitizing mechanism at the excitation energies we use, 12,[28][29][30] in contrast to what we observe.
To address this issue, we report in Fig. 5 A Fast (direct contribution to the first excited state) as a function of the excitation energy (wavelength).A continuous monotonic decrease can be observed across the whole excitation range suggesting the existence of only one erbium sensitizer which we relate to Si-nc. 13he presence of a saturation region below 600 nm (see Fig. 4) with a value of A Fast /A All ratio equal to 0.6 implies that direct energy transfer to the first excited state remains to be a dominant excitation mechanism even under short wavelength excitation.

IV. CONCLUSIONS
In conclusion, we reported a systematic study of the energy transfer process in silicon nanoclusters and Er 3þ co-doped thin films under low energy optical excitation.The study presented here complements a recent work focused on PL quantum yield of SRO:Er 3þ material under similar excitation conditions. 18We find profound differences in the fast dynamic of the visible PL with respect to the high energy optical excitation regime which we attribute to a decrease of the energy transfer efficiency and/ or decrease of excitation to higher (than first) excited states of Er 3þ .We demonstrate that the energy transfer to a higher energy state of Er 3þ ions ceases to be effective for photon energies between 2.1 and 1.8 eV (0.7-0.55 eV of pump excess energy with respect to the energy of 4 I 11/2 state).We explain this behavior in the framework of the intraband model in terms of sub-bandgap states participation in the energy transfer.Although we do not provide the definitive proof of their physical nature, we correlate them with the presence of Si-nc.We confirm that the energy transfer to the first excited state of Er 3þ remains to be a dominant excitation mechanism in the range of considered excitation energies, implying that even with the opening of the new excitation channels, through the higher Er 3þ excited states, only modest improvements in the efficiency of the Er 3þ ions excitation should be expected.fundamental state, see Fig. 1, main text) is characterized by two contributions (see Fig. 2, main text): a very fast direct one (on %ns timescale) and a slow (on %ls timescale) process caused by the internal relaxation from higher excited states of Er 3þ ions.The very fast decaying initial PL contribution is not considered since regardless of its origin, its contribution to the total PL intensity is insignificant.Therefore, the time evolution of the PL signal can be described by the following equation: I Background (background level) and t 0 (laser pulse arrival time) are fit parameters, t 1 ¼ 4.2 ls and t 2 ¼ 5.5 ms are fixed quantities and have been independently measured. 10t 2 is the decay constant of the first excited state while t 1 is the measure of the internal relaxation time.The other fit parameters are A Slow and A Fast .A Fast is the direct contribution to the total PL while A Slow gives the contribution by the internal relaxation from higher energy states.
The first exponential term describes the PL signal evolution coming from the fraction of the Er 3þ ions population that has been directly excited to the first excited state while the second term gives the PL signal of the Er 3þ ions that has been excited to higher states.In this last case, PL follows an internal relaxation from the higher states to the first excited state.On the timescale of the observation, the amplitude of the later one is a function of time as the internal relaxation continues (Eq.(A1)) causing the complex exponential dependence of the PL signal in time.
We assumed that the direct excitation to the first (and higher) excited states is instantaneous (faster than the time resolution of our detection system %40 ns) and that the relaxation from the higher excited states to the 4 I 13/2 state can be well described by a decaying single exponential function with a characteristic time t 1 ¼ 4.2 ls.Note that Eq. (A1) and parameter physical interpretation are different respect to what can be found in similar works. 17,34y introducing the parameter A All , which is the sum of the previous two contributions, or in other words, the total contribution to the first excited state Eq. (A1) could be rewritten as: Knowing that t 1 is more than three orders of magnitude smaller than t 2 , Eq. (A3) can be simplified to This form is the one used for the fitting procedure. 10

TABLE I .
FIG.2.Fast decay dynamics of the visible PL of samples A (red and green line) and B (black and blue line) under 470 nm excitation (upper two lines) and 640 nm (lower two lines).The time decay traces were recorded at 750 nm using a 90 nm wide spectral window.50 ns time gate (inset) was used in order to filter out the initial fast contribution.Sample specifications.
4I 13/2 -4 I 15/2 transition is frequently described by an initial microseconds PL rise followed by a very slow PL decay (on millisecond time FIG.1.Spectrum of the 4 I 13/2 -4 I 15/2 transition of Er 3þ ions (transition from the first excited state to the ground state) under non-resonant (476 nm) continuous optical excitation.Inset: Er 3þ energy states scheme with Russel-Saunders notation and characteristic radiative transitions.