Figure a shows the PL spectra of SRSO films doped with Er3+ ions measured at 500 and 10 K for samples with two Si atomic concentrations: 37 and 39 at.%. Two main emission bands at 1.6 and 0.81 eV have been observed. The first band at 0.81 eV is assigned to a radiative intra-4f shell transition of Er3+ ions (4I13/2 → 4I15/2). The shape of this band at a high temperature can be modeled with a Boltzmann distribution for thermal populations of the crystal-field split manifold of 4I13/2 and 4I15/2 sublevels that have a total of 56 possible transitions between them, giving significant contribution to the observed broadening of this band.
Figure 1 Results of photoluminescence measurements. PL spectra of Si-NCs (VIS) doped with Er3+ (NIR) measured at 10 and 300 K at 488-nm excitation together with normalized PLE spectra detected at 0.81 eV for two Si concentrations: (a) 37 at.% and (b) 39 at.% of (more ...)
The second band at 1.6 eV can be assigned to the recombination of excitons localized in the SRSO matrix. Moreover, from Figure a, it can be seen that all VIS emission bands have a complex structure. This is due to interference effects caused by the refractive index contrast between SRSO and the Si substrate [35
]. These interferences will modify the shape of the emission spectra in the entire VIS spectral range. However, Er3+
emission is not affected by this effect.
Additionally, Figure a shows the PLE spectra measured for Er3+
at room temperature at 0.81 eV in a broad UV-VIS excitation band energy range. The obtained PLE spectra are also very similar to those obtained by us for undoped SRSO samples [36
]. The appearance of strong Er3+
emission at excitation wavelengths far from resonance with erbium energy levels clearly indicates that we are dealing here with an efficient excitation transfer from the levels responsible for VIS emission (i.e., a
Si-NCs, Si-NCs, or defects) to erbium ions. The main argument behind the conclusion that defect states can be excluded in this case is the Si-concentration-dependent position of the excitation spectra for Er3+
ions and VIS emission bands. It can be seen that when the Si content increases, the edge of excitation as well as emission bands shifts towards lower energies due to reduction of quantum confinement. This suggests that the observed VIS emission can be related either to a
Si-NCs or to Si-NCs. Moreover, the position of these excitation bands at 4.3 and 3.4 eV for 37 and 39 at.% of Si, respectively, seems to be different than energies typically obtained for excitation bands of defects in SiO2
films: ‘non-bridging oxygen hole center’ at 4.8 and 5.8 eV [38
’ center at 5.4 to 6.2 eV [39
], or ‘oxygen-deficient center’ (ODC) at 7.6, 6.9, and 5.0 eV [40
Another important conclusion from Figure a is that the emission band in the VIS spectral range cannot be assigned to Si-NCs or a
Si-NCs only, but some contribution from defect states can also be clearly observed, especially for the sample with 39 at.% where weak emission bands at around 450 nm can be observed. These defect states are most probably due to ODC in the SiO2
] or self-trapped excitons (STE) [42
]. It has been shown that emission from ODC at this energy is characterized by a long emission decay time of 10 ms [40
]. On the other hand, the emission decay time of STE should rather be in the nanosecond range. However, the nature of STE in SiO2
is not clear at the moment. Nevertheless, we believe that emission at 1.6 eV originates mainly from a
Si-NCs where the recombination is due to transitions between the tails of local density of states (LDOS) related to a
Si-NCs rather than to the band-to-band excitonic transitions like in Si-NCs. One of the arguments strengthening our hypothesis can be seen in Figure c,d where the VIS emission peak position has been monitored with temperature ranging from 10 to 500 K for two excitation wavelengths. The PL peak position shows abnormal blueshift with increasing temperature. Usually, the PL peak position for unalloyed semiconductors shows a redshift with increasing temperature in accordance with Varshni’s formula [43
] shown also in Figure b with parameters typical for bulk Si. The temperature dependence of the PL peak position shown in Figure d is rather similar to the S-shaped phenomenon observed due to localized states caused by potential fluctuations in semiconducting alloys [44
]. This should be a similar case for amorphous clusters. This is mainly because the tail states (Ntail
) of a
Si-NCs can be approximated as an exponential distribution [45
Based on Equation 1, the carrier density trapped at localized tail states (ntail) can be estimated using the Fermi-Dirac statistics,
where f(E) is the Fermi probability function defined as f(E) = [1 + exp(E - EF/kT)]-1, where k is Boltzmann’s constant and T is the ambient temperature. Thus, at a low temperature, carriers relax to the lowest levels within the tails of LDOS. However, when the temperature increases, carriers move to higher lying levels and recombine at higher energies. Moreover, due to the increased role of non-radiative channels at a high temperature, the emission decay time is reduced, and thus, carriers can recombine from higher levels, also moving the emission band towards higher energies. Thus, the observed emission band at 1.6 eV can be related mainly to aSi-NCs. However, we cannot exclude additional contributions to the observed emission from Si-NCs.
From Figure , we can clearly see the redshift of the total VIS emission with increasing Si content. Based on the above results, the observed shift can be explained as due to changes in a
Si-NC sizes (redshift due to quantum confinement effect), changes in number of defect states making contributions to tails of LDOS (blue- or redshift), relative contribution of emission bands from matrix-related defect states, or Si-NC- and a
Si-NC-related emission. Moreover, increasing strain at the Si-NCs/SiO2
interface with Si atomic percent should also be included as it has been shown by us recently elsewhere [46
]. This can introduce defect states and can also influence the position of the energy levels related to Si-NCs inducing both red- and blueshift.
To analyze in detail the origin of the observed VIS emission bands, time-resolved PL spectra (TRPL) have been measured for two samples at 266-nm excitation wavelength. Obtained results are shown in Figure . Figure a,d shows emission spectra obtained just after the excitation with a laser pulse of less than 2 ns wherein the signal was collected during 1,000 μs. This condition should best reflect the emission signal obtained at the CW excitation shown in Figure . As it has been discussed already, the observed emission is composed of at least three independent emission bands overlapping each other spectrally. When the delay between the pulse and detection is set to 100 μs, two extreme bands disappear (Figure b,e). This means that their kinetics is much different (faster) than the one related to the main emission band centered at around 600 or 650 nm for 37 and 39 at.% of Si, respectively. To analyze this aspect further, the same TRPL spectra have been collected in a 100-ns window and recorded just after the 2-ns pulse. From the obtained results shown in Figure c,f, it can be seen that only the band on the high-energy side of the main emission can be observed. In this case, the integration window is too small to see the slow, main emission band. This band is related to the levels which just started to be populated. Some indication of this band can be seen as a second emission component shown in Figure c. Moreover, the position of defect-related bands is the same for both samples and does not depend on Si content. This is opposite to the behavior of the main band which shifts with Si content towards lower energies. This type of fast short-wavelength emission has been observed already and is considered to be caused most probably by STE. For this band, we were also able to measure the emission decay time, which is equal to 20 ns for both samples. Due to system limitations and weak signal of the main emission band (aSi-NCs), we were only able to estimate from TR-PL the average decay time as 500 μs.
Time-resolved PL spectra. SRSO:Er3+ samples obtained at 266-nm excitation for (a, b, c) 37% and (d, e, f) 39% of Si. Δt, integrating time; Δt, delay time.
Based on the results obtained so far, we conclude that the observed wide emission band obtained usually at CW excitation is a superposition of three emission sub-bands coming from spatially resolved objects with very different kinetics: (1) a band at around 450 nm, with 20-ns decay, which is not changing its position with Si content and is related to optically active defect states and STE in the SRSO matrix; (2) a band at around 600 nm related to aSi-NCs with hundreds of microsecond emission decay and strong dependence on Si content following the predictions of the quantum confinement model; (3) and a third band at around 800 nm (1.54 eV) (Si-NCs, defects) with either very fast (<3 ns) or very slow (>100 μs) emission kinetics also depending on Si content. In this case, however, an increase in Si content influences only the relative intensities between this band and the aSi-NC emission bands. This band can be related to Si-NCs or defect-related states. The weak dependence of the position of this band on Si content can be due to the weak quantum confinement regime. Based on our previous XRD and Raman results for similar samples, we can assume that the size of Si-NCs is in the range of 4 to 6 nm.
In summary, two components often obtained in emission decay times when the signal is recorded at one energy can be due to different spatially resolved objects (a
Si-NCs and Si-NCs or defects) rather than two relaxation mechanisms different in timescale related with one object only, i.e., Si-NCs or a
Si-NCs. The second conclusion that can be given based on the obtained preliminary results is that in many cases, the shift of the emission band at CW excitation observed for samples either annealed at different temperatures or obtained at different excess Si contents can be due to different contributions of defect states into this band. This shift is often related to changes in Si-NC size only. However, at the same time, these two technological parameters change also the number of defects in the matrix, induce a phase transition of Si clusters from amorphous to crystalline, influence the lanthanide distribution [3
], and modify the strain at the clusters’ interface, increasing/reducing the tails of density of states [46
To better understand the dynamics of the Er3+-related emission, the time evolution of the 1,535-nm band has been analyzed at different excitation wavelengths: 266 and 488 nm. Figure shows the obtained results together with maximum entropy method (MEM) analysis expressed in the form of α(τ).
Figure 3 Time evolution of the 1,535-nm band. (a) PL decay obtained for samples with 37 and 39 at.% of Si at 266 and (b) 488 nm. (c) MEM distribution of emission decay at 266-nm excitation for 37 and 39 at.% of Si and (d) MEM distribution of emission decay at (more ...)
In the analysis of kinetic experiments involving the relaxation of complex materials, such as rare-earth-doped glasses, it is often very difficult to choose appropriate models to fit the data. In particular, it is difficult to distinguish between non-exponential models (such as the ‘stretched exponential’) and models that consist of a few discrete exponentials. Thus, many authors use stretched exponential functions to fit the Er3+-related emission decay which, in many cases, is not justifiable. To prove the well-grounded use of two exponential functions to fit our data instead of one exponential or a stretched exponential function, we calculated the inverse Laplace transform of the decay curves obtained by us. This solution allows us to seek a representation for the relaxation process in a space of decay rates, thus obviating the necessity of forcing a particular functional form to fit the data. In this case, the PL decay can be written as
where g(k) is a distribution of decay rate constants for the process I(t). Given an experimental I(t), we would like to obtain the appropriate distribution g(k) that obeys Equation 3, without any assumption about the analytical form of g(k). This essentially involves performing a numerical inverse Laplace transform of the measured decay I(t) which can be written as
where the integration is carried out over the appropriate Bromwich contour. The calculation of an inverse Laplace transform on a noisy data function is known from information theory to be an ill-conditioned problem, and a large number of distributions can fit the data equally well. Nevertheless, it is possible to find the distribution g(k) using the maximum entropy method. The MEM is based on maximizing a function called the Skilling-Jaynes entropy function
where α(τ) is the recovered distribution and m(τ) is the assumed starting distribution. In this equation, τ = 1/k, and the relation between g(k) and α(τ) is α(τ) = τ-2g(1/τ). MEM allows finding α(τ) without any previous knowledge that we may have about the rate distribution. This method has been successfully applied in many situations where the inverse problem is highly degenerate, owing to the presence of noise in the data or the large parameter space one is working with.
Thus, based on the above approach, we fit our data with two exponential functions. It should be mentioned that an important aspect of MEM is that even purely exponential decay processes have decay time distributions with finite width (unless the data is completely noiseless). Therefore, the broad distributions obtained by MEM, i.e., in the case of 488-nm excitation for 37 at.% of Si sample, do not necessarily imply non-exponential dynamics. A test to verify this is to fit the data with exponential decays taking the peaks of the distributions as the decay times. In the investigated case, the PL decay can be fitted very well with a two-exponential decay (χ2
≈ 1.0), yielding decay times of 4,860 and 885 μs and 2,830 and 360 μs for the samples with 37 and 39 at.% of Si, respectively. The obtained decay times are almost the same as the distribution peaks shown in Figure . This result allows us to conclude that the PL decay for both samples can be described by two exponential functions. It should be emphasized that this conclusion could not be drawn without MEM analysis since the PL decays can be fit well also with other models, e.g., the stretched exponential function of the form I
) ~ tβ-1
). However, in the case of the stretched exponential function, the distribution α
) should exhibit the power-law asymptotic behavior of the form α
) ~ tβ-1
, for t
→ 0, which is not the case.
Thus, at 266-nm excitation for both samples, we obtained emission decay times characterized by two components: a fast one (<1 ms) and a slow one (approximately 3 ms). Since the radiative transitions in Er3+
are only weakly allowed, the cross sections for optical excitation and stimulated emission are quite small, typically in the order of 10-21
. Because of that, the radiative lifetime of the 4I13/2
transition in Er3+
ions excited directly in SRSO should lie between 14 ms for pure silica [47
] and 1 ms for silicon [48
The longer time obtained by us is typical for times obtained by other authors (i.e., SiO, 2.5 to 3.5 ms [49
] and SRSO, 2 to 11 ms [11
]). To explain the second component of our samples, we have three options: (a) Er3+
ions are excited via a
Si/Si-NCs, and there is only one optically active Er3+
site excited by two temporally different mechanisms; (b) Er3+
ions are excited via a
Si/Si-NCs, and there are two different Er3+
sites, i.e., the isolated ion and clusters of ions; and (c) optically active Er3+
ions are excited via Si-NCs and a
Si-NCs or defect states separately with a different kinetics [53
Nevertheless, even if the above models could explain two different times recorded for Er3+
emission, the short time observed for Er3+
seems to be much shorter than expected. This could be explained only by the assumption that the short emission decay can be related to Er3+
ions which interact with each other, and due to ion-ion interaction, their emission time can be significantly reduced. Efficient clustering of lanthanides and especially Er3+
ions has already been shown by us and other authors [3
]. Thus, we propose that the slow component is due to emission from isolated ions, while the fast component is related with the ions in a cluster form.
Moreover, from Figure , it can be seen that with increase of Si content, the Er3+
-related emission decay is reduced. We believe that this is due to changes in the refractive index of our matrix for both samples and its contribution to the expression defining the radiative emission time for lanthanides [54
where n is the refractive index of the matrix, <ΨJ′| and |ΨJ> are the initial and final states of single parity, U(λ) is the irreducible tensor form of the dipole operator, λ is the emission wavelength, and Ωλ are the Judd-Ofelt parameters, describing the local environment of the ion. We have observed similar effects of the influence of n on the emission decay time recently for Tb3+ ions introduced into a SRSO matrix where the Si concentration was changed from 35% to 40%, increasing the refractive index from 1.55 to 1.70. Additionally, this reduction in decay time can be also due to an increased number of non-radiative channels with increasing Si content making contributions to the final emission decay as τPL-1 = τR-1 + τNR-1. Similar results have been obtained when 488 nm was used as the excitation wavelength. Moreover, reduction in emission decay time has been observed when the excitation wavelength is changed. The emission decay time at 488 and 266 nm can be different when two different sites are excited at different wavelengths. To verify this, emission spectra of Er3+ ions obtained at 10 K have been compared at different excitation wavelengths. In the limit of our system resolution, we did not find any difference in the emission peak position at different excitation wavelengths. Thus, we believe that the same sites emit at 1,535 nm at all excitation wavelengths.
To investigate the effect of emission quenching, we have performed PL measurements as a function of temperature for different excitation wavelengths. In order to interpret these results, we considered the temperature dependence of the PL intensity at low pump power according to the Arrhenius law with EQ as deactivation (ionization) energy.
Based on the FTIR and Raman spectroscopy done on our samples previously [46
], we found several absorption bands related with phonons or SRSO matrix vibrations which can participate in thermal quenching. Typical Raman spectra obtained by us for these samples consist of two bands: a broad low-frequency band (LF) with maximum at around 485 cm-1
(59 meV) and a narrower, asymmetrically broadened high-frequency (HF) peak centered at 520 cm-1
(64 meV). The LF band may be attributed to a
Si present in the matrix, whereas the HF originates from Si-NCs. Moreover, from the FTIR spectra, there are three main bands located at 1,000 to 1,300 cm-1
(123 to 161 meV) and 800 cm-1
(100 meV) related to the asymmetric stretching and bending Si-O-Si modes, respectively.
In general, the quenching of the luminescence with temperature can be explained by thermal emission of the carriers out of a confining potential with an activation energy correlated with the depth of the confining potential. Since the observed activation energy is much less than the band offsets between Si/SiO2
(approximately 3.4 eV), the thermal quenching of the a
Si/Si-NC-related emission is not due to the simple thermal activation of electrons and/or holes from the a
Si/Si-NCs potential into the SiO2
barriers. Instead, the dominant mechanism leading to the quenching of the VIS-related PL is due to the phonon-assisted tunneling [55
] of confined carriers to states at the interface between a
Si/Si-NCs and the matrix.
As it can be seen from Figure c,f, for the excitation wavelength of 980 nm, thermal quenching of Er3+
-related emission for both samples can be well characterized with only one deactivation energy (EErQ1
) equal to approximately 20 meV. Since the f
levels of Er3+
ions weakly couple to any matrix states due to screening effects of electrons filling higher orbitals, we believe that the observed quenching energy can be related with two mechanisms: Boltzmann distribution of carriers among the Stark levels having different radiative and non-radiative decay probabilities with one multiplet, or phonon-assisted dipole-dipole coupling between the 4I13/2
transition and energy levels related with a
Si/Si-NCs or defect states. The matrix-related emission in this spectral range with nanosecond dynamics has been shown already by other authors [16
], making this process highly probable. Moreover, we can see that the intensity of the Er3+
-related emission at this excitation varies by factors of 4 and 6 for samples with 37 and 39 at.% of Si. This is quite a significant change for RE3+
, suggesting that the main quenching is due to the coupling of Er3+
ions with some defect states. We can also see that this quenching is almost twice as large for the sample with 39 at.% of Si, suggesting correlation of these quenching centers with Si content in the SRSO matrix.
Figure 4 Emission thermal quenching. Obtained for Si-NCs and Er3+-related bands at different excitation wavelengths (266, 488, and 980 nm) as function of temperature for two samples with 37 (a, b, c) and 39.at % of Si (d, e, f). Photon flux used for the experiment (more ...)
Analyzing the data presented in Figure a,d, we can see that when the Er3+ is excited with 266 nm, PL thermal quenching can be well fitted only when two quenching energies are used. For both samples, these energies are equal to EErQ1 ~ 15 meV and EErQ2 ~ 50 meV. For comparison, in Figure a,d, two fits have been shown with one and two quenching energies. It is clear that two energies are needed to obtain a statistically good fit. Once we look at thermal quenching recorded for the emission related to aSi/Si-NCs, we can see that the thermal quenching can also be fitted with two energies similar for both samples: EVISQ1 ~ 10 and EVISQ2 ~ 65 meV.
The EVISQ2 energy corresponds exactly to the energy of phonons related to oscillations of Si-Si bonds obtained in Raman experiments. In more detail, this value is closer to the amorphous phase of silicon rather than the crystalline phase. This could be related to the fact that amorphous nanoclusters are responsible for the observed emission in the VIS range as well as for the indirect excitation of Er3+ ions. Thus, most probably at a temperature corresponding to 65 meV, one of the carriers is moved from the potential related with aSi-NCs to defects states at their surface, where it recombines non-radiatively or diffuses over longer distances inside the matrix. The second energy (EVISQ1) is much less clear at the moment. Nevertheless, correlation between the second quenching energy (55 meV) observed for Er3+ emission with the quenching energy obtained for aSi-NC emission (65 meV) suggests efficient coupling between these two objects and confirms that most of the quenching appears before the excitation energy is transferred from aSi-NCs to Er3+ ions. Also, at this excitation, Er3+-related emission is quenched by factors of 6 and 11 for samples with 37 and 39 at.% of Si, respectively.
Figure e shows results of thermal emission quenching at 488-nm excitation wavelength for a sample with 39 at.% of Si. It can be seen that the Er3+-related emission is also characterized by two quenching energies equal to about 20 and 60 meV. These values are almost the same as for 266-nm excitation and very similar to VIS emission where values of 15 and 70 meV have been obtained. This indicates that in this case also, we deal with indirect excitation of Er3+ ions. Since 488 nm corresponds also to direct excitation of Er3+ ions, most probably, we deal with both kinds of excitation simultaneously. We believe, however, that indirect excitation is in this case dominant. Nevertheless, the results obtained at this excitation wavelength for 37 at.% of Si are not so obvious. In this case, two statistically equal fits with one (20 meV) and two energies (20 and 6 meV) were possible to achieve. The higher energy is clear and has the same origin as in the previous cases. One explanation of this fact would be the excitation spectrum for this sample where its edge is much shifted to blue as compared to samples with 39 at.% of Si. Thus, in this case, we can indeed observe a major contribution from a direct excitation of Er3+ ions rather than via intermediate states.