1. Introduction

During the last two decades Er-doped Si-based systems have attracted a considerable attention as materials for the development of efficient sources to be used in silicon microphotonics [1]. The Er emission wavelength of about 1.54 μm is in fact very important, since it corresponds to a minimum in the loss spectrum of silica optical fibers. The Er content that can be inserted in solid hosts is however limited to about 10²⁰ at/cm³, due to the occurrence of segregation or clustering phenomena, that limit the number of emitting centers [2]. A promising alternative approach is represented by Er-based compounds, such as oxides or silicates, in which Er can be inserted in higher concentration [3–6], about 10²² at/cm³, by avoiding the Er-Er clustering. It has been demonstrated that all Er ions are optically active in Er₂Si₂O₇ [3]. However extremely high Er concentration introduces also strong non-radiative recombination paths, such as concentration quenching and cooperative up-conversion, that limit the 1.54 μm luminescence. Yttrium-Erbium silicates have been suggested in order to introduce gradually the Er content by reaching the best compromise between a high number of optically active centers and the occurrence of the deleterious non-radiative paths [7–9]. In these systems a very low cooperative up-conversion coefficient, about 10⁻¹⁸ cm³/s, has been found for 10²¹ Er/cm³ [8, 9], thus demonstrating the possibility to reach high optical gain potentialities.

Another common technique, successfully used in diode pumped glass lasers, and especially in fiber lasers [10–13], for increasing the amount of excited Er³⁺ ions in the ⁴I_13/2 level is the Yb³⁺ sensitization. Thanks to the energy match between the ⁴I_11/2 level of Er³⁺ and the ²F_5/2 level of Yb³⁺, the energy transfer between an excited Yb³⁺ ion and an Er³⁺ ion in the ground state can occur resonantly. This process is very efficient since the absorption cross section of Yb³⁺ (about 10⁻²⁰ cm²) is one order of magnitude higher than that one of Er³⁺ (about 10⁻²¹ cm²).

In this work we have studied the Yb-Er couple in (Yb-Er) disilicate, α−(Yb_1-xEr_x)₂Si₂O₇, thin films grown on Si. The choice takes advantage of the Er-based compounds (for inserting controlled Er concentrations), of the efficient Er³⁺ sensitization from Yb³⁺ ions and of the compatibility with the Si platform. The disilicate host has also the advantage of a high phonon energy (≈1100 cm⁻¹). This leads to a high ⁴I_11/2→⁴I_13/2 transition probability, thus reducing the back-energy transfer from Er³⁺ to Yb³⁺ and guaranteeing a high population of the ⁴I_13/2 level. The Er concentration, N_Er, was varied between 0.2 at.% and 16.5 at.%, by keeping constant the total RE concentration (N_Er + N_Yb = 18 at.%), in order to study the Er³⁺ excitation and de-excitation mechanisms and the Yb-Er coupling in the α−(Yb_1-xEr_x)₂Si₂O₇. Moreover two sets of reference samples, α−(Y_1-xEr_x)₂Si₂O₇ and α−(Yb_1-xY_x)₂Si₂O₇, have permitted to evaluate the optical properties of the single RE without the influence of the second one. These reference samples are very important since Y³⁺ has the same chemical properties of a RE but it is optically inactive. In our best sample, a very high energy-transfer coefficient has been reached, about 2 × 10⁻¹⁶ cm⁻³s⁻¹. The best compromise between the number of excited Yb³⁺ donors and the available Er³⁺ acceptors is obtained for 1.6 at.% of Er (corresponding to 1.4 × 10²¹ Er/cm³). At this concentration a very high excited population at the ⁴I_13/2 level has been estimated suggesting that material is very promising as an active medium for planar optical amplifiers at 1535 nm.

2. Experimental section

We have deposited (Yb_1-xEr_x)₂Si₂O₇ thin films, about 150 nm thick, in a ultra high vacuum magnetron sputtering system on (100) c-Si substrates by the co-sputtering from Yb₂O₃, Er₂O₃ and SiO₂ targets. (Y_1-xEr_x)₂Si₂O₇ and (Yb_1-xY_x)₂Si₂O₇ thin films have been also synthesized, as reference samples, by substituting respectively the Yb₂O₃ or the Er₂O₃ with the Y₂O₃ target. Further details on the apparatus and on the deposition procedure can be found elsewhere [9]. By properly changing the powers supplied to the three targets we have synthesized several films having different ratio between the two involved REs but keeping always fixed their sum, 18 at.%, and the disilicate composition RE:Si:O = 2:2:7. All the films have been treated at 1200 °C for 30 s in O₂ ambient in a rapid thermal annealing system, in order to induce the α-phase crystallization.

Thin films composition has been evaluated by Rutherford Backscattering Spectrometry (RBS) and by Particle Induced X-Ray Emission (PIXE). RBS measurements were performed by using a 2 MeV He⁺ beam, with the detector placed at an angle of 165° with respect to the incident beam. PIXE analyses were realized by using a 2.4 MeV He⁺ beam; a higher energy with respect to RBS measurements was chosen in order to increase the ionization cross section, and hence the probability of X-ray emission. A Si-PIN covered by a thin Be window was used as a detector; an Al filter was placed in front of the detector, in order to cut the low-energy X-rays originating from the Si substrate.

Room temperature photoluminescence (PL) measurements have been performed by a Titanium-sapphire laser pumped through a laser diode at 532 nm and mechanically chopped at a frequency of 11 Hz. The wavelength of the Ti-sapphire laser has been varied with continuity between 750 and 1000 nm. The PL signal was analyzed by a single grating monochromator and detected by a germanium photodetector. Time resolved PL measurements were performed by first detecting the modulated luminescence signal with an Hamamatsu infrared-extended photomultiplier tube and then by analyzing the signal with a photon counting multichannel scaler. The overall time resolution of the system is of 1 μs.

3. Results and discussion

3.1 Structural properties

RBS analyses have been performed for all the samples and the spectra were fitted by using the SIMNRA 6.0 software [14], in order to estimate their chemical composition. Figure 1(a) reports some examples of RBS spectra. At a first glance it is evident that all the elemental signals are constant, thus indicating a uniform chemical composition along all the film thickness.

 

Fig. 1 (a) RBS spectra of (Y_1-xEr_x)₂Si₂O₇, Yb₂Si₂O₇ and (Yb_1-xEr_x)₂Si₂O₇ thin films. In the latter case P(Yb₂O₃) = 140 W, P(Er₂O₃) = 70 W. The vertical lines in the bottom axis indicate respectively the surface energy edges of O, Si, Y, Er and Yb atoms at increasing energies. (b) PIXE spectra of (Yb_1-xEr_x)₂Si₂O₇ thin films obtained by varying the powers applied to the two RE oxide targets, Yb₂O₃ and Er₂O₃. The x-ray transitions associated to Yb and Er are labeled.

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All the compounds obtained by changing the powers applied to the Y₂O₃ and Er₂O₃ targets, and by keeping constant at 300 W the one to the SiO₂ target, have the disilicate stoichiometry (Y + Er):Si:O = 2:2:7 (see the example in Fig. 1(a), green line and open triangles). A similar composition, i.e. (Yb + Y):Si:O = 2:2:7, has been confirmed for all the samples obtained by varying the powers supplied to the Yb₂O₃ and Y₂O₃ targets (not shown). In both kinds of disilicates the atomic concentration of the single RE is also evaluated, and it varies in the range between 0.2 at.% and 18.0 at.%.

In contrast in (Yb-Er) compounds it is not possible to distinguish the Yb and Er contributions to the RBS signal. This is evident by looking at the spectra in Fig. 1(a) regarding Yb₂Si₂O₇ (blue continuous line) and (Yb-Er) compound (red line and open circles). In fact the energy difference between their surface edges is lower than the energy resolution of the detector as a consequence of their very similar masses. In this case the experimental spectra were fitted by assuming that the RE RBS signal is related only to a single RE (while in effect it is the sum of both REs). In fact Yb and Er Rutherford backscattering cross sections, σ_R, differ only by 5%. Since the detected RBS signal is directly proportional to σ_R, the highest error in the total RE estimation is 5% in the worst case. By fitting the RBS spectra we can conclude that all the as-deposited (Yb-Er) compounds have a disilicate composition (Yb + Er):Si:O = 2:2:7.

In order to evaluate independently the concentrations of each RE, we have performed PIXE analyses. Figure 1(b) reports the PIXE spectra of two reference samples Yb₂Si₂O₇ and Er₂Si₂O₇ and of the (Yb_1-xEr_x)₂Si₂O₇ compounds obtained for different powers applied to the two RE oxide targets. In the case of Yb₂Si₂O₇ film (blue continuous line) only the Yb-related peaks are visible (Lα_1,2, Lβ and Lγ as labeled in the figure). Analogously for Er₂Si₂O₇ (black line and open squares) peaks related to Er transitions appear. Finally in the (Yb_1-xEr_x)₂Si₂O₇ films peaks related to both Yb and Er are present and their intensities vary depending on the content of each species. In PIXE spectra the peaks associated to Yb and Er are well separated, and then it is possible to analyze them individually.

The quantitative estimation of the single RE concentrations was done by combining RBS and PIXE measurements and by using the Yb₂Si₂O₇ and Er₂Si₂O₇ films as calibration standards. In fact through RBS analyses it is possible to determine the atomic areal density of the sum of Yb and Er, while PIXE allows to identify their mutual weight. In order to have the best sensitivity we have chosen the Lα_1,2 peak due to its higher intensity with respect to the other ones. By using the two calibration standards we can obtain a parameter that directly correlates the RE areal density (expressed in cm⁻²) to the area of the Lα_1,2 peak individually for each RE, equal to 3.26 × 10⁻³ and 3.44 × 10⁻³ cm⁻²keV⁻¹ for Yb and Er respectively.

Measuring the areas of the Er Lα_1,2 and Yb Lα_1,2 peaks, reported in Table 1 , in all the as-deposited (Yb_1-xEr_x)₂Si₂O₇ samples we have directly extracted the atomic areal density of Yb and Er, N_Yb and N_Er. This procedure is justified by the fact that both the ionization cross section and the fluorescence yield can be considered unchanged for all the samples because they do not depend on the film composition. This is a reasonable assumption since the atom ionization by ion impact is an atomic process, which does not involve the material structure in which the atom is embedded. In addition also the x-ray absorption of the materials is unchanged. The estimated atomic concentrations of Yb and Er have been reported in atomic percentage in Table 1, as obtained by considering the total atomic density estimated by RBS measurements.

Table 1. The powers applied to the Yb₂O₃ and Er₂O₃ targets and the corresponding measured PIXE area of Yb Lα_1,2 and Er Lα_1,2 (expressed in counts × keV) and estimated atomic concentration (in atomic percentage) for all the (Yb_1-x-Er_x)₂Si₂O₇ thin films

View Table

All the as-grown films have a disilicate composition with an extended range of Er concentration (and Yb one accordingly), spanning from 0.2 at.% (corresponding to about 5 × 10²⁰ at/cm³) to 18.0 at.% (corresponding to about 10²² at/cm³).

After the thermal treatment at 1200 °C for 30 s in O₂ ambient the disilicate films crystallize in the α-crystalline phase (XRD spectra not shown), as already known for Er and (Y-Er) disilicates [9, 15-16]. Moreover it has been demonstrated that in the (Y-Er) disilicate Er³⁺ can be substituted by Y³⁺ ions [2, 8]. Also all the (Yb_1-xY_x)₂Si₂O₇ and (Yb_1-xEr_x)₂Si₂O₇ thin films crystallize in α-phase even by varying the relative REs amount. This confirms that also in these two disilicates we can insert gradually Yb³⁺ ions in substitution of Er³⁺ (or of Y³⁺ ions), thanks to the similarities of Y, Yb and Er ionic radii and of their chemical properties.

3.2 Optical properties: Yb-Er coupling

We have investigated the photoluminescence properties of α-(Yb_1-xEr_x)₂Si₂O₇ thin films by exciting all the samples under low pump flux (ϕ = 1.6 × 10¹⁹ cm⁻²s⁻¹) at room temperature. In order to study the excitation mechanisms of Er³⁺ and Yb³⁺ ions we have also analyzed the PL properties of both REs in some reference samples, α-(Y_1-xEr_x)₂Si₂O₇ and α-Yb₂Si₂O₇. Since the Y³⁺ ions are optically inactive, these two samples permit to distinguish the role of each single RE without the influence of the other one. By exciting under 980 nm the typical PL peak of Er³⁺ in α-crystalline phase [15] is observed from α-(Y_1-xEr_x)₂Si₂O₇, as shown in Fig. 2(a) . By varying the excitation wavelength, λ_exc, between 750 nm and 1000 nm, the photoluminescence excitation (PLE) spectrum recorded at 1535 nm is characterized by two sharp peaks depicted in Fig. 2(b). The peaks centered respectively at 800 nm and at 980 nm correspond to the ⁴I_15/2→⁴I_9/2 and ⁴I_15/2→⁴I_11/2 Er³⁺ transitions. This is true because Er³⁺ ions can be excited only by direct excitation, since Y³⁺ ions are optically inactive.

 

Fig. 2 PL spectra (a) from α-(Y_1-xEr_x)₂Si₂O₇ under λ_exc = 980 nm, (c) from α-Yb₂Si₂O₇ and (e) from α-(Yb_1-xEr_x)₂Si₂O₇ under λ_exc = 920 nm. In addition we reported the PLE spectra recorded (b) at 1535 nm from α- (Y_1-xEr_x)₂Si₂O₇, (d) at 1025 nm from α-Yb₂Si₂O₇ and (f) at 1535 nm from α-(Yb_1-xEr_x)₂Si₂O₇. The inserts report the levels schemes of the Er³⁺ and Yb³⁺ ions. Note that spectrum (b) has been multiplied by a factor of 10. This same amplification factor has been used in (f) in the wavelength range 750-850 nm.

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The PL properties of Yb³⁺ ions have been instead studied in α-Yb₂Si₂O₇ (N_Yb = 18 at.%). Under λ_exc = 920 nm the PL emission has the typical broad band shape between 900 and 1100 nm associated to the ²F_5/2→²F_7/2 Yb³⁺ de-excitation, see Fig. 2(c). A further band has been found between 1100 and 1200 nm due to the band edge recombination of carriers in Si. Therefore we have measured the PLE spectrum by recording the PL intensity at 1025 nm, shown in Fig. 2(d). It is characterized by a main peak at 980 nm and a further band around 920 nm, both associated to the ²F_7/2→²F_5/2 transitions of Yb³⁺ ions typically observed in several other matrices [10–13, 17–20].

When we excite the α-(Yb_1-xEr_x)₂Si₂O₇ under λ_exc = 920 nm, that is not resonant with any Er³⁺ transitions, the PL spectrum, in Fig. 2 (e), shows not only the Yb³⁺ emission between 900 and 1200 nm but also the typical peak of Er³⁺ at 1535 nm. Therefore in this case Er³⁺ can be excited only by Yb³⁺ sensitization, thanks to the good matching between the Yb^{3+ 2}F_5/2 and the Er^{3+ 4}I_11/2 levels and the thermalization process within the Yb³⁺ system, possibly involving migration of excitation [18,19]. In order to understand the role of Yb³⁺ in the Er³⁺ excitation mechanism the PLE spectrum recorded at 1535 nm has been analyzed, as reported in Fig. 2(f). It is worth noticing that its shape is a superposition of the two PLE spectra already described for Er³⁺ in α-(Y_1-x-Er_x)₂Si₂O₇ and for Yb³⁺ in α-Yb₂Si₂O₇. We can conclude that Er³⁺ in α-(Yb_1-xEr_x)₂Si₂O₇ can be excited both by the direct absorption and by the mediated excitation from Yb³⁺ ions.

Moreover by comparing the PL intensity at 1535 nm of the two samples having the same Er³⁺ content, in presence (Fig. 2(f)) and in absence (Fig. 2(b)) of Yb³⁺, a very similar signal is observed under λ_exc = 800 nm. Instead under λ_exc = 980 nm PL at 1535 nm is surprisingly one order of magnitude higher when Er³⁺ ions are in presence of Yb³⁺, in the α-(Yb_1-xEr_x)₂Si₂O₇ (note that in Fig. 2(b) the whole spectrum is multiplied by a factor of 10). This is due to the superposition of the two contributions, the direct Er³⁺ excitation and the mediated excitation from Yb³⁺ ions.

By comparing all the α-(Yb_1-xEr_x)₂Si₂O₇ thin films we have observed very similar PLE shapes. Therefore the relevant mediated contribution observed for all the samples demonstrates the efficient Yb-Er energy transfer also for the lowest N_Yb values. By increasing N_Yb the PL signal observed under mediated excitation condition increases with respect to the PL recorded under λ_exc = 980 nm that is resonant with both the direct and the mediated excitation. The ratio of the PL signals at 1535 nm recorded under pure mediated excitation (λ_exc = 935 nm) and under resonant plus mediated excitation (λ_exc = 980 nm) can give important quantitative information on the Er³⁺ excitation mechanisms. In fact for pure resonant excitation this ratio should be zero, while for pure mediated excitation could be 0.45 (as for the emission of a pure Yb sample, Fig. 2(d)). The PL(λ_exc = 935 nm)/PL(λ_exc = 980 nm) ratio is reported as a function of N_Yb (or N_Er, upper scale) in Fig. 3 .

 

Fig. 3 PL(λ_exc = 935 nm)/PL(λ_exc = 980 nm) ratio recorded at 1535 nm as a function of N_Yb, bottom scale, or N_Er, top scale (N_Er + N_Yb = 18 at.%). In the right hand scale is reported the estimation of mediated contribution.

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This ratio raises by increasing N_Yb and it reaches its maximum value for all the samples containing N_Yb higher than 10.0 at.% (or N_Er lower than 8.0 at.%). It is very interesting to note that this maximum value corresponds exactly to the ratio PL(λ_exc = 935 nm)/PL(λ_exc = 980 nm) recorded at 1025 nm from Yb³⁺ ions in the α-Yb₂Si₂O₇ thin films. This value is therefore characteristic of Yb³⁺ and it comes from the dependence of its absorption cross section on λ_exc. By normalizing the PL ratios detected at 1535 nm from the α-(Yb_1-xEr_x)₂Si₂O₇ to the maximum value we obtain an estimation of the percentage mediated contribution under λ_exc = 980 nm. It means that for the regime with N_Yb> 10.0 at.% (and N_Er< 8.0 at.%), 100% mediated contribution is reached and the PL at 1535 nm is mainly due to the sensitization of Er³⁺ ions from Yb³⁺ ones. This regime corresponds to the condition for which the Yb³⁺ donors overcome the Er³⁺ acceptors.

In order to quantify the energy-transfer efficiency in α-(Yb_1-xEr_x)₂Si₂O₇ we have analyzed the Yb³⁺ decay rate, W_Yb-Er. In fact if an Yb-Er interaction is present, then it is expected that new non-radiative channels increase the Yb³⁺ intrinsic decay rate, W_Yb, under the relationship

We have estimated W_Yb-Er and W_Yb (inverse of the lifetime) by analyzing the PL decay curves recorded at 980 nm under λ_exc = 935 nm respectively from the α-(Yb_1-xEr_x)₂Si₂O₇ and α-(Yb_1-x-Y_x)₂Si₂O₇ films having the same Yb contents (see Fig. 4(a) ). By single exponential fits we have estimated the decay times for all the samples and then extracted the respective rates. W_Yb-Er was found to be always 0.1 μs⁻¹, much higher than the typical radiative decay rate of Yb (0.7 ms⁻¹) [17]. On the other hand W_Yb was found to be strongly dependent on N_Yb. By increasing N_Yb from 1.5 at.% to 17.8 at.%, W_Yb increases from 3.9 ms⁻¹ to 62 ms⁻¹, but always lower than W_Yb-Er. The W_Yb trend is due to the energy migration among Yb³⁺ ions and their interaction with impurities, such as OH^- radicals [17], dependent respectively on the square of N_Yb and on N_Yb.

 

Fig. 4 (a) PL decays recorded at 980 nm for N_Yb = 1.5 at.% and N_Yb = 17.8 at.% in absence (N_Er = 0 at.%) and in presence of Er³⁺. Continuous red lines are the single exponential fits of the experimental data. (b) Energy-transfer efficiency η (left hand scale) and energy-transfer coefficient C_ET (right hand scale) as a function of N_Yb, calculated by Eq. (1) and Eq. (2).

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Then η is evaluated for each N_Yb according to Eq. (2) and the obtained values are reported in Fig. 4(b). Note that η is almost 1 for 1.5 Yb% (and 16.5 Er%). This means that for the lowest N_Yb all the power absorbed by Yb³⁺ ions is lost by energy transfer to Er³⁺ ions, given that for each donor there are 8 available acceptors. By increasing N_Yb η slightly decreases down to 0.4, because the excited Yb³⁺ fraction that efficiently transfers to a nearby Er³⁺ ion is decreasing as well. This is due to the stronger Yb-Yb interaction, demonstrated by the W_Yb increase, at the expenses of the Yb-Er coupling. However η decreases only by about a factor of 2.4 by rising N_Yb by a factor of 10. This means that the number of excited Yb³⁺ ions that efficiently transfer to Er³⁺ are still increasing by a factor of 4, corresponding to 6.0 × 10²¹ sensitizers/cm³. Such a number is much larger than the available acceptors, 1.6 × 10²⁰ Er/cm³.

The energy-transfer coefficient, C_ET, is obtained through Eq. (1) and it is reported in the right hand scale of Fig. 4(b). It has a slight increase by increasing N_Yb and a sharp increase for N_Yb> 10 at.%, reaching a value of about 2 × 10⁻¹⁶ cm⁻³s⁻¹. Since we have demonstrated that the actual sensitizers are always more than the acceptors, the simultaneous decrease of N_Er implies that each Er³⁺ feels a stronger coupling with Yb³⁺ population. The maximum C_ET value is very high and comparable to the best energy-transfer coefficient reported in literature in other phosphate glasses containing typically about 10¹⁹ Er/cm³ and 10²⁰ Yb/cm³ [21]. Therefore we have demonstrated that Er³⁺ excitation through Yb³⁺ is still efficient in (Yb-Er) disilicates even by increasing the RE concentrations up to one order of magnitude.

3.3 Optical properties: efficient PL emission from Er³⁺ ions

When Er³⁺ ions in α-(Yb_1-xEr_x)₂Si₂O₇ are excited to the second excited level, ⁴I_11/2, they fastly decay to the first excited level, ⁴I_13/2, and then radiatively to the ground state, ⁴I_15/2, by emitting a photon at 1535 nm [9]. In order to study the Er³⁺ emission properties we have measured the decay time, τ_1,Er, as a function of N_Yb (and N_Er) under λ_exc = 980 nm. Figure 5(a) shows some traces at different Er contents taken at low pump flux of 1.6 × 10¹⁹ cm⁻²s⁻¹. In the same figure the decay curve in absence of Yb (in Y-Er disilicates) is also reported for a particular N_Er, 1.6 at.%. It is interesting to note that the Er³⁺ lifetime depends only on Er³⁺ content and is not affected by the presence of Yb (or Y).

 

Fig. 5 (a) PL decays recorded at 1535 nm for α-(Yb_1-x-Er_x)₂Si₂O₇ at different N_Er. For N_Er = 1.6 at.% the decay curve for α-(Y_1-x-Er_x)₂Si₂O₇ is also reported. Continuous black lines are the single exponential fits of the data. (b) PL intensity (left hand scale) and lifetime (right hand scale) at 1535 nm as a function of N_Yb (bottom scale) in α-(Yb_1-x-Er_x)₂Si₂O₇. For comparison the decay times (black open triangles) at 1535 nm in α-(Y_1-x-Er_x)₂Si₂O₇ as a function of N_Er (top scale) have been reported. The blue line is a guide for the eye. The measurements of both panels are obtained under λ_exc = 980 nm and at ϕ = 1.6 × 10¹⁹ cm⁻²s⁻¹.

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The lifetime values, τ_1,Er, have been evaluated for all the samples by single exponential fits of the decay curves and reported in the right hand scale of Fig. 5(b) (blue line and open squares). It is evident that by decreasing N_Er, τ_1,Er varies between 0.3 ms and 5.6 ms. The same trend is observed in the case of α-(Y_1-xEr_x)₂Si₂O₇ samples (black open triangles). Therefore the τ_1,Er behavior can be associated only to the Er-Er interactions not involving Yb³⁺ ions. For the highest N_Er, the very short lifetime can be justified by the occurrence of concentration quenching between Er³⁺ ions owing to the short mean Er-Er distance. This phenomenon consists in a resonant energy transfer from one excited Er³⁺ ion at the first excited level to a nearby Er³⁺ ion in the ground state. Hence energy travels along the sample by eventually being lost when a quenching center is encountered [2]. By increasing N_Yb and, as a consequence, by decreasing N_Er the deleterious Er-Er interactions are reduced. It means that the decay time of the ⁴I_11/2→⁴I_13/2 transition and the Yb-Er energy-transfer time are faster than the Er³⁺ de-excitation time from the ⁴I_13/2 level. In this α-(Yb_1-xEr_x)₂Si₂O₇ host the good Yb-Er coupling and the reduced back-transfer from Er³⁺ to Yb³⁺ are guaranteed for the whole N_Er range under investigation.

In Fig. 5(b) data on the PL intensity at 1535 nm as a function Yb and Er contents are also summarized (left hand scale). A very strong PL emission has been already demonstrated from Er³⁺ in Er₂Si₂O₇ (N_Yb = 0 at.%) [3], because all Er³⁺ ions are optically active. By introducing just 2 at.% of Yb, PL intensity at 1535 nm already increases by a factor of three though the emitting Er³⁺ ions are reducing from 18 at.% to 16.5 at.%. This is due to the occurrence of mediated excitation from Yb³⁺ ions as already demonstrated. The PL intensity continues to increase by further increasing N_Yb. This trend cannot be justified only by the simultaneous slight increase of τ_1,Er but it is mainly due to the raising of the mediated contribution at λ_exc = 980 nm (see Fig. 3). When we reach the maximum mediated excitation contribution for N_Yb> 10 at.% the PL intensity continues to increase, reaching its maximum for 1.6 Er% and 16.4 Yb%. This further increase is justified by the strong increase of τ_1,Er that compensates the reduction of the number of Er³⁺ emitting centers. By further increasing N_Yb, though the maximum radiative efficiency and the maximum C_ET (see Fig. 4(b)) is reached, the number of Er³⁺ ions available for excitation is too low. This determines that the overall Er emission at 1535 nm drops down.

For the sample having the best PL emission at 1535 nm the PL trend has been recorded as a function of pump flux, ϕ, in the range between 10¹⁸ cm⁻²s⁻¹ and 10²² cm⁻²s⁻¹ as reported in Fig. 6 . A comparison with the α-(Y_1-x-Er_x)₂Si₂O₇ sample with the same Er content, but in absence of Yb, is also shown. In the two cases the PL trend is very similar, it increases linearly and then it exhibits a sublinear regime. This is associated with the occurrence of up-conversion phenomena where two Er³⁺ ions both excited at the ⁴I_13/2 level interact with one being de-excited to the ⁴I_15/2 ground state and the other being resonantly excited to the ⁴I_9/2 level [2] thus determining a depletion of the first excited level (as reported in the scheme of Fig. 6).

 

Fig. 6 Photoluminescence intensity at 1535 nm as a function of ϕ for the α-(Yb_1-xEr_x)₂Si₂O₇ and the α-(Y_1-xEr_x)₂Si₂O₇ film having the same N_Er. The excitation wavelength is λ_exc = 980 nm. The continuous curves are fits of the experimental data, obtained by using Eq. (3). A scheme of the up-conversion phenomenon is depicted on the right-hand corner.

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In order to fit the data, the PL intensity has to be correlated with the Er³⁺ population in the first excited level, N_1,Er. As already pointed out, Er³⁺ quickly de-excites from the ⁴I_11/2 level to the ⁴I_13/2 one and the back-energy transfer probability to the Yb³⁺ ions is negligible. This allows to describe the Er³⁺ dynamics as a two-levels system. Therefore, by solving the rate equations in steady state conditions, the population N_1,Er is obtained as a function of ϕ, as reported in literature [2, 9]:

In this expression σ_Er is the Er³⁺ effective excitation cross section under λ_exc = 980 nm, τ_1,Er is the lifetime in absence of up-conversion and C_up is the up-conversion coefficient. Note that since at ϕ = 1.6 × 10¹⁹ cm⁻²s⁻¹ up-conversion is negligible, for τ_1,Er we have used the value reported in Fig. 5(b). In particular, Er³⁺ has the very same lifetime in the two considered hosts. Moreover, since the PL intensity is proportional to N_1,Er, the correlation can be done with a proper calibration procedure reported in [9] and by using a standard reference sample of Er-doped silica (see right-hand scale in Fig. 6).

Now it is possible to fit the curves of PL intensity as a function of ϕ with Eq. (3), thus obtaining the values of σ_Er, C_up for both samples. We have found σ_Er values of 2.0 × 10⁻²¹ cm² in α-(Y_1-xEr_x)₂Si₂O₇, corresponding to the typical absorption cross section of Er³⁺ ions under λ_exc = 980 nm observed in silica glasses [22], and 2.0 × 10⁻²⁰ cm² in α-(Yb_1-xEr_x)₂Si₂O₇. This further confirms that Er³⁺ ions are indeed excited with an excitation cross section one order of magnitude higher if in presence of Yb³⁺ ions. Moreover it is very interesting to note that in this case σ_Er is indeed equal to the direct Yb³⁺ absorption cross section, as measured in Yb₂Si₂O₇ (data not shown) and also reported in literature [17], thus confirming the efficient excitation of Er³⁺ ions by Yb-Er energy transfer.

As far as the C_up estimation is concerned, we have obtained the same value (6 × 10⁻¹⁹ cm³/s) in the two cases and this is a direct proof that the interactions between Er³⁺ ions in the first excited level are not influenced by the presence of Yb³⁺. Moreover this value is of the same order of magnitude of that reported for Er-doped silica [23] or for (Y-Er) silicate [8,9].

The higher σ_Er and similar C_up for Er³⁺ in (Yb-Er) disilicate determine that the PL intensity is always higher than the one in α-(Y-Er) disilicate for the whole ϕ range. Moreover it is very interesting to note that in α-(Yb_1-x-Er_x)₂Si₂O₇ almost 20% of Er³⁺ ions can be excited at the first excited level at photon fluxes of about 10²³ cm⁻²s⁻¹. This excited fraction is almost one order of magnitude higher than the one obtained in the case of Er³⁺ in absence of Yb³⁺. This remarkable result demonstrates that the α-(Yb_1-xEr_x)₂Si₂O₇ system is a very promising material for optical amplifiers at 1535 nm.

4. Conclusion

We have demonstrated that by introducing simultaneously Yb³⁺ and Er³⁺ inside an α-disilicate an efficient coupling between the two RE ions is possible for an extended range of RE concentrations. Though the high RE contents introduce deleterious non-radiative paths in all the cases Yb³⁺ ions can efficiently transfer energy to Er³⁺. In particular, for N_Yb increasing from 0 at.% to 10 at.% the effective excitation of Er³⁺ passes from 2.0 × 10⁻²¹ cm² (direct Er³⁺ photon absorption) to 2.0 × 10⁻²⁰ cm² (Yb³⁺ mediated energy transfer). With further increasing Yb concentration (and consequently decreasing Er) up to 16.4 at.% the PL intensity at 1535 nm further increases due to a decrease of Er-Er concentration quenching. These results are made possible by the high phonon energy that characterizes the host thus guaranteeing high probability for the ⁴I_11/2→⁴I_13/2 relaxation and therefore a reduced back-energy transfer from Er³⁺ to Yb³⁺, favouring the population of the ⁴I_13/2 level. Though the strong Yb³⁺ absorption cross section allows an efficient Er³⁺ excitation, in waveguide applications Yb³⁺ itself could hinder the overall amplifying performance. In fact, given the higher absorption cross section of Yb³⁺, the propagation length of the pumping signal through the waveguide is lower than in the case of a waveguide with Er³⁺ only, thus shortening the overall length for which the 1535 nm signal can be amplified [19]. The study of the Yb-Er interaction in such (Yb-Er) silicates in which the Er content can be continuously increased is then fundamental to find a trade-off between the waveguide length and the absolute number of excited Er³⁺ ions. Moreover the very high excited population at ⁴I_13/2 level obtained for the optimized (Yb_1-xEr_x)Si₂O₇ film (having 1.6 Er%, corresponding to 1.4 × 10²¹ Er/cm³) makes this material very promising as active medium for amplification at 1535 nm.