Iaroslav Nekrashevych

Vadim S Nikolayev
email: vadim.nikolayev@cea.fr

Pulsating heat pipe simulations: impact of PHP orientation

Keywords: Pulsating heat pipe, Oscillation, Liquid films, Phase change, Simulation Nomenclature

The pulsating (called also oscillating) heat pipe (PHP) is a simple capillary tube bent in meander and filled with a two-phase fluid. We discuss numerical simulations of the 10-turn copper-water PHP under vertical favorable (bottom-heated), vertical unfavorable (top-heated), and horizontal orientations. Within the present approach, the horizontal orientation is equivalent to the microgravity conditions. The simulations are performed with the in-house CASCO software. The time-averaged spatial distribution of the liquid plugs inside the PHP is influenced by gravity. This affects the overall PHP performance. We show that, independently of the PHP orientation, contribution of the latent heat transfer is large with respect to the sensible heat transfer. We discuss the phenomena occurring inside the PHP during startup and the stable regimes (intermittent and continuous oscillations followed by dryout).

The pulsating (called also oscillating) heat pipe (PHP) is a simple capillary tube bent in meander and filled with a pure fluid that forms inside the vapor bubbles and liquid plugs. When the heat power is applied to one meander (evaporator) side, the sequence of bubbles and plugs inside the tube begins to oscillate spontaneously. This oscillation causes an efficient heat transfer from evaporator to the cooled meander side (condenser). In spite of such a simple structure, the PHP functioning is not completely understood both from experimental and theoretical points of view [START_REF] Marengo | Pulsating heat pipes: Experimental analysis, design and applications[END_REF]. Tools for the PHP dimensioning are still absent. The numerical simulation seems to be the only way to predict the heat transfer for a given PHP design.

There are many works where the influence of PHP orientation on the PHP performance has been studied experimentally [START_REF] Marengo | Pulsating heat pipes: Experimental analysis, design and applications[END_REF]. By testing a 10-turn transparent (teflon) PHP filled with R-114 refrigerant during a parabolic flight, [START_REF] Gu | Microgravity performance of micro pulsating heat pipes[END_REF] found that its performance was better in microgravity that in the vertical favorable position. However most authors agree that the PHP performance in the vertical favorable orientation (evaporator below condenser, called 90 • below) is better than in the horizontal (0 • ) orientation, which is in its turn, more advantageous that the vertical unfavorable (evaporator above condenser, -90 • ) orientation. In the present work we simulate a 10-turn water-copper PHP by considering the flow pattern inside the PHP and heat transfer for these three orientations. In other words, we compare the functioning of PHP under the Earth gravity influence (for 90 • and -90 • ) and in microgravity (within the present simulation, equivalent to 0 • ).

The principles of PHP simulation have been established by [START_REF] Shafii | Thermal modeling of unlooped and looped pulsating heat pipes[END_REF]. Because of the non-stationary functioning that involves multiple vapor liquid interfaces, the 3D or even 2D direct numerical simulation are too costly; 1D modeling appears to be an only viable choice to make the parametric investigation. The simulation techniques has been recently reviewed in detail by [START_REF] Nikolayev | Pulsating heat pipes: Basics of functioning and numerical modeling[END_REF]. To our knowledge, the orientation effect has been studied by simulation only by [START_REF] Mameli | Numerical investigation of the effects of orientation and gravity in a closed loop pulsating heat pipe[END_REF]. However their study used the code of [START_REF] Holley | Analysis of pulsating heat pipe with capillary wick and varying channel diameter[END_REF] who for some reason used an incorrect vapor energy equation (the initial approach of [START_REF] Shafii | Thermal modeling of unlooped and looped pulsating heat pipes[END_REF] was entirely correct), see [START_REF] Nikolayev | Pulsating heat pipes: Basics of functioning and numerical modeling[END_REF] for the discussion.

We present here the simulation results obtained with CASCO (French abbreviation of Code Avancé de Simulation de Caloduc Oscillant: Advanced PHP Simula- tion Code, cf. Fig. 1). It is the 1D simulation in-house software [START_REF] Nikolayev | A dynamic film model of the pulsating heat pipe[END_REF]. The plug flow regime (most commonly observed in PHP) can be simulated. Thin liquid films deposited by the receding liquid menisci on the internal tube walls are assumed to be of fixed thickness (cf. Table 1). This is a "minimal" model adopted in many previous simulation approaches (including those cited above). The film thickness value depends on the velocity of the receding meniscus (cf. [START_REF] Nikolayev | Oscillatory instability of the gas-liquid meniscus in a capillary under the imposed temperature difference[END_REF] for the discussion). The characteristic meniscus velocity adopted here is 0.7 m/s, which is an average value that we observe in our simulations. The film thickness is kept fixed for all simulation runs presented here to exclude the thickness effect on the results. Unlike older approaches, the liquid films around bubbles have a varying length defined by meniscus motion and film evaporation dynamics [START_REF] Nekrashevych | Effect of tube heat conduction on the pulsating heat pipe start-up[END_REF].

Similarly to previous simulation approaches, the gravity is assumed to be constant along each branch; its variation along the curved parts is neglected while the additional pressure drop in the curved parts has been accounted for. In the present simulation, the vapor phase model of [START_REF] Nikolayev | Vapor thermodynamics and fluid merit for pulsating heat pipe[END_REF] is used. More details about the simulation model were described previously by [START_REF] Nekrashevych | Effect of tube heat conduction on the pulsating heat pipe start-up[END_REF].

Oscillation startup at different orientations

The thermal boundary conditions chosen for the simulation are the imposed heat power per unit length of the tube in evaporator (which mimics e.g. the heating with electric isolated wires wound around the tube) and fixed temperature T c on the internal tube walls in the condenser. The feedback section (vertical in Figs. 1) is assumed to situate in the middle of the condenser section and inside the condenser block. Since there is no thermal spreader in the evaporator, thermal coupling between the PHP turns is absent there. Such a design is not practical for applications because the dryout in one turn can cause the overall PHP dryout. However this design reveals the local thermal coupling between the tube wall and the fluid. The total evaporator power P e and other PHP material and working fluid properties used in simulation are shown in Table 1.

Initially (at t = 0 s), the whole PHP is isothermal at T c . Between 10 and 20 liquid plugs of the same length are distributed uniformly throughout the PHP tube. The start-up scenario depends on the PHP orientation. As previously discussed [START_REF] Nekrashevych | Effect of tube heat conduction on the pulsating heat pipe start-up[END_REF], because of expansion of the vapor bubbles initially located in the evaporator, all the bubbles outside evaporator are compressed and disappear by condensation. This occurs for all orientations, typically in less than a second after the P e switching. After this, the plug distribution is the same for different orientations, see Figs. 1a,1c. For this reason, further PHP evolution is almost independent on the initial liquid phase distri-bution. We checked this by varying the initial number of plugs and adding/removing liquid films between them.

The distribution of different fluid phases (liquid plugs, liquid films and dry areas) in the evaporator are considered below for each orientation. The distribution of a particular phase can be characterized by an averaged over evaporator length fraction F . One distinguishes the fraction covered by the liquid plugs F l , liquid films F f and dry area F d (Figs. 2); at each time moment

F l + F f + F d = 1.
In the -90 • (unfavorable) case, all the liquid gathers in the condenser during the first second as discussed above (Fig. 1a). The plug fraction F l drops to zero, see Fig. 2a. The film edges recede (F f decreases while F d increases) and the vapor pressure grows due to the film evaporation. The vapor pressure becomes so high that the plugs lose their ability to penetrate into the evaporator. This causes entire evaporator (and partially adiabatic zone) overheating, and the oscillatory motion ceases at about t = 2 s for the case of P e = 200 W (cf.

-90 • curve in Fig. 3a). The averaged over evaporator tube temperature T e grows. However, this is not a dryout state as the film edges keep receding, which signifies their evaporation; it is just the PHP stopover. At some point (which typically coincides with the disappearance of the film adjacent to the closest to evaporator liquid meniscus), the menisci suddenly begin to oscillate with the increasingly large amplitude (this occurs at t 12 s, cf. -90 • curve in Fig. 3a) until one of them penetrates into the evaporator so F l rises. One or several vapor bubbles nucleate and grow inside the fluid. This bubble growth causes a displacement of neighboring liquid plugs to other hot evaporator sections, so bubbles can be nucleated there. As a result, the whole PHP startsup within a fraction of a second and T e sharply drops.

For the 90 • (favorable) orientation (Fig. 1c), all the liquid first gathers in the evaporator but the bubbles nucleated there soon expel the liquid into the condenser in spite of the gravity force. The phase distribution becomes the same as in the -90 • case (Fig. 1a). Being hydrostatically unstable, this configuration is destabilized much sooner than in the -90 • case where it is stable. The liquid plugs penetrate into the evaporator at t 4 s for P e = 200 W, cf. Fig. 2c. Bubble nucleation begins and the stationary oscillations start-up. Figures 3 show that the functioning becomes stable in 90 • case much earlier than in the -90 • case.

For the 0 • orientation, in the beginning of evolution, some bubbles (among those situating in the evaporator) begin to expand at the expense of the others. The plugs are large so their inertia is strong. The smaller bubbles (even those situating in the evaporator) compressed during the plug motion. They cannot stop the plug motion and finally disappear, i.e. the liquid plugs coalesce. This means that thee plugs become longer; their inertia becomes even larger, which causes further disappearance of small bubbles. As a result, several long liquid plugs (longer than one PHP branch) form during first several seconds so the evaporator sections of some turns are completely covered by liquid (Fig. 1b). Vigorous oscillations appear when the superheating of tube walls in the evaporator section become high enough to overcome the nucleation barrier.

3 PHP stable operation at different orientations [START_REF] Karthikeyan | Infrared thermography of a pulsating heat pipe: Flow regimes and multiple steady states[END_REF] described the regimes of stable operation which are observed experimentally in the PHP: continuous oscillations, intermittent or stopover regime and dryout. Our simulations also produce these regimes. Let us continue the description of the -90 • case for P e = 200 W. The initial startup that occurs at t 12 s is short-lasting and stops at t 14 s. The liquid films deposited by the receding plug menisci slowly (with respect to the system dynamics during the initial oscillation burst) evaporate; F f remains to be nonzero for a much longer time than F l , cf. Figs. 2a,3a. The evaporator temperature keeps rising because F f is not large enough to provide efficient evaporator cooling. The system is thus again in the stopover configuration that lasts during the film drying. This second stopover is similar to the first stopover discussed in sec. 2. At t 21 s, a new oscillation burst occurs and T e drops sharply again. Then another stopover follows. The stopovers and oscillation bursts (that correspond to the sharp T e drops in Fig. 3a) alternate but their duration is irregular. This is a signature of the intermittency well known from the theory of dynamical chaos [START_REF] Ott | Chaos in Dynamical Systems[END_REF]. Such a process finally leads to a stable regime (Fig. 3b) where the temperature T e oscillates around an average value T e . This regime can be seen in Fig. 4a where the heat exchanged with the evaporator section is analyzed. The total power Qe transferred from the evaporator can be divided into three distinctive parts: the latent heat Qlat e associated with the phase change at the surface of the liquid films and plug menisci, the heat Qsens e received by the fluid via the sensible heat transfer and the heat conducted via the tube. The latter is not represented separately in Figs. 4 but can be deduced from them by subtraction of two other contributions from Qe . The sensible heat exchange appears mostly due to the thermal interaction of the liquid plugs with the tube walls appearing during the oscillating motion inside the PHP. Another part of the sensible heat exchange (the vapor phase heat exchange with the walls appearing within the dry areas) that has been accounted for is much smaller.

The stopovers can be clearly seen in Fig. 4a because during them both Qlat e and Qsens e drop sharply and the heat is transferred only through the tube walls; the wall contribution to Qe slightly grows in time because during the stopovers T e grows (cf. Fig. 3a). During the oscillation bursts, the instantaneous heat exchange is extremely strong and can be an order of value larger than P e . The heat is transferred mainly as the latent heat; the sensible contribution is negligibly small because of the rare and brief residence of the liquid plugs in the evaporator. This can be seen from a very low average value of F l , see Table 2. The predominance of the latent heat transfer (see Table 2) discussed earlier by [START_REF] Nikolayev | A dynamic film model of the pulsating heat pipe[END_REF] imentally by [START_REF] Jo | Experimental investigations of heat transfer mechanisms of a pulsating heat pipe[END_REF] who measured experimentally its relative value situating between 0.66 and 0.74 for the 90 • case. A regime that can be characterized as intermediate between intermittent and continuous oscillations occurs for P e ≥ 180 W in the horizontal (0 • ) orien-tation. It develops after an initial transient, where a long stopover typically occurs (15 s< t < 20 s for P e = 200 W, cf. Fig. 3a). Such a regime shows very short (one or several seconds) and rare complete stopovers. The stable regime is achieved after first 30 s (cf. the 0 • curve in Fig. 3a; see the curve in Fig. 7 below corresponding to ∆t = 10 -5 s for the long time evolution). In spite of almost continuous motion, the liquid plugs situate in the condenser and adiabatic sections most of the time. Their excursions to the evaporator are short-lasting so F l is of the order of several percent (Fig. 2b). This value is intermediate between the respective values for intermittent (Fig. 2a) and continuous oscillations (Fig. 2c) regimes.

When one performs the simulations for larger and larger power P e , the stopover periods become longer and longer until the oscillation bursts do not occur any more. Such a situation corresponds to the dryout.

When P e < 100 W at the same horizontal orientation (0 • ), the continuous oscillation regime is observed. The PHP then behaves exactly like in vertical favorable orientation (90 • ). This can be seen in Fig. 5 where we present the dependence of the thermal resistance calculated as

R th = T e -T c P e (1)
on P e . The data for 0 • and 90 • coincide in this region.

The continuous oscillation regime occurs almost in the whole P e range in the 90 • case. The evaporator cooling in continuous oscillation regime is more efficient than in the intermittent regime: R th values are lower in qualitative agreement with experimental results of [START_REF] Lips | Experimental evidences of distinct heat transfer regimes in pulsating heat pipes (PHP)[END_REF]. This is explained by a much more frequent and durable residence of the liquid plugs (cf. Table 2) in the evaporator. The moving plugs deposit the liquid films that provide the efficient heat transfer. In addition, when the plugs situate within the evaporator, the bubble generation occurs inside the plugs. The bubbles escape quickly from the evaporator and their condensation occurs in the adiabatic section and condenser. Therefore, a permanent presence of the liquid plugs in the evaporator is a necessary condition for a good PHP performance. Accordingly to the frequent liquid plug presence in the evaporator, the sensible heat exchange (Fig. 4c) can in this regime be comparable to the latent heat exchange. The behavior of the thermal resistance with the heat load (Fig. 5) is similar to the experimental observations of [START_REF] Lips | Experimental evidences of distinct heat transfer regimes in pulsating heat pipes (PHP)[END_REF]; [START_REF] Mangini | A pulsating heat pipe for space applications: Ground and microgravity experiments[END_REF]. The curves for both vertical orientations are monotonously decreasing. The quantitative agreement is not bad either, at least the order of value is similar. This is satisfactory (the PHP structures are not the same). The curve for 0 • is non monotonous. As mentioned above, it nearly coincides with the 90 • curve at low P e (where the oscillations are continuous) and is thus decreasing too. At high P e , R th is nearly constant and the oscillations are intermittent. There is a transition region at 100 W< P e < 180 W where the system is sensible to small change in simulation parameters. It should be recalled at this point that the system is chaotic, which means that a very small change in any parameter like initial condition or numerical precision (related e.g. to different processor models) results in different instantaneous values at a given t. However the simulation model is robust, which means that the average values of simulated variables are independent of these small changes. The situation is however different in the transition region where there is some data scatter shown in Fig. 5.

Simulation reliability

The heat and mass conservation in the system is important to be satisfied throughout the simulation. In any stable regime, the average heat power transferred from the evaporator should be equal to the amount received by the liquid: on average, there is no heat accumulation both in the tube wall and in the fluid. The sum Qe of all the contributions (latent and sensible heat transfer through the fluid and the solid) should be equal to the input power P e , see Fig. 4. Since the oscillations are chaotic, a small error always appears in the summation. We verified that this error does not exceed at most one percent for the simulated time t = 5 min.

The total fluid mass that consists of the mass of the liquid plugs, liquid films, and the vapor should ideally be conserved throughout the simulation. However, a small deviation always exists. The most evident reason is the overlap of the film edges and the menisci during their coalescence. Such an overlap appears because of the numerical error associated with the finiteness of the time step. The plug coalescence (i.e. bubble deletion) events are frequent, their number can be as large as 10 6 during a run. The numerical algorithms used in CASCO were carefully worked out to minimize the mass deviation. In a typical continuous oscillation regime run, where the number of generated and deleted bubbles is of the order of 10 3 , the relative mass deviation is smaller than 10 -4 . A case of high thermal load where the regime is intermittent and the total number of the processed bubbles is about 10 5 is shown in Fig. 6. Another important issue concerns the grid and time step independence of the results. It has been verified that the frequency of the liquid plug spatial remeshing applied during the simulation does not impact the results. The influence of the time step is shown in Fig. 7 for the "worst" case of the intermittent regime that exhibits strong chaotic fluctuations. One can see that a change of the time step as large as ten times does not have a strong impact on the long-time T e average value after the start-up.

To give an idea about the CASCO efficiency, a typical simulation of 300 s of the PHP functioning takes about 8 hours on an Intel Core i7 based computer for ∆t = 10 -5 s and 1 hour for ∆t = 10 -4 s.

Conclusions

The 10-turn copper-water PHP with separately heated turns has been simulated for three different orientations with respect to gravity and for different power inputs. The CASCO software is capable of long-time reliable simulations with a reasonably small required computer resources and good numerical stability. In the vertical favorable orientation (evaporator below condenser) the continuous oscillations were observed for all heat loads. In the horizontal position, continuous oscillations occur until a threshold power, then a transition to the intermittent (stopover) regime was encountered. In the vertical unfavorable orientation (condenser below evaporator) the intermittent oscillations occur for all powers. The PHP dryout is observed for each regime when the heat load exceeds a threshold. The thermal resistance is obtained as a function of heat load. The obtained change of the thermal resistance with the heat load corresponds at least qualitatively to the experimentally obtained curves. The order of value of the resistance is similar to the experimental measurements. More detailed quantitative comparisons are necessary to tune the simulation parameters.

Our analysis shows that the difference in PHP performance at different orientations is linked to the difference in the phase distribution inside the PHP evaporator.

The contribution of the phase change to the overall heat exchange in the PHP is large in all the oscillation regimes. The relative contribution of the latent and sensible heat transfer rates controlled by the presence of the liquid plugs and liquid films inside the evaporator. The average fractions of evaporator sections covered by these phases are different at each PHP orientation. When PHP works efficiently (vertical favorable orientation and horizontal at small heat loads), the major part of the transferred heat is the latent heat. This agrees with recent experimental data. The sensible heat exchange through the fluid is usually larger than that through the tube walls. In the intermittent oscillation regime (vertical unfavorable and horizontal for large heat loads), the fluid sensible contribution is very low.

Acknowledgment

The financial contribution of ESA within MAP INWIP is acknowledged. This work has been presented during the joint 19th International Heat Pipe Conference and 13th International Heat Pipe Symposium, Pisa, Italy (2018).

Fig. 1 :

 1 Fig. 1: Start-up phase distribution for P e = 200 W and t = 3 s pictured by the CASCO software for different orientations: (a) -90 • , (b) 0 • , and (c) 90 • . The direction of gravity is shown by arrow for two vertical orientations. The round turns are not represented for simplicity; black lines are simply connectors linking the equivalent points of neighboring branches. Thin liquid films (in violet) cover the internal tube walls inside the vapor bubbles, except of the dry areas (white), see the image (b). The liquid plugs are blue. The tube wall temperature is shown with color varying from blue to red, which corresponds to 22 • -40 • C interval. The notations for the PHP sizes are shown in the image (b).

Fig. 2 :

 2 Fig. 2: Evaporator coverage by liquid plug, liquid film and dry area during the first 50 s of functioning at different PHP orientations for P e = 200 W.

Fig. 3 :Fig. 4 :

 34 Fig. 3: Evaporator temperature evolution for P e = 200 W. (a) Short-time curves (during the first 50 s of functioning) for different PHP orientations and (b) Long time evolution for -90 • case. The dashed line shows the average temperature T e 109 • C for the stable intermittent regime.

  The PHP thermal resistance as a function of P e at different orientations. Triangles show the -90 • data, circles, 0 • and squares, 90 • . The lines are the eye guides.

Fig. 6 :

 6 Fig.6: The relative mass deviation from the initial value for the liquid plugs, liquid films, and the total fluid mass during the simulation for 0 • and P e = 400 W.

Fig. 7 :

 7 Fig. 7: T e evolution calculated with two different time steps for 0 • and P e = 200 W.

Table 1 :

 1 Parameters used for the simulation.

	Length of one evaporator tube section Le = 126 mm
	Length of adiabatic section	La = 126 mm
	Length of one condenser tube section	Lc = 110 mm
	Number of turns	Nturns = 10
	Feedback section length	L f b = 130 mm
	Filling ratio	φ = 0.5
	Inner diameter	d = 1.4 mm
	Outer diameter	3.2 mm
	Condenser temperature	Tc = 22 • C
	Working fluid	Water
	Tube material	Copper
	Time step	∆t = 0.01 ms
	Tube mesh size	2 mm
	Film thickness	20 µm
	Bubble deletion threshold	L thr = 10 µm
	Nucleated bubble length

L nucl = 100 µm Nucleation barrier ∆T nucl = 15 • C

Table 2 :

 2 Relative contributions of average latent and sensible heat transfer (normalized by P e ) and of coverage fractions of evaporator by different phases for different PHP orientations at P e = 200 W.

		Qlat e	Qsens e	F f	F l	F d
	-90 •	0.73	0.02	0.14 0.01 0.85
	0 •	0.80	0.02	0.24 0.04 0.72
	90 •	0.73	0.17	0.42 0.37 0.21


M M Klak

G Zatryb

L W Golacki

P Benzo

C Labbé

J Cardin

J Misiewicz

F Gourbilleau

A Podhorodecki
email: artur.p.podhorodecki@pwr.edu.pl

Influence of rapid thermal annealing temperature on the photoluminescence of Tb ions embedded in silicon nitride films

Keywords:

In this work, silicon nitride films containing terbium were deposited by reactive magnetron co-sputtering in a nitrogen enriched plasma and subjected to rapid thermal annealing treatments. The influence of annealing temperature on the emission and absorption properties of these films was investigated by photoluminescence, photoluminescence decay and photoluminescence excitation measurements. An increase in the photoluminescence intensity and photoluminescence decay time was observed upon annealing for the main 5 D 4 -7 F 5 transition of Tb 3+ ions. This observation was attributed to decrease of the non-radiative recombination and increase of the number of excited Tb 3+ ions upon annealing. Moreover, high temperature annealing was found to shift the spectral position of absorption bands observed in the photoluminescence excitation spectra. In general, these excitation spectra were shown to have a rather complicated structure and were decomposed into three Gaussian bands. It was suggested that two of these excitation bands might be due to indirect excitation of Tb 3+ ions via defects and the third excitation band could be due to direct 4f-5d transition.

Introduction

Silicon nitride films have been extensively studied in recent years as a promising material for a wide variety of applications in the microelectronic industry, including use as the gate dielectric in field effect and thin film transistors [START_REF] Tsai | Approaching defect-free amorphous silicon nitride by plasma-assisted atomic beam deposition for high performance gate dielectric[END_REF], an important antireflection coating layer for crystalline silicon solar cells [START_REF] Dumont | SiNx:Tb3+--Yb3+, an Efficient Down-conversion Layer Compatible With a Silicon Solar Cell Process[END_REF], a charge storage layer in MNOS non-volatile memories [START_REF] Gritsenko | Nature of traps responsible for the memory effect in silicon nitride[END_REF] and as an active material for light emitting diodes (LEDs) [START_REF] Museur | Photoluminescence and electronic transitions in cubic silicon nitride[END_REF]. Research on this material has been additionally stimulated by its full compatibility with Si-based transistor technology, which could lead to easy integration with various microelectronic devices. Among Si-based films designated for application in light sources, rare earth (RE) doped SiN x structures have received considerable attention, owing to the interesting optical properties of rare earth elements. Up to now, most research in this field has focused on Er, Nd and Yb doped SiN x films [START_REF] Dumont | SiNx:Tb3+--Yb3+, an Efficient Down-conversion Layer Compatible With a Silicon Solar Cell Process[END_REF][START_REF] Zanatta | Visible photoluminescence from Er3+ ions in a-SiN alloys[END_REF][START_REF] Ribeiro | Spectroscopic study of Nd-doped amorphous SiN films[END_REF][START_REF] Yuan | Photoluminescence of Tb3+-doped SiNx films with different Si concentrations[END_REF], obtained either by plasma-enhanced chemical vapor deposition (PECVD) or sputtering. For these dopants, efficient near-infrared photoluminescence and electroluminescence have been demonstrated, which is important for telecommunication. Considerably less attention has been paid to other RE dopants, such as Tb, showing emission in the visible range, which is interesting from the point of view of applications in color LEDs and (when co-doped with Yb) frequency conversion layers for silicon solar cells [START_REF] Dumont | SiNx:Tb3+--Yb3+, an Efficient Down-conversion Layer Compatible With a Silicon Solar Cell Process[END_REF].

The previous studies of Tb-doped SiN x thin films focused primarily on the influence of film stoichiometry on the Tb photoluminescence intensity [START_REF] Yuan | Photoluminescence of Tb3+-doped SiNx films with different Si concentrations[END_REF][START_REF] Yuan | Photoluminescence of Tb3+ doped SiNx films grown by plasma-enhanced chemical vapor deposition[END_REF]. In these studies, after deposition films were annealed at high temperatures in conventional furnaces what probably caused their non-intentional oxidation, confirmed by infrared absorption measurements. It is noteworthy that such contamination of Tb:SiN x films with oxygen can influence optical properties of Tb 3+ ions, giving rise to a more ionic chemical environment. When analysed from this perspective, it is interesting and important to study non-contaminated Tb:SiN x films and to test alternative annealing techniques, such as rapid thermal annealing. Moreover, to our knowledge, no systematic experimental study exists which investigates the influence of annealing temperature on the non-radiative recombination of Tb 3+ ions embedded in SiN x matrix. Furthermore, while the previous studies emphasized the importance of host-mediated excitation of Tb 3+ ions in SiN x matrix [START_REF] Guerra | Thermal activation and temperature dependent PL and CL of Tb doped amorphous AlN and SiN thin films[END_REF], there are still many open questions regarding the actual excitation mechanism of Tb 3+ ions.

In this paper, we investigated the most efficient paths of optical excitation of Tb 3+ ions embedded in silicon nitride films deposited by reactive magnetron co-sputtering in a nitrogen enriched plasma. The deposited films were subjected to rapid thermal annealing treatments and the temperature allowing to obtain the strongest Tb 3+ emission intensity was determined. Finally, we discussed the physical mechanism responsible for the observed photoluminescence enhancement of Tb 3+ ions after high-temperature annealing.

Experimental details

The rare earth doped layers have been deposited by co-sputtering reactively a Si and Tb cathodes in a nitrogen-rich plasma. The films were grown on a 2" Si wafer heated at 200 °C and the nitrogen enriched atmosphere was achieved by injecting 8 sccm of Ar and 2 sccm of N in the deposition chamber. The plasma pressure was set at 3 mTorr and the RF power density applied on the Si target was fixed to 4.5 W.cm -2 while the optimized RF power density applied on the Tb target was 0.45 W.cm -2 . All the deposited layers had a thickness of about 90 nm to avoid any interference effects in the emission spectrum. After deposition, the samples were subjected to rapid thermal annealing (RTA) treatment at different annealing temperatures (T A ), ranging from 600 °C to 1100 °C during 10 min. The composition of the thin layers has been determined by means of RBS measurements as described elsewhere [START_REF] Dumont | SiNx:Tb3+--Yb3+, an Efficient Down-conversion Layer Compatible With a Silicon Solar Cell Process[END_REF]. All the Tb:SiN x films were found to contain 42.3 at. % of Si, 56.3 at. % of N and 1.4 at. % of Tb. In other words, the chemical composition of films investigated in this study is very close to stoichiometric Si 3 N 4 and no oxygen contamination was clearly visible in RBS measurements for the as-deposited films. Nevertheless, since the relative error in determined N concentration is around 6%, a small amount of oxygen contamination cannot be excluded.

The Fourier-transform infrared (FTIR) absorbance spectra were collected using a Nicolet iS10 spectrometer (Thermo Fisher Scientific Instruments). These measurements were conducted in attenuated total reflectance mode (ATR) using a VariGATR accessory with germanium crystal (Harrick Scientific) at an angle of incidence set to 65°. The measured spectra were not corrected for the typical ATR effects e.g. the effect of anomalous dispersion in the vicinity of an absorption peak. For this reason, the ATR absorption peaks may be slightly shifted from their corresponding locations in a transmission spectrum. Here, it is also worth to mention that since the investigated thin films were deposited on Si substrate, our germanium ATR accessory allows to significantly enhance the FTIR signal intensity [START_REF] Milosevic | Single-reflection attenuated total reflection of organic monolayers on silicon[END_REF] and should be sensitive to effects such as superficial film oxidation.

Finally, the optical properties of investigated samples were determined by means of photoluminescence (PL), photoluminescence excitation (PLE) and PL decay measurements, conducted at room temperature. For both PL and PLE measurements, the signal emitted from the sample was collected and detected by a Si CCD camera (HR4000 Ocean Optics). For PLE experiments, a continuous wave (cw) xenon lamp connected to a monochromator (Jobin Yvon TRIAX 180) was used as the tunable excitation source. For such measurements, the recorded signal was corrected for the xenon lamp spectral intensity profile. For PL decay measurements, a pulsed excitation line (λ EXC = 266 nm, repetition rate 100 Hz) of an actively Q-switched diode pumped solid state laser (Elforlight Ltd) was used, together with a multichannel detection system equipped with a monochromator and a PMT detector. The detection wavelength (λ EM ) was set to λ EM = 545 nm. The time resolution in all PL decay measurements presented in this study was better than 1 μs. Finally, in the case of cw-PL measurements, the same laser was used for excitation, but the repetition rate was increased to 40 kHz which allowed to operate in quasi-continuous excitation regime.

Results and discussion

Fig. 1 shows FTIR absorbance spectra of (a) Tb:SiN x sample annealed at 1100 °C measured shortly after deposition (b) the same Tb:SiN x sample after storage in ambient atmosphere for one year and (c) reference SiO x N y sample annealed at 1000 °C and containing 22.42 at. % Si, 13.410 at. % N and 41.120 at. % O (this sample is shown for reference purposes only and it was deposited by Plasma Enhanced Chemical Vapor Deposition method as described elsewhere [START_REF] Ramírez | On the photoluminescence of as-deposited Tb-doped silicon oxides and oxynitrides fabricated by ECR-PECVD[END_REF]), as determined by RBS measurements. It should be underlined that spectra (b) and (c) are used only for the purpose of FTIR absorbance discussion and the emission properties of these samples are not the subject of this article. It can be seen in Fig. 1 that in the case of spectrum (a) of Tb:SiN x sample, only one peak can be seen at around 803 cm -1 , which is assigned to Si-N asymmetric stretching mode [START_REF] Scardera | Fourier transform infrared spectroscopy of annealed silicon-rich silicon nitride thin films[END_REF][START_REF] Debieu | Structural and optical characterization of pure Si-rich nitride thin films[END_REF]. When the annealing temperature increases from 600 to 1100 °C, this peak shifts only slightly, from 799 cm -1 to 803 cm -1 , indicating a weak bond rearrangement. The broad and asymmetric peak shape is characteristic to silicon nitride and is consistent with reported results for this material [START_REF] Scardera | Fourier transform infrared spectroscopy of annealed silicon-rich silicon nitride thin films[END_REF][START_REF] Lattemann | Investigation and characterisation of silicon nitride and silicon carbide thin films[END_REF]. Due to the fact that after deposition our samples were stored in ambient atmosphere, it should be noted that Si-O bending mode (796 cm -1 ) could be superimposed on the Si-N asymmetric stretching mode. Nevertheless, there is no clear signature of the Si-O asymmetric stretching mode at 1058 cm -1 in spectrum (a). This suggests that high temperature annealing did not result in film oxidation, as reported in some other studies [START_REF] Yuan | Photoluminescence of Tb3+-doped SiNx films with different Si concentrations[END_REF][START_REF] Yuan | Photoluminescence of Tb3+ doped SiNx films grown by plasma-enhanced chemical vapor deposition[END_REF]. For comparison, the effect of oxidation is clearly seen in spectrum (b), obtained for the same Tb:SiN x sample stored in ambient atmosphere for one year. As can be seen, spectrum (b) is far different from spectrum (a): for spectrum (b) two separate peaks can be distinguished at 803 cm -1 , assigned to Si-O bending mode, and at 862 cm -1 , assigned to Si-N asymmetric stretching mode. Such assignment can be confirmed when looking at spectrum (c) measured for Si x O y N z film. It can be seen that for this silicon oxynitride film there are three distinguishable peaks assigned to Si-O asymmetric stretching mode (1058 cm -1 ), Si-O bending mode (796 cm -1 ) and Si-N asymmetric stretching mode at 950 cm -1 . Moreover, as can be seen in Fig. 1, the position of Si-N asymmetric stretching mode shifts significantly towards higher wavenumbers when oxygen amount in the silicon-nitride films increases. This observation is consistent with the previous reports stating that Si-N vibrational modes can be found between 490 and 1020 cm -1 [START_REF] Giorgis | Optical, structural and electrical properties of device-quality hydrogenated amorphous silicon-nitrogen films deposited by plasma-enhanced chemical vapour deposition[END_REF] and their position depends on the oxygen content [START_REF] Zhou | Comparative investigation of infrared optical absorption properties of silicon oxide, oxynitride and nitride films[END_REF]. Indeed, the dotted arrow drawn on the Fig. 1 shows that Si-N related peak can be shifted from 803 cm -1 to 950 cm -1 . Additionally, there is no detectable Si-O asymmetric stretching mode in the spectrum (a) of Tb:SiN x samples. As demonstrated in spectrum (b) in Fig. 1, our ATR-FTIR measurement technique is sensitive to superficial oxidation of silicon nitride films. Nevertheless, such oxidation has not been clearly detected in any spectra of the samples investigated in this study. Together with RBS data, this result indicates that if there is any oxygen present in the investigated films, its concentration is very low. This is in contrast to some other studies [START_REF] Yuan | Photoluminescence of Tb3+-doped SiNx films with different Si concentrations[END_REF][START_REF] Yuan | Photoluminescence of Tb3+ doped SiNx films grown by plasma-enhanced chemical vapor deposition[END_REF] where strong signature of Si-O bonds was observed in FTIR spectra of Tb:SiN x films, most probably as a result of superficial oxidation that took place as soon as the samples were removed at high temperature from the conventional furnace.

Fig. 2 shows a PL spectrum of Tb:SiN x film annealed at 1000 °C. Four main PL bands can be seen that originate from radiative transitions within the 4f shell of Tb 3+ ions. The observed transitions are 5 D 4 → 7 F 6 (490 nm), 5 D 4 → 7 F 5 (545 nm), 5 D 4 → 7 F 4 (589 nm) and 5 D 4 → 7 F 3 (623 nm) [START_REF] Zatryb | Optical properties of Tb and Eu doped cubic YAlO3 phosphors synthesized by sol-gel method[END_REF]. The same emission bands were identified also for samples annealed at other temperatures (not shown here). These transitions and their spectral positions are very similar to the emission lines of Tb 3+ ions embedded in silicon oxide [START_REF] Podhorodecki | Green light emission from terbium doped silicon rich silicon oxide films obtained by plasma enhanced chemical vapor deposition[END_REF], silicon oxynitride [START_REF] Ramírez | Amorphous sub-nanometre Tb-doped SiO x N y /SiO 2 superlattices for optoelectronics[END_REF][START_REF] An | Highly efficient infrared quantum cutting in Tb 3+ -Yb 3+ codoped silicon oxynitride for solar cell applications[END_REF], or silicon carbide films [START_REF] Guerra | Effect of thermal annealing treatments on the optical activation of Tb 3+ -doped amorphous SiC:H thin films[END_REF] and their overall shape does not change after annealing. Finally, it should be underlined that measured PL spectra did not show any signature of the broad matrix-related PL which has been reported by other authors for undoped SiN x films [START_REF] Debieu | Structural and optical characterization of pure Si-rich nitride thin films[END_REF][START_REF] Deshpande | Optical properties of silicon nitride films deposited by hot filament chemical vapor deposition[END_REF]. Recently, such matrix-related PL on Tb 3+ emission lines has been reported by Guerra et al. [START_REF] Guerra | Thermal activation and temperature dependent PL and CL of Tb doped amorphous AlN and SiN thin films[END_REF], but it was detectable only at low measurement temperatures (≤250 K) and for 488 nm excitation wavelength, which is almost resonant with 5 D 4 level of Tb 3+ ions. It is noteworthy that this broad emission band was assigned to different radiative defects present in SiN x matrix. According to Guerra et al. these defects can transfer the excitation energy to nearby Tb 3+ ions and such process is phonon-mediated. Since at low temperatures the population of phonons decreases, the efficiency of excitation transfer also drops and emission from defects becomes visible.

Next, to study Tb 3+ emission properties in more details, measurements of photoluminescence decay were conducted for each sample. An example of such PL decay, measured for the most intense 5 D 4 → 7 F 5 PL band (λ EM = 545 nm), has been shown in the inset of Fig. 2 for the sample annealed at 1000 °C. In general, all measured PL decays were slightly non-single-exponential and were fitted with double-exponential decay function I PL (t) = A 1 exp(-t/τ 1 ) + A 2 exp(-t/τ 2 ), where I PL (t) denotes total PL intensity at time t, τ 1 and τ 2 are PL lifetimes and A 1 , A 2 are contributing intensity amplitudes. It should be noted that fitting of these PL decays with a single-exponential decay function I PL (t) = Aexp (-t/τ PL ) was also possible but resulted in somewhat lower fit quality at the end of the decay curves. While the obtained PL lifetimes are discussed later, here, it should be underlined that the model selection does not affect any of our later conclusions. Finally, it is worth to mention that similar non-single-exponential shape of PL decay has been also reported for the emission of Yb 3+ ions embedded in Tb:Yb:SiN x films [START_REF] Dumont | SiNx:Tb3+--Yb3+, an Efficient Down-conversion Layer Compatible With a Silicon Solar Cell Process[END_REF] or for Al-Tb:SiO 2 multilayers [START_REF] Blázquez | Structural and optical properties of Al-Tb/SiO2 multilayers fabricated by electron beam evaporation[END_REF]. Unfortunately, we failed to find any reports on the PL decay of Tb 3+ ions in SiN x films. Nevertheless, the slightly non-single-exponential character of the PL decay is not unusual and is probably caused by the presence of Tb 3+ ions at several different sites in the SiN x matrix.

To study the effect of annealing on the Tb 3+ PL intensity, the most intense 5 D 4 → 7 F 5 band was chosen to represent the emission of Tb 3+ ions. For this band, the integrated emission intensity is shown in Fig. 3(a) as a function of annealing temperature. It can be seen that in general annealing treatment results in an increase in the Tb 3+ PL intensity by up to a factor of 2.0. It should be noted that similar increase in the Tb 3+ emission intensity after annealing was reported in an earlier study [START_REF] Guerra | Thermal activation and temperature dependent PL and CL of Tb doped amorphous AlN and SiN thin films[END_REF], but without mentioning what was the actual composition of Tb:SiN x films, what makes quantitative comparison difficult. Nevertheless, these results allow us to suspect that the observed temperature tendencies are rather general for Tb 3+ ions embedded in SiN x , and that the optimal annealing temperature is around 900 °C because above this temperature PL intensity does not change significantly. Nevertheless, it should be pointed out that the optimal annealing temperature can be different if the annealing conditions change or Tb concentration is different. As shown by Guerra et al. [START_REF] Guerra | Effect of thermal annealing treatments on the optical activation of Tb 3+ -doped amorphous SiC:H thin films[END_REF] the annealing of Tb-doped thin films is a rather complicated issue and depends on many factors.

To study these annealing effects in more detail, the average PL decay times 〈τ PL 〉 were calculated for each sample. As it was mentioned before, PL decays were fitted with double-exponential function and for this reason the average PL lifetime has been defined as 〈τ PL 〉 = (A 1 τ 1 + A 2 τ 2 )/(A 1 + A 2 ) [START_REF] Sillen | The correct use of average fluorescence parameters[END_REF]. Here, it is worth mentioning that for a given PL decay the maximum difference between 〈τ PL 〉 and 〈τ PL 〉 calculated from the fit with single-exponential decay function does not exceed 2%. For this reason and to simplify further discussion, we do not assign any physical meaning to τ 1 and τ 2 separately. Nevertheless, we use the interpretation of the average PL lifetime, consistent with the general definition of average surviving time of an excitation. According to this definition, 〈τ PL 〉 is simply the average amount of time which Tb 3+ ions spend in their excited 5 D 4 states [START_REF] Lakowicz | Principles of Fluorescence Spectroscopy[END_REF]. For this reason, in the simplest case scenario, if there is a non-radiative recombination from 5 D 4 excited states of Tb 3+ ions (such as non-radiative energy transfer to some defect states, energy transfer between Tb 3+ ions [START_REF] Guerra | Effect of thermal annealing treatments on the optical activation of Tb 3+ -doped amorphous SiC:H thin films[END_REF][START_REF] Benz | Tuning the emission colour by manipulating terbium-terbium interactions: terbium doped aluminum nitride as an example system[END_REF] or multiphonon relaxation), 〈τ PL 〉 will become shorter. Strictly speaking, this behavior is expected only when a competition between radiative and non-radiative recombination is possible for 5 D 4 excited state. In other words, for 5 D 4 excited state, the rate of radiative recombination has to be comparable with the rate of nonradiative recombination. On the other hand, if the non-radiative recombination rate from 5 D 4 state is much higher than the radiative recombination rate, a fraction of Tb 3+ ions becomes non-luminescent (undetectable in PL measurements). In this case, 〈τ PL 〉 remains constant and a lowered PL intensity is observed.

Fig. 3(b) shows the average PL lifetimes as a function of annealing temperature. It can be seen that the average PL lifetime increases with temperature up to 850 °C and remains fairly constant at around 530 μs for higher temperatures. Such an increase is attributed to a reduction of non-radiative recombination from 5 D 4 -excited state and can partly explain the observed enhancement of the PL intensity in that temperature range. However, to first approximation, at low flux of excitation photons ϕ, the PL intensity I PL should increase proportionally to the PL lifetime [START_REF] Polman | Optical doping of waveguide materials by MeV Er implantation[END_REF]. In our case, the intensity increases by a factor of 2.0 upon annealing, while 〈τ PL 〉 increases only by a factor of 1.2. Taking into account that PL intensity I PL does not change proportionally to 〈τ PL 〉, it is reasonable to suspect that thermal annealing also increases the concentration of excited ions N Tb * , since

I PL = k R N Tb *
. The increase of N Tb * , could be due to many reasons. For example, annealing treatment could influence the concentration of optically active (available for excitation) ions, by inducing the necessary structural changes of SiN x matrix, providing the environment for the Tb atoms to be incorporated in their optically-active trivalent state (e.g. from over-or undercoordinated ions to Tb 3+ [START_REF] Guerra | Effect of thermal annealing treatments on the optical activation of Tb 3+ -doped amorphous SiC:H thin films[END_REF]). Such mechanism has been reported for Er-implanted semiconductors, where annealing treatment is necessary in order to obtain Er at an optically active site [START_REF] Michel | Impurity enhancement of the 1.54-μm Er3+luminescence in silicon[END_REF][START_REF] Tang | Characteristics of rare-earth element erbium implanted in silicon[END_REF]. Furthermore, if the excitation of Tb 3+ ions is indirect, annealing could be responsible for increase of the effective absorption cross-section of Tb 3+ ionsin such case, the concentration of optically active ions does not have to change, but the number of excited ions N Tb * should be larger due to more efficient excitation energy transfer from some donor states. Similar mechanism has been reported for Nd 3+ and Er 3+ ions embedded in SiO x matrices [START_REF] Kenyon | Broad-band and flashlamp pumping of 1.53 μm emission from erbium-doped silicon nanocrystals[END_REF][START_REF] Steveler | Low-temperature photoluminescence properties of Nd-doped silicon oxide thin films containing silicon nanocrystals[END_REF][START_REF] Podhorodecki | On the origin of emission and thermal quenching of SRSO:Er3+films grown by ECR-PECVD[END_REF]. Nevertheless, based on the obtained results it is not possible to determine which mechanism is responsible for the increased N Tb * in our case.

To investigate the excitation mechanism of Tb 3+ ions, we conducted PLE measurements by monitoring the intensity of main 5 D 4 → 7 F 5 emission band of Tb 3+ for different excitation wavelengths. The normalized PLE spectra measured for samples annealed at 600 and 1100 °C are shown in Fig. 4. Similar PLE spectra were obtained also for other samples. It can be seen that there are two distinct peaks in the PLE spectra of both samples, which shift to higher energies upon annealing. For both samples, the first peak appears above 4.5 eV, while the second peak appears below 4.5 eV. On closer inspection, it turns out that each PLE spectrum can be fitted with three Gaussians, what suggests presence of at least three different excitation bands of Tb 3+ ions. An example of such decomposition is shown in Fig. 4. For the purpose of further discussion, each Gaussian component was labeled as B1, B2 and

B3.

The decomposition of measured PLE spectra into three Gaussian components allows us to make several important observations. First, Fig. 5(a) shows the integrated intensities of bands B1, B2 and B3 as a function of the annealing temperature. It can be seen that in general, the integrated intensities are higher for annealed samples, except for the intensity of band B2 which first increases and then drops above 850 °C. More importantly, according to Fig. 5(a), band B3 almost completely dominates the PLE spectrum, being probably the most efficient excitation channel of Tb 3+ ions. As a matter of fact, for each annealing temperature, this broad band contains 61-64% of the total integrated PLE intensity.

The second important observation is that in general, the energy of each band maximum shifts upon annealing. As can be seen in Fig. 5(b), the peak position of band B1 and B2 significantly increases as a function of the annealing temperature while the peak position of band B3 increases only slightly up to T A = 800 °C and does not change above this temperature. It is important to underline that the tendency obtained for band B3 is clearly different from the tendencies obtained for band B1 and B2. In particular, the increase of peak energy is 143 meV (3.4%) and 174 meV (3.8%) for band B1 and B2, respectively, and only 68 meV (1.5%) for band B3. Clearly, the peak position of band B1 and B2 is more sensitive to the annealing temperature than the peak position of band B3. This result suggests that mechanism of excitation of Tb 3+ ions is similar in the case of bands B1 and B2 but different in the case of band B3.

Based on the obtained results, only a tentative explanation of the Tb 3+ ions excitation mechanism can be given. First, it is important to note that the PLE spectra of Tb 3+ ions (Fig. 4) show remarkable similarities to PLE spectra of pure silicon nitride films. For example, several broad excitation bands peaking at around 4.2, 4.4, 4.6 and 5.2 eV have been reported for undoped amorphous SiN x [START_REF] Gritsenko | Nature of traps responsible for the memory effect in silicon nitride[END_REF][START_REF] Deshpande | Optical properties of silicon nitride films deposited by hot filament chemical vapor deposition[END_REF] films and crystalline Si 3 N 4 [START_REF] Museur | Photoluminescence and electronic transitions in cubic silicon nitride[END_REF][START_REF] Zhang | Optical properties of singlecrystalline α-Si3N4 nanobelts[END_REF], showing that there are optically active states in silicon nitride which have energies in the range of efficient excitation of Tb 3+ ions. Moreover, as demonstrated by ab initio calculations [START_REF] Valentin | Ab initio study of transition levels for intrinsic defects in silicon nitride[END_REF], there are many defects in β-Si 3 N 4 with transition levels at 3.1, 3.4, 4.0, 4.5 and 4.6 eV. Similar optical transitions at 3.8-3.85, 4.19-4.27, 4.58 and 4.82 eV were reported for SiN x films [START_REF] Aozasa | Analysis of carrier traps in silicon nitride film with discharge current transient spectroscopy, photoluminescence, and electron spin resonance[END_REF] prepared by low-pressure chemical vapor deposition and assigned to defect states. The above examples suggest that indirect excitation of Tb 3+ ions through some defect states in SiN x matrix is possible. Taking this into account, we assign bands B1 and B2 to indirect excitation of Tb 3+ ions through SiN x defect states. First of all, it is reasonable to expect that the energies of defects should change upon annealing because high temperature treatment induces structural changes in SiN x matrix. As can be seen in Fig. 5(b), bands B1 and B2 fulfil this criterion and significantly shift after annealing, in contrast to band B3 which moves only slightly. Second, if the excitation transfer occurred from a band tail defect states to some discrete Tb 3+ states, we would expect to observe an increase of the excitation band position since annealing results in a more ordered silicon nitride network with narrower band tail. Again, this kind of tendency was observed for bands B1 and B2, suggesting indirect excitation of Tb 3+ ions. Here, it is worth mentioning that the decrease of Urbach energy and simultaneous increase of the Tauc-gap as a function of annealing temperature has been observed before [START_REF] Guerra | Effect of thermal annealing treatments on the optical activation of Tb 3+ -doped amorphous SiC:H thin films[END_REF] for Tb-doped SiN x films, which is consistent with our interpretation. Finally, it should be noted that energy of band B1 is close to energies of different defects in SiN x [START_REF] Valentin | Ab initio study of transition levels for intrinsic defects in silicon nitride[END_REF] and the similarity of tendencies obtained for band B1 and B2 suggest rather similar nature of these excitation bands.

As for the band B3, the situation is more complicated. The peak position of band B3 is much less sensitive to T A and the energy of band maximum at ~4.75 eV is close to typical values reported for 4f-5d transitions of Tb 3+ ions in different host materials [START_REF] Dorenbos | The 4fn↔4fn-15d transitions of the trivalent lanthanides in halogenides and chalcogenides[END_REF]. Moreover, 4f-5d transition of Tb 3+ is known for high absorption cross-section compared to parity forbidden intra-4f shell transitions. Thus, it is possible that band B3 is related to direct excitation of Tb 3+ ions through 4f-5d transition. As a matter of fact, this kind of transition was suggested as the excitation mechanism of Tb 3+ and Ce 3+ ions in crystalline α-Si 3 N 4 powders [START_REF] Li | Photoluminescence properties of rare earth doped α-Si3N4[END_REF]. From this point of view, the large broadening of B3 could be due to electron-phonon coupling which is usually very strong for f-d transitions [START_REF] Podhorodecki | Excitation mechanism and thermal emission quenching of Tb ions in silicon rich silicon oxide thin films grown by plasma-enhanced chemical vapour deposition-do we need silicon nanoclusters?[END_REF][START_REF] Zatryb | Effect of hydrogen passivation on the photoluminescence of Tb ions in silicon rich silicon oxide films[END_REF][START_REF] Huang | Synthesis and photoluminescence of doped Si3N4 nanowires with various valence electron configurations[END_REF].

In general, our PLE results show that the excitation mechanism of Tb 3+ ions in SiN x films is a complicated issue. For this reason, only tentative interpretation of the experimental data is possible at the moment. Finally, we would like to suggest that measurements of PL and PLE as a function of sample temperature could help to clarify this problem in the future. In particular, if the indirect excitation of Tb 3+ ions is phonon-mediated process, the contribution of respective excitation bands to total PLE spectra should decrease at low temperatures. Moreover, if the band B3 is indeed related to direct 4f-5d transition, the full-width at half maximum (FWHM) of B3 should also decrease at low temperatures [START_REF] Podhorodecki | Influence of pressure-induced transition from nanocrystals to nanoceramic form on optical properties of Ce-doped Y3Al5O12[END_REF].

Conclusions

In this work, Tb 3+ -doped SiN x (x ≈ 4/3) films were deposited by reactive magnetron co-sputtering in a nitrogen rich plasma and subjected to rapid thermal annealing treatments. It was shown that annealing at elevated temperatures up to 1100 °C influences both absorption and emission properties of these films. In particular, it was found that annealing generally enhances the photoluminescence intensity of Tb 3+ ions and increases the average photoluminescence decay time measured for the main 5 D 4 → 7 F 5 transition of Tb 3+ ions. This effect was explained by decrease of the non-radiative recombination rate and increase of the number of excited Tb 3+ ions upon annealing. Furthermore, according to our results, photoluminescence excitation spectra measured for 5 D 4 → 7 F 5 emission of Tb 3+ ions show a rather complicated structure with excitation maxima located in the energy range of 4-5 eV. According to our results, these excitation maxima shift to higher energies as a function of the annealing temperature. After decomposition of each photoluminescence excitation spectrum into three Gaussian components it was demonstrated that two excitation bands are especially sensitive to the annealing temperature, suggesting that SiN x defects might participate in the indirect excitation of Tb 3+ ions. Nevertheless, the dominant photoluminescence excitation component was shown to be much less sensitive to the annealing temperature what could suggest that excitation of Tb 3+ ions in SiN x matrix might occur also as a result of direct 4f-5d transition.

Fig. 1 .

 1 Fig. 1. FTIR absorbance spectra measured for (a) Tb:SiN x film annealed at 1100 °C shortly after deposition process (b) Tb:SiN x film annealed at 1100C measured after storage in ambient atmosphere for one year (c) SiO x N y film (22.42 at. % Si, 13.410 at. % N and 41.120 at. % O). Spectra (b) and (c) are used only for the purpose of FTIR absorbance discussion and the emission properties of these samples are not the subject of this article. Dashed arrow represents the shift of Si-N absorbance peak and is only a guide to the eye. The spectra were vertically shifted for clarity.

Fig. 2 .

 2 Fig. 2. Room temperature photoluminescence spectrum of Tb:SiN x film annealed at 1000 °C. The inset shows photoluminescence decay measured for this sample for 5 D 4 → 7 F 5 emission line, together with double-exponential fit.

Fig. 3 .

 3 Fig. 3. Photoluminescence intensity (a) and average photoluminescence decay time (b) measured as a function of the annealing temperature for the 5 D 4 → 7 F 5 emission of Tb 3+ ions. The dotted lines are only a guide to the eye.

Fig. 4 .

 4 Fig. 4. Normalized photoluminescence excitation spectra (solid dots) measured for 5 D 4 → 7 F 5 emission of Tb:SiN x films annealed at 600 and 1100 °C. Each spectrum was fitted with three Gaussian components (dotted lines labeled as B1, B2 and B3). The cumulative fits are shown with solid lines.

Fig. 5 .

 5 Fig. 5. Integrated band intensity (a) and band peak position (b) obtained for each of the three PLE Gaussian components B1, B2 and B3, shown as a function of the annealing temperature.

Acknowledgments

In Poland, this work was funded by National Science Centre under Project No.DEC-2012/05/D/ST7/01121.

In France, this work was financially supported by the French Research National Agency through the GENESE project (No ANR-13-BS09-0020-01), and the LABEX EMC3 ASAP project.