A Belasri

K Khodja

S Bendella

Z Harrache

One-dimensional modeling of DBDs in Ne-Xe mixtures for excimer lamps

Keywords: DBDs, Ne-Xe mixtures, Excimer lamp, Sheath, Modeling PACS: 51.50.+v, 52.20.-j, 52.80.-s, 82.33.Xj

Dielectric barrier discharges (DBDs) are a promising technology for high-intensity sources of specific UV and VUV radiation. In this work, the microdischarge dynamics in DBDs for Ne-Xe mixtures under the close conditions of excimer lamp working has been investigated. The computer model including the cathode fall, the positive column and the dielectric is composed of two coupled sub-models. The first submodel describes the electrical properties of the discharge and is based on a fluid, two-moments description of electron and ion transport coupled with Poisson's equation during the discharge pulse. The second submodel, based on three main modules: a plasma chemistry module, a circuit module and a Boltzmann equation module, with source terms deduced from the electric model, describes the time variations of charged and excited species concentrations and the UV photon emission. The use of the present description allows a good resolution near the sheath at high pressure and it predicts correctly the waveform of the discharge behavior. The effects of operation voltage, dielectric capacitance, gas mixture composition, gas pressure, as well as the secondary electron emission by ion at the cathode on the discharge characteristics and the 173 nm photon generation have been investigated and discussed.

Introduction

The dielectric barrier discharges are more and more used in technology for generating non-local thermal equilibrium (non-LTE) plasmas near atmospheric pressure [1][2][3][4], in particularly for ozone generation [4][5][6], surface treatment and thin film deposition [7,[START_REF] Massines | Proc. of the International Conference on Gas Discharges and Their Applications[END_REF], flue gas treatment [START_REF] Chang | [END_REF]10], pollution control [11,12], laser pumping [START_REF] Yagi | IEEE/OSA Conference on Lasers and Electro[END_REF][START_REF] Yasui | [END_REF][15] and production of ultra-violet (UV) and vacuum ultra-violet (VUV) radiation [4,[16][17][18][19][20]. The DBDs are used due to their simplicity, stability, low cost, high power, and easy maintenance. In the last decade, excimer lamps excited by dielectric barrier discharges have received much attention by scientific communities.

In particularly, because they provide an efficient scheme for generating incoherent spontaneous UV and VUV [23,47] bases itself on the resolution of the continuity equations of electrons and ions, the energy conservation equation and Poisson's equation. Liu and Neiger [48] have developed a dynamic electrical model. The model used by Carman et al [22,49,50] analyzes the spatiotemporal evolution of species populations and electrical parameters. Also, in order to investigate the spatiotemporal characteristics of the short-pulsed DBDs in pure xenon, a 1D and 2D fluid models was used by Bogdanov et al [24,51]. S. Belezenai et al in Ref. [START_REF] Sz | [END_REF], reported that in xenon discharge lamp most power is deposited in the high field region in the vicinity of the dielectric barriers, about 21% of the total input power was used by ion heating. X. Jing-zhon et al [56] have investigated the influence of the gas temperature in DBDs on the excimer emission.

In this work, computer model including the sheath, the dielectric and the positive column has been developed to investigate the microdischarge dynamics in dielectric barrier discharges operating in Ne-Xe mixtures. The context of this study is the modelling of the DBDs with a reasoned approach for controlling VUV emission in excimer lamp. The model predicts the optimal operating conditions and describes the electrical and chemical properties of the excimer lamp. We present in Sec. 2 an overview of the physical and the kinetic models. In Sec. 3, the salient numerical results are presented and discussed. The conclusion of the present work is summarized in Sec. 4.

Model

The computer model including the cathode fall, the positive column and the dielectric was based on two coupled sub-models as used in Refs. [57,58]. In this model, the space gradients are supposed to exist only in the cathode sheath described by the one-dimensional fluid model, and the positive column which is supposed to be spatially uniform was studied by a zero-dimensional model. The gap length d is considered to be equal to d cr + d plas , where d cr is the length of cathode sheath limited by the cathode and the plasma and d plas is the plasma length (see Figure 1). In order to have a good numerical resolution the length of the cathode sheath region described with the onedimensional model is typically d cr =3 mm in the calculation presented below. This region includes the (timevarying) sheath and a small part of positive column plasma. The boundary condition on the plasma side of the cathode region (x=d rc ) is such that the charged-particle density gradients are zero. This discharge region is supposed to be in series with the rest of the plasma (described with the zero-dimensional model). For the considered operating conditions of excimer lamp in this work, the maximum value of the sheath length d s (the sheath end, i.e., the sheath-plasma boundary defined here as the point where the electron density become larger than half the ion density) reached before the plasma formation is about 2 mm, which will be small to cathode region length, and then to the gap distance (d s <d cr <d). In the frame of this study, the cathode region length d cr is supposed equal to 3 mm (region studied with the 1D model) which will be greater than the maximum value of the sheath length d s reached before the plasma formation under different lamp operation conditions. The applied voltage through the discharge is given by:

V ap (t)= V D (t)+ V cr (t)+ V plas (t) (1)
where V plas (t), V D (t) and V cr (t)=V(d cr , t) are the voltage across the positive column, the dielectric and the cathode region respectively for a given time t. The relation between the current I cr and the voltage V cr in the cathode region is described by the current equation:

I cr t = -ε 0 A d cr ∂V cr ∂t + A d cr J e x, t + J p (x, t) dx d cr 0 ( 2
)
where A represents the electrode area, and J e x, t and J p x, t are, the electron and ion current density respectively for a given position x and time t.

The zero-dimensional model consists of three main modules: a plasma chemistry module, a circuit module and a Boltzmann equation module. The plasma chemistry module constructs differential equations for the evolution of the density of species. The system of equations describing the dielectric, the positive column and the cathode region are solved in two steps as follows; for a given voltage V cr across the cathode region at a time t, the plasma kinetic equations coupled with the dielectric equation are solved with the classical GEAR method [START_REF] Gear | Numerical Initial Value Problems in Ordinary Differential Equations[END_REF] between the instants t and t+dt. Taking I cr in equation (2) from the above calculation (I cr =I plas ) at time (t+dt), where I plas is the plasma current calculated in the positive column, the one-dimensional fluid equations are integrated in space (0<x<d cr ) and time between t and (t+dt).

For the kinetic scheme, we consider the Ne-Xe mixture used in Refs. [START_REF] Meunier | [END_REF]61], including the charged particles of electrons (e), atomic ions ( Xe + , Ne + ), molecular ions (Ne ), Ne * and the photonic species hν (173 nm), hν (147 nm) and hν (150 nm) (see Table 1). The bibliographic research on Ne-Xe gas mixture shows that this kinetic scheme constitutes the basis of the set of models used for the description of plasma display panels (PDPs) [START_REF] Meunier | [END_REF]61,72], excimer lamps and lasers. The transport coefficients and the electronic collision frequencies which depend on the reduced electric field E/N are therefore precalculated and tabulated by solving the steady state, homogeneous electron Boltzmann equation in the considered gas mixture, using Bolsig+ software [START_REF] Bolsig+ | KINEMA Software[END_REF].

The one-dimensionnel fluid model, based on two-moments description of electron and ion transport coupled with Poisson's equation during the discharge pulse, describes the space and time variations of the electron and ion densities, the electric field and the current density. The positive column model describes the time variations of charged and excited species concentrations and of the UV photon emission.

Results and discussion

Input conditions

The DBDs lamp parameters and operating conditions used in the present work are shown in Table 2. These parameters of the discharge configuration and operating conditions are chosen, in the range order of that used in recent experimental and theoretical works [21-24, 47-51, 53] on excimer lamp, in the objective to have a spatially uniformity of the plasma across the discharge area and a high lamp efficiency.

Discharge behavior

In this paragraph, we illustrate the formation and the quenching of a single discharge in a mixture of 10% xenon in neon, with a total pressure of p r = 400 Torr, the applied voltage is equal to 2 kV, and the capacity of the dielectric layer above each electrode is 460 pF/cm 2 (the equivalent capacitance of the two layers, C diel , is therefore 230 pF/cm 2 ). In this work, a secondary emission coefficient [24,47,[START_REF] Meunier | [END_REF]61,74] of 0.25 has been assumed for neon ions. Usually, in DBD's configuration for display panels or lamps a MgO thin film is deposited above the dielectric layers in order to protect the dielectric layers, and decrease the breakdown voltage due to the relatively large value of the secondary electron emission coefficient of MgO bombardment by neon ions. Note that the value of the secondary emission coefficient due to xenon ions is about ten times smaller to that of neon ions During this time the electrons have drifted a distance of about 1.3 mm, which is the maximum sheath length.

Current and voltage across the gap

Electric field and charged particle densities

After about 20 ns, which is the time for breakdown, the plasma is formed and an ionic space charge is created near the cathode, accompanied by a field increase to high values. These large values lead to high ionization in front of the sheath, followed by a rapid motion of the sheath-plasma boundary toward the cathode. Two discharge regions are distinguished. At first, a cathode fall region exists where the electric field drops drastically from a maximum value of about 1.6 10 V/cm at the moment of the peak current (t=243 ns), also the ion density reaches its largest value of 3.7 10 13 cm -3 and the sheath length is about 0.005 cm. Secondly, a positive column plasma is observed characterized by quasi neutrality and a very low value of the electric field.

Species concentrations and UV photon emission

The with maximum values of 1.5×10 11 cm -3 and 2×10 11 cm -3 respectively. This variation of the atomic and molecular excited species is confirmed in Ref. [START_REF] Meunier | [END_REF]. It is due to the kinetic scheme used (see Table 1). In the Xe DBDs plasma, VUV emission is generated via the radiative decay of the four excited xenon states: the Xe * ( P ), both at 173 nm. The time variation of the photonic species, hν (173 nm), hν (147 nm) and hν (150 nm), was shown in figure 4(c).

Parametric studies

The dielectric discharge lamps convert electrical energy into radiation by transforming electrical energy into kinetic energy of moving electrons, which in turn is converted into electromagnetical radiation as a result of some kind of collision process with atoms of gas. The luminous efficacy of the excimer lamp is determined by the vacuum ultraviolet VUV photon emission which transfers into visible light by the phosphor. However it is interesting to look at how the energy gained by electrons and ions from the electric field is dissipated inside the cell. Recently, several experimental and theoretical works have focused on the lamp efficiency [4, 21-24, 46, 47, 49-51, 60, 61], and it has been shown that the efficiency of excimer lamps is directly dependent on the electron energy deposition in xenon excitation, and can be drastically increased in a pulsed regime. It seems possible to modify the power deposition in the plasma by varying external discharge parameters such as the amplitude and the rise time of the applied voltage, and to modify the plasma composition by changing the gas mixture and pressure. In this subsection, we discuss the dependence of VUV photon generation and the DBDs behaviour on the dielectric properties, the gas mixture composition, the gas mixture total pressure, the applied voltage and the secondary electron emission process.

Effect of the applied voltage

In order to study the interactions between the power supply and the lamp, we illustrate in figure 5 V/cm. These large values of electric field in the vicinity of the dielectric will lead to a large power deposition [START_REF] Sz | [END_REF][START_REF] Meunier | [END_REF], however a significant ion heating will be noticed which will probably limit the lamp efficiency. Figure 6 investigates the effect of varying the applied voltage amplitude V ap on photon hν (173 nm) emission in DBDs.

It is known that increasing V ap increases the light emission due largely to increasing energy deposition, and the most of the energy dissipated in exciting xenon is used in the VUV production.

Effect of the Xe concentration

In order to see how the electrical and chemical characteristics of the plasma can be affected by xenon concentration in Ne-Xe gas mixtures, it is interesting to look at the time variations of the discharge current and the photon hν (173 nm) density, as displayed in figures 7(a)-(b) respectively, for three concentrations of xenon in neon and an applied voltage of 3 kV at a fixed pressure of 400 Torr. We can see clearly that, the generation of 173 nm photons increases with the increasing of the xenon mole fraction in the mixture [21,22,[73][74][75].

However for low concentrations of xenon, the discharge current is higher because an important fraction of power deposition goes into producing ionization. Figure 8 illustrates the effect of the xenon concentration on the secondary electron current due to photon impact on the cathode J e, hν . The photoelectron current [49,57,58,[START_REF] Levin | [END_REF] is obtained by the relation:

J e, hν = 1 2 e Q d S hν
where Q is the quantum efficiency for photon electron generation, which represents the number of electrons released from the electrode per incident photon. In this work we have assumed a quantum efficiency of Q=10 , which represents an upper limit for the 173 nm incident photons on a 4 eV work-function cathode material. The production rate S hν of the 173 nm photons has been obtained from the density of excited molecule Xe 2 * .

Effect of pressure

We also investigated the consequences of gas mixture total pressure on the discharge current, the photon generation and excited species under the same conditions of subsection 3.2, in figures 9, 10, and 11. As pressure increases, the discharge sustaining voltage becomes larger. Then for a constant value of applied voltage V ap = 2 kV, the current peak will be decreased when the gas pressure increases (see Figure 9). The emissions of the three photons (147 nm, 150 nm and 173 nm) increase with increasing gas pressure due to higher gas density resulting in more UV emission. However the efficiency of 173 nm photon generation is high at high-pressures because the three body collisions are more efficient to generate Xe 2 * ( u + ) [22] as shown in figures 10(a)-(b).

Figures 11(a)-(b) report the effect of the total pressure on the time variation of the metastable state Xe * ( P

and the resonant state Xe * ( P 1 3 ) respectively. We see that the density of the metastable state decreases with the increasing of the gas pressure. This diminution in metastable density is due in part to its conversion to Xe 2 * ( 3 Σ u + ), collision with the fundamental state of xenon [21,22,[START_REF] Meunier | [END_REF]. However, we can expect that the reaction R3 (see Table 1) can also contribute to this diminution as the pressure increasing induces a decrease in the plasma electric field.

Effect of dielectric capacitance

The consequences of the dielectric capacitance on the deposed power and the 173 photon generation, for three values of C diel =100, 230, 400 pF/cm 2 and under the same conditions of subsection 3. Figure 12(a) shows also, that the power density has a similar profile as the discharge current pulse and the time to breakdown is not affected by the presence of the dielectric.

Effect of the secondary electron emission

The presence of the cathode sheath in series with the plasma of the positive column can have a big influence on the evolution of the voltage, current, and chemical kinetics in the plasma. In order to illustrate this effect, we plotted in figure 13, the time evolution of the discharge current, plasma voltage and the dielectric voltage when the sheath is not considered. This result has been obtained by solving the zero-dimensional model plasma kinetic equation described in the model section (see Table 1) for the case when the positive column has a distance equal to the total gap distance (i.e., without considering the cathode region) coupled with the dielectric equation and under the same conditions of subsection 3.2. We see that the pulse duration is about 200 ns and the discharge current density has a peak of 23 A/cm 2 . We report on figures 14(a)-(b), the time variation during the discharge pulse of the current and the 173 nm photon density, obtained with the complete one-dimensional model, including positive column, cathode region, and the circuit equations, for two values of secondary emission coefficient γ = 0.25 and 0.1. We see clearly from these figures, that the plasma electrical characteristics and kinetics are strongly affected by the presence of this cathode region; however, the presence of the sheath cannot be neglected in theoretical models developed to study the DBDs characteristics. We note that the current of the discharge and the 173 nm photon production increase with the large values of secondary emission coefficient at the cathode.

Conclusion

The fundamental objective of the dielectric discharge lamps is to convert electrical energy into radiation by transforming electrical energy into kinetic energy of moving electrons, which in turn is converted into VUV radiation. This work presents a reasoned approach to deliver electric energy into a dielectric barrier discharge excimer lamp, with the aim of controlling its VUV emission. The computer model including the cathode fall, the positive column and the dielectric, describes under the same conditions of excimer lamp working, the spatial and time variations of the electrical and chemical discharges properties during the pulse; current, electric field, voltage across the micro-discharge, charged and excited species concentrations and the VUV photon emission.

The results discuss the microdischarge dynamics and the optimization of discharge conditions for excimer lamp and photon generation. The efficiency of VUV photon generation in DBDs depends on the dielectric properties, gas mixture composition, gas mixture pressure, applied voltage and the sheath via secondary electron emission at the cathode. The increase of the applied voltage, xenon concentration, gas pressure, and the dielectric capacitance induces an increasing in 173 nm photon generation. From the result of the secondary electron emission effects on the discharge behavior, one can deduce that taking account of the sheath is indispensable to have a realistic approach, in theoretical models developed to study DBD's for excimer lamp. Finally, the results of this work can be considered as important design data of excimer lamps for practical applications. ) Time (ns)

V ap =1,5kV

V ap =2kV

V ap =3kV

Figure 2

 2 Figure2shows, the time variations of the voltage across the positive column V plas , the voltage across the cathode region V cr , the voltage across the dielectric V D , and the current. It seems, that at any time during the discharge pulse, the voltage equality V ap V cr V plas V D is realized, and the transition from capacitive to resistive behaviour of the sheath is observed by a voltage increase and decrease across the cathode region to reach the desired operating point. This figure shows also, that the discharge is initiated in the gap after a delay time of about 20 ns. The current density increases this time and reaches a peak value of 2.7 A/cm 2 at the instant t= 243 ns. The current density then decreases rapidly to reach a low value at the end of the discharge pulse. The decrease of the current density is due to the charging of the dielectric layers by electrons and ions generated in the discharge volume and flowing to the walls. The voltage induced by the charging of the dielectric layers opposes the applied voltage and increases to reaches a maximum value at the end of the pulse. This value of V D is sufficient to ensure the next discharge.

Figure 3

 3 Figure 3 illustrates the spatial distribution of the electric field, electron and ion densities in the cathode region at six different times of the discharge pulse. These times (t = 5, 10, 19.7, 156, 243 and 940 ns) are indicated on the current curve in figure 2. During the first pulse period, the electric field is spatially uniform, and the electrons move towards the anode (the cathode is defined at the position x=0), inducing gas ionization.

  (a), the time variations of the discharge current pulse, under the same conditions of subsection 3.2 and for three value of applied voltage V ap = 1.5, 2 and 3 kV. In this figure, it appears clearly the strong effect of the applied voltage on the breakdown time and the current peak. It is instructive to look at the time variation of the electric field at the cathode, for different values of the applied voltage. The time variation of the cathode electric field as plotted in figure 5(b) is similar to that of the current discharge. For the three values of applied voltage 1.5, 2 and 3 kV, the peak of the electric field reaches respectively the following values 4.5 10 , 1.6 10 and 8.8 10

2 ,

 2 figures 12(a)-(b). With a larger dielectric capacitance, more current is required to charge the dielectric.

Figures listFigure1.Figure 2 .

 2 Figures listFigure1. Scheme of the dischargeFigure 2. Time evolution of the discharge current I, voltage across the positive column V plas , voltage at the cathode region V cr and the voltage across the dielectric V D.

Figure 3 .

 3 Figure 3. Spatial distribution of the electric field, electron and ion densities in the cathode region at six different times of the discharge pulse.

Figure 4 .

 4 Figure 4. Temporal evolution of the concentration of: (a) charged particles, (b) excited atoms and molecules, (c) photonic species.

Figure 5 .

 5 Figure 5. Time variations of: (a) the discharge current pulse, (b) the electric field at the cathode for three values of applied voltage V ap = 1.5, 2 and 3 kV.

Figure 6 .

 6 Figure 6. Time variations of the photon hν (173 nm) density for three values of applied voltage V ap = 1.5, 2 and 3 kV.

Figure 7 .

 7 Figure 7. Time variations of the: (a) discharge current, (b) photon hν (173 nm) density for three values of xenon in neon 10%, 20% and 30%.

Figure 8 .

 8 Figure 8. Time variations of the secondary electron current due to the photon impact on the cathode J e, hυ for three values of xenon percentage in neon 10%, 20% and 30%.

Figure 9 .

 9 Figure 9. Time evolution of the discharge current for three values of gas pressure p r = 300, 400 and 600 Torr.

Figure 10 .

 10 Figure 10. Time evolution of: (a) the 173 nm photon concentration, (b) the Xe 2 * Σ u 3

Figure 11 .

 11 Figure 11. Time evolution of: (a) the metastable state Xe * ( 3 P 2 ) concentration, (b) the resonant state Xe * ( 3 P 1 )concentration for three values of gas pressure p r = 300, 400 and 600 Torr.

Figure 12 .

 12 Figure 12. Time evolution of: (a) deposed power density, (b) the 173 nm photon concentration for three values of dielectric capacitance C diel = 100, 230 and 400 pF/cm 2 .

Figure 13 .

 13 Figure 13. Time evolution of the discharge current I, plasma voltage V plas and the dielectric voltage V D when the sheath is not considered.

Figure 14 .

 14 Figure 14. Time evolution of: (a) the discharge current, (b) the 173 nm photon density for two values of secondary electron emission coefficient γ=0.1 and 0.25.

  Figure 1

Figure 2 Figure 3

 23 Figure 2

  Figure 7

  Figure 8

2 C

 2 Figure 12

  Figure 13

  temporal evolution of the Ne-Xe mixture concentrations, obtained with the kinetic model, is presented in figures 4(a)-(c). These figures show that after the breakdown phase, a fast growth of excited and charged species densities are noticed. The dominant ions in positive column are Xe + and Xe 2

	+ , as appeared in
	figure 4(a), which represents the time variations of the Xe + , Ne + , Xe 2 + , Ne 2 + , and NeXe + concentrations, together
	with the electron density n e . The time variations of the excited atoms and molecules Xe * ( P 2 3 ), Xe * ( P 1 3 ), Xe ** ,
	Ne * , Xe 2 * ( Σ u + 3 ), Xe 2 * ( Σ u + 1 ), and Xe 2 * (O u ) are plotted in figure 4(b). The metastable state Xe * ( P 2 3 ) reaches a
	maximal value of 1.58×10 14 cm -3 , then decreases much slower during the discharge pulse, while the resonant
	state Xe * ( P 1 3 ) reaches a maximum of 7.5×10 13 cm -3 and decreases rapidly. Note that the excited molecular state
	Xe 2 * ( Σ u + 3 ) density has a maximum of 3.4×10 11 cm -3 and follows closely the time variation of Xe * ( P 2 3 ).
	However, the time variations of Xe 2 * ( Σ u + 1 ) and Xe 2

* (O u ) concentrations are almost identical to those of Xe * ( P 1 3 )

Table 1 .

 1 List of reaction processes and their rate coefficients used in the present work (T e is the electron temperature).

Table 2 .

 2 Lamp parameters and operating conditions.

	Table 1.

Table 2 .

 2

	Parameter	Value
	Gas mixture Ne-Xe	10, 20, 30% of xenon in neon.
	Gas pressure	p r = 300, 400, 600 Torr
	Gas temperature	T g = 300 °K
	Gap length	d= 5 mm
	Cathode region length	d cr = 3 mm
	Electrode area	A= 1 cm 2
	Applied voltage	V ap = 1.5, 2, 3 kV
	Dielectric capacitance	C diel = 100, 230, 400 pF/cm 2
	Coefficient of secondary emission	γ = 0.1, 0.25
	Initial electron density	10 9 cm -3

Acknowledgments

This work was funded by the Algerian Ministry of Education and Research. Z. H. is grateful to Professor M.D.

Calzada for the kind hospitality during the realization of this work.


R Fabbro
email: remy.fabbro@gmail.com

Melt Pool and Keyhole Behavior Analysis for Deep Penetration Laser Welding

Keywords: laser welding, keyhole, melt pool hydrodynamics, instability, penetration depths Pacs numbers: 42.62.-b, 81.20.Vj

One usually defines the main characteristic of the welding performances of a given laser system by its "penetration curve" that corresponds to the welding depth as a function of the welding speed V w for a given set of operating parameters. Analysis of a penetration curve is interesting and gives very fruitful results. Coupled with high speed video imaging of melt pool surface and ejected plume behaviors, the analysis of this penetration curve on a very large range of welding speeds, typically from 0 to 50 m/min, has allowed us to observe very different and characteristic regimes. These regimes are mainly characterized by the physical processes by which they impede the laser beam penetration inside the material. We show that it is only at rather high welding speeds that these limiting processes are reduced. Consequently the scaling law of welding depth with welding speed is in agreement with adapted modeling of this process. On the other hand, as the welding speed is reduced, different effects depending of the weld pool dynamics and plume interaction, strongly disturb the keyhole stability and are responsible of the deviation of the penetration curve from the previous modeling that agrees with a 1/V w scaling law. A corresponding criterion for the occurrence of this effect is defined.

Introduction

The hydrodynamics of a melt pool generated during deep penetration laser welding has always appeared to be very complex. This melt flow is a result of the interaction of many driving forces [START_REF] Matsunawa | Understanding physical mechanism in laser welding for mathematical modeling and process monitoring[END_REF]. The role of these different driving forces (such as ablation pressure, vapor plume effects, surface tension, gravity, possible induced electromagnetic forces, ...) is not totally defined, as their relative importance with the operating conditions, for example when the welding speed or incident laser intensity varies. In order to improve the understanding of these complex processes, different experiments have been performed and the evolution of melt pool dynamics for a range of welding speeds, wider than the one usually used, has been analyzed. Five typical hydrodynamic regimes can be defined by varying the welding speed from a few m/min to several tens of m/min and thus discriminate some of the driving forces. As a final result, the importance of the dynamic pressure induced by the vapor plume emitted by the keyhole front is emphasized. In a first part of this paper, the main characteristic regimes related to the different flows observed with the variation of the welding speed, are recalled. In a second part, a dynamical model is presented. This model describing the stationary equilibrium of the keyhole front, shows how the main derived parameters (such as penetration depth, keyhole tilting angle, evaporation pressure, ...) vary with the operating parameters. Finally in the third part, these experimental results are discussed in the frame of this model. The importance of the perturbing effect of the collapse of the keyhole, due to surface tension, usually observed at low welding speeds for limiting depth penetration, is highlighted by the results.

Experimental results

I recall here the main experimental results, concerning the visualization of the melt dynamics observed with the high-speed video camera at a frame rate of 20 kHz, for variable welding speeds. The incident laser power and laser spot diameter are kept constant at 4 kW and 0.6 mm respectively. 304 Stainless steel samples were welded, in partial penetration. The experimental setup used as well as the main results have already been presented and detailed [START_REF] Fabbro | Analysis of the various melt pool hydrodynamic regimes observed during CW Nd-Yag deep penetration laser welding[END_REF][START_REF] Fabbro | Experimental study of the humping process during Nd:Yag CW laser welding[END_REF]. The films analysis allows defining five main characteristic contiguous regimes, which are only controlled by the welding speed. It appears that these behaviors can be interpreted as the result of a very different action of the vapor plume on the melt pool. This action is controlled by the geometry of the keyhole front, itself defined by the welding speed and incident laser intensity.

Welding speeds below 5 m/min: "Rosenthal" regime

This regime, which is observed for welding speeds lower than 5 m/min, is characterized by a rather large melt pool, even in front of the keyhole, due to the rather low welding speed. The melt pool surface shows many chaotic surface fluctuations and large swellings of liquids fluctuating around the keyhole aperture, which is rather well defined and remains circular (see figure 1).

Confidential: not for distribution. Submitted to IOP Publishing for peer review 9 September 2010 Because of these fluctuations, one cannot emitted from the keyhole rim, and parti decrease of the penetration depth as well can be correlated with the previously des seam show a gradual transition of the sha (typically about 1 to 3 m/min) to a more welding speeds, which will be discussed fluctuations, one can schematized this reg limited hydrodynamics. So the descriptio surface is uniformly heated at some tempe

Welding speeds between 6 to 8 m/min

This regime is observed for welding spee single swelling generated near the top of are emitted. This large wave is ejected r pool therefore leading to quite periodic cl and collides with the melt pool and so, t keyhole front is tilted; as the vapor plume rearwards [START_REF] Fabbro | Study of keyhole behavior for full penetration Nd-Yag CW laser welding[END_REF]. The analysis of plume defle One can observe that only the tilted keyho regime where the luminosity characterizi the keyhole surface). More interestingly corresponding local heating of the liquid observed. So the vapor plumes not only tr rather high temperature.

2 t observe a clear laminar flow around the keyhole. Al cularly on its front side. On this range of welding as large fluctuations of ejection direction of the vapo scribed melt pool swellings fluctuations. Macrograph ape from the well-known "wine cup shape" character slender shape for 5 m/min. From the analysis of the d in § 2.7, we know that the keyhole is quite vertic gime by a vertical cylindrical keyhole surrounded by on of this situation by a kind of "Rosenthal" heat flow erature close to the evaporation temperature, could be gime. Typical view of melt pool (scale: 1mm) and cro n: "Single wave" regime eds ranging from 6 to 8 m/min. It is characterized by t the rear keyhole wall (see figure 2). It is only from t rearwards quite periodically and generates back and f osures of the keyhole. The vapor plume is emitted rath triggers these oscillations. The more the welding spe e is emitted perpendicularly from the keyhole front sur ection variations has already confirmed this result [START_REF] Fabbro | Experimental study of the dynamical coupling between the induced vapor plume and the melt pool for Nd-Yag laser welding[END_REF]. ole front is clearly heated by the incident laser beam ( ng the laser heated surface was more uniformly and y, when the ejected vapor plume collides with the d surface as a result of the impact by this energetic ransfers impulse momentum, but also a non-negligible

Swellings

Local evaporation

Spatters

Vapor jet lso, many spatters are mainly speeds, one can see a rapid or plume. These fluctuations hs cross sections of the weld ristic of a low welding speed keyhole tilting for these low cal. Therefore, despite these y a large melt pool with very w regime, where the keyhole used.

ss-section (scale: 0.5 mm).

the presence of a rather large this region that melt droplets forth oscillations of the melt her deeply inside the keyhole eed is increased the more the face, it is then rather directed (contrarily to the "Rosenthal" randomly distributed around e melt pool and lifts it, the heated vapor plume can be e amount of energy due to its However its length presents also some fl previous regime, and the height of the ind shows two characteristic zones that are common to all regimes, and the second Moreover, vapor plume seems to be also regime, heating by the collision of the vap much less intense than in the te that this elongated keyhole inclined keyhole front wall, eyhole, inside the melt pool. frontward. As in the previous ble.

Welding speeds between 12 to 19 m/m

This regime is observed for welding spee that contours the keyhole front wall, wh elongated (but with a shorter length tha fluctuations characterized by only surface There is also a central melt flow that is rearwards with its surface reaching a leve zone observed in the "elongated" regime spatters or droplets are emitted, even from the level of the surface sample and wets on the sides of the seam. In that case, on upper sides, at the rear of this elongated k from the keyhole front wall collides with is very stable; it does not fluctuate anymor

Welding speeds above 20 m/min: "Hu

For our operating conditions, above 20 m occurrence of a weld seam with very str separated by smaller valleys. The melt flow that is coming from the key the main central flow is always emerging rearwards and it rises up to a level that i distance of about 2 mm and then a liquid j propagates rearwards at high velocity. It i detachment point [START_REF] Fabbro | Experimental study of the humping process during Nd:Yag CW laser welding[END_REF]. In fact, a shrinkage be observed at a certain distance, typicall jet and so attaches it to the sample. The f can grow.

4 min: "Pre-humping" regime eds ranging from 12 to 19 m/min. It is characterized hose tilting angle begins to become important. This an in the previous regime) and the surface of the waves with rather small amplitudes.

regime. Typical view of melt pool (scale: 1mm) and cr emerging from the bottom of the very stable keyhol el close to the initial sample surface (see figure 4). T seems very small here, only located at the bottom of m the rear rim of the keyhole as in the previous regim both sides. But above 15-16 m/min welding speeds, s ne can observe that the emerging melt does not reach keyhole. These undercuts begin to be important becaus the central emerging flow and press it towards its cen re and is precisely ejected perpendicularly to the keyh umping" regime m/min, we reach the very characteristic humping regim rong undercuts, composed of solidified large swelling yhole region presents very particular characteristics [3 g from the bottom of the keyhole front wall (see Figu is much lower than the surface sample. It stays attac jet from the central part of this flow is detached and f is along this strip of liquid jet that the humps appear a of this melt jet strip, due to the Rayleigh instability d ly 2 mm from the detachment point. This shrinkage co fluid flowing inside this strip of melt jet is then stopp lateral side flow interaction zone

Undercut

Emerging flow by a rather strong melt flow s resulting "keyhole" is then following melt pool shows ross-section (scale:0.5 mm).

le front wall and is deflected The characteristic heated rear the emerging flow. No more me. Melt pool surface reaches some undercuts are observed h the sample surface near its se the two side flows emitted nter. Finally, the vapor plume hole front wall. me that can be defined by the gs of quite ellipsoidal shape, 3]. As in the previous regime, ure 5); it is strongly deflected ched to the sidewalls along a forms a thin vertical strip that at a certain distance from the driven by surface tension, can ools locally this strip of melt ped at this point, and a hump m the detachment point which of section of the groove, very not modified.

, in the incident laser power -. Linear best fits for the R/S, meter used here is 0.45 mm.

incident laser power of 4 kW eters, these experiments have er to have a greater range of e observed but with modified imited the regions where the me is observed (labeled C). wer greater than 0.5 kW. Of olds between the Rosenthal / abeled respectively R, S, E, P, dent laser power. One can see that best-fit lines passing through the origin can be plotted through these 3 series of experimental points of these consecutive regimes.

For the P/H transition, it is interesting to note that for incident laser powers smaller than 2.5 kW, no humping instability is observed, even at very high welding speed. Also, when the incident power increases, the P/H welding speed threshold decreases; this behavior is similar to previous experimental results but obtained for different conditions [START_REF] Thomy | Humping in welding with single mode fiber lasers[END_REF]. The very different behavior of this P/H transition compared to the 3 previous one, results probably from the very different mechanisms driving this humping instability. It is also interesting to notice that if we extrapolate the P/H transition at higher incident powers, the pre-humping region should disappear. This behavior could be verified by using higher laser powers, for example with new fiber or discs lasers.

Penetration depths scaling

Figure 7 shows the variation of the corresponding penetration depth e as a function of the welding speed. Despite the various phenomena described above, this curve appears quite continuous. The 1/e variation has also been reported and one can observe that above a certain welding speed, around 6-8 m/min, this scaling is quite linear. It is interesting to note that this behavior occurs for regimes where the keyhole remains opened and beam incidence on front keyhole wall is not disturbed by the fluctuating keyhole closures (so corresponding to "elongated" regimes). In fact, this is a general result that can be observed for any set of operating parameters: above a critical welding speed V wc , the penetration curve always scales as the 1/V w . For welding speeds lower than V wc , of course the penetration depths still increases, but with a smaller rate that 1/V w , and even saturates for static conditions (V w = 0). Moreover, one can also observe from many results reported by different laboratories that this critical welding speed V wc is a decreasing function of the focal spot diameter, i. e. as the focal spot increases, the 1/V w scaling remains valid for smaller welding speeds. An example of this behavior is shown on figure 8, where penetration curves obtained for very different focal spot diameters have been plotted [START_REF] Beyer | High power laser materials processing -New developments and trends[END_REF][START_REF] Luft | A New applications for welding with diode lasers[END_REF]. The range on which the 1/V w scaling is observed is more extended for large focal spots. Similar behaviors on the effect of spot size have been observed in several publications [START_REF] Verhaeghe | The effect of spot size and beam quality on welding performance when using high-power continuous wave solid-state lasers[END_REF][START_REF] Weberpals | Fundamental understanding of spatter behavior at laser welding of steel[END_REF][START_REF] Suder | Absolute spot size effect on penetration depth in laser welding[END_REF].

Keyhole front tilting angle

The tilting angle of the keyhole front is also another experimental data that plays an important role in the keyhole dynamics.

Its value has been reported on Figure 9 as a function of the welding speed, for a 4 kW incident power and 0.6 mm focal spot diameter. Two methods have been used for its determination [START_REF] Fabbro | Importance of the Coupling Between the Induced Vapor Plume and the Melt Pool, for Nd-Yag CW Laser Welding[END_REF]: one uses the measurement of the maximum plume deflection observed on a video sequence (assuming that the vapor plume is emitted perpendicularly from the keyhole front), the other one uses measurements of the longitudinal front keyhole extension through coaxial view during full penetration experiments. These results show that the KH front angle scales quite linearly with the welding speed. Very similar behaviors and scaling, but resulting from the measurement of spatters ejection angle, have been obtained by Weberpals et al. [START_REF] Weberpals | Fundamental understanding of spatter behavior at laser welding of steel[END_REF]. 3. Dynamical model of keyhole.

Basic modeling

The previous experimental results have been analyzed in the frame of our dynamical model of keyhole front equilibrium [START_REF] Fabbro | Keyhole modelling during laser welding[END_REF][START_REF] Fabbro | Dynamical description of the keyhole in deep penetration laser welding[END_REF]. This scheme is based on the local equilibrium of the keyhole front wall under the two opposite effects that tend to displace it, which are the welding speed V w and the drilling velocity V d that results of the penetration of the laser beam inside material. For a uniform incident intensity profile, a scheme of the longitudinal section of the front and rear keyhole walls with corresponding notations is shown on figure 10. The keyhole front wall is tilted with an angle α relatively to the vertical laser beam. The kinematic condition of equilibrium of the keyhole front, which states that there is no displacement along its normal, means that the projection along the normal to the keyhole front wall of the welding speed V w has to be equal to the "drilling" velocity V d that results of the penetration of the laser beam inside material (this drilling velocity is always normal to the local surface). This allows us to write the basic equation of equilibrium for stationary conditions [START_REF] Fabbro | Keyhole modelling during laser welding[END_REF][START_REF] Fabbro | Dynamical description of the keyhole in deep penetration laser welding[END_REF]:

V d = V w . cos α (1)
We will now consider the well-known "piston model" [START_REF] Semak | The role of recoil pressure in energy balance during material processing[END_REF][START_REF] Fabbro | Study of keyhole behavior for full penetration Nd-Yag CW laser welding[END_REF] and make the assumption that the resulting drilling velocity V d , is proportional to the local absorbed laser intensity. This is a very convenient approximation that can be checked in a certain range of operating parameters such as low laser irradiances. As a consequence one can write:

V d = k I abs = k I 0 A(α) sinα (2)
where I 0 is the incident laser intensity, A(α) the local absorptivity and sinα, the cosine of the local angle of incidence of the laser beam. The parameter k ( 3 10 -11 m 3 /J, for our experimental conditions, on 304-stainless steel), is the proportionality factor that can be also determined experimentally for similar conditions of incident laser intensity [START_REF] Fabbro | Study of keyhole behavior for full penetration Nd-Yag CW laser welding[END_REF]. One can determine that k mainly depends on the thermal properties of the used material. The absorptivity A(α) depends of the angle of incidence and one can use a Fresnel-like equation for A(α) [START_REF] Semak | The role of recoil pressure in energy balance during material processing[END_REF]:

A(α) = A 0 (sinα) q (3)
where A 0 is the absorptivity under normal incidence and q has a rather small value (q 0.1). By combining equations 1 to 3, in the limit of small values of q and for low welding speed V w , one obtains the variation of angle α with operating parameters:

α V w /(k I 0 A 0 ) (4)
It is interesting to note that this scaling of α is in agreement with our previous results for the welding speed variation. Weberpals et al. [START_REF] Weberpals | Fundamental understanding of spatter behavior at laser welding of steel[END_REF] have also observed a similar scaling with the incident intensity I 0 .

For defining the maximum penetration depth e, one can consider that this depth is obtained when the incident beam is entirely intercepted by the keyhole front, i. e. when the relation:

tanα D/e (5)
is fulfilled.

In fact this relation would be exact if the absorptivity A 0 was very large. Typically, for these conditions, we have shown that A 0 0.7 (on stainless steel). So, one can expect some multireflections. By taking into account these multireflections, one can show that for these conditions of incident intensity, 1 to 2 more reflections occur, and the maximum keyhole depth is increased by about 30%. Nevertheless, we will use equation 5 for closing the problem and combined it with equations 1 and 2. One can therefore determine this penetration depth that is given by: (

) 6
where P is the incident laser power (for deriving [START_REF] Thomy | Humping in welding with single mode fiber lasers[END_REF], we have only considered that q 0). Again, the equation 6 shows that the penetration depth scales as 1/V w , as previously observed experimentally for high welding speeds. It also shows a 1/D scaling (where D is the spot diameter): it is important to note that this scaling has also been observed experimentally, but only when these focal spots are rather large [START_REF] Verhaeghe | The effect of spot size and beam quality on welding performance when using high-power continuous wave solid-state lasers[END_REF][START_REF] Weberpals | Fundamental understanding of spatter behavior at laser welding of steel[END_REF][START_REF] Suder | Absolute spot size effect on penetration depth in laser welding[END_REF]. For small focal spots, the penetration depth appears to be quite constant with the spot diameter. An attempt of explanation of this behaviour will be discussed in the next paragraph.

By using this model one can also determine the absorbed intensity I abs on the keyhole front, which is given by: I abs = I 0 A 0 sinα (for the sake of simplicity, we will also consider here that q 0). In the limit of low values of α, it is easy to see that I abs is given by:

I abs = I 0 A 0 sinα = V w /k ( 7
)
Equation 7 is interesting because it shows that for low angles (obtained for low welding speeds and/or for high incident intensity), the absorbed intensity on the keyhole front is totally independent of the incident intensity (or focal spot diameter); it only depends of the welding speed. This is a self-regulating mechanism: for a given welding speed, when the incident laser intensity increases, the keyhole front tilting angle decreases (equation 4), correspondingly the penetration depth also increases (equation 6), but the absorbed intensity on the keyhole front (equation 7) remains constant! Of course, when the welding speed increases or the incident laser intensity decreases, the angle α increases and the absorbed intensity also increases and tends to the limit I 0 A 0 . We will see the importance of this behavior in the next paragraph.

Discussion

Regime transition thresholds.

From our previous analysis of the keyhole front equilibrium, one can relate the slope of the 3 best-fit lines plotted on Figure 6 through the experimental thresholds of the corresponding transitions, with the mean tilting of the keyhole front. It is easy to verify that in a (P -V w ) diagram, a linear relation occurs between incident laser power P and welding speed V w :

w 0 D V P k A 4 e π = P = B . V w , (8)
Where by using equations 5 and 6, the slope B of this linear relation between P and V w , is given by: B = (9)

From equation 9, the angle α that reproduces the slopes of these 3 best-fit lines drawn on Figure 6 are 15°, 30°and 45°for respectively the R/S, S/E and E/P transitions. One can note that these angles are in fair agreement with the experimental observations that can be obtained by using the high speed videos. Moreover, our model also shows that this slope B is proportional to the penetration depth (equation 9). Therefore, for a given transition (R/S, or S/E, or E/P) all the welding speed thresholds corresponding to that transition occur at the same penetration depth or angle α. Of course as expected, when one goes from R to P regimes, the corresponding penetration depths decrease as the welding speeds increase. So these results would indicate that the transition between these first 4 regimes is basically controlled by a characteristic tilting angle of the keyhole front wall. As we know that this angle also defines the direction and the dynamic pressure of the emitted vapor plume (this vapor plume being directed perpendicularly to its emitting surface), these results confirm that it is the level of interaction of the vapor plume with the rear melt pool that defines the type of its hydrodynamic regime [START_REF] Fabbro | Analysis of the various melt pool hydrodynamic regimes observed during CW Nd-Yag deep penetration laser welding[END_REF]. At low welding speeds, the keyhole front wall is slightly tilted; the absorbed intensity is then rather small, as well as the dynamic pressure of vapor. The vapor plume is directed quite horizontally inside the melt pool and so perturbs the melt pool from its bottom. This would correspond to the occurrence of the Single wave regime. As the welding speed increases, the tilting angle increases, as well as the absorbed intensity and correspondingly the dynamic pressure of the vapor plume. But this vapor plume is more likely emitted quite vertically and therefore perturbs more efficiently the top part of the melt pool as in the Pre-humping regime.

Penetration curve analysis.

We have seen that at low welding speeds, the experiments show that the penetration curve strongly deviates from the 1/V w scaling and even saturates at very low welding speeds. A perturbing mechanism is probably responsible of this limitation. Our video movies show that for these conditions ("Rosenthal" regime), strong keyhole fluctuations are observed and one cannot anymore consider a stationary regime in these conditions. Equation 7shows that at low welding speed, the absorbed intensity on the keyhole front, which is only a function of this welding speed, is rather low for these conditions. On the other hand, we know that the evaporation pressure resulting of the absorbed intensity is a direct function of this absorbed intensity. In previous experiments, by using a deflection technique [START_REF] Fabbro | Analysis of basic processes inside the keyhole during deep penetration Nd-yag CW laser[END_REF], we have estimated this evaporation pressure P evap that can be given by the following relation:

P evap C I abs [START_REF] Weberpals | Fundamental understanding of spatter behavior at laser welding of steel[END_REF] where C 6 10 -6 s m -1 (for 304-stainless steel). The constant C is also strongly dependent on the thermal properties of the used material.

It is this evaporation pressure that maintains opened the keyhole: the metallic vapor generated by the evaporation process from the keyhole front wall impinges the rear keyhole wall and impedes its collapse. Of course, this effect is only possible if this evaporation pressure is greater than the closing pressure P σ , resulting from the local surface tension, which is defined by the relation:

P σ = 2σ/D ( 11
)
where σ is the surface tension of the melt pool liquid. Therefore, by using equations 7, 10 and 11, the condition P evap > P σ for maintaining an opened keyhole for these conditions of low welding speeds becomes:

(C/k) V w >2σ/D (12)
Typically, for σ 1.5N/m, the equation 12 shows that the welding speed must be greater than 1.8 m/min in order to maintain opened a 0.5 mm keyhole diameter. These low values of welding speed agree fairly well with those observed for different experiments. The scaling obtained with the equation 12 is also in agreement with the previously described results that indicate a greater range of welding speeds for disturbed penetrations depths when smaller focal spots diameters are used. In fact for this regime, the keyhole cannot be stationary; after its internal collapse, it is continuously re-opened by the continuous incoming incident laser beam. As equation 12 defines a maximum value for the product D.V w (> 2σk/C), from equation 6, one can finally determine the corresponding maximum penetration depth e max given by ( 13):

e max [START_REF] Fabbro | Dynamical description of the keyhole in deep penetration laser welding[END_REF] Equation 13 gives the maximum penetration depth for achieving a stable keyhole regime; above e max , as explained previously, one can expect strong fluctuations that may lead for example to some defects such as porosity of the weld seam and correspondingly some reduction of the penetration depth. One can note that this maximum depth is only dependent of the incident laser power P. As a conclusion, for achieving a given deep penetration, this analysis shows the interest of using high power laser with the largest focal spot diameter compatible with the required welding speed. Using the previously defined parameters, equations 13 and 12 can be expressed in practical units as follows (for 304 stainless steel):

e max (mm) 1.5 P(kW) and V w (m/min) . D(mm) > 1 ( 14)

3.2.3. Effect of a side gas jet. In the previous paragraph we have seen that for low welding speeds, the evaporation pressure is not enough intense for maintaining an opened keyhole, in stationary conditions. A possible method for helping this opening consists in using a side gas jet that delivers a neutral gas inside the keyhole [START_REF] Kamikuki | Prevention of welding defect by side gas flow and its monitoring method in continuous wave Nd:Yag laser welding[END_REF][START_REF] Fabbro | Importance of the Coupling Between the Induced Vapor Plume and the Melt Pool, for Nd-Yag CW Laser Welding[END_REF] (see figure 11). If the gas is correctly delivered, the dynamical pressure of the gas jet can be adjusted in order to balance the closing pressure due to surface tension effects. Typically a flow rate of 20 l/min of Argon gas, delivered through a 2 mm diameter nozzle, generates on the nozzle axis a dynamical pressure of 20 kPa, at 5 mm from the keyhole aperture. By adjusting the Argon flow rate, one can therefore generate any dynamical pressure inside the keyhole. Figure 12 (a) and (b) show characteristic images extracted from a video sequence of two experiments: one experiment (a) is obtained without the use of the gas jet and the other (b) is obtained when the gas jet delivers a dynamical pressure of 8 kPa inside the keyhole. When the gas jet is properly used, the hydrodynamic flow of the melt pool is completely controlled: it is ejected rearwards in a continuous, stationary and quite laminar flow that is completely different from what is observed without the gas jet; we have shown in § 2.1 that in that case, this corresponds to the previous "Rosenthal regime", where the flow is chaotic and non-stationary with many bumps generated around the keyhole rim. Moreover, the penetration depth obtained with the gas jet is about 40% greater than without the gas jet, and porosities have disappeared [START_REF] Fabbro | Importance of the Coupling Between the Induced Vapor Plume and the Melt Pool, for Nd-Yag CW Laser Welding[END_REF]. So, we consider that this experiment confirms the previous given scheme that for these low welding speeds, the internal pressure inside the keyhole, generated by the ejected metallic vapor from the keyhole front, is not large enough for counterbalancing the closing pressure of the keyhole due to surface tension effects. In these conditions, a stationary keyhole can no longer exist; this keyhole must be "re-drilled" quite periodically and therefore the corresponding keyhole depth is limited compared to a situation where the keyhole has enough time to be fully developed. In fact one could consider that this behavior could be also an initiating phenomenon for producing "humps" that generate disturbances of the keyhole front. The local collapse of the keyhole walls generates a "normal" surface to the incident beam, which is then pushed downwards very efficiently due to the very high resulting local intensity, as in the drilling phenomena,. But the welding displacement makes a perturbation of this drilling process that stops it and induces a small angle of the keyhole front from which the local absorbed intensity decreases. This generates the following cycle: decreased evaporation pressure, followed by local collapses of the keyhole, and the process is then repeated.

Conclusion.

Coupled to previous experimental results where the geometry of the keyhole front [START_REF] Fabbro | Study of keyhole behavior for full penetration Nd-Yag CW laser welding[END_REF], and the dynamic pressure of ejected vapor plume [START_REF] Fabbro | Experimental study of the dynamical coupling between the induced vapor plume and the melt pool for Nd-Yag laser welding[END_REF], have been analyzed, for various conditions, the analysis of induced flow inside melt pool has led us to conclude that the interaction of this vapor plume with the melt pool generates or modifies its hydrodynamics, which was initially defined by the side flows of the melt generated underneath the focal spot by the local "piston effect" [START_REF] Semak | The role of recoil pressure in energy balance during material processing[END_REF]. The tilting of the keyhole front wall and the corresponding dynamic pressure of the ejected vapor plume control the degree of coupling between the vapor plume and the melt pool, which finally defines the induced regime: Friction stresses induced by the vapor flowing along the walls of a quite vertical keyhole in case of low welding speeds [START_REF] Fabbro | Analysis of the various melt pool hydrodynamic regimes observed during CW Nd-Yag deep penetration laser welding[END_REF], or direct collision of the vapor with the keyhole rear wall, generate strong waves and perturbations in the melt pool at higher welding speeds. Above a critical welding speed, the liquid jet rearwards accelerated by the evaporation pressure generates the humping instabilities.

The previous experiments have been performed with a rather large focal spot (0.6 or 0.45 mm) compared to those achievable with recent high beam quality lasers, which are thus able to deliver intensities more than one order of magnitude greater. The importance of the keyhole front wall tilting in the appearance of the different regimes has been highlighted. Whereas this parameter is a monotonic function of the ratio V w /I 0 (I 0 : incident laser intensity, see equation 4), similar characteristic regimes with these high beam quality lasers should also be observed, but they should appear at much higher welding speed thresholds. Some experiments with high beam quality lasers have already shown that critical welding speeds for "melt flow dynamic" humping process was largely increased [START_REF] Behler | Melt pool dynamics in high speed welding with modern high power solid state lasers[END_REF][START_REF] Myamoto | High-speed microwelding by single-mode fiber laser[END_REF]. So, future corresponding detailed experiments will be welcomed for confirming the occurrence of these regimes in these extreme conditions. In a second part of this article, we have analyzed the penetration depth curve. It has been shown that at high welding speeds the scaling of 1/V w , in agreement with our dynamical model of keyhole front equilibrium, is generally observed, and that the focal spot diameter is the main parameter that controls the range of this 1/V w scaling: the greater the focal spot diameter, the larger extent of this velocity range. At low welding speed, our dynamical model predicts that the absorbed intensity on the keyhole front is independent of incident intensity and only depends of the welding speed. As this absorbed intensity defines the resulting evaporation pressure, which is therefore decreased for these conditions, the collapse of the keyhole can occur at low welding speed and this effect limits the penetration depth of the keyhole that becomes non-stationary. This result is important because it shows the limited interest of small focal spots when large penetration depths are required. In fact, we show that it is the available incident laser power that defines the maximum stable penetration depth. The recent advent of lasers delivering output powers above about 10 kW, should allow the achievement of correct weld seams of about 10 to 15 mm in depth, at interesting welding speeds and with adapted focal spot diameters. Finally, a side gas jet of Ar gas, with a correctly adjusted induced dynamical pressure, allows to keep open the keyhole, with an increased penetration depth for these low welding speeds. These experiments have therefore emphasized the importance and the complexity of the hydrodynamics of the melt pool during laser welding. It is clear that if one wants a correct description of the melt pool and beyond it, the final weld seam geometry, particularly at high welding speeds, it is necessary to master 3-D simulations dealing with free surface problems. Moreover, if one wants to take into account the complete process of vapor effect during the laser welding process, it is also necessary to describe the vapor-free surface interaction, which is presently a very complex issue for numerical simulations, which has been addressed up to now in very few publications [START_REF] Ki | Modeling of Laser Keyhole Welding: Part I[END_REF][START_REF] Fabbro | Modeling of the melted bath movement induced by the vapor flow in deep penetration laser welding[END_REF].

Figure 1 :

 1 Figure 1: Sketch of the "Rosenthal" reg

Figure 2 :

 2 Figure 2: Sketch of the "single-wave" r2.3 Welding speeds between 9 to 11 m/miThis regime is observed for welding spee with its maximum length of typically abou

Figure 3 :

 3 Figure 3: Sketch of the "elongated" reg

  view of melt pool (scale: 1mm) and cr in: "Elongated keyhole" regime eds ranging from 9 to 11 m/min. It is characterized by ut 2 mm, observed at 11 m/min (see figure3). gime. Typical view of melt pool (scale: 1mm) and cro luctuations, but the resulting liquid oscillations are m duced swellings is much smaller. It is interesting to not heated: the first one corresponds of course to the one is located at the rear end of this elongated ke emitted from the second heated spot and so directed f por plume emitted from the keyhole front is also possib (scale:0.5 mm) y a keyhole that is elongated, oss-section (scale: 0.5mm).

Figure 4 :

 4 Figure 4: Sketch of the "pre-humping" r

Figure 5 :Figure 6 :

 56 Figure 5: Sketch of the "humping" reg Typical view of melt p

Figure 7 :

 7 Figure 7: Penetration depth e and 1/e variations as a function of the welding speed. Incident laser power: 4 kW; Focal spot diameter: 0.6 mm; Material: 304-stainless steel.

Figure 8 :

 8 Figure 8: Penetration depths as a function of welding speed for 4 different focal spot diameters: -125 and 200 microns, (from ref. [7], 4 kW, Nd-Yag laser) -600 and 1000 microns, (from ref. [8], 4 and 6.3 kW, diode laser) Corresponding critical welding speeds delimiting the 1/V w scaling are shown by vertical bars (Material: Mild Steel).

Figure 9 :

 9 Figure 9: Keyhole front tilting angle as a function of welding speed for two different methods of observation.

Figure 10 :

 10 Figure 10: Scheme of the longitudinal section of a keyhole in a case of full penetration. Incident beam has a uniform intensity I 0 , with a diameter D. Material is moving from left to right with the welding speed V w .

Figure 11 :

 11 Figure 11: Scheme of the positioning of the gas jet used for opening the keyhole during welding. Each configuration of rear or front jet can be used, they both give very similar results.

Figure 12 :

 12 Figure 12: Images extracted from a video sequence obtained without (a) and with (b) an optimized side gas jet. Welding speed: 3 m/min. P laser : 3 kW. White vertical arrows show the axis of incident laser beam location.


Yigang Li
email: yigang.li@ist.utl.pt

Rui M Almeida
email: rui.almeida@ist.ult.pt

Photoluminescence from Tb-doped photonic crystal microcavity for white light generation

Keywords: 42.70.Qs, 42.72.Bj, 68.65.Ac, 78.55.Qr, 78.67.Pt, 81.20.Fw

Terbium-doped one-dimensional triple microcavities have been prepared by sol-gel processing. The photoluminescence (PL) of Tb 3+ ions outside a microcavity structure, when excited by blue laser light at 488 nm, consisted of three distinct peaks at 542 nm, 587 nm and 619 nm. When embedded in the microcavities, the three Tb 3+ PL peaks were enhanced, balanced and broadened by the photonic crystal structure and combined into a continuous broad band. An analysis in the CIE colour space showed that white light can be obtained by mixing the modified Tb 3+ PL with the blue exciting light, while this is impossible with the original PL profile. This novel technique may improve white light generation by enhancing and modifying the spontaneous emission of current phosphors. It may also lead to the development of new rare earth phosphor materials based on 4f-4f transitions, able to generate white light more efficiently, via simpler and cheaper alternatives to the current phosphor compositions. A novel configuration to combine this kind of structure with a white light-emitting-diode (LED) is also proposed.

Introduction

Fluorescent materials enable a key technology for white light generation since, whether fluorescent or LED lamps are used, the excitation of a phosphor by ultraviolet (UV) or blue light to generate white light output is always an important technique [1][2][3][4][5]. For the current white LED lamps, Cerium(III)-doped yttrium aluminium garnet (Ce:YAG) and the various Europium(II)-doped ceramics are the most popular types of phosphors. Ce:YAG phosphors are usually combined with blue light excitation, whereas the Eu(II)-doped ceramics are excited in the near-UV [3][4][5]. The transitions from 4f N-1 5d 1 to 4f N states of the Ce 3+ or Eu 2+ ions (N, the number of electrons in the ground state 4f shell, is 1 for Ce 3+ and 7 for Eu 2+ ) cause PL emission. The peak wavelengths of the emitted light range from blue to red and can be mixed with each other, or with the blue exciting light, in order to generate the white appearance. The transitions between the 4f and 5d states are electric-dipole allowed [3,6]. That is why the Ce 3+ and Eu 2+ ions have strong absorption and emission cross sections. The 5d electrons are strongly affected by the environment surrounding these ions, including the ligand field, chemical environment, temperature, etc.. This causes the 4f-5d absorption and emission bands to be broad. The broad band emission and high PL intensity are the advantages of the current phosphors. But the sensitivity of the 5d states is also the reason why almost all these phosphors must be lightly doped (~0.1 at.%), single-phase ceramic powders. They must have high chemical purity and have to be fabricated and stored carefully to guarantee their fluorescent quality. These factors limit the development of new phosphors, decrease their working lifetime and increase their cost. On the other hand, rare-earth (RE) ions are also known to have extremely rich 4f N (N = 1-14, from Ce 3+ to Yb 3+ ) electronic energy configurations [7]. Many transitions between the 4f N states are located in the visible range. And one outstanding advantage of the 4f-4f transitions is that they are little influenced by the environment since the 4f orbits are shielded by the completely filled 5s and 5p electronic sub-shells [3,6]. That means that these active RE ions do not need to be located in a specific crystal lattice position, as in the case of 4f-5d transitions. They can heavily dope ceramics, glasses, amorphous or organic materials freely and still keep their fluorescence properties without too much change. This is an obvious advantage for the development of new types of phosphors, which may decrease the fabrication costs as well. However, the 4f-4f transitions of the RE ions are not utilized in the current white LED techniques because they also have two significant shortcomings. The first problem is that the 4f-4f transitions are electric-dipole forbidden [8]. They can only happen through magnetic-dipole or electric-quadruple mechanisms, but mainly through electricdipole transitions induced by crystal field effects. This forbidden character makes the 4f-4f transitions much weaker than the 4f-5d ones. But this is still not fatal, since the weak absorption and emission intensities of 4f-4f transitions may be compensated by additional active ions through heavy doping. The other problem stems from the fact that the 4f electrons are well shielded. This makes the 4f-4f transition peaks quite narrow, so that the spontaneous emission (SE) from any of the 4f N levers of the RE ion always manifests itself as one or more distinct peaks, according to their fluorescence branching ratios. It is difficult to generate a continuous white light spectrum based on distinct peaks with different intensities. In the present paper, a technique using one-dimensional (1-D) photonic bandgap (PBG) structures is firstly introduced for white light generation. It is demonstrated that this novel technique may also be a way to improve the application of 4f-4f transitions for white light generation. PBG structures, also known as photonic crystals, are periodic dielectric structures which can manipulate the SE of fluorescent materials embedded inside them, by changing the optical mode density which surrounds the active ions [9,10]. It has been proved in our previous work that a 1-D PBG structure can effectively change the SE properties of RE doping ions, namely broadening their PL bandwidth and simultaneously enhancing the emitted light intensity [11]. In the present work, this technique has been extended to white light generation and a 1-D terbium-doped triple coupled microcavity was prepared as a demonstration of this novel idea. When pumped by blue light at 488 nm, the PL from Tb 3+ ions outside a PBG structure includes three distinct peaks. But when a triple microcavity structure is doped with terbium, these three peaks are enhanced, balanced and broadened, combining into a continuous fluorescence band ranging from green to red. This result supports a new method to explore the white light generation phenomenon through an increased member of RE-containing materials. A possible scheme to apply this technique to white LED illumination is also discussed.

Experiments

The multilayer microcavity samples were prepared by sol-gel processing. Silicate glass and titania films were alternately deposited on single crystal silicon substrates. The silicate sol was prepared by mixing 3 ml of tetraethylorthosilicate (TEOS), 6 ml of isopropanol and 0.48 ml of 0.01N HCl, with continuous stirring at 70 ºC for 3 hours; then, an additional 16 ml of isopropanol, 0.5 g of Al(NO 3 ) 3 and 0.3 g of Tb(NO 3 ) 3 were added, corresponding to a dopant concentration of 5 mol% Tb 3+ ions (on a cation basis). The titania sol was prepared by mixing 2.5 ml of titanium isopropoxide with 3 ml glacial acetic acid, followed by stirring for 1 hour; then, 16 ml of ethanol and 0.21 g of Tb(NO 3 ) 3 were added, leading to a dopant concentration of 5 mol% Tb 3+ ions (Tb/Ti ratio of 5:100). The additional 16 ml of isopropanol and the 16 ml of ethanol were volumes empirically determined to adjust the single layer silicate and titania film thickness to the designed values. All sols were aged for 24 hours, before the multilayer spincoating deposition process. Each individual layer was heat treated at 1050 ºC for 30 s. More details about the fabrication technique can be found in [12]. A reference sample with the structure of H 10 L 14 , having the same number of silicate glass and titania layers, but without the PBG structure, was also prepared, in order to determine the effects which originated specifically from the triple microcavity structure. The SEM cross section micrograph of one sample was taken with a FEG-SEM JEOL JSM-7001F, in the back-scattered electron mode. The reflection spectra of all samples and their PL spectra from green to red were recorded by two standard setups. A top view of the reflection measurement setup is sketched in figure 1. White light from a tungsten lamp (Cuda products corporation, I-150) was focused by a lens. It went through an iris and a beam splitter and then irradiated the surface of the sample, which was held on a rotation stage. The diameter of the light spot on the sample was about 5 mm. The iris could control the brightness of the light spot and it helped to confirm that the sample was in the perpendicular direction, by turning the rotation stage until the reflected light spot coincided with the iris hole. A piece of borosilicate glass was used as the splitter and the ~4 % of light it reflected entered a 10X microscope objective and was then coupled into a multimode optical fiber with a core diameter of 600 µm. The collected light was sent to a spectrometer consisting of a 0.85 m double monochromator (Spex 1403) and a photomultiplier tube (PMT, Hamamatsu, R928). The spectrum of the light reflected by an aluminium mirror was recorded as the 100 % reflectivity reference; the reflection spectra of other unknown samples were obtained by rationing their reflection and the reference spectra. The measurement setup for PL was similar to the reflection one. The differences were: the removal of the iris, the splitter and the microscope objective; the replacement of the white light beam with the 488 nm line of an Ar + ion laser (Spectra-Physics mod. 2017) with a power of 200 mW; and a rotation of the sample, pumping it at a large incidence angle (~45º), while collecting the PL directly by the multimode optical fiber in the perpendicular direction.

Results

The PL of Tb 3+ ions ranges from green to red outside a PBG structure and it includes three distinct peaks at 542 nm, 587 nm and 619 nm, respectively. The idea is to enhance, balance and broaden these three PL peaks by means of a PBG structure and make them combine into an appropriate continuous fluorescence band. For this purpose, a triple coupled microcavity with the structure (LH) 3 L 2 HLHL 2 HLHL 2 (HL) 3 was designed, where L and H represent low and high refractive index quarter-wave films. The reflection spectrum of this structure can be simulated by the transfer matrix method (TMM) [11,13]. Generally, this reflection profile contains three defect peaks (or "pass bands") located inside the stop band. The wavelength range covered by the stop band and the position of the defect peaks can both be tuned through the refractive index and thickness of each layer. In the present work, the proposed structures were prepared by the sol-gel method and the low and high refractive index materials were sol-gel derived silicate glass and titania films, respectively. Based on the refractive indices of these two materials, 1.45 for silicate glass and ~2.2 for titania in the visible range, when the thickness of the silicate layers is ~110 nm and that of the titania layers is ~50 nm, the stop band of the proposed structure will cover the visible range and the three defect peaks will closely match the three PL peaks of Tb 3+ . The two best results obtained in the present work are reported in this paper. One of the samples was labelled sample #1 and the other sample #2. The SEM cross section micrographs of sample #1 and the reference sample are shown in figure 2. The reflection spectrum of sample #1 is plotted in figure 3 (solid line on top). The PL of the Tb 3+ ions outside a microcavity is also drawn at the bottom of figure 3, measured on the reference sample. The PL spectra of both PBG samples are plotted in figure 4 (solid lines at bottom), together with their reflection spectra (solid lines on top) and the reference PL spectrum (dashed lines). Figure 4 (a) refers to sample #1 and figure 4 (b) to sample #2. Since the reference sample was prepared with the same sols and processing methods of sample #1, the PL intensities of both can be compared directly in figure 4 (a). Generally, the PL was enhanced near the resonance wavelengths and changed very little outside the defect peaks. According to that, the PL spectrum of sample #2 in figure 4 (b) was normalized to the reference spectrum by the PL intensity emitted outside the resonance wavelengths (around 542 nm and 587 nm). Compared to the reference PL, it is clear that the PL near the resonance wavelengths of each microcavity spectrum was enhanced and the three distinct PL peaks of Tb 3+ ions were broadened and combined into a continuous fluorescence band.

Discussion

The top-left of figure 3 illustrates the designed triple coupled microcavity structure, in which the light blocks represent the silicate glass layers and the dark blocks represent the titania ones. Compared to this illustration, figure 2 shows that the proposed structure was prepared successfully. The bright thin strips in the SEM micrograph are titania layers and the darker thick strips are silicate glass. In the middle of the cross section, there are three silicate glass layers (D1-D3) whose thickness is double that of the other silicate layers and which correspond to the cavity defect layers. According to this picture, it can be estimated that the thickness of each silicate layer in sample #1 was 114 ± 8 nm and that of each titania layer was 52 ± 6 nm, close to the designed values of ~110 nm and ~50 nm, respectively. The optical quality of the samples can be judged from their reflectivity spectra. The reflection spectrum of sample #1 is represented by the solid line at the top of figure 3, while the simulated reflection spectrum calculated by TMM is plotted as a dashed line. The refractive indices used in the TMM model were from our previous work [12] and the thickness of each layer was determined from the best fit of the simulated to the measured spectrum. The final fitting results were 110 nm for the silicate and 49.5 nm for the titania layers. These two values match the thicknesses obtained from the SEM micrograph (figure 2) very well, since 1 pixel in figure 2 represents ca. 4.5 nm. It is shown in figure 3 that the profile of the measured reflection spectrum coincided with the theoretical curve almost perfectly, including the stop band, the defect peaks and the fringes, demonstrating the high quality of sample #1. The conclusion was the same for sample #2, based on similar considerations. The three defect resonance wavelengths of sample #1 were 536 nm, 571 nm and 617 nm, respectively and the average Q factor (λ/∆λ) of these three defect peaks was 54. The three defect resonance wavelengths of sample #2 were 528 nm, 565 nm and 613 nm, respectively and their average Q factor was 49. The Tb 3+ PL outside the microcavity consists of three distinct peaks at 542 nm, 587 nm and 619 nm, with most of the PL energy concentrated on the green peak (542 nm). The three distinct PL peaks correspond to the 4f-4f transitions from the 5 D 4 state of Tb 3+ ions to their 7 F 5 , 7 F 4 and 7 F 3 states, respectively, as denoted in figure 3. The diagram of the eight lowest energy states of Tb 3+ ion is given in figure 5 [14]. The relative intensity of all these transitions depends on the SE branching ratios. Tb 3+ ion is a typical example of the shortcomings of the 4f-4f transitions discussed in the introduction. It has strong absorption bands in the blue and UV and its 5 D 4 level has very high PL quantum efficiencies. In fact, Tb-doped phosphors are widely used in the current fluorescent lamps, but only for their green emission [1,3]. Although the transitions of Tb 3+ ions from the 5 D 4 state to the 7 F J multiplets cover the visible range from blue to red, they cannot generate proper white light individually. In figure 4 (a) and (b), the PL spectra from the Tb 3+ ions embedded in the triple coupled microcavity structure of the two samples are plotted. By comparison with the spectrum of the reference sample, it is obvious that the PL near the resonance wavelengths has been enhanced by the PBG structure. This PL enhancement has modified the profiles of the three original distinct PL peaks of Tb 3+ ions, causing them to broaden and overlap. The physical explanation of a similar phenomenon concerning the SE from an erbium-doped double microcavity has been discussed in great detail in a previous publication [11], where it was shown how the 1-D PBG structure can enhance and modify the SE of fluorescent materials. For the red PL at 619 nm, the corresponding pass bands of samples #1 and #2 were both located very close to this peak wavelength, which significantly enhanced the red PL. At the same time, the green pass bands of the two samples were both somewhat blue-shifted relatively to the green PL at 542 nm, thus not enhancing the green PL too much, but clearly broadening it on the blue side. The most interesting change was at the yellow pass band (571 nm for sample #1 and 565 nm for sample #2), whose defect peak was located between the green (542 nm) and yellow (587 nm) PL peaks of Tb 3+ . As a result, a new PL peak was generated at the resonance position, combining the green and yellow emissions of Tb 3+ into a continuous PL band. These new PL peaks, as well as the new green PL peak at 528 nm for sample #2, can be explained by the Stark splitting of the 4f energy states, shown at the right hand side of figure 5. In general, when RE ions are embedded in a solid, the crystal field interaction can split a free RE ion level with total angular momentum J into 2J+1 distinct sublevels, if J is an integer and into (J+1/2) sublevels, if J is a half-odd integer [START_REF] Morrison | Handbook on the physics and chemistry of rare earths[END_REF]. But the actual number of sublevels and their energy splitting are ultimately determined by the symmetry of the crystal field surrounding the RE ion. The diagram on the right hand side of figure 5 is an example of how the eight lowest energy levels of Tb 3+ ions split into many sublevels, according to the PL data from Tb:YAG [14]. For the heavily doped silicate glass and titania films in the present case, the Tb 3+ ions are located in environments of varying geometries and the crystal fields surrounding them are of much lower symmetry and much more random than those in YAG crystal, especially in the glassy matrix. So the actual Stark splitting of each state was much larger in samples #1 and #2 than in YAG crystal and the 7 F J states in these two samples became a quasi-continuous energy band. When outside the PBG structure, the excited ions are mainly located in the lowest sublevels of 5 D 4 state, because of the Boltzmann distribution law and the transitions between each two sublevels still obey the SE branching ratios. That is why the reference PL spectrum included three distinct peaks and most of its energy was concentrated in the green peak. But once the Tb 3+ ions were embedded into the triple coupled microcavity, the SE branching ratios changed and the transitions between any two sublevels resonant with the defect peaks become strongly enhanced. This is where the "new" PL peaks come from. To the best of our knowledge, this kind of modification combining several distinct PL peaks into a continuous broad band by means of multiple coupled microcavities has not been reported before. For white light sources, a lamp possessing a continuous broadband spectrum will give higher colour rendering index (CRI) than those which have only several narrow bands. The effective optical spectra of a 1-D PBG structure undergo blue-shifts when the propagating light deviates from the perpendicular direction. So the observed modified Tb 3+ PL spectrum changes depending upon the detection angle. The final profile observed at different angles depends on the resulting enhancement at the effective resonant wavelengths for each propagation direction. However, both the theoretical simulations and the experimental results show that the blue-shift of the resonance wavelengths for deviations of up to 10º off-normal are less than 3 nm and the observed Tb 3+ PL spectrum doesn't change too much. Such deviations correspond to a LED emitting with a 20º full viewing angle. For example, the blue-shift for a 15º deviation from the normal, corresponding to a 30º full viewing angle, is also still only 7 nm. The profile modification in figure 4 has balanced the green and red proportions of the Tb 3+ PL to a good extent. The CIE colour coordinates of the reference PL spectrum and those of samples #1 and #2 PL have all been plotted in figure 6. The latter two points totally overlapped each other and they obviously moved to a "redder" position compared to the reference PL. The centre excitation wavelength of the current blue-excited white LED is ca. 465 ± 15 nm, but sometimes may even be located at 420 nm [4,[START_REF] Hirosaki | [END_REF]. The area covered between the two lines connecting the sample coordinate and the exciting wavelengths represents the possible colours that result from the sample PL and the excitation light. The white point E is shown at the centre of the CIE diagram. It is clear from figure 6 that, from the Tb 3+ PL outside PBG structure, it is impossible to obtain white light simply by mixing blue light into it. However, the E point can be reached, in theory, by using the PL from the triple coupled microcavity. Besides the profile modification, the absolute PL intensity of the PBG samples was enhanced as well. The total PL energy from sample #1 was ~1.7 times larger than that from the reference sample under similar pumping conditions. The normalized PL energy from sample #2 was ~1.9 times larger, similar to the result from sample #1. This SE energy enhancement can be attributed to an increase in the emission rate of Tb 3+ ions embedded in the triple microcavity, similarly to the explanation given in ref. [11]. Finally, a possible scheme to apply the 1-D PBG structure to a white LED is proposed in figure 7. It is similar to the typical architecture of a common white LED [3]. The base block connected with two wires is the semiconductor chip emitting the blue or UV excitation light. For the current white LED, this chip is buried under phosphor powders to down-convert the exciting light to a hybrid light having a white appearance. The present new scheme replaces the phosphor powders with a phosphor patch pasted onto the semiconductor chip directly. The configuration of the phosphor patch is sketched on the right hand side of figure 7. It consists of a very thin transparent glass substrate; a short-pass filter is deposited on its bottom side to let the exciting light pass, but to reflect all the other light of longer wavelength emitted by the phosphor. On the top side, a fluorescent PBG structure is deposited to convert the exciting light into a white one. Because the novel, PBG-assisted white light generation technique introduced in the present paper depends on an optical structure and not on a specific fluorescent material or a fabrication technique, any phosphors, from the traditional Ce:YAG to other possible fluorescent materials working based on 4f-4f transitions, can be applied in this scheme, as long as they can be incorporated into the PBG structure. Obviously, this will considerably improve the development of novel materials for white light generation. The current phosphors may also benefit from the enhancement and modification effects provided by the PBG structure. An added advantage of this scheme is that it will avoid most of the light scattering from the phosphor powders, which may be beneficial to the LED thermal management and energy efficiency [17].

Conclusion

In summary, terbium-doped triple coupled microcavities were prepared by sol-gel processing in the present work. The three pass bands of the triple microcavities were designed to match the three visible PL peaks of Tb 3+ ions. The PL of Tb 3+ ions outside a microcavity consisted of three distinct peaks. Once embedded into the microcavities, the three Tb 3+ PL peaks were enhanced, balanced and broadened by the PBG structure and combined into a continuous broad band. The CIE coordinates of the original and the modified Tb 3+ PL profile were calculated and compared. It was shown that white light can be obtained by mixing the modified PL emission with the blue exciting light, while this is impossible for the original PL profile. While the results obtained do not mean that the present terbium-doped PBG structure can immediately be used in a white LED, they clearly highlight the functions and potential of this novel PBG-assisted technique, which may improve white light generation by enhancing and modifying the SE of current phosphors. It may also significantly help the development of new RE phosphor materials based on 4f-4f transitions. These new improvements may be able to generate white light more efficiently, allowing simpler and cheaper alternatives to the current phosphor compositions. A novel configuration to apply the PBG structure to a white LED has also been proposed.

Figure 1 .

 1 Figure 1. Experimental setup for the measurement of reflection spectra.

Figure 2 .

 2 Figure 2. FEG-SEM cross section micrographs of (a) sample #1 and (b) the reference sample, in the back-scattered electron mode. The bright strips are titania layers and the dark strips are silicate glass. The estimated thickness of each silicate layer in sample #1 is 114 ± 8 nm and that of each titania layer is 52 ± 6 nm. The three layers labelled D1-D3 in (a) are the cavity defect layers.

Figure 3 .

 3 Figure 3. Simulated (dashed line) and measured (solid line) reflection spectra of sample #1. The structure of this triple coupled microcavity is illustrated at the top-left: the light blocks represent silicate glass layers and the dark blocks represent titania layers; all layers are doped with 5 mol % Tb. The Tb 3+ PL without microcavity, for a reference sample pumped by the 488 nm Ar +

Figure 4 .

 4 Figure 4. PL from terbium-doped triple coupled microcavity samples #1 (a) and #2 (b) (solid lines) and from the reference sample (dashed line), under the same pumping conditions at 488 nm. The PL of sample #2 in (b) has been normalized by the PL intensity emitted outside the resonance wavelengths. The reflection spectrum of each PBG sample is plotted as a solid line at the top of the figures.

Figure 5 .

 5 Figure 5. The lowest eight electronic energy states of Tb 3+ ion. The right hand side shows a diagram with the Stark splittings of each state, drawn from data of Tb:YAG [14].

Figure 6 .

 6 Figure 6. CIE coordinates for the PL of samples #1 and #2, plus the reference sample. The points corresponding to samples #1 and #2 overlap completely. The area covered between the two lines connecting the PL emission point and the exciting wavelengths represents the possible colours resulting from a mixture of the PL and the excitation lights. The E point at the centre of the diagram is the white colour point.

Figure 7 .

 7 Figure 7. Proposed scheme for the application of the PBG structure to a white light LED. The block connected with two wires is the light emitting semiconductor chip and the block on top of it is a proposed phosphor patch whose architecture is sketched on the right hand side.

Author to whom any correspondence should be addressed.Confidential: not for distribution. Submitted to IOP Publishing for peer review 16 September 2010

Acknowledgements

We would like to acknowledge the financial support of FCT (Fundação para a Ciência e a Tecnologia). One of us (Y.G. Li) would also like to thank FCT for support under an Assistant Researcher contract at IST (Instituto Superior Técnico).