A Hennad

Dr M Yousfi
email: yousfi@laplace.univ-tlse.fr

Ion collision cross sections with transport and reaction coefficients in Ar, Cl 2 and N 2 and their mixtures for photonic crystal applications

Keywords: numbers(s): 52.20.Hv, 51.50.+v, 52.25.Fi

The ion swarm transport coefficients such as reduced mobility, diffusion coefficients and reaction rates of the following systems Ar + /Cl 2 , Ar + /N 2 , N 2 + /Cl 2 and N 2 + /Ar have been determined from a Monte Carlo simulation using calculated elastic and experimentally estimated inelastic collision cross sections. The elastic momentum transfer cross sections have been determined from a semi-classical JWKB approximation based on a rigid core interaction potential model. The inelastic cross sections have been fitted using the measured reaction coefficients as for instance ion conversion reaction coefficients. Then, the cross sections sets are fitted using either the measured reduced mobility when available in the literature or the zero-field mobility calculated from the Satoh's relation. From the sets of elastic and inelastic collision cross sections thus obtained in Ar + /Cl 2 , Ar + /N 2 , N 2 + /Cl 2 and N 2 + /Ar systems, the ion transport and reaction coefficients are then calculated in pure gases and also in binary and ternary mixtures involving Cl 2 , Ar and N 2 over a wide range of reduced electric field. These ion data are very useful for modelling and simulation of non equilibrium low pressure electrical discharges used more particularly for etching of the III-V compounds in the case of crystal photonic applications.

Introduction:

In the frame work of photonic crystal applications, inductively coupled plasmas (ICP) in chlorine gas mixtures (Cl 2 /Ar, Cl 2 /N 2 , Cl 2 /H 2 , etc.) are very promising candidates for etching the III-V compounds. The presence of Cl 2 in the mixture favours the volatility of chloride species formed during plasma etching while the presence of N 2 increases the anisotropy of the etching and removes the roughness of the hole surfaces (see for instance Refs [1] up [4] and the references given therein). Furthermore, ICP sources are able to generate high ion fluxes with an ion energy controlled thanks to the bias potential of the substrate holder thus leading to operating parameters very favourable to a high etching velocity. In order to better understand the plasma formation and its stability in presence of negative chlorine ion and also to optimise the positive ion flux arriving to the etched surface, the experimental investigations have to be completed by discharge modelling. The electrodynamics and kinetics discharge modelling needs more particularly a good knowledge of ion collision cross sections and also transport and reaction coefficients in the chlorine mixtures used in photonic crystal applications. In the literature there are some compilations on ion data as for instance those of Ellis et al (refs [5]) or Viehland [6] or more recently Petrovic et al [7] on negative ion for nanotechnology applications, Nelson et al [8] for ion in air and flue gases and Yousfi et al [9] on ions in gas mixtures for PECVD thin film deposition. However, in the gas mixtures of our interest involving chlorine, ion data are very sparse more particularly in the case of ions interacting with their non parent gases. In fact, ion collision cross sections are available in the literature only in the case of ion interacting with their parent species as for instance in the case Ar + /Ar [10] or N 2 + /N 2 [11]. For binary or ternary mixture involving Cl 2 , Ar and N 2 , several ions can be formed in the low pressure discharges of our interest as for example Ar + , N 2 + , N + , Cl -, Cl 2 + and Cl + (see e.g. [12]). Obviously, the transport and the interactions of such ions with the neutral gas mixture directly affect the electro-dynamics and the reactivity of the ICP discharge and therefore its etching efficiency. So, the aim of our first work in these chlorine mixtures is to give the collision cross sections of Ar + and N 2 + interacting either with Cl 2 , or Ar or N 2 . These concern more particularly the systems Ar + /Cl 2 , Ar + /N 2 , N 2 + /Cl 2 and N 2 + /Ar whose the cross sections are not available in the literature. The calculation method of elastic momentum transfer cross section based on JWKB approximation using a rigid core interaction potential model is given in section 2 with the choice of inelastic cross sections. An optimized Monte Carlo method [13] is used for the fitting of the collision cross sections from comparison with measured mobility data or Satoh's relation [14] in the case of elastic processes and from comparison with measured reaction coefficients in the case of inelastic processes. In section 3, from the present fitted sets of elastic and inelastic collision cross sections of Ar + and N 2 + in their non parent gases (Ar, Cl 2 and N 2 ) and from the literature (refs [10] and [11]) sets in the case of these ions in their parent gases (Ar + /Ar and N 2 + /N 2 ), the ion transport and reaction coefficients are calculated and analysed over a wide range of reduced electric field E/N in binary and ternary mixtures including Cl 2 , Ar and N 2 used as gas mixture filling inside ICP reactor for crystal photonic applications.

Method of calculation and analysis of collision cross sections

Method of calculation

The ion transport and reaction coefficients are calculated from an optimized Monte Carlo method well adapted to both symmetric and asymmetric ion/gas system [13]. This needs as input data both elastic and inelastic collision cross sections. The elastic momentum transfer cross section has been calculated using a semi classical formalism based on JWKB approximation for the phase shift using a rigid core potential model describing the ion/molecule interaction [15]:

             - - -              - - - = 4 3 12 12 3 a r a r a r a r n n n ) r ( V m n m m ε (1)
r is the intermolecular distance, ε m the minimum energy of the potential, r m the position of the minimum, n is the power of the repulsive part of the potential and a is the shift between the mass and the charge centres.

In the framework of JWKB approximation, the phase shift δ l using depends on impact parameter b and interaction potential V(r) as following:

1 / 2 1 / 2 2 2 2 2 ( ) ( ) 1 - 1 c l b r r V r b b b k - - dr k - dr r r δ δ ε ∞ ∞     ≈ =   ∫       ∫ (2) with b= k l 2 / 1 +
where l is the angular momentum quantum number, b the impact parameter, and k the wave number of the relative motion proportional to the ion/neutral relative energy ε r

The elastic momentum transfer cross section Q m (ε r ) is calculated from :

∑ ∞ = + - + = 0 1 2 2 1 4 l l l r m ) ( sin ) l ( k ) ( Q δ δ π ε (3)
Then , the inelastic cross sections have been either taken from literature or fitted using the available data on reaction coefficients.

The set of calculated elastic cross sections Q m and estimated inelastic cross sections in Ar + /Cl In the case of Ar + /Cl 2 , according to the literature, the most probable collision processes in the energy range of our interest are: Ar Cl Ar Cl

+ + +  → + (1) 2 2
Ar Cl Cl Ar 4.28 eV

+ + +  → + + (2) 2
Ar Cl Cl Cl Ar 0.20 eV

+ + +  → + + + (3)
Reaction (1) corresponds to the classic elastic collision with momentum transfer cross section Q m (see figure 1) while reaction (2) is a non resonant charge transfer. This exothermic reaction is observed by Murrel [16] and Spanel et al [17]. Reaction (3) is a dissociative charge transfer producing Cl + . According to Spanel et al., the ion production of Cl ( )

+ + Σ or 2 2 u Cl ( ) + Π
is the largest reaction (75%). This total inelastic cross section Q(Cl 2 + ,Cl + ), corresponding to reactions (2) and (3) and shown in figure 1, is validated from the good agreement obtained between the measurement (k in =1.49 ± 0.5 x 10 -10 cm 3 s -1 Ikezoe and al. [START_REF] Ikezoe | Ion reaction research group of mass spectroscopy society of Japan[END_REF]) and the Monte Carlo calculations of the total non-resonant charge transfer rate k in .

In the case of Ar + /N 2 system, the most probable collision processes in the energy range our interest are: Ar N Ar N

+ + +  → + (4) 2 2
Ar N N Ar -0.07 eV

+ + +  → + (5) 2
Ar N N N Ar -8.53 eV

+ + +  → + + (6) 2
Ar N ArN +N -8.20 eV

+ + +  → (7)
Reaction (4) corresponds to the elastic momentum transfer cross section Q m . Reaction ( 5) is a non-resonant charge transfer. The threshold and the collision cross section corresponding to reaction (5) are given in the literature (Viggiano and al. [START_REF] Viggiano | [END_REF], Smith and Adams [20], Liao et al. [21], Liao et al [22], Flesch and Ng [23]). The total non-resonant transfer charge cross section Q(N 2 +

) by Ar + ( 2 P 3/2 ) and Ar + ( 2 P 1/2 ) impacts is shown in figure 2. This cross section is measured by Liao et al [22] and Flesch and Ng [23]. Reaction (6) leading to the production of N + is observed by Flesch and Ng ( [23] and [24]) while reaction (7) corresponding to production ArN + has been detected by Flesch and Ng [23] and also Tosi et al. [25]. Concerning the magnitudes of the inelastic cross sections of reactions ( 5), ( 6) and ( 7), it is worth noting that reaction ( 5) is a largely dominant process in comparison to reactions ( 6) and (7). This is why the inelastic cross section of theses two later reactions have been neglected and not shown in figure 2.

In the case of N 2 + /Cl 2 system, in addition to the elastic collision (reaction 8), there is the non-resonant charge transfer (reaction 9). N Cl N Cl

+ + +  → + (8) 2 2 2 2
N Cl Cl N 4.10 eV

+ + +  → + + (9)
Reaction ( 8) is characterized by its elastic momentum transfer collision cross section Q m shown in figure 3 with the inelastic cross section for asymmetric charge transfer reaction (9). This interaction is an exothermic process because the energy difference between the ionization potentials of N 2 (15.58 eV) and Cl 2 (11.48 eV) is positive and equal to 4.10 eV. This inelastic cross section Q(Cl 2 + ) corresponding to reaction ( 9) is validated from the good agreement obtained between the measurement (k in =6.0 x 10 -10 cm 3 s -1 ± 20% Anicich [26]) and the Monte Carlo calculations of the non-resonant charge transfer rate coefficient.

In the case of N 2 + /Ar system, the dominant interactions between N 2 + and Ar occurring in our energy range (thermal energy up to about 100 eV) are, respectively, the elastic momentum transfer cross section (reaction 10) (Qm in figure 4) and the non resonant charge transfer (reaction 11) (Q(Ar + ) in figure 4). In fact reaction (reaction 12) producing ArN + is also observed by Tosi et al [27] but has a much more lower magnitude cross section and therefore has been neglected. 2 2

N Ar N Ar

+ + +  → + (10) 2 2
N Ar Ar N +0.185 eV

+ + +  → + (11) 2
N Ar ArN N 5.70 eV

+ + +  → + - (12)
The inelastic cross section of reaction (11) is measured by Amme and Hayen [28] for energy range 50 eV to 10 3 eV. At low energy, the shape is given by the classical Firsov relation [29] also applicable to symmetric system while the magnitude of this cross section is fitted using the literature data (Ref [START_REF] Ikezoe | Ion reaction research group of mass spectroscopy society of Japan[END_REF]). As previously emphasized, the sets of collision cross sections shown in figures 1 up 4 for Ar + /Cl 2 , Ar + /N 2 , N 2 + /Cl 2 and N 2 + /Ar systems have been fitted in order to lead to the best agreement possible between calculated and measured ion mobility data and rate coefficients of asymmetric charge transfer. For the considered ion/gas systems, there are experimental ion mobility data only in the case of N 2 + /Ar system. Therefore, in the other systems (Ar + /Cl 2 , Ar + /N 2 and N 2 + /Cl 2 ) where there are no experimental data on ion mobility, the momentum transfer cross section fitting fulfils to the following conditions: -at low E/N (in the E/N region where mobility shows a plate as a function of E/N), the set of cross sections is chosen to have a good agreement between Monte Carlo simulation and Satoh's relation which already shows confident results in numerous ion/gas systems where there are experimental mobility data at low E/N, -at higher E/N (after the mobility plate), the potential parameters (ε m , r m and n ) needed to calculate the elastic momentum transfer cross section (relation 3) are chosen to have a mobility shape similar to the measurements already available in the literature for ion/gas systems having a behaviour close to the studied system in terms of reduced mass and colliding target. For instance, the E/N position of the maximum mobility bump shown in figure 5 in the case of Ar + /N 2 system is chosen close to 180 Td corresponding to the case of a similar ion/gas system taken from literature (K + /N 2 [5]).

Ion transport and reaction coefficients in

Figure 5 shows the Ar + mobility data over a wide E/N range (from 1 Td up to 1000 Td) in the case of pure N 2 , Ar and Cl 2 . The available experimental literature data for Ar + /Ar systems and the Satoh's data at low E/N (E/N=1 Td) are also displayed. First, as previously emphasized, the different sets of collision cross sections are chosen to fit the Satoh's value at low E/N. Then, we also observe the good agreement in the case of Ar + /Ar system obtained from the set of the collision cross section taken from the literature (ref [10]). In the case of Ar + /N 2 system, as already emphasized, the potential parameters are chosen in order to have a mobility shape near the E/N bump region (180 Td) similar to mobility data given in the literature in the case of a similar system (K + /N 2 [5])). In the case of Ar + /Cl 2 which has an asymmetric charge transfer process exothermic (effective even at low or thermal ion energy), the chosen potential parameters leads to a small bump near about 300 Td. The magnitude of the mobility data shown in figure 5 are directly linked to the inverse of the magnitude to the total collision cross sections (or Q tot collision frequency). Indeed, the relation between mobility K 0 (E/N), isotropic part of ion distribution φ 0 (ε r ) and total collision frequency ν tot (

1/ 2 tot r r r tot r ( ) N( 2 / M ) Q ( ) ν ε ε ε =
) can be written as:

( )

3/2 0 r r 0 r tot r r 0 ( ,E / N ) K E/N d ( ) ∂φ ε ε ε ν ε ∂ε ∞ ∝ ∫ (13)
This is why the mobility of Ar + in N 2 corresponding to the lowest total collision cross section (or collision frequency) is the highest one and the Ar + /Cl 2 mobility is the lowest one.

Figure 6 shows the N 2 + mobility data over a wide E/N range in the case of the same pure gases (N 2 , Ar and Cl 2 ). The available experimental literature data for N 2 + /Ar and N 2 + /N 2 systems and the Satoh's data at low E/N (E/N=1 Td) are also displayed. First, figure 6 confirms that the different sets of collision cross sections fit the Satoh's value at low E/N. Then, there are a good agreements between the calculated and measured mobility data in the case of the fitted N 2 + /Ar set and the N 2 + /N 2 set taken from the literature (ref [11]). In the case of N 2 + /Cl 2 which has also an asymmetric charge transfer process exothermic (effective like Ar + /Cl 2 even at low or thermal ion energy), the chosen potential parameters leads to a small bump near about 400 Td due to an energy ε m of the well depth potential higher than the one corresponding to Ar + /Cl 2 system. Furthermore as already emphasized, the magnitude of mobility data is inversely proportional to the total collision frequency. Therefore the mobility of N 2 + in Ar corresponding to the lowest total collision frequency is the highest one and the N 2 + /Cl 2 mobility is the lowest one. Figure 7 displays as a function of mean ion energy a comparison between measured (Ref [START_REF] Viggiano | [END_REF]) and calculated reaction rate coefficients of asymmetric charge transfer for Ar+/N 2 system for three gas temperatures. The good agreement between measurement and calculation confirms the good choice of the inelastic collision cross section shown in figure 2 for the asymmetric charge transfer process.

Figure 8 shows the variation over a wide E/N range (1 Td up to 1000 Td) of the inelastic reaction coefficients for asymmetric charge transfer for Ar + /N 2 , Ar + /Cl 2 , N 2 + /Ar and N 2 + /Cl 2 . The available experimental data at thermal or gas energy are also displayed at low E/N (1 Td). Obviously these inelastic reaction rate coefficients are very useful for the modelling of the ion chemistry inside the plasma discharge reactor particularly in the case of the crystal photonics applications.

The behaviour as a function of E/N of other ion data as for instance the longitudinal diffusion coefficients ND L (very useful for a better understanding of the ion transport in plasma discharge of our interest) are shown in figures 9 and 10. The shape and the magnitude of the diffusion coefficient of each ion/gas systems are obviously completely determined by the total collision frequency tot r ( ) ν ε behaviour. In fact the isotropic diffusion coefficient D which is an average between transversal D T and longitudinal D L diffusion coefficients (D= (D L + 2D T )/3) is inversely proportional to tot r ( ) ν ε :

3 / 2 r 0 r r tot r 0 ND( E / N ) ( ,E / N )d ( ) ε φ ε ε ν ε ∞ ∝ ∫ (14)
For instance in figure 9 showing Ar + in the different gases (Ar, N 2 and Cl 2 ), at relatively low E/N the lowest diffusion coefficient corresponds to Ar + /Cl 2 system due to the highest total collision frequency. The crossing of ND L of Ar + /Cl 2 with the one of Ar + /Ar at E/N around 150 Td is due to the inelastic charge transfer that becomes larger for Ar + /Ar. This obviously leads to a lower ion mean energy in presence of such inelastic processes with the same consequence on the longitudinal characteristic energy or diffusion coefficient. A quite similar behaviour of ND L in the case of N 2 + ion in Ar, N 2 and Cl 2 can be also observed in figure 10.

Ion swarm coefficients of Ar + and N 2 + in binary and ternary mixtures involving Ar, Cl 2 and N 2

From the knowledge of the sets of elastic and inelastic collision cross sections in the different pure gases (Ar + /Cl 2 , Ar + /N 2 , N 2 + /Cl 2 and N 2 + /Ar), it is therefore possible to calculate from Monte Carlo simulations the transport and reaction coefficients of Ar + and also N 2 + in the case of the different binary (Ar-Cl 2 or N 2 -Cl 2 ) and ternary (Ar-Cl 2 -N 2 ) mixtures. It is worth noting that the ion data in the gas mixtures are generally obtained from linearity laws as for instance Blanc's law giving the ion mobility K mix for a gas mixture from the knowledge of mobility data K n of pure gases (x n being the mole fraction of the gas of the species n and K n the corresponding ion mobility).

n mix n n 1 x = K K ∑ (15)
However, the validity of Blanc's law is normally limited to the cases where there are only elastic processes and when the ion energy distribution function is maxwellian. In the following the ion mobility data obtained from Monte Carlo simulations are given in different binary and ternary mixtures and compared to Blanc's law.

Figures 11a and11b show the inverse of Ar + mobility in the binary Ar-Cl 2 mixtures as a function of the proportion of Cl 2 at 100 Td (Fig 11a) and 1000 Td (Fig. 11b). At 100 Td, the increase of 1/K mix as a function Cl 2 proportion in the Ar-Cl 2 mixture obviously corresponds to a case where the total collision frequency is lower for the low Cl 2 proportion and then becomes higher with the Cl 2 proportion rise because the inverse of mobility is directly proportional to the total collision frequency (see relation 13). This trend is reversed at 1000 Td due to the presence of inelastic processes which play a larger role. Furthermore, there is a small but visible deviation between Monte Carlo calculation and Blanc's law at 100 Td (about 3%). This deviation is paradoxically lower or negligible at 1000 Td because the inelastic processes are supposed to play a larger role when E/N increases. In fact the negligible deviation from Blanc's law at 1000 Td is due to the specific shape and magnitude of inelastic processes at intermediate energy range (corresponding to the ion energy distribution for 1000 Td) in both Ar + /Ar (large symmetric charge transfer) and Ar + /Cl 2 (lower asymmetric charge transfer in the same energy range). Figures 12a and12b show the inverse of N 2 + mobility in the binary Ar-Cl 2 mixtures as a function of the proportion of Cl 2 at 100 Td (Fig 12a) and 1000 Td (Fig. 12b). In this case the trend of the variation of the inverse of the mobility is the same as in figures 11: 1/K mix increases with Cl 2 proportion at 100 Td and decreases at 1000 Td. However, whatever E/N (100 Td or 1000 td) there is a deviation that reaches about 5% between Monte Carlo simulation and Blanc's law. Figures 13a and13b show the inverse of Ar + mobility in the ternary Ar-N 2 -Cl 2 mixtures as a function of the proportion of Cl 2 at 100 Td (Fig 13a) and 1000 Td (Fig. 13b). It is worth noting that Ar and N 2 have the same proportion whatever the Cl 2 proportion. In this case the trend of the variation of the inverse of the mobility is not the same as in the previous case at 1000 Td. Indeed, 1/K mix increases with Cl 2 proportion for both E/N values (100 Td and 1000 Td). This increase of 1/K mix at E/N=1000 Td from about 1.1 V s cm -2 (1/K mix value for Ar + in 50%N 2 -50%Ar) up to 1.4 V s cm -2 (value for Ar + in 100% Cl 2 ) is coherent with the results already shown in figure 11b in the case of Ar + in the binaryAr-Cl 2 mixture. This is due to the specific shape and magnitude in the intermediate energy range of the elastic and inelastic collision cross sections of Ar + interacting with the different neutral species (Ar, N 2 and Cl 2 ). Figures 14a and14b show the inverse of N 2 + mobility in the ternary Ar-N 2 -Cl 2 mixtures as a function of the proportion of Cl 2 at 100 Td (Fig 13a) and 1000 Td (Fig. 13b). The proportions of Ar and N 2 are the same in the mixture when the Cl 2 proportion varies. In this case, the trend of the variation of 1/K mix is also similar to the trend already observed in figures 11 and 12: 1/K mix increases with Cl 2 proportion at 100 Td and decreases at 1000 Td. Furthermore, whatever the E/N value (100 Td or 1000 td) the deviation between Monte Carlo simulation and Blanc's law is always present and reach a maximum of 10%.

Conclusion

The ion swarm transport coefficients (reduced mobility, diffusion coefficients and reaction rate coefficients) of Ar + /Cl 2 , Ar + /N 2 , N 2 + /Cl 2 and N 2 + /Ar have been determined from a Monte Carlo simulation using calculated elastic and experimentally estimated inelastic collision cross sections. The calculation of elastic momentum transfer cross sections are based on a semi-classical JWKB approximation using on a rigid core interaction potential model while the inelastic cross sections have been fitted using the measured ion conversion reaction coefficients. Then, the cross sections sets are fitted using at low E/N range the zerofield mobility calculated from the Satoh's relation and the measured mobility data available in the literature for N 2 + /Ar. For the other systems where there are no experimental mobility data at higher E/N range, we used the physical properties of each considered ion/gas system. The sets of elastic and inelastic collision cross sections are then given for the first time in the literature in Ar + /Cl 2 , Ar + /N 2 , N 2 + /Cl 2 and N 2 + /Ar systems. Then, the ion transport and reaction coefficients are calculated also for the first time in the literature over a wide range of E/N for Ar + and N 2 + in pure gases and also in binary and ternary mixtures involving Cl 2 , Ar and N 2 . The deviations between the mobility data calculated from Monte Carlo simulations and the linear Blanc's law are also analysed in the case of different gas mixtures ; these deviations do not exceed 10% in the chosen E/N range. The ion swarm data given in this work are needed for the modelling and simulation of non equilibrium low pressure electrical discharges used more particularly for etching of the III-V compounds in the field of crystal photonic applications. [START_REF] Ikezoe | Ion reaction research group of mass spectroscopy society of Japan[END_REF] and the compilation of Anicich [26] Figure 9: Longitudinal ion diffusion coefficient as a function of E/N in the case of Ar + interacting with pure Ar, Cl 2 and N 2 + /Cl 2 and N 2 +/Ar systems Symbols are taken from the experimental data of Ikezeo et al [START_REF] Ikezoe | Ion reaction research group of mass spectroscopy society of Japan[END_REF] and the compilation of Anicich [26] E/N (Td)

Figure Captions:

pure and gas mixtures 3 . 1

 31 Ion swarm coefficients of Ar + and N 2 + in pure Ar, Cl 2 and N 2

Figure 1 :Figure 2 :Figure 3 :Figure 4 : 2 +Figure 5 :

 123425 Figure 1 : Set of collision cross sections for elastic momentum transfer Qm and non-resonant charge transfer Q(Cl 2 + ,Cl + ) processes in the case of Ar + /Cl 2 system Figure 2: Set of collision cross sections for elastic momentum transfer Qm and non-resonant charge transfer Q(N 2 + ) processes in the case of Ar + / N 2 system Figure 3: Set of collision cross sections for elastic momentum transfer Qm and non-resonant charge transfer Q(Cl 2 + ) processes in the case of N 2 + /Cl 2 system Figure 4: Set of collision cross sections for elastic momentum transfer Qm and non-resonant charge transfer Q(Ar + ) processes in the case of N 2 + / Ar system Figure 5: Reduced ion mobility as a function of E/N for Ar + in pure Ar, Cl 2 and N 2 with comparison with Satoh's relation (▲) at low E/N and comparison with experimental mobility data (Basurto et al [30]) in the case of Ar + /Ar

Figure 10 : 2 Figure 11a :

 10211a Figure 10: Longitudinal ion diffusion coefficient as a function of E/N in the case of N 2 +

Figure 13b :

 13b Figure 13b: The inverse of Ar + mobility in the Ar-N 2 -Cl 2 mixtures as a function of the proportion of Cl 2 at 1000 Td. Noting that Ar and N 2 have the same proportion whatever the Cl 2 proportion. Monte Carlo calculations (Solid line) are compared to Blanc's law (Symbols)

Figure 14b :Figure 1 :Figure 2 :Figure 3 :

 14b123 Figure 14b: The inverse of N 2 + mobility in the Ar-N 2 -Cl 2 mixtures as a function of the proportion of Cl 2 at 100 Td. Noting that Ar and N 2 have the same proportion whatever the Cl 2 proportion. Monte Carlo calculations (Solid line) are compared to Blanc's law (Dashed line).

Figure 4 : 2 + 2 Figure 5 : 2 Figure 6 : 2 Mean

 4225262 Figure 4: Set of collision cross sections for elastic momentum transfer Qm and non-resonant charge transfer Q(Ar + ) processes in the case of N 2 + / Ar system

Figure 7 :Figure 8 :

 78 Figure 7: Comparison between measured and calculated reaction rate coefficients of nonresonant charge transfer process for interactions of Ar + with N 2 (reaction 5). Experimental data (Viaggiano et[START_REF] Viggiano | [END_REF]) are given for different gas temperatures.

Figure 9 : 2 EFigure 10 :Figure 11a :Figure 11b :

 921011a11b Figure 9: Longitudinal ion diffusion coefficient as a function of E/N in the case of Ar + interacting with pure Ar, Cl 2 and N 2

2.2 Ar + and N 2 + ions in pure Ar, Cl 2, and N 2

	2 , Ar + /N 2 , N 2 + /Cl 2 , and N 2 100 eV. In the following, the literature information available in the studied systems Ar + /Cl 2 , + /Ar are shown in figures 1 to 4 from thermal energy up to Ar + /N 2 , N 2 + /Cl 2 , and N 2 + /Ar are given.

  Ar + in pure Ar, Cl 2 and N 2 with comparison with Satoh's relation (▲) at low E/N and comparison with experimental mobility data (Basurto et al[30]) in the case of Ar + /Ar Figure6: Reduced ion mobility as a function of E/N for N 2 + in pure Ar, Cl 2 and N 2 with comparisons with Satoh's relation (▲) at low E/N and comparison with the experimental mobility data (Ellis et at compilation[5]) in the cases of N 2 + /Ar and N 2 + / N 2 Figure 7: Comparison between measured and calculated reaction rate coefficients of nonresonant charge transfer process for interactions of Ar + with N 2 (reaction 5). Experimental data (Viaggiano et al [19]) are given for different gas temperatures. Figure 8: Inelastic collision rate coefficients as a function of E/N in the cases of Ar + /Cl 2 , Ar + /N 2 , N 2 + /Cl 2 and N 2 +/Ar systems Symbols are taken from the experimental data of Ikezeo et al

Acknowledgement:

This work has been undertaken in the framework of an international cooperation between CNRS (French Center of Scientific Research) and MESRS (Algerian Ministry of higher Education and Research).


M Hamamda

V Bocvarski

F Perales

J Baudon

G Dutier

C Mainos

M Boustimi

M Ducloy

Dynamics of evanescent matter waves in negative-index media

Keywords: numbers: 03, 75, -b Matter Waves 03, 75, Be Atom and Neutron Optics 37, 10, Gh Atom Traps and Guides 42, 25, -p Wave Optics

Semi-evanescent and evanescent matter-waves produced by an atom wave packet impinging a repulsive barrier can be back-refracted and reconstructed by the application of negative-index "comoving" potential pulses. One shows that those collapses and revivals generate a matter wave confined on both sides of the barrier border ("surface matter wave") and should be observable via the retardation of atom reflection from the barrier interface. This property, joined to the possibility recently demonstrated of inducing negative refraction of atom waves, makes such potentials a matter-wave counterpart of negative-index materials or "meta materials" well-known in light optics.

With the fast development of matter-wave optics, many of the functions previously operated in light optics have been realised: atom diffraction and mirrors, beam splitters, atom lasers, atom holography, quantum reflection, etc. [START_REF] Meystre | Atom Optics[END_REF]. Specific characters of those processes originate in the properties of the associated particle: non-zero atom mass, vacuum dispersion for the "de Broglie" waves (implying longitudinal wave packet spreading), scalar character of the atomic wave function, influence of the internal atomic degrees of freedom, etc. Along this viewpoint, novel areas in the field of atom optics are presently explored, including e.g., the devising of non-diffracting atom nano-beams via a specially designed transverse Stern-Gerlach interferometer [START_REF] Perales | [END_REF]. Recently, we have proposed to extend the concept of "metaoptics" (known as negative index materials, NIM-s, in light optics [3][4]) to matter waves [5]. The main specificity of NIM-s for atom optics is their transient character, linked to the fact that for matter waves the reversal of atom group velocity is operated and can be only transient -contrary to the equivalent process in light optics where the phase velocity is reversed. In [5], it was proposed to use a "comoving" potential pulse [6] to reverse the atom group velocity. Previously only the trajectory of the wave packet centre has been investigated and a negative refraction predicted. In this letter, we examine the behaviour of the wave packet itself in negative-index media and analyse its dynamics both in free space and classically forbidden regions (evanescent or semi-evanescent matter wave packets). The dynamics of matter waves impinging a static potential barrier is strongly altered by the comoving potential. In particular, we investigate here the possibility of evanescent wave-packet engineering and predict the generation of atom reflection replicas as well as matter waves confined in the vicinity of the barrier edge.

It is commonly admitted that, in the semi-classical regime, light and matter waves involving a single direction of space (e.g. x), behave identically provided they are monochromatic, i.e. provided they involve a single value of the wave number k (or particle's energy). For both kinds of waves, the evanescent wave appears, at a normal incidence with respect to a planar interface, as soon as the refractive index of the second medium is imaginary. This means for light a conducting medium (metal, plasma). For particles, a constant potential energy barrier V 0 , extending from x = 0 to x infinite, higher than the initial kinetic energy E 0 of the particle, or, in the case of a wave packet, higher than the kineticenergy distribution, provides an imaginary index since the index for matter waves in the region x > 0 is n = (1 -V 0 /E 0 ) 1/2 . In a 2D geometry (x, z) with the same potential barrier, the motion along z is free, which leads to a total reflection in the x < 0 half plane and to an evanescent wave in the x > 0 side. The corresponding index is static. As shown in [5], a negative index for matter waves is necessarily a transient process, thus needing incident wave packets, i.e. some k-momentum distribution. As a consequence, light and matter evanescent waves behave differently. While light evanescent waves are factorized in x and t (at least in a non-dispersive medium), such a factorisation does not hold for evanescent matter waves, simply because of intrinsic vacuum dispersion: the time dependence is in exp [-i h k 2 t /(2m)], instead of exp[-i ck t], where m is the atomic mass and c the light velocity. The existence of evanescent matter waves is one of the fundamental processes introduced by quantum mechanics and has many outstanding consequences, mainly explored, up to now, for electrons (like electron tunnelling, as in tunnelling microscopy [7], or Josephson Effect in superconductivity [8]). For atomic systems, it has not been much studied, except in molecular spectroscopy [9], collision physics [START_REF] Instance Ch | Quantum Collision Theory[END_REF] and more recently cold atom physics [START_REF] Schumm | [END_REF], where evanescent waves are commonly involved (e.g. quasi-bound states and resonances of various types).

The evolution in x and t of a partially evanescent matter-wave packet, experiencing a pulse of comoving potential, will be described in the following. This comoving potential has the general form:

V(t, x) = s(t) cos (2π x / Λ) (1a)
where s(t) is a real signal restricted to a finite time interval (0, τ 1 ) and Λ is the spatial period.

To really construct a "comoving" potential, it is necessary that the spectrum H(ν) of s(t) contains a frequency matching the atomic velocity (ν 0 = h k 0 /(mΛ), k 0 being the central atomic momentum. A simple -while not fully optimized -form is:

s(t) = C e +20t/τ for t in the interval [-∞, 0] s(t) = C ε 2 (t + ε) -2 e -t/τ for 0 ≤ t ≤ τ 1 ; = 0 for t > τ 1 (1b)
where C, ε, τ, τ 1 are constants. We consider here atoms the spin of which is J = 2, like argon metastable atoms (Ar* 3 P 2 ) having a velocity along x axis of 4 m/s (de Broglie wavelength λ dB ≈ 2.8 nm, central momentum value k 0 = 2.244 10 9 m -1 , momentum dispersion δk = 0.005 k 0 ), polarized in the M = +2 Zeeman sublevel. For such atoms, a magnetic potential can be used, with C = g L μ B B max M, where g L is the Landé factor, μ B the Bohr magneton, B max the maximum value of the magnetic field magnitude and M the magnetic quantum number. Evanescent wave packets appear when k < k 0 within a repulsive potential barrier of momentum height a = k 0 (this corresponds to a magnetic field of 127 Gauss). For Ar* atoms, the repulsive potential barrier can be created using a static magnetic field B 0 in the half-space x > 0 (see figure 1).

B 0 y z RF pulse

x Figure 1. Principle scheme of an experiment on evanescent and semi-evanescent wave packets submitted to comoving magnetic potential pulses (see text). A static potential barrier is generated by the static magnetic field B 0 . Potential pulses, comoving in the x direction, are produced by a generator ("RF pulse"). The incident wave packet propagates in plane (x, z). The reflected wave packets propagate in a direction of the (x, z) plane, symmetric of the incident direction with respect to the x axis.

The magnetic potential actually takes the form (1a) -plus a constant within the barrier -, provided that a given value of M, e.g. +2, referred to the comoving field axis (y) is prepared and maintained, which implies the presence of a tiny static field (b of a few Gauss) on both sides of the barrier edge. The easiest way to realize this condition is to use a collinear configuration, i. e. to make B 0 parallel to y axis. In fact, the static field cannot be abruptly increased from zero (or b) up to B 0 , which means that the barrier edge has necessarily a finite thickness. It should be possible to analyse in some detail the effect that it causes to the reflection/transmission at the barrier edge (e.g. in the case of a linear increase, by use of a combination of Airy functions). Nevertheless, provided that the thickness is less than the spatial period Λ, and owing to the fact that the comoving field starts at a given time, this thickness is expected to be of little importance on the dynamics of incident, reflected and transmitted wave packets.

We are dealing here with three wave functions, namely ψ i (t, x), the incident wave packet propagating from x = -∞ to x = 0, ψ r (t, x), the reflected wave packet propagating backwards from x = 0 to x = -∞, and the transmitted evanescent wave ψ tr (t, x) in the region x > 0. For a specific value of the wave number k, i.e. a specific value E of the total incident energy, the three wave functions have the same time-dependence, in exp [-i h k 2 t / (2m)]. In the absence of comoving field, the conservation of the probability flux leads to the usual reflection and transmission factors (in amplitude):

R(k) = κ + κ - i k i k ; T(k) = κ + i k k 2 (2)
, with κ = . Let Ψ tr0 (t, x) be the solution for x > 0 in absence of comoving potential, that is (up to a multiplicative constant):

ψ tr 0 (t, x) = (4a) ) k , x , t ( ) k ( ) k ( T dk 0 tr φ ρ ∫ +∞ ∞ -
ρ(k) being the momentum distribution and φ tr0 the evanescent k-spectral component:

φ tr 0 (t, x, k) = exp(-κx) exp[-i k 2 t /(2m)] (4b)
h Expansions similar to (4a) are obtained for incident and reflected waves, namely:

ψ i 0 (t, x) = ) k , x , t ( ) k ( dk 0 i φ ρ ∫ +∞ ∞ - ψ r 0 (t, x) = (5a) ) k , x , t ( ) k ( ) k ( R dk 0 r φ ρ ∫ +∞ ∞ -
with spectral components :

φ i 0 (k, t, x) = exp(i k x) exp[-i k 2 t /(2m)] h φ r 0 (k, t, x) = exp(-i k x) exp[-i k 2 t /(2m)] (5b)
h Let us assume that the effect of the comoving potential pulse on the spectral components of the wave packets consists of simple multiplicative factors: φ i, r, tr = φ i 0, r 0, tr 0 f i, r, tr (k, t, x)

The time dependent Schrödinger equation in half-space x > 0 is:

tr 0 tr 2 x 2 tr t )] x , t ( V V [ m 2 i Ψ + + Ψ ∂ - = Ψ ∂ h h (7)
whereas in "free" half-space x < 0, it is :

r , i r , i 2 x 2 r , i t ) x , t ( V m 2 i Ψ + Ψ ∂ - = Ψ ∂ h h (8)
Provided that the "perturbation factors" f evolve, as functions of x, much slower than the φ 0 -s, then the terms in ∂ x 2 f can be neglected with respect to κ ∂ x f or k ∂ x f. The validity of this latter approximation will be verified a posteriori. It leads for the f-s to the equations:

tr tr x 2 tr t f V f m f i + ∂ κ + = ∂ h h (9a) r , i r , i x 2 r , i t f V f ik m f i + ∂ + = ∂ h h (9b)
Let us define two new variables, in half-space x > 0:

u = t x m i κ + h ; v = t x m i κ -h (10a)
and similarly in "free" half-space x < 0:

u 0 = t x k m h + ; v 0 = t x k m h - (10b) Using (9a) it is readily verified that (∂ t + m i κ h ∂ x ) = 2 ∂ v .
Then, using variables u, v, eq. (9a) becomes:

h 2 i f f tr tr v - = ∂ V(u, v) (11)
where V(u, v) is the comoving potential expressed as a function of u and v.

Setting f tr = exp[i ϕ tr (u, v)], one gets from [START_REF] Schumm | [END_REF], ∂ v ϕ tr = -V /(2 ) and finally: h

ϕ tr (u, v) = ∫ - v ' dv 2 1 h V(u, v') + F tr (u) (12)
where F tr (u) is an arbitrary function of u.

For a comoving potential of the form (1a, b), setting at a given value of u, v' = 2t' -u, Eq. ( 12) yields:

ϕ tr = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ - κ Λ π -∫ ) ' t u ( m i 2 cos ) ' t ( s ' dt 1 ) t ( 0 h h + F tr (u) (13a)
where the upper bound is (t) = Min [t, τ 1 ]. Finally, the phase shift ϕ tr (a complex number in general) depends on 3 independent variables, k (via κ), t and x (via u).

A similar treatment can be carried out for incident and reflected waves in the free halfspace, by setting f i = exp[i ϕ i (u 0 )] and f r = exp[i ϕ r (v 0 )]. One readily gets:

ϕ i = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ - Λ π ∫ - ) ' t u ( m k 2 cos ) ' t ( s ' dt 1 0 ) t ( 0 h h + F i (u 0 ) (13b)
and a similar expression for ϕ r , u 0 being replaced by v 0 . The arbitrariness in the choice of the additional functions F i, r, tr corresponds to all possible constraints applicable to the incident, reflected and transmitted waves. To define them we have to specify the problem under consideration, namely at infinite negative values of x and t, a well defined and unperturbed incoming incident wave packet impinging the barrier. Under such a condition, F i is a constant, which can be assumed to be 0.

The continuity conditions at the barrier edge (x = 0) also hold for φ i , φ r and φ tr . The continuity condition for the modified wave functions is :

f i + R f r = T f tr ( 14
)
where f i , f r , f tr are taken at x = 0. The continuity condition of the x-derivative at x = 0, [∂ x ] x=0 being noted ('), is:

ik f i + f i ' + R (-ik f r + f r ') = T (-κ f tr + f tr ') (15)
It can be noted that the previous expressions of ϕ i (eq. 13b) and ϕ r become identical at x = 0 since at that point u 0 = v 0 . It then appears as a reasonable assumption to impose ϕ r = ϕ i , i.e. F r = F i = 0. Under this condition, (i) one readily gets from ( 14) that, at x = 0, ϕ tr = ϕ i = ϕ r. , from which the additional function F tr (u) can be deduced; (ii) eq. 15 becomes (f i + R f r -T f tr )' = 0. At this point, it is interesting to compare these expressions of the ϕ-s to that of the phase shift -let us call it ϕ pro -previously used in the case of a purely propagating matter wave (cf. Ref. [5], Eq. 8):

ϕ pro (k, t) = ∫ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Λ π - t 0 ' t m k 2 cos ) ' t ( s ' dt 1 h h ( 16
)
The integral part in expressions (13a) becomes identical to (16) when iκ is replaced by k, provided that ⎜u ⎜can be considered as much smaller than ⎜v⎜. This also readily holds for ϕ i, r .

In other words, this equivalence holds provided that (respectively for incident and reflected

waves) ⎜t m x k m h ⎜ << ⎜t x k m h ± ⎜.
This means that, in the case of propagation, all relevant values of t and x are close to those related to the propagation of the wave packet centre. Such an approximation, possibly valid for the incident and reflected wave packets, is clearly not valid for an evanescent wave packet. In the following calculations, time parameters in s(t) [eq. ( 1b)] have been chosen to be adapted to typical characteristics of the wave packets in the region x > 0. In the present case we take ε = 7.4 µs, τ = 0.37 µs, τ 1 = 0.6 or 1.10 µs. The spatial period is Λ = 2 or 3 μm [12]. The effect of the comoving pulse on the wave functions ψ i , ψ r , ψ tr is simply derived by incorporating the factors exp (iϕ i, r, tr ) into the expansions of these wave functions over k. At this point, let us examine the validity of approximation used previously to get the simplified equations (9a, b). It turns out that, with the parameters used here, this approximation is quite good in the free half-space. Within the potential barrier (x > 0), it becomes rather poor when the original comoving potential in cos (2πx/Λ) is used, in the sense that the ratio │κ ∂ x f tr │/│∂ x 2 f tr │, which is zero for κ = 0 (k = k 0 ), becomes larger than 1 only when │k -k 0 │> δk. The reason is that such a potential starts too abruptly at x = 0. The situation is greatly improved by slightly shifting the spatial dependence into, for instance, cos (2πx/Λ -π/10), which should be easily realized in an experiment. In such a case the ratio is larger than 10 as soon as │k -k 0 │> δk/20. In other words, only a narrow central slice of the spectrum violates the approximation. It is expected -and it has been verified -to be of little importance in so far as it involves large distances from the barrier edge (x > 20/δk = 1.57 μm). This modified spatial dependence has been adopted for semi-evanescent wave packets. For almost purely evanescent ones (i.e. a ≥ 1.01 k 0 ), this correction is not useful since the questionable part of the spectrum (κ ≈ 0) corresponds to very low values of ⎜ψ tr ⎜.

The profiles in t and x of the squared modulus ⎜ψ tr0 ⎜ 2 of unperturbed semi-evanescent (a ≤ k 0 ) and almost purely evanescent (a > k 0 ) waves are shown in figure 2. In a first step, we examine the effect of the comoving potential pulse in the semievanescent case. Figure 3 shows the squared moduli of the wave functions, in free space ⎜ψ i + ψ r ⎜ 2 and within the barrier, ⎜ψ tr ⎜ 2 , for B max = 370 Gauss, v 0 = 4 m/s, τ 1 = 0.6 µs, Λ = 2 µm, a = 0.95 k 0 . Within the barrier, a negative refraction effect brings the wave packet back to the edge. Note the (transient) narrowing of the transmitted wave packet. It is produced by the time-reversal property of the meta-medium [START_REF]Narrowing of the matter-wave packet in negative-index media is a general feature of atom "meta-optics[END_REF]. In the free half-space x < 0, a rebound of the wave packet is seen at the same time as that observed within the barrier (t ≈ 0.2 µs), as expected from the continuity conditions at the boundary. As a consequence the wave packet finally reflected at this time is retarded with respect to that obtained in absence of comoving pulse. Other features appear when the pulse duration is increased.

x (nm) t (ns) Figure 3. Profiles in t and x (3D surface and contour plot) of the squared modulus ⎜ψ tr ⎜ 2 of the transmitted wave function (in the x > 0 half-space) and ⎜ψ i + ψ r ⎜ 2 of the total wave function in the x < 0 half-space, when a comoving pulse is applied. The parameters (see text) are as follows: v 0 = 4 m/s, a/k 0 = 0.95, Λ = 2 µm, τ 1 = 0.6 µs, B max = 370 Gauss. A negative refraction of the transmitted semi-evanescent wave is seen. It generates a rebound in the free half-space (x < 0) and a retardation of the reflected wave packet.

Figure 4 shows the squared modulus of the wave functions on both sides of the barrier edge, under the following conditions: B max = 150 Gauss, v 0 = 4 m/s, τ 1 = 1.1 µs, Λ = 3 µm, a = 1.01 k 0 . On the positive-x side, the rebound previously seen for semi-evanescent wave packets is replaced by two evanescent contributions, one appearing at t = 0, the other one at t ≈ 0.43 µs. In the free half-space, a real rebound connects these two times and the finally reflected wave packet is delayed to by the same amount of time with respect to the ordinary reflected wave packet.

x (nm) t (ns) Repeated similar effects are observed when two additional pulses, delayed by 0.605 µs and 1.210 µs, are applied (see fig. 5). This is a clear evidence for the beginning of a temporal series of collapses and revivals of the evanescent matter wave at the potential barrier, accompanied by rebounds on the negative-x side. The same type of result is obtained with almost purely evanescent wave packets. This behaviour of the wave packets when subsequent pulses of comoving potential are applied strongly suggests the existence of a sort of a surface matter wave, which remains confined on both sides of the barrier edge (x = 0 axis) while exhibiting a series of temporal rebounds or echoes along the t axis. The related delay on the reflected wave packet should be a signature of the behaviour of the evanescent wave packet inside the barrier. Another observation mode would consist in cutting off the potential barrier at some distance, smaller than or equal to the evanescent decay length, and measuring the transmitted intensities.

x (nm) barrier edge t (ns) To summarize, adequate pulsed comoving potentials have been proven not solely to induce a negative refraction of matter waves, but also to cause drastic effects on the dynamics of evanescent or semi-evanescent matter waves in a static potential barrier. It generates repeated enhancements, giving rise to a guided atomic "surface" wave, confined within an interval smaller than 1 µm on both sides of the barrier edge and resulting into a retarded reflection. This makes these "negative index media" a counterpart of left-handed media in light optics, with however important differences related to the different natures of matter and light waves. Various applications can be imagined for matter waves. Some of them are similar to those of left-handed materials in light optics, such as atom wave focusing (meta lenses and atom nano-lithography), cloaking, etc. Some others are specific of matter waves such as beam splitters and interferometers and guided matter wave along a potential barrier edge. In this letter, we have mainly considered the special case of atoms with spin experiencing magnetic comoving potential pulses. Actually any type of potential possessing the same spatio-temporal characteristics as the present comoving pulses would induce effects quite similar to those described here. As an example we could envision electric comoving potential pulses acting on dipolar molecules and Rydberg atoms or molecules [START_REF] Bethlem | [END_REF].

  a 2 = (2m/ ) V 0 > k 2 . As expected, the evanescent wave does not carry any probability flux then2 h 1 = R. Similar expressions of R and T are obtained for k ≥ a (partial propagation through the barrier), by replacing iκ by k'

Figure 2 .

 2 Figure 2. Profile in t and x of the squared modulus ⎜ψ tr0 ⎜ 2 of the unperturbed semi-evanescent wave function. (a) The height a (in momentum) of the potential barrier is chosen equal to central value k 0 of the incident momentum distribution. At x = 0, the time dependence is Gaussian. For x > 0, one observes as expected the decay characteristic of the evanescent part together with a partial wave packet propagating at a positive group velocity and broadening in time. (b) Same as (a) for an almost pure evanescent wave (a = 1.1 k 0 ). No more propagation is seen.

Figure 4 .

 4 Figure 4. Same as fig. 3 (3D surface), with an almost purely evanescent wave (barrier height: a = 1.01 k 0 ). The comoving pulse parameters are as follows: v 0 = 4 m/s, Λ = 3 µm, τ 1 = 1.1 µs, B max = 150 Gauss. An evanescent "echo" delayed by 0.43 µs is generated within the barrier, whereas a rebound is seen in the free half-space causing a retardation of the finally reflected wave packet by the same amount of time.

Figure 5 .

 5 Figure 5. Same profiles as in figs 3, 4 (contour plot). A sequence of three identical comoving potential pulses is applied. Numerical parameters are as follows: v 0 = 4 m/s, a/k 0 = 0.9975 (semi-evanescent transmitted wave), Λ = 3 µm, τ 1 = 0.6 µs, B max = 120 Gauss. Second and third pulses are delayed by 0.605 µs and 1.210 µs with respect to the first one. Note the difference by a factor 10 in x-scales in regions x > 0 and x < 0.

Authors are members of the Institut Francilien deRecherche sur les Atomes Froids (IFRAF).


Yongxin Liao
email: yongxin.liao@cran.uhp-nancy.fr

Mario Lezoche
email: mario.lezoche@cran.uhp-nancy.fr

Hervé Panetto
email: herve.panetto@cran.uhp-nancy.fr

Nacer Boudjlida
email: nacer.boudjlida@loria.fr

Why, Where and How to use Semantic Annotation for Systems Interoperability

Keywords: Semantic Annotation, Models, Ontology, Systems Interoperability.

Semantic annotation is one of the useful solutions to enrich target's (systems, models, metamodels, etc.) information. There are some papers which use semantic enrichment for different purposes (integration, composition, sharing and reuse, etc.) in several domains, but none of them provides a complete process of how to use semantic annotations. This paper identifies three main components of semantic annotation, gives a formal definition of semantic annotation method and presents a survey of current semantic annotation methods which include: languages and tools that can be used to develop ontology, the design of semantic annotation structure models and the corresponding applications. The survey presented in this paper will be the basis of our future research on models, semantics and architecture for systems interoperability.

INTRODUCTION

Nowadays, the need of systems collaboration across enterprises and through different domains has become more and more ubiquitous. But because the lack of standardized models or schemas, as well as semantic differences and inconsistencies problems, a series of research for data/model exchange, transformation, discovery and reuse are carried out in recent years. One of the main challenges in these researches is to overcome the gap among different data/model structures. Semantic annotation is not only just used for enriching the data/model's information, but also it can be one of the useful solutions for helping semi-automatic or even automatic systems interoperability.

Semantically annotating data/models can help to bridge the different knowledge representations. It can be used to discover matching between models elements, which helps information systems integration [START_REF] Agt | Semantic Annotation and Conflict Analysis for Information System Integration[END_REF]. It can semantically enhance XML-Schemas' information, which supports XML documents transformation [START_REF] Köpke | Semantic Annotation of XML-Schema for Document Transformations[END_REF]. It can describe web services in a semantic network, which is used for further discovery and composition [START_REF] Talantikite | Semantic annotations for web services discovery and composition[END_REF]. It can support system modellers in reusing process models, detecting cross-process relations, facilitating change management and knowledge transfer (Bron, et al., 2007). Semantic annotation can be widely used in many fields. It can link specific resources according to its domain ontologies.

The main contribution of this paper is identifying three main components of semantic annotation, gives a formal definition of semantic annotation and presenting a survey, based on the literature, of current semantic annotation methods that are applied for different purposes and domains. These annotation methods vary in their ontology (languages, tools and design), models and corresponding applications.

The remaining of this paper is organized as follows: Section 2 describes the definition of annotation and gives a formal definition of semantic annotations. Section 3 provides the answers to why and where to use semantic annotation. Section 4 first presents an introduction to ontologies and semantic annoation structure models, and then discusses the usage of semantic annotations. Section 5 concludes this paper, together with some related work and potential extensions.

WHAT IS SEMANTIC ANNOTATION?

In this section, we first illustrate the types of annotations from different papers (section 2.1), and then propose a formal definition of semantic annotation together with its three main components (section 2.2).

Definition and Types of annotation

In Oxford Dictionary Online1 , the word "annotation" is defined as "a note by way of explanation or comment added to a text or diagram". It is used to enrich target object's information, which can be in the forms of text descriptions, underlines, highlights, images, links, etc. Annotation has special meanings and usages in different fields. In software programming, an annotation is represented as text comments embedded in the code to expand the program, which is being ignored when the program is running. In mechanical drawing, an annotation is a snippet of text or symbols with specific meanings. In Library Management, an annotation is written in a set form (numbers, letters, etc.), which helps the classification of books.

Further, different annotation types are identified by the following papers [START_REF] Bechhofer | The Semantics of Semantic Annotation[END_REF] and [START_REF] Boudjlida | A practical experiment on semantic enrichment of enterprise models in a homogeneous environment[END_REF] distinguished annotation as (i) Textual annotation: adding notes and comments to objects; (ii) Link annotation: linking objects to a readable content; (iii) Semantic annotation: that consists of semantic information which is machine-readable. Similarly, three types of annotation are described in the research of [START_REF] Oren | What are Semantic Annotations?[END_REF]: (i) Informal annotation: notes that are not machine-readable; (ii) Formal annotation: notes that are formally defined and machinereadable (but it does not use ontology terms); (iii) Ontological annotation: notes that use only formally defined ontological terms that are commonly accepted and understood. [START_REF] Bechhofer | The Semantics of Semantic Annotation[END_REF] According to the above classification, semantic annotation can be considered as a kind of formal metadata, which is machine and human readable. This will be further discussed in the following sections.

Semantic annotation

The term "Semantic Annotation" is described as "the action and results of describing (part of) an electronic resource by means of metadata whose meaning is formally specified in an ontology" (electronic resource can be text contents, images, video, services, etc.) by [START_REF] Fernández | Semantic Annotation Introduction[END_REF]. [START_REF] Talantikite | Semantic annotations for web services discovery and composition[END_REF] introduced it as "An annotation assigns to an entity, which is in the text, a link to its semantic description. A semantic annotation is referent to an ontology". In the research of [START_REF] Lin | Semantic Annotation for Process Models: Facilitating Process Knowledge Management via Semantic Interoperability[END_REF], semantic annotation is concerned as "an approach to link ontologies to the original information sources". All above definitions from different papers show one thing in common: a semantic annotation is the process of linking electronic resource to a specific ontology. Ontology here is only one of the possible means to provide a formal semantic.

As it can be seen on Figure 1, the left side represents an Electronic Resource (ER) and on the right side, there are the three main components of semantic annotation: (1) Ontology, which defines the terms used to describe and represent a body of knowledge [START_REF] Boyce | Developing Domain for Course Content[END_REF]. It can be reused from existing ontologies or designed according to different requirements. (2) Semantic Annotation Structure Model (SASM), which organizes the structure/schema of an annotation and describes the mappings between electronic resources and an ontology. (3) Application, which is designed to achieve the user's purposes (composition, sharing and reuse, integration, etc.) by using SASM. This figure also shows the three main steps on how to use semantic annotation, which is introduced in section 4: ontology (section 4.1), semantic annotation structure model (section 4.2) and application (section 4.3).

Fig. 1. Semantic Annotation components

The following definition formally defines a semantic annotation: a Semantic Annotation is a tuple ( ) consisting of the SASM and an application .

{ ( ( )) } Where:

* +, is the set of ontology that bring some meaning to any annotated element.

An Ontology is a 4-tuple ( , is_a, , ), where is a set of concepts, is_a is a partial order relation on , is a set of relation names, and ( ) is a function which defines each relation name with its arity (Stumme and Maedche, 2001a).

Formally, { 〈 〉 ( )} and represents the set of relationships between an element of the set of electronic resources and an element of the powerset of the ontology set .

A mapping ( ) may represent three different kinds of semantic relations:

(1) ( ) is a binary equivalence relation. If (
) then an electronic resource is semantically equivalent to , an element of the powerset ( ), in the context of an application .

(2) ( ) is a binary relation stating that the semantic of an electronic resource subsumes the semantic of an element of the powerset ( ), in the context of an application .

(3) ( ): is a binary relation stating that the semantic of an electronic resource is subsumed by the semantic of an element of the powerset ( ), in the context of an application . can be further extended, including also some additional parameters or constraints c k , generally expressed using, in the worst case, natural language, or, better, a formal logical expression.

is then defined as * +.

The main issue, related to mappings such as in (2) and in (3), is being able to measure the semantic gap (2) or the over semantic (3), brought by the semantic annotation. Such measures have been studied by researchers in the domain of information retrieval [START_REF] Ellis | The Dilemma of Measurement in Information Retrieval Research[END_REF] or in the domain of ontology matching [START_REF] Maedche | Measuring Similarity between Ontologies[END_REF], mapping [START_REF] Doan | Learning to map between ontologies on the semantic web[END_REF], merging [START_REF] Stumme | FCA-MERGE: Bottom-Up Merging of Ontologies[END_REF], alignment [START_REF] Noy | PROMPT: Algorithm and Tool for Automated Ontology Merging and Alignment[END_REF].

In addition, [START_REF] Peng | A Novel Approach to Semantic Annotation Based on Multi-ontologies[END_REF] also gave a very simple definition of semantic annotation in their paper, which is ( ) , where is set of resources and is an ontology. Furthermore, [START_REF] Luong | A Rule-based Approach for Semantic Annotation Evolution[END_REF] defined it as * +. In this definition, is a set of resources; is a set of concept names; is a set of property names; L is a set of literal values; and is a set of triple (

) , where ( ) . To the best of our knowledge, in this definition is duplicated.

WHY, WHERE TO USE SEMANTIC ANNOTATION

A semantic annotation uses ontology objects for enriching resource's information that tells a computer the meanings and relations of the data terms. It can be used in many areas, such as Business Process Models, Web services, XML Schema, Strategic Data Models, Information Systems, etc. Several usages of semantic annotation are introduced: Business Process Models: In the research of [START_REF] Lin | Semantic Annotation for Process Models: Facilitating Process Knowledge Management via Semantic Interoperability[END_REF], a semantic annotation framework is designed to manage the semantic heterogeneity of process model, to solve the discovery and sharing of process models problems in/between enterprise(s). [START_REF] Born | User-Friendly Semantic Annotation in Business Process Modeling[END_REF] used semantic description of process artefacts to help a modeller in graphical modelling of business processes.

Web Services: [START_REF] Talantikite | Semantic annotations for web services discovery and composition[END_REF] used a semantic annotation to represent web services as a semantic network. Based on the network and submitted requests, the composition algorithm produces the best composition plan. [START_REF] Patil | Meteor-S Web Service annotation framework[END_REF] proposed an annotation framework for semi-automatically marking up web service descriptions (WSDL files) with domain ontologies to help web services discovery and composition.

XML Schema:

In the research of [START_REF] Köpke | Semantic Annotation of XML-Schema for Document Transformations[END_REF], a path expression method is used to add annotation to XML-Schemas. Then they transform paths to ontology concepts and use them to create XML-Schema mappings that help XML document transformation.

Strategic Data Models: [START_REF] Diamantini | Semantic enrichment of strategic datacubes[END_REF] presented a novel model that uses a mathematical ontology in semantic annotation to describe mathematical formulas in Data Warehouse schemas.

Information System: [START_REF] Agt | Semantic Annotation and Conflict Analysis for Information System Integration[END_REF] used semantic annotations to help information system integration. They annotate the model/object at CIM (Computation Independent Model), PIM (Platform Independent Model) and PSM (Platform Specific Model) levels of the MDA approach [START_REF] Mellor | Model-Driven Architecture[END_REF]2004), and then they discover some matching between model elements with respect to semantic process requirements.

In short, semantic annotation can be considered as a semantically enrichment of models or data, which may be widely used for many purposes. In business process models and Information system, it can be used to bridge the gap between two models. In Web service and Strategic Date Models, it can be used as additional information that helps description, discovery and composition. To the best of our knowledge, the path expression method in XML Schema will lead to lose information in Schema (e.g. restrictions of maxoccur/min-occur, sequence or choice of elements, etc.), which still needs to be improved.

HOW TO USE SEMANTIC ANNOTATION

In this section, we present an introduction to the three main components of semantic annotation: the languages and tools which can be used in designing ontology; semantic annotation model's structure and mappings; and the applications of semantic annotation.

Introduction to Ontology

Designing an appropriate ontology for semantic annotations is the first step of the annotation process. Ontology has been actively studied for a long period of time, and there are many research works proposing ontology engineering techniques. We are not going to give, here, a complete overview of every ontology languages, but we provide a brief introduction to the three more representative languages. We will show also some simple examples and typical development tools.

Ontolingua was developed by KSL (Knowledge Systems Lab, Stanford University) [START_REF] Fikes | Tools for Assembling Modular Ontologies in Ontolingua[END_REF]. It is an extension of KIF2 (Knowledge Interchange Format) through adding frame-based representation and translation functionalities. But because of the newly development of semantic web ontology, Ontolingua is not frequently used recently. Figure 2-a) shows a simple Ontolingua example from [START_REF] Mizoguchi | Tutorial on Ontological Engineering: Part 2: Ontology Development, Tools and Languages[END_REF]. Ontolingua Server3 provides an editor, which can be used to browse, create, edit, modify, and use Ontolingua ontologies.

F-Logic was presented by Michael Kifer (Stony Brook

University) and Georg Lausen (University of Mannheim) [START_REF] Kifer | Logical Foundations of Object-Oriented and Frame-Based Languages[END_REF]. It is an object-oriented language that is frequently used for Semantic Web. It also can map straightforward to most frequent ontological constructs. Figure 2-b) shows a simple F-logic example from [START_REF] Liao | Model-driven Rule-based Mediation in XML Data Exchange[END_REF]. Flora24 is an F-logic ontology development application, which extends F-logic with HiLog and Transaction Logic. OWL (Web Ontology Language) was developed by World Wide Web Consortium, which shares many characteristics with RDF5 (Resource Description Framework) and RDF Schema [START_REF] Horrocks | From SHIQ and RDF to OWL: the making of a Web Ontology Language[END_REF]. It is written using the XML syntax, and contains three sublanguages: OWL Lite, OWL DL and OWL Full. OWL is considered as a standard language for ontology representation for semantic web. Figure 2-c) shows a simple OWL example from OWL Guide6 . Protégé7 ontology editor is a Java-based tool that can export ontology into formats such as OWL, RDF and XML Schema. OntoStudio8 supports the modelling of RDF(S), OWL and Object-Logic with possible transformation between them. The design methods of ontology for annotations have their own purposes and structures. [START_REF] Lin | Semantic Annotation for Process Models: Facilitating Process Knowledge Management via Semantic Interoperability[END_REF] used Protégé OWL editor to design the ontology. In order to separately annotate meta-models (modelling language) and their process models, the author designs two ontologies: General Process Ontology (GPO) and Domain Ontology. The design of GPO is based on Bunge-Wand-Weber (BWW) Ontology [START_REF] Bunge | ): Ontology I: The Furniture of the World[END_REF][START_REF] Wand | On the ontological expressiveness of information systems analysis and design grammars[END_REF]. GPO contains nine main concepts: Activity, Artifact, Actor-role, Input, Output, Precondition, Postcondition, Exception and WorkflowPattern. Relations between above concepts are has_actor-role, has_artifact, has_subActiviy, has_input, has_output, related_to, has_precondition, has_postcondition, has_exception, handled_by (e.g. Activity uses has_actor-role relation to link Actor-role). The Domain ontology is formalized according to SCOR 9 specifications (Supply Chain Operations Reference-model).

Agt, et al. ( 2010) designed a semantic meta-model (SMM) to describe domain ontologies. Artefacts in ontology are castigated as DomainFunction and DomainObject. The relations (predicates) among Objects and Functions are defined as: IsA, IsInputOf, IsOutputOf, Has, IsListOf, IsEquivalentTo, etc. A RDF-like triple (e.g., Tax Has TaxNumber) is used as the statement in SMM. [START_REF] Born | User-Friendly Semantic Annotation in Business Process Modeling[END_REF] used two kinds of ontologies: sBPMN 10 ontology and a domain ontology. The first ontology is used to represent BPMN process models. The second ontology defines domain objects, states and actions according to objects lifecycle, which is used to provide the user advices during the modelling process. More details of above ontologies can be found in references.

Introduction to Semantic Annotation Structure Model

The second component of a semantic annotation is SASM. It is the connection between electronic resources and ontology concepts. A study in this direction is pursued by SAWSDL Working Group 11 that developed SAWSDL (Semantic Annotation for Web Services Definition Language) which provides two kinds of extension attributes as follow: (i) modelReference, to describe the association between a WSDL or XML Schema component and a semantic model concept; (ii) liftingSchemaMapping and loweringSchema-Mapping, to specify the mappings between semantic data and XML [START_REF] Martin | Towards Semantic Annotations of Web Services: OWL-S from the SAWSDL Perspective[END_REF][START_REF] Kopecký | SAWSDL: Semantic Annotations for WSDL and XML Schema[END_REF].

To be more specific, we analyse four SASMs that are designed for different requirements. Figure 3 below gives an overview of these four SASMs: Model A is the annotation schema for enterprise models from [START_REF] Boudjlida | Enterprise semantic modelling for interoperability[END_REF]; Model B is designed to annotate the business process model from [START_REF] Born | User-Friendly Semantic Annotation in Business Process Modeling[END_REF]; Model C is proposed to conceptually represent a web service from [START_REF] Talantikite | Semantic annotations for web services discovery and composition[END_REF]; and Model D is the annotation model for an activity element which is part of the Process Semantic Annotation Model (PSAM) from [START_REF] Lin | Semantic Annotation for Process Models: Facilitating Process Knowledge Management via Semantic Interoperability[END_REF]. Class and Individuals: <owl:Classrdf:ID="Wine"> <rdfs:subClassOfrdf:resource="&food;PotableLiquid"/> <rdfs:labelxml:lang="en">wine</rdfs:label> <rdfs:labelxml:lang="fr">vin</rdfs:label> </owl:Class> Properties: <owl:ObjectPropertyrdf:ID="hasWineDescriptor"> <rdfs:domainrdf:resource="#Wine" /> <rdfs:rangerdf:resource="#WineDescriptor" /> </owl:ObjectProperty>

In order to compare above semantic annotation structure models, we identify five types for classifying the contents in SASM:

(1) identity of annotation (e.g. id, name, etc.);

(2) reference to ontology concept (e.g. element Customer has a reference "same_as" which is referenced to ontology concept Buyer); (3) reference to element (represent the relationship between element themselves. e.g. element manufacture has a reference "has_input" which is referenced to element material); (4) text description, the natural language definitions of annotation contents; ( 5) others (extinction contents, such as: execution time, restriction, annotation types, etc.). The classification results of each SASM are described by linking model contents to type numbers

We can easily find that the basic components of SASMs are: identity of annotation and reference to ontology concepts; reference to element, text description and others are added for different usages. As an example, Lin ( 2008) adds "has_Actor-role" to denote the relationship between activity element and actor-role element; [START_REF] Boudjlida | Enterprise semantic modelling for interoperability[END_REF] added "Informal Content" for explaining the intent of the annotation; [START_REF] Talantikite | Semantic annotations for web services discovery and composition[END_REF] added "exec-time" into SASM to record the execution time of a web service request.

In the rest of this section, the discussion is focused on the design of reference to ontology concepts. As can be seen from above figure, reference to ontology concepts in model A is just a conceptual reference without meanings. Model B describes the references with meaning of states of objects (current, before and after). Model C uses inputs and outputs to represent the relationships. Model D gives more meanings to references like same_as, kind_of, phase_of, etc. Further, one to one mapping is not the only mapping type in SASM. For example, in Model C, there can be more than one input, which means the mapping between model content and ontology concept is one to many. Here, we analyses "reference to ontology concepts" according to mapping types and definitions of mappings.

Mappings are separated into two levels in the research of Lin 2 shows the comparison and classification of the mappings from [START_REF] Agt | Semantic Annotation and Conflict Analysis for Information System Integration[END_REF] and [START_REF] Lin | Semantic Annotation for Process Models: Facilitating Process Knowledge Management via Semantic Interoperability[END_REF]. In order to classify those mappings, we assume the mapping direction in the table is from a model element to an ontology concept.

Composition

In our opinions, there are three high level mapping types: 1 to 1 mapping, 1 to n mapping and n to 1 mapping (n to n is a combination of 1 to n and n to 1). For each of the mapping, we can design different semantic relationships for further usages. Figure 4 shows the mapping types and semantic relationships for each kind of mapping. [START_REF] Han | Survey of semantic annotation platforms[END_REF]. In the research of [START_REF] Lin | Semantic Annotation for Process Models: Facilitating Process Knowledge Management via Semantic Interoperability[END_REF], mapping is manually linking the process models to ontology. In the work [START_REF] Patil | Meteor-S Web Service annotation framework[END_REF], mapping is semi-automatically computed. They developed algorithms to match and annotate WSDL files with relevant ontologies. Automatic mapping is, for the moment, restricted to some simple cases because of the impossibility to completely explicit knowledge from the different models.

Introduction to Application

Once the semantic annotation structure model is defined, designers can begin to design the application to achieve their purpose (composition, sharing and reuse, integration, etc.). Several applications of semantic annotation are introduced as follow: Talantikite, et al. (2008) designed an application, which uses a matching algorithm to process the "input" and "output" (SASM model C, Figure 3) of elements, and builds a semantic network for web services. This semantic network is explored by a composition algorithm, which automatically finds a composite service to satisfy the request. Authors implement a prototype in java, which includes: Pellet 12 Reasoner (matching algorithm), RSsw (Réseau Sémantique des Services Web), Request and Composor (returns an optimal composite service for requesters). [START_REF] Born | User-Friendly Semantic Annotation in Business Process Modeling[END_REF] used Tensegrity Graph Framework 14 as environment to support graphical design functions. Namebase and Process Context-base matchmaking functionalities are designed to help user annotating process models. Namebase matching uses string distance metrics method for the matching between business process models and domain ontology, and it supports the user for specifying or refining the process. Process Context-base matching uses the lifecycle (state before, state after, etc.) in domain ontology for suggesting the next activity during modelling.

Indeed, there are many tools and technologies that enable designing applications in semantic annotation. The selections of tools are always depending on the design of semantic annotation structure models and ontologies. In any case, all three components of semantic annotation are closely related

CONCLUSIONS

In this paper, a brief survey of semantic annotation in different domains is presented. We identify three main components of semantic annotations that are Ontology, Semantic Annotation Structure Model and Application. In addition, a formal definition of semantic annotation is proposed. It contributes to better understand what a semantic annotation is and then contributes to a common reference model. How to use semantic annotation? There are still many problems can be further discussed during the annotation process. For example, how to optimize ontology and an annotated model? How to solve the inconsistency or conflicts during the mapping? How to add consistent semantic on models in different levels of a system? How to achieve semiautomatic or automatic annotation?

We are currently investigating how semantic annotations can help collaborative actors (organizations, design teams, system developers, etc.) in co-designing, sharing, exchanging, aligning and transforming models. In particular, this research work will be based on general systems with several kinds of interactions. We can have interoperation between systems that with different versions (during many years, systems may have been modified or updated). We can also have systems with same functions but used by different enterprises.

Semantic annotations can bridge this knowledge gap and identify differences in models, in schemas, etc. In some case, interoperation is a process between a set of related systems throughout a product lifecycle (Marketing, Design, Manufacture, Service, etc.), and semantic annotations can influence the existing foundations and techniques which supports models reuse, semantic alignment and

  further classified the annotation according to six possible uses that are not always clear and disjoint: (a) Decoration, comments on an object; (b) Linking, link anchors; (c) Instances Identification, strong assert that an object is an instance of a particular class. It may use a URI; (d) Instance Reference, less clear than instance identification, reference depending on background and world knowledge; (e) Aboutness, loose association of the object with a concept; (f) Pertinence, assertions about the concepts within an ontology without encoding that information.

Fig. 2 .

 2 Fig. 2. Examples of Ontolingua (a), F-logic (b) and OWL (c).

  9 http://supply-chain.org/ 10 http://www.ip-super.org 11 http://www.w3.org/2002/ws/sawsdl/#Introduction b) F-logic General class information: person[name*=>string, children*=>person]. Database facts: John:person[name->'John Doe', children-> {Bob, Mary}]. Mary:person[name->'Mary Doe', ciildren->{Alice}] Deductive rule: ?X:human:-?X:person Query: ?X:person[name->?Y, children->Mary] a) Ontolingua (define-class Tutoring-objective (?t-obj) "Attributes are also represented as slots" :def (and (individual ?t-obj) (value-type ?t-objTuroring.policy Policy)) :axiom-def (subclass-partition Tutoring-objective (setof Transfer-ofknowledge Remedy))) c) OWL

Fig. 3 .

 3 Fig. 3. Semantic Annotation Structure Model Examples.

  (2008): meta-model level and model level. In the meta-model level, mapping direction is from ontology to model contents. The mappings are defined as: Atomic Construct (one to one. e.g. Activity is mapped to Task), Enumerated Construct (one to many. e.g. Artifact is mapped to Information or Material) and Composed Construct (one to combination. e.g. Workflow Pattern is mapped to a combination of Flow and Decision Point). In model level, semantic relationships are: Synonym (same_as, alternative_name), Polysemy (different_from), Instance (instance_of), Hyponym (superConcept_of), Meronym (part_of, member_of, phase_of and partial Effect_of), Holonym (composition Concept_of) and Hypernym (kind_of). (e.g. Meronym: Airline member_of Air Alliance). Agt, et al. (2010) described five mapping types in their work: single representation (one model element to one ontology concept), containment (one model element to multiple ontology concepts), compositions (multiple model elements to one ontology concepts), multiple and alternative representation (the mappings with AND and OR/XOR operators). Table

  : equal_to, similar_to, etc. 1 to n means one element is annotated by the composition/aggregation of several ontology concepts. Semantic relationships can be: contains, has, etc. n to 1 means the composition/aggregation of several elements are annotated by one ontology concept. Semantic relationships can be: part_of, member_of, etc. One element can have several semantic relationships, but for each relationship, they belong to one mapping type.

Fig. 4 .

 4 Fig. 4. Mapping types and semantic relationshipsSince the structure and semantic relationships of SASM are designed, we should consider how to implement the annotation process. The annotation process can be performed manually, semi-automatically or automatically (Reeve and[START_REF] Han | Survey of semantic annotation platforms[END_REF]. In the research of[START_REF] Lin | Semantic Annotation for Process Models: Facilitating Process Knowledge Management via Semantic Interoperability[END_REF], mapping is manually linking the process models to ontology. In the work of[START_REF] Patil | Meteor-S Web Service annotation framework[END_REF], mapping is semi-automatically computed. They developed algorithms to match and annotate WSDL files with relevant ontologies. Automatic mapping is, for the moment, restricted to some simple cases because of the impossibility to completely explicit knowledge from the different models.

  14 http://www.tensegrity-software.com/ . Above all, our research work will focus on designing, and reusing appropriate ontologies in relationship with a formal semantic annotation structure model.

Table . 1

 . . Mappings from Model to Ontology

	Types	Lin (2008)	Lin (2008)	Agt, et al.(2010)
	1 to 1	Atomic Construct	Instance	Single represent
			Synonym
			Polysemy
			Hyponym
			Hypernym
	1 to n			Containment,
				Multiple
				Alternative
	n to 1	Enumerated Construct	Meronym
		Composed Construct	Holonym

  integrating Protégé OWL API to provide the OWL ontology browser. Ontologies (GPO, Domain ontology, etc.) are stored on an ontology server, which can be loaded by annotators. The output of the annotation is an OWL instance file, which is used by a knowledge repository service to support the process knowledge query, discovery and navigation from users.

	Lin (2008) developed a prototype Process Semantic
	Annotation tool (Pro-SEAT) to describe the relationship
	between process models and ontologies. They use Metis 13 as

12 http://clarkparsia.com/pellet/ 13 http://www.troux.com/ a modelling environment

http://oxforddictionaries.com

http://www-ksl.stanford.edu/knowledge-sharing/kif/

http://www.ksl.stanford.edu/software/ontolingua/

http://flora.sourceforge.net/

http://www.w3.org/RDF/

http://www.w3.org/TR/2004/REC-owl-guide-20040210/

http://protege.stanford.edu/

http://www.ontoprise.de/en/products/ontostudio/