Enrico Cavalli
email: enrico.cavalli@unipr.it

Gianluca Calestani

Francesco Mezzadri

Raffaele Faoro

Mauro Tonelli

Philippe Boutinaud

Structural effects on the emission properties of Pr 3+ -doped Ba 2 NaNb 5 O 15 crystals

Keywords: 78, 55, Hx; 61, 66, Fn

Single crystals of Ba 2 NaNb 5 O 15 doped with Pr 3+ have been grown from sodium tetraborate flux. Their emission properties have been measured as a function of the doping level under different excitation and temperature conditions. The experimental observations have been accounted for by considering the effects of the crystal structure, of the doping mechanisms and of the interactions between host lattice and doping ions. The proposed conclusions have been verified by means of single crystal X-ray diffraction measurements and the resulting site occupancies of the active ions have been discussed in the light of the synthesis procedure.

Introduction

Ba 2 NaNb 5 O 15 (BNN) belongs to the family of the niobates with the tungsten bronze (TB) structure. These compounds have attractive photorefractive, ferroelectric and non linear optical properties [1]. BNN is also an interesting host material for luminescent ions. Nd 3+ -doped crystals have been investigated in order to develop self doubling laser media [2,3]. Studies extended to BNN activated with Yb 3+ [4], Er 3+ [5], Tm 3+ and Ho 3+ [6,7] have confirmed its potentialities as host lattice for laser ions. We have recently explored the visible emission properties of BNN crystals activated with Eu 3+ , Dy 3+ , Tb 3+ and Sm 3+ [8], pointing out the issues concerning the site occupancy in this host lattice and the analogies with SBN:Ln 3+ (Ln 3+ = rare earth ions). In this paper we thoroughly investigate the emission properties of Pr 3+ -doped BNN (hereafter Pr:BNN) crystals as a function of the temperature, of the doping concentration and of the excitation conditions. Our interest in this system is related to different interconnected aspects: the development of a new visible emitting material, the analysis of its excited states dynamics and of the interactions between optical centres and lattice constituents in the light of the structural properties of the host and of the Pr 3+ site occupancy, the possibility of extending the obtained information to other members of the TB niobate family, and so on.

Experimental 2.1 Crystal growth.

Single crystals of BNN singly doped with Pr 3+ were grown by means of the flux growth method. Pure BaO, Nb 2 O 5 and Na 2 B 4 O 7 were used as starting materials. The doping ions were added as Pr 6 O 11 with nominal 0.5%, 2% and 8% molar ratios with respect to Ba. The starting mixture was placed in a Pt crucible and heated to melt (1250 °C) in a horizontal furnace. After a 12 h soaking time, the temperature was slowly lowered (2-3 °C/h) to 400 °C, then the furnace was turned off. Crystals with size up to of 2×2×3 mm 3 and of sufficient optical quality were separated from the flux by dissolving it in hot diluted HCl. The structural properties of the grown crystals will be discussed in details in Sect. 4. For the moment it is sufficient to point out that the incorporation of Pr 3+ ions into the BNN lattice requires charge compensation that, combined with the intrinsic disorder of the TTB structure, results in the formation of different non equivalent optical centers and then in a significant inhomogeneous broadening of the absorption and emission features.

Characterization.

Single crystal X-ray diffraction (XRD) data were collected on a modified Philips PW1100 single crystal diffractometer using graphite monochromatized Mo K radiation. Experimental details are reported in Table 1. The room temperature emission and excitation spectra were measured using a Fluoromax-3 (Jobin-Yvon) spectrofluorimeter. The low temperature spectra were measured in the 485-760 nm range by using an Argon laser in single-line configuration to pump the 3 P 0 manifold. The crystal was mounted on the cold finger of a closed-cycle He cryocooler. The luminescence was chopped and focused by a 75 mm focal lens on the input slit of a D330 Hillger & Watts monochromator with 300 mm focal length (resolution: 0.1 nm), processed by a lock-in amplifier and revealed by means of a S20 photomultiplier. A Glan-Thomson prism was placed at the entrance slit of the monochromator in order to perform polarized measurements. The decay time measurements were carried out upon 445 nm excitation by means of the second harmonic of tunable Ti-Sa pulsed laser (pulse duration ~30 ns, repetition rate 10Hz).

Luminescence spectroscopy

10 K emission spectra.

The 10 K polarized emission spectra of 0.5%, 2% and 8% Pr:BNN measured upon 476.5 nm CW laser excitation are shown in figure 1. They are composed of four emission manifolds: the intense 3 P 0 3 H 4 transition at 495 nm, the weak 3 P 0 3 H 5 multiplet at around 550 nm, a complex band system in the 600-670 nm range, including the 1 D 2 3 H 4 (~605 nm), 3 P 0 3 H 6 (610-650 nm) and 3 P 0 3 F 2 (650-670 nm) transitions, and the weak 3 P 0 3 F 3,4 emission at around 750 nm. The intensity ratio between the observed manifolds as well as the polarization behaviour of their components change with the doping level. This in our opinion is the consequence of the presence of different (and interacting) optical centres whose relative concentrations vary with the total Pr 3+ content independently one from the other. As expected, all features are inhomogeneously broadened, the sharpest ones having FWHM (full width at half maximum) values of the order of 30-40 cm -1 . The broadness of the emission features depend on the excitation wavelength: as an example, Figure 2 (a) compares the 600-670 nm manifold measured upon 476.5 and 458 nm laser excitation. The latter is significantly broader, indicating that the 458 nm radiation excites a number of non-equivalent centres larger than that excited by the 476.5 nm one. It is clear from in figure 2 (b) that that the relative intensity of the 1 D 2 3 H 4 emission transition strongly decreases with the doping level. This is an expected result, since the emission properties of Pr 3+ -doped compounds are significantly affected by the activator concentration. In the case of the 3 P 0 level the concentration quenching is ascribed to cross relaxation processes of the type [9]:

[ 3 P 0 , 3 H 4 ]→[ 1 G 4 , 1 G 4 ] (i) [ 3 P 0 , 3 H 4 ]→[ 1 D 2 , 3 H 6 ] (ii)
shown in Fig. 3(a). Process (i) is not resonant, since the two involved transitions occur at energies differing by about 950 cm -1 , and process (ii) is nearly but not fully resonant. In consequence, both are expected to be favoured by phonon assistance, since phonons of suitable energy are available in the IR or Raman spectrum [10]. This mechanism is concomitant with the 3 P 0 → 1 D 2 multiphonon relaxation. The cross relaxation involving the 1 D 2 state (figure

3 (b)): [ 1 D 2 , 3 H 4 ]→[ 1 G 4 , 3 F 4 ] (iii)
is in practice a resonant process, then we have to expect a strong concentration and a weak temperature dependence. In addition to these processes, the mechanism involving charge transfer states have to be considered.

298 K emission spectra.

As the temperature increases the emission bands broaden and their intensity decreases. At 300 K the spectra present a broad luminescence in the 600-660 nm range, with two components: the more intense (composed by the 1 D 2 3 H 4 and 3 P 0 3 H 6 transitions) has maximum at 605 nm that shifts to 620 nm as with concentration increasing as a consequence of the quenching of the 1 D 2 emission, the minor one ( 3 P 0 3 F 2 ) peaks at 655 nm (Fig. 4 (a)). The relative intensities of the spectral components depend on the excitation wavelength: this is a typical consequence of the presence of the IVCT state that favours the population of the 1 D 2 state. The spectrum of the diluted crystal is rather similar to that reported for SBN:Pr (1%) [11], indicating similar environments for the optically active ions in the two lattices. The excitation spectrum (Fig. 4 (b)) is characterized by three band systems located in the 420-500, 340-410 and <300 nm regions. The last one corresponds to the host absorption band feeding the Pr 3+ emission through an energy transfer process. The manifold in the blue region, resolved into three well separated components, is ascribed to the 3 H 4 3 P J (J= 0, 1,2), 1 I 6 absorption of Pr 3+ . The band located in the 340-410 nm range is to low in energy to be assigned to a 4f 2 4f 1 5d 1 transition and it is ascribed to the intervalence charge transfer (IVCT) process: Pr 3+ +Nb 5+ Pr 4+ +Nb 4+ already observed in Pr 3+ -doped niobates [12]. It is interesting to note that the IVCT maximum shifts to higher energy as the doping level increases: it is located at 374 nm in the 0.5% case, at 368 nm in the 2% and at 345 nm in the 8% case. As pointed out by Boutinaud et al. [12], the position of the IVCT state is related to the optical electronegativity of the involved transition metal ion (Nb 5+ in the present case) and to its minimum distance with respect to the lanthanide ion. This dependence is formalized by the empirical equation: M n+ ) is the shortest interatomic distance between Pr 3+ and M n+ . In the diluted crystals the shortest Pr 3+ -Nb 5+ distance calculated using eq. ( 1) is 2.89 Å. In the BNN lattice however, Pr 3+ is expected to replace Na + (A 2 site) or Ba 2+ (A 1 site). In both cases the shortest Pr 3+ -Nb 5+ distances, 3.36 and 3.60 Å respectively, are not consistent with the calculated value. Only in the case of C site occupancy the resulting distance, 2.90 Å, is practically coincident with the evaluated one. In addition, the IVCT shift with increasing Pr 3+ concentration indicates that the average shortest Pr 3+ -Nb 5+ distance increases with the doping level. These are unexpected and interesting issues that we have decided to investigate in more details by XRD techniques. c Calculated on the reflections used in the refinement.

Decay time measurements

The emission kinetics of both 3 P 0 (655 nm) and 1 D 2 (605 nm) states have been measured at different temperatures upon 455 nm excitation (Fig. 5). The profile of the 3 P 0 emission is a single exponential only in the case of the diluted sample at 10 K. As the temperature and/or the concentration increases the curves significantly deviates from the exponential behaviour. Possible reasons of this effect can be: I. as the concentration increases the distribution of the Pr 3+ ions among the different sites tend to vary, as well as the effect of the related charge compensation mechanisms. II. the 3 P 0 → 1 D 2 multiphonon relaxation process requires at least four high energy (840 cm -1 ) host phonons to occur, since the gap between the involved levels is of the order of 3300-3500 cm -1 . It then constitutes a temperature dependent contribution to the 3 P 0 depopulation. III. the temperature dependent cross relaxation mechanisms. IV. the de-excitation through the IVCT state can be favoured by suitable phonon assistance and then could have some temperature dependence. It is clearly impossible to analyze the profiles on the basis of a single reliable model. We have then evaluated the effective emission decay times using the eq (2) [START_REF] Nakazawa | Phosphor Handbook[END_REF]:

( ) ( ) t I t dt I t dt τ ⋅ = (2)
where I(t) represents the luminescence intensity at time t. The obtained values, reported in Fig. 5 in proximity of the corresponding curves, evidence a relatively small variability, despite the number of processes potentially involved. The 10 K 1 D 2 profiles are characterized by a risetime, approximately of the order of 1 µs, confirming the feeding from the 3 P 0 upper level through the II-IV processes above mentioned. At 298 K the risetime disappears because the above mentioned temperature dependent relaxation processes from 3 P 0 become much more effective and the feeding process faster. The decays are non exponential in consequence of the presence of non equivalent optical centres. The values of the effective decay times, calculated with eq. ( 2), reveal a strong concentration dependence compatible with the resonant character of the [ 1 D 2 , 3 H 4 ]→[ 1 G 4 , 3 F 4 ] cross relaxation responsible of the non radiative depopulation of the 1 D 2 level.

Structural characterization

Three single crystals with nominal Pr/Ba ratios 0.5%, 2% and 8% were characterized by single crystal XRD. Crystal data are very similar, as reported in Table 1, and consistent with the typical tetragonal tungsten bronze (TTB) structure, characterized by the structural formula (A 1 ) x (A 2 ) y C z B 10 X 30 , where x can ideally vary in the 0-2 range and y, z in the 0-4 range. The typical framework (Fig. 6) can be thought as derived from the perovskite structure by rotation of some [BX 6 ] polyhedra and is formed by corner sharing [BX 6 ] octahedral units whose linking produces three different types of channels (also called tunnels) containing the extraframework cations in A 1 , A 2 , and C sites, respectively. In terms of coordination polyhedra, the A 2 cations are 15-fold coordinated in the tunnel with a pentagonal section, the A 1 cations are 12-fold coordinated in the surviving perovskite cage, and the C cations are 9-fold coordinated in channels characterized by a triangular section. In our case the structure was solved with SIR2002 [START_REF] Altomare | SIR2002, Program for Crystal Structure Solution and Refinement[END_REF] and refined with SHELX97 [START_REF] Sheldrick | SHELXL97, Program for Crystal Structure Refinement[END_REF]. After a preliminary structure refinement in which only the presence of Ba 2+ and Na + (located in A 2 and A 1 , respectively) as extra-framework cations was taken into account, difference Fourier maps revealed in all cases a residual electron density in the triangular channels, suggesting a partial cationic occupation of the corresponding C sites. Since these residuals were not detected in undoped BNN crystals previously characterized, a possible site occupation by praseodymium was considered. Owing to the reduced cage dimension, this hypothesis could appear quite rash, unless to evaluate carefully the local effects produced by structural modulation. In fact TTB structures, known for a great number of oxides and fluorides, are usually characterized in the low temperature region of the phase diagram (very often extending well above RT) by a typical structural modulation along the [110] crystallographic direction, ranging from incommensurate to commensurate depending on chemical composition and connected to the doubling of the c parameter ( 8 Å). The structural modulation, ascribed to the existence of a cooperative tilt of the [NbO 6 ] octahedra that reduces the real symmetry from tetragonal to orthorhombic, is at the basis of ferroelasticity in these systems. The fundamental averaged structure of BNN at room temperature was determined at the end of the 1960s by Jamieson et al. [START_REF] Jamieson | [END_REF]. The first attempt to describe the modulated structure was made by Lin and Bursill [17] on the basis of electron diffraction (ED) data in an orthorhombic supercell with a b 2 a TTB √2, c = 2 c TTB and space group Im2a. Further studies on de-twninned crystals by Labbe´et al. [18] demonstrated that the supercell describing the quasi-commensurate modulation is in reality half in volume, being b a TTB √2, and its symmetry is consistent with the Bbm2 space group.The results of Labbé were then confirmed by Fabbrici et al. [19] for K 0.525 FeF 3 and by Mezzadri et al. [20] for K 0.6 FeF 3 , confirming this modulation as generally distinctive of TTB phases and not only of BNN. The use of de-twninned crystals revealed to be fundamental in structural studies of BNN, where ferroelastic domains connected to the exchange of the a and b axes of the superstructure occurs on a scale that is below the coherence length of X-ray, so that the modulation satellites are usually observed only by electron diffraction (ED). In spite of the typical absence of modulation satellites, the existence of the structural modulation leaves a characteristic trace in single crystal XRD data, consisting in an anomalous elongation of the anisotropic displacement parameters (a.d.p.'s) of the atoms, that is indicative of static disorder. The phenomenon is particularly significant for the apical O atoms of the [NbO 6 ] octahedra (the mostly affected by the cooperative tilt) and for the Ba atoms hosted in the large pentagonal channels (that moves in the ab plane in agreement with the displacements of the apical O atoms lying on the same plane). Once the structural modulation is taken into account (at least partially) by refining these atoms on disordered positions, the triangular channels become able to host Pr 3+ ions (Fig. 7). Following this idea the occupancies of the extra-framework cations were refined in the final cycles, by constraining the total charge to compensate the anionic framework. The Pr 3+ concentration of the most diluted crystal estimated by this approach significantly exceeds the nominal doping level and cannot be considered quantitatively reliable. Nevertheless these results allow concluding that in this sample praseodymium occupies the C site, compensating a small Ba deficiency in the A 2 site. The presence of some Pr 3+ in the A 1 site of BNN:Pr (0.5%) cannot be excluded. However, being the refined occupancy of the order of the standard deviation, the Na occupancy of A 1 site was fixed to the unit in the last refinement cycles. The occupation of the C site by Pr is probably forced by the large Na excess in the flux that inhibits the competitor role of Pr for the A 1 site. As the doping level increases Pr 3+ starts to occupy preferentially the A 1 site as usual for lanthanides in TTB structures, decreasing its occupancy in the C site. Refinement and atomic parameters are reported in Tables 1 and2, respectively; selected bond lengths are reported in Table 3. In the Tables 2 and3 we have indicated with Pr1 and Pr2 the Pr 3+ ions located at the A 1 and C sites, respectively. The distribution of Pr 3+ over the two sites influences the shortest Pr-Nb distance that represents a critical spectroscopic parameter. The average Pr-Nb shortest distance, determined for the three samples and weighted on the refined site occupancy (Table 3), is in good agreement with the values predicted from the spectroscopic behaviour, indicating the effectiveness of the proposed model.

Conclusions

The luminescence spectra of Pr:BNN crystals are influenced by the host properties and by the substitution mechanisms. Measurements as a function of the temperature, of the excitation wavelength and of the doping level have evidenced the presence of non equivalent optical centres whose emission properties are affected by different and concomitant non radiative processes. The interaction between host and doping ions results in the formation of an IVCT state that actively participates to the excited states dynamics of the system. In this context, the concentration shift of the IVCT band has been accounted for on the basis of a previously developed empirical model that allows formulating a hypothesis about the site occupancy of the Pr 3+ ion in this host. The structures of the investigated materials have been determined by single crystal XRD measurements and are consistent with the supposed Pr 3+ occupancy, and the connection with the growth procedure has been pointed out.

Figure 1 .

 1 Figure 1. Polarized emission spectra measured upon 476.5 nm laser excitation.

Figure 2 .

 2 Figure 2. The 600-680 nm emission manifold (π polarization) measured for different excitation wavelengths (a) and Pr 3+ concentrations (b).

Figure 3 .

 3 Figure 3. Non radiative mechanisms affecting the 3 P 0 (a) and 1 D 2 (b) emission of Pr 3+ in oxide lattices.

  optical electronegativity of the closed-shell transition metal ion M n+ and d(Pr 3+ -

Fig. 4 .

 4 Fig. 4. Room temperature unpolarized emission (a) and excitation (b) spectra of Pr:BNN.

Fig. 5 .

 5 Fig. 5. Emission decay profiles of Pr:BNN.

Figure 6 .

 6 Figure 6. TTB structure with the conventional sites nomenclature.

Fig. 7 .

 7 Fig. 7. Configurations of the triangular channels resulting from the modulation of the BNN structure and allowing the accommodation of the Pr 3+ ions in the C site.

Table 1 .

 1 Crystal data and refinement parameters

	Compound	Pr:BNN (0.5%)	Pr:BNN (2%)	Pr:BNN (8%)
	Formula weight	998.92	999.12	998.67
	Crystal habit	needle	needle	needle
	Crystal colour	colorless	colorless	colorless
	Crystal dimensions, mm	0.53 x 0.07 x 0.05	0.41 x 0.07 x 0.07	0.50 x 0.08 x 0.08
	Crystallographic system	tetragonal	tetragonal	tetragonal
	Space group	P4bm	P4bm	P4bm
	Cell parameters:
	a, Å	12.465(5)	12.464(4)	12.463(4)
	c, Å	3.986(2)	3.986(2)	3.984(2)
	, °90 β, °90	90 90	90 90
	, °90	90	90
	V, Å 3	619.3(5)	619.2(4)	618.8(4)
	Z	2	2	2
	-3 D calc , Mg m Linear abs. coefficient, cm -1	5.357 10.784	5.359 10.818	5.360 10.865
	Absorpt. correction type	ψ-scan	ψ-scan	ψ-scan
	Absorpt. correction T max	0.411	0.468	0.421
	Absorpt. correction T min	0.576	0.404	0.351
	Temperature, K	293	293	293
	Radiation, Å	0.71073	0.71073	0.71073
	2θ range, °3.27-35.01	3.27-35.01	3.27-45.02
	Total measured reflections	2974	2976	5473
	Unique reflections	802	804	1451
	Unique observed reflection	792	740	1212
	Criterion for obs. reflections	I>2σ(I)	I>2σ(I)	I>2σ(I)
	Reflections used (NO) a	802	804	1451
	Refined parameters (NV)	64	66	66
	NO/NV ratio	12.53	12.18	21.98
	R = Σ∆F / ΣF o  b wR2 = [Σw∆F 2  2 /	0.0274 0.0664	0.0238 0.0575	0.0439 0.0999
	ΣwFo 2  2 ] ½ c GOF=[Σw∆F 2  2 / (NO-	0.998	1.132	1.007
	NV)] ½
	Flack parameter	0.08(6)	0.09(6)	0.04(6)
	Extinction coefficient	0.0154(9)	0.0092(5)	0.0091(10)
	Maximum shift/esd, last cycle 0.002	0.001	0.04
	Maximum residual peak, e/Å 3 1.50	1.98	2.06
	a Refinement based on the reflections with I > 0.

b Calculated on the observed reflections.

Table 2 .

 2 Atomic coordinates and displacement parameters (Å 2 ).

	Pr:BNN (0.5%)

Table 3 .

 3 Selected bond lengths and distances (Å). Bonds denoted by a and b superscripts represents possible alternatives produced by the disordered description of the modulation in the fundamental cell.


M Bakr

H Wang

H Fuess

Dielectric relaxation and magnetic properties of Cr doped GaFeO 3

Polycrystalline GaFe 1-x Cr x O 3 (x= 0.05, 0.1 and 0.15) samples were prepared by solid state reaction. The monophasic compounds crystallize in the orthorhombic space group P c 2 1 n and the unit cell volume decreases with increasing Cr content. The saturated magnetization and magnetic transition temperature of the ceramics decrease due to the dilution of the magnetic interaction with Cr concentration. The dielectric properties were investigated from 133 to 353 K at various frequencies (100-10 7 Hz). Whereas the dielectric constant decreases with Cr-content an increase of dielectric loss tangent was observed. The activation energy of the compounds (calculated both from loss and modulus spectrum) are the same and have values ~0.22 and 0.27 eV for Cr=10 and 15%, respectively, and hence the relaxation process may be attributed to the same type of charge carrier. A separation of the grain and grain boundary properties has been achieved using an equivalent circuit model. The capacitance and resistances associated with the grain boundary were found to be higher than that associated with grain.

Introduction

The study of multiferroics is a very hot topic. It is interesting not only from the point of view of fundamental physics but also for many potential applications in electronics [1,2].

GaFeO 3 has an orthorhombic crystal structure (space group P c 2 1 n) with four different cation sites labeled Ga1, Ga2 (mostly occupied by gallium) and Fe1, Fe2 (mostly occupied by iron). This material has a spontaneous polarization along the b axis and a ferrimagnetic structure below room temperature result from unequal distribution of Fe spins of nearly equal magnitude on the sublattices with a magnetic moment of the spin along the c axis [3,4].

GaFeO 3 contains only trivalent metals in the structure like rare earth orthoferrites, making them attractive systems for investigations of isovalent substitutions. In particular, the replacement of Fe 3+ by Cr 3+ and its effect on structural, magnetic and other properties have been reported [5][6][7] for rare earth orthoferrites. For example, in the lanthanum orthoferrites, partial replacement of Fe by Cr leads to a reduction in the Néel temperature from 750 K in LaFeO 3 to 280 K in LaCrO 3 . Moreover, Cr doping is one of the most adopted strategies to tailor the dielectric and piezoelectric properties of ferroelectrics for practical applications. It is well known that Cr is effective in decreasing the aging effect and the dielectric loss; thus, the effect of doping of Cr 3+ is that of a stabilizer of the piezoelectric and dielectric properties [8,9].

In the present work we study the (a) magnetic properties, (b) apply the variablefrequency technique of impedance spectroscopy to the samples over a wide temperature range, and (c) characterize the grain and grain boundary resistance using IS, from which one can calculate their capacitance and can model the equivalent circuit for Cr-substituted GaFeO 3 samples.

Experimental procedures

The polycrystalline GaFe 1-x Cr x O 3 (x=0.05, 0.1 and 0.15) samples were prepared by solid state reaction method. Appropriate amounts of Ga 2 O 3 (99.99%), Fe 2 O 3 (99.9%), and Cr 2 O 3 (99.9%) were mixed together and ground in an agate mortar till a homogeneous mixture was formed. This mixture was precalcined at 900 C (20h) and then at 1050°C (50h). These powders were reground thoroughly, palletized and sintered at 1300 C (10h). The crystal structure of the samples was examined by x-ray diffraction using MoK with wavelength =0.709703 Å. The lattice constants and structural parameters of the samples were refined by the FULLPROF program package [10]. Magnetization evaluation was executed a SQUID magnetometer in the temperature range of 5-320 K under a magnetic field of 100 Oe. M-vs-H hysteresis curves were measured at 10 K in applied magnetic fields H ranging up to 6 T. For dielectric measurements, the uniaxially pressed powder (heated at 1050°C) was then cold pressed using a "wet-bag" pressing technique in weber presser KIP100E Isostatic press to achieve uniform distribution throughout the pellet and then sintered at 1300°C (10h). Silver electrodes were prepared for the samples and the dielectric measurement was controlled by a programmable electrometer (KEITHLEY 617). The complex dielectric permittivity was investigated using a Novocontrol Alpha-A analyzer (f = 100-107 Hz), in the temperature from 133K-350K with a ZGS active sample cell. Surface morphologies were investigated on High Resolution Scanning Electron Microscopy (HRSEM).

Results and discussion

Structure and microstructure

Figure 1(a) shows the XRD patterns of the sintered GaFe 1-x Cr x O 3 (x 0.05, 0.1 and 0.15) samples recorded at room temperature. The Rietveld analysis results reveal that all samples have orthorhombic structure (P c 2 1 n) as shown in Figure1(b) for the GaFe 0.85 Cr 0.15 O 3 sample. The unit cell volume of the solid solution GaFe 1-x Cr x O 3 slightly decrease from about V= 417.38 [4] nm 3 to V= 415,55 nm 3 , when x is changed from 0 to 0.15.This decrease in unit cell volume with increasing Cr substitution is expected since the ionic radius of Cr 3+ is slightly smaller than that of Fe 3 + . .The SEM micrograph of the sintered pellet is shown in Figure 2 (a and b). The micrograph revealed a uniform distribution of the grains of varying shape with well defined boundaries with average grain size in the range of ~1-3 µm. The energy dispersive X-ray spectrum in the SEM mode is shown in Figure 2(c andd), which determines the chemical composition of the samples.

Magnetic properties

The magnetic properties of GaFe 1-x Cr x O 3 (x=0.05, 0.1 and 0.15) samples are shown in Figure 3(a). The temperature dependence of the magnetization (zero field cooling; ZFC and field cooling, FC), measured over the temperature range from 5 to 300 K under 100 Oe field, indicates that the magnetization is decreased by Cr doping. The magnetization of GaFe 0.85 Cr 0.15 O 3 , which is 3.7 emu/g, is found to be less than that of the undoped sample (6.3 emu/g) at 5 K [4]. The magnetic transition temperatures (T C ) calculated from the minimum position of the dM/dT versus temperature curve are around 148, 120 and 104 K for Cr=5, 10 and 15 %. The Curie temperature T C decreases with increasing Cr content in GaFe 1-x Cr x O 3 as compared to the parent compound where its T c =190K [4]. A similar behavior has been observed in the CoCr x Fe 2-x O 4 system [11]. The lowering of T c may be related to the weak Cr 3+ (3µ B )-O-Cr 3+ (3µ B ) [12] and Fe 3+ (5µ B )-O-Cr 3+ (3µ B ) interaction [13] as compared to Fe 3+ (5µ B )-O-Fe 3+ (5µ B ).

Figure 3(b) presents the magnetization as a function of field. All samples exhibit hysteresis behavior in the M-H curve, indicative of ferrimagnetism. The saturation magnetization (M s ), remnant magnetization (M r ), and coercivity (H c ) of the samples obtained from the hysteresis curves are presented in Table 1. It is seen that M s , M r and H c exhibit decreasing trends with increasing x. If the spin of the substituting Cr 3+ ion align with the Fe 3+ ion, the spin magnetic moment (SMM) of Cr 3+ (d 3 ) ion is 3 µ B , thus, the net SMM is expected to be reduced by 2 µ B per formula unit [14].

The frequency dependence of the dielectric constant, , and the dielectric loss, tan , at 353 K for Cr=10 and 15 % are shown in Figure 4. clearly shows a Debye-like relaxation from a high value at low frequency to a small saturated value at higher frequency for both samples. The decrease of the dielectric constant and the higher dielectric loss as a function of Crcontent may be related with the grain size. In general the dielectric constant and the dielectric polarization are proportional to the grain size [15]. In the present study, however, a different behavior was observed similar to Cr doped Ba 0.6 Sr 0.4 TiO 3 thin films [16]. A possible explanation may be a change in concentration of oxygen vacancies and defect related dipoles due to variable oxidation state of both Fe and Cr.

In general, the dielectric constant of any material is due to dipolar, electronic, ionic, and interfacial polarizations [START_REF] Jonscher | Dielectric Relaxation in Solids[END_REF][START_REF] Singh | [END_REF]. The dipolar and interfacial polarizations contribute significantly to the dielectric constant at low frequencies. Both these polarizations are strongly temperature dependent. In the high frequency region is almost the same for all samples as the contribution to the dielectric constant arises from electronic and ionic polarizations at high frequencies which are frequency independent. The frequency dependence of dielectric loss spectrum (tan ) shown in inset of Figure 4 implies that the hopping of charge carriers plays an important role in their transport process because a loss peak is an essential feature of the charge carrier hopping transport [19]. The monotonous increase in the loss factor at low frequency is probably due to the contribution of the d.c. conductivity [20].

The dielectric constant and the dielectric loss at 100 Hz-10 MHz for the sample of Cr=15% versus temperature (T) are shown in Figure 5. The dielectric constant is high at 1 KHz and decreases very sharply with increasing frequency at temperatures above 350 K. Jen Hsiao et.al. found similar situation in Li 0.01 Ni 0.94 Ta 0.05 O composition [21] and they explained the decrease in dielectric constant at higher frequencies in terms of the interfacial space charge polarization. Where the space charge polarization increases with increasing temperature due to the increase in dc conductivity, moreover, it decreases with increasing frequency due to the decrease in ac conductivity [22]. The values of (dielectric constant, dielectric loss) at 1 KHz and 298 K are (22.7, 0.01), (22.8, 0.6) and (16, 0.2) for GaFe 1-

x Cr x O 3 (x=0.0 [4], 0.1 and 0.15), respectively. Which indicates the doped of Cr decrease dielectric constant and increase the dielectric loss opposite to the situation of Cr doped BiFeO 3 [START_REF] Yi | Thin Solid Films[END_REF], where the dielectric constant increase considerably with the Cr doping level. The frequency (f) dependence of the and tan of GaFe 0.85 Cr 0.15 O 3 as a function of temperature are shown in Figure 6 (a) and (b).The peak in tan , shifts to a lower frequency on lowering the temperature. The values of the most probable relaxation time m were obtained from the peak frequencies m ( m m =1) of tan . The variation of m vs 10 3 /T shown in Figure 6 suggest that the relaxation time follows the Arrhenius law

= o exp(E a /K B T) (1)
where E a is the activation energy for the dielectric relaxation, K B is the Boltzmann constant and T is the absolute temperature. The activation energy for the dielectric relaxation obtained from the slope of the fitted line is 0.24 and 0.28 eV for Cr=10 and 15%, respectively. It has to be mentioned that the samples have been synthesized at high temperature 1200 ºC; a slight amount of oxygen loss can occur and may be expressed as by the Kroger-Vink notation [START_REF] Kroger | [END_REF]:

O o x =V o .. +1/2O 2 (gas)+2e ,
where O o x is the loss of lattice oxygen, V o .. is the presence of oxygen-ion vacancy and e is the electron released or captured. The electron release may be captured by Fe 3+ to generate Fe 2+ for charge compensation such as in LaFe 0.9 Ni 0.1 O 3 [25].The V o .. and Fe 2+ , contribute not only to the conductivity but also to the dielectric response. So, the activation energy values obtained above are almost equal to the activation energy of electron hopping between an Fe 2+ and an Fe 3+ ion in the oxide [26]. Again the strong increase in the dielectric characteristics with increasing temperature may be due to thermally induced oxygen ion vacancies and enhancement of hopping conduction as we will see later [27].

Polycrystalline samples may be analyzed by considering the impedance Z( ) spectra as an electric modulus M( ) spectra in order to emphasize the grain and grain boundary contributions to the electric properties [START_REF] Macdonald | Impedence spectroscopy: Theory, Experiment, and application[END_REF]. From the physical point of view, the electric modulus corresponds to the relaxation of the electric field in the materials when the electric displacement remains constant [START_REF] Molak | [END_REF]. The logarithmic frequency dependence of the electric modulus M' and M'' for various temperature are shown in Figure 7 for GaFe 0.9 Cr 0.1 O 3 .In terms of the dielectric constant ( ), the electric modulus is given by M*( )=M'( )

+ jM''( )= 1/ * 2(a) M'( ) = '( ) /[ '( ) 2 + ''( ) 2 ] 2(b) M''( )= ''( )/[ '( ) 2 + ''( ) 2 ]
2(c) It can be clearly seen that values of M'( ) increase with frequency and reach a constant value at higher frequencies [Figure 7(a)], while M ( ) exhibits a maximum (M max ) [Figure 7(b)]centered at the dispersion region of M′( ). It may be noted from Figure 7(b) that the position of the peak M max shifts to lower frequencies as temperature decreased. The frequency region below the peak maximum (M'' max ) determines the range in which charge carriers are mobile on long distances. At frequency above peak maximum the carriers are confined to potential wells, being mobile on short distances [30]. Figure 7(c) shows the frequency dependence of normalized M /M max peaks for GaFe 0.9 Cr 0.1 O 3 . The M /M max curves are overlap for all the temperatures into a single master curve, indicating that they describe the same mechanism at various temperatures relaxations. The temperature dependence of the characteristic relaxation time was determined and plotted in Figure 7 (d), which follows the Arrhenius law [31]. From the least square fitting, the activation energies are calculated, and are found to be 0.22 and 0.27 eV for Cr=10 and 15%, respectively. The nearly equal values of activation energy (calculated from loss and modulus spectrum) suggests that the relaxation process may be attributed to the same type of charge carriers.

Figure 8 shows Complex impedance (Z'' vs. Z' ) plot for GaFe 1-x Cr x O 3 samples measured at 353 K. The impedance diagrams clearly demonstrate that Cr influences the values of impedance, the real and imaginary components of the impedance decrease with an increase of Cr amount. Impedance spectra have been analyzed by an equivalent circuit, as displayed in the inset of Figure 8. The two sub-circuits represent the grain (g) and grain boundary (g b ) effects. The impedance spectra reveal semicircles whose centres do not lie on the abscissa of the axis, suggesting departure from ideal Debye-type behavior [START_REF] Behera Banarji | [END_REF]. Hence, in the equivalent circuit, the constant phase elements (Q) capacitance Q ( ) = B (i ) n-1 are assumed to describe the depressed semicircle [START_REF] Macdonald | Impedance spectroscopy[END_REF], where B is constant. The exponent n varies between 0 and 1(n= 1 for an ideal capacitor and n=0 for ideal resistor). The best fitting of equivalent RC circuit at 353 K using the software" ZsimpWin" are R g = 0.7 and 3,51 M , R gb = 88,81 and 40.89 M , C g = 8.186 x10 -12 and 6.506 x10 -12 F, C gb = 0.995 7 x10 -9 and 0.477 9 x10 -9 F for Cr=10 and 15 %, respectively. Thus, the impedance spectroscopy analysis clearly demonstrates that the grain boundaries are more resistive than the grain in GaFe 1-

x Cr x O 3 system.

In order to further elucidate the transport mechanism in this system, the electric conductivity at different temperatures is studied. Electric conductivity can be calculated from the dielectric data as ( )= 0 tan , (3) where is the angular frequency and 0 is the vacuum permittivity. Figure 9 (a) shows frequency dependence of a.c. conductivity ( a.c. ) at various temperatures for GaFe 1.85 Cr 0.15 O 3 . It can be seen that at low frequencies and above room temperature plateaus of a.c. (frequency independent values of conductivity) exist which corresponds to d.c. conductivity.

The observed frequency dependent conductivity can be described by the equation [START_REF] Jonscher | Dielectric Relaxation in Solids[END_REF] (

)= d.c +A n , ( 4
)
where n is the frequency exponent in the range of 0<n<1 and for an ideal Debye-type behavior it is equal to 1, A and n are thermally activated quantities, hence electrical conduction is a thermally activated process [START_REF] Behera Banarji | [END_REF].Extrapolating these curves towards low frequency gives the dc conductivity ( d.c. ). The resulting d.c . is plotted as a function of reciprocal temperature in Figure 9 (b) and it well obeys the Arrhenius law, = 0 exp (E cond /K B T), where 0 is the pre-exponential term, E cond is the conduction activation energy, and K B is the Boltzmann constant. From the fitting E cond are 0.22 and 0.28 eV, for Cr=10 and 15%, respectively. This thermal activation energy of the intragrain conductivity is very close to that obtained from the dielectric relaxation, which suggests that the conductivity may play a very important role in these materials.

Conclusion

Polycrystalline GaFe 1-x Cr x O 3 (x=0.05, 0.1 and 0.15) was prepared by solid state reaction. Xray diffraction of the samples confirmed the orthorhombic crystal structure. The surface morphology of the compounds is studied through SEM, which gives the average grain size as the order of ~1-3 µm. The magnetic properties decrease due to the weakening of the Fe 3+ -O-Fe 3+ superexchange interaction strength when the Cr 3+ ions replaces some of the Fe ions. The frequency dependent maxima in the imaginary electric modulus at various temperatures are found to obey Arrhenius law with activation energies of ~0.22 and 0.27 eV, for GaFe 1-x Cr x O 3 , x=0.1 and 0.15, respectively, which has been interpreted by hopping of electrons between ions of the same element but in different oxidation states. The scaling behavior of the imaginary part of electric modulus (M'') suggests that the relaxation describes the same mechanism at various temperatures. Impedance spectroscopy along with the equivalent circuit model was used to determine the resistance and capacitance associated with the grain and grain boundary.

Figure 1 .

 1 Figure 1. (a) XRD patterns of GaFe 1-x Cr x O 3 (x = 0.05, 0.1, 0.15) ceramic samples. (b) Rietveld analysis results of XRD pattern at RT for the GaFe 0.85 Cr 0.15 O 3 sample. Solid circles indicate the experimental data and the calculated data are the continuous line overlapping them. The lowest curve shows the difference between experimental and calculated patterns. The vertical bars indicate the Bragg reflection positions.

Figure 2 .

 2 Figure 2. The SEM surface images of GaFe 1-x Cr x O 3 samples: (a) x = 0.1, (b) x = 0.15, (c and d) Energy dispersive X-ray spectrum of Cr=10 and 15% doped samples.

Figure 3 .

 3 Figure 3. (a) Temperature dependence of magnetization for ZFC (open) and FC(solid) modes measured at 100 Oe (b) Magnetic hysteresis loop M(H) measured at 10K for the GaFe 1- x Cr x O 3 samples.

Figure 4 .Figure 5 .

 45 Figure 4.Frequency dependence of (a) ' and (b) tan of GaFe 1-x Cr x O 3 ; x=0.1 and 0.15 at 353 K

Figure6.

  Figure6. Frequency dependence of (a) ' and (b) tan of GaFe 0.85 Cr 0.15 O 3 at different temperature, and the inset is ln vs. 1000/T.

Figure 8 .

 8 Figure 8.Nyquist plots of GaFe 1-x Cr x O 3 samples at 353 K, inset represents the proposed circuit model.

Figure 9 .

 9 Figure 9.(a) Frequency dependent electric conductivity at various temperature for GaFe 0.85 Cr 0.15 O 3 , (b) Arrhenius plot of dc conductivity for GaFe 1-x Cr x O 3 , x=0.1 and 0.15 samples, read color represent linear fit.

  Figure 2

  Figure 4

  Figure 6

Figure 1

 1 GaFe 0.9 Cr 0.1 O 3 GaFe 0.85 Cr 0.15 O 3

	Element	Wt%	At%	Wt%	At%
	Ga	45.15	28.26 45.84	28.86
	Fe	36.64	28.63 34.67	27.24
	Cr	3.48	2.92	5.03	4.25
	O	14.74	40.19 14.45	39.65

Table 1 .

 1 Details of structure refinements with error bar and magnetic properties GaFe 1-x Cr x O 3 .

	Figure 9

Acknowledgements

One of us (M.Bakr Mohamed) would like to thank the Egyptian Ministry of Higher Education, Scientific Research and Technology for a research grant.


R R A Syms
email: r.syms@imperial.ac.uk

L Solymar

I R Young

T Floume

Thin-film Magneto-Inductive Cables by

Keywords: Metamaterial, periodic structure, magneto-inductive wave PACS numbers 41.20.-q Applied classical electromagnetism 81.05.Zx New materials: theory, design and fabrication 84.30.Bv Circuit theory

Magneto-inductive cables for low (ca 100 MHz) radio frequencies are demonstrated in thin-film form. 20 cm long resonant elements are formed using double-sided patterning of copper-clad polyimide, based on single-turn inductors and parallel plate capacitors that use the substrate as an interlayer dielectric. Continuous cables are formed by overlaying elements, in an arrangement that allows a high, positive coupling coefficient (κ > 0.6) to be achieved despite the use of a planar geometry. Equivalent circuit parameters are extracted from experiments on integrated coupling transducers, and propagation characteristics are compared with simple theory. Low propagation loss (4 dB/m at 55 MHz, falling to 2.3 dB/m at 130 MHz) is demonstrated near the operating frequencies of magnetic resonance imaging, for a potential application as patient-safe cable in internal imaging.

Introduction

Recently there has been considerable interest in artificial electromagnetic structures that may have novel properties such as negative permittivity, permeability and refractive index [1][2][3]. Many are based on periodic arrays of resonant elements, and are therefore similar to those historically used in filters and slow wave circuits [4,[START_REF] Silin | Slow wave structures[END_REF]. However, wideranging research has extended the range of applications and operating frequencies very considerably [6][7][START_REF] Solymar | Waves in metamaterials[END_REF].

One example of a simple metamaterial is the magneto-inductive (MI) waveguide [START_REF] Shamonina | Magneto-inductive waveguide[END_REF], sometimes called a metasolenoid [START_REF] Maslovski | Artificial magnetic materials based on the new magnetic particle: metasolenoid[END_REF][START_REF] Jylhä | Traveling waves along the metasolenoid[END_REF]. The resonant element is a simple L-C circuit, which is magnetically coupled to its neighbours by a mutual inductance M as shown in Figure 1a. There are two main variants: the axial (Figure 1b) and planar (Figure 1c) configurations, in which M is positive and negative, respectively. MI waves have been studied extensively, in one-dimensional (1D) waveguides [START_REF] Wiltshire | Dispersion characteristics of magneto-inductive waves: comparison between theory and experiment[END_REF][START_REF] Shamonina | Magneto-inductive waves supported by metamaterial elements: components for a one-dimensional waveguide[END_REF][START_REF] Syms | Low-loss magneto-inductive waveguides[END_REF][START_REF] Syms | Higher order interactions in magneto-inductive waveguides[END_REF] and in 2D and 3D arrays [START_REF] Shamonina | Magnetoinductive waves in one, two and three dimensions[END_REF][START_REF] Syms | Positive and negative refraction of magnetoinductive waves in two dimensions[END_REF]. Applications have been identified in magnetic field concentration [START_REF] Wiltshire | Resonant magnetic concentrator[END_REF], delay-lines [START_REF] Freire | Planar magnetoinductive wave transducers: Theory and applications[END_REF], phase shifters [START_REF] Nefedov | On potential applications of metamaterials for the design of broadband phase shifters[END_REF], filters and splitters [START_REF] Syms | Magneto-inductive waveguide devices[END_REF] and near-field lenses [START_REF] Freire | Planar magnetoinductive lens for three-dimensional subwavelength imaging[END_REF][START_REF] Sydoruk | Mechanism of subwavelength imaging with bilayered magnetic metamaterials: theory and experiment[END_REF].

A recent application is patient safety during in-vivo internal magnetic resonance imaging (MRI) [START_REF] Syms | MR-safe cables -an application of magnetoinductive waves?[END_REF][START_REF] Syms | Periodic analysis of MR-safe transmission lines[END_REF], a generalisation of earlier work in which co-axial cables carrying the signal from catheter-mounted detectors were subdivided using thin-film transformers [START_REF] Weiss | Transmission line for improved RF safety of interventional devices[END_REF]. Here, division into lengths shorter than the resonant length for external excitation prevents heating by the electric field of the powerful RF transmitter [START_REF] Konings | Heating around intravascular guidewires by resonating RF waves[END_REF][START_REF] Nitz | On the heating of linear conductive structures as guidewires and catheters in interventional MRI[END_REF]. The critical length is c/(2f√ε r ), where c is the velocity of light, f is the frequency and ε r is the relative dielectric constant of any surrounding tissue. For 1 H MRI in a 1.5 T field, f = 63.8 MHz, ε r = 77 for human tissue and the critical length is around 27 cm.

Previously, MI waveguides have been constructed as discrete elements based on wirewound [START_REF] Wiltshire | Dispersion characteristics of magneto-inductive waves: comparison between theory and experiment[END_REF] or printed circuit board [START_REF] Syms | Low-loss magneto-inductive waveguides[END_REF] inductors and surface mount capacitors.

However, construction has involved tedious assembly and tuning, and propagation losses have been extremely high. Taking into account the element spacing, published attenuation figures of ≈1.5 dB/El in [START_REF] Wiltshire | Dispersion characteristics of magneto-inductive waves: comparison between theory and experiment[END_REF] and ≈ 0.12 dB/El in [START_REF] Syms | Low-loss magneto-inductive waveguides[END_REF] translate into propagation losses of ≈150 dB/m and ≈ 50 dB/m, respectively. These high values rule out most practical applications.

A key requirement is therefore low-cost fabrication of high-performance material, especially in long lengths, large areas or flexible formats. Metamaterials such as dipoles, Jerusalem crosses, wire pairs and split-ring resonators are now being fabricated using single-sided patterning of metal layers on flexible dielectric substrates [START_REF] Shelton | Fabrication of periodic microstructures on flexible polyimide membranes[END_REF][START_REF] Shelton | Gangbuster frequency-selective surface metamaterials in terahertz band[END_REF][START_REF] Awad | Negative-index metamaterial with polymer-embedded wire-pair structures at terahertz frequencies[END_REF][START_REF] Tao | Terahertz metamaterials on free-standing highly-flexible polyimide substrates[END_REF][START_REF] Tao | Flexible and reconfigurable THz metamaterials[END_REF][START_REF] Peralta | Large-area metamaterials on thin membranes for multilayer and curved applications at terahertz and higher frequencies[END_REF][START_REF] Miyamaru | Characterization of terahertz metamaterials fabricated on flexible plastic films: towards fabrication of bulk metamaterials in terahertz region[END_REF]. This approach has been successful at terahertz frequencies, when only small effective component values are required and sufficient capacitance can be obtained using a coplanar geometry [START_REF] Tao | Terahertz metamaterials on free-standing highly-flexible polyimide substrates[END_REF][START_REF] Tao | Flexible and reconfigurable THz metamaterials[END_REF][START_REF] Peralta | Large-area metamaterials on thin membranes for multilayer and curved applications at terahertz and higher frequencies[END_REF][START_REF] Miyamaru | Characterization of terahertz metamaterials fabricated on flexible plastic films: towards fabrication of bulk metamaterials in terahertz region[END_REF]. However, for a MI waveguide operating at MHz frequencies, large values of L and C are required.

In this paper, a novel resonant element that allows low-loss, low frequency magnetoinductive waveguides to be formed as continuous thin-film cables is introduced. Doublesided patterning of flexible copper-clad polyimide is used to form elements that combine loop inductors with integrated parallel-plate capacitors, and low-loss propagation is demonstrated at MRI frequencies over the two-metre lengths typical of catheter-based internal imaging probes. We believe these to represent the longest continuous metamaterial structures demonstrated to date. The approach also allows the incorporation of integrated coupling transducers. The design is introduced in Section 2, fabrication and experimental characterisation are described in Section 3, experimental results are compared with the predictions of simple theory in Section 4 and conclusions are presented in Section 5.

Design

We first briefly review the underlying theory of magneto-inductive waveguides [START_REF] Shamonina | Magneto-inductive waveguide[END_REF].

Applying Kirchhoff's laws to the n th loop in Figure 1a, we obtain:

{jωL + 1/jωC + R}I n + jωM{I n-1 + I n+1 } = 0 (1)
Here ω = 2πf is the angular frequency and f is the corresponding temporal frequency.

Here we have introduced resistors R to denote lossy inductors. Assuming that the currents I n may be taken in the form of a travelling wave as I n = I 0 exp(-jnka), where ka is the phase shift per element, k is the propagation constant and a is the period, the dispersion equation may be obtained as:

{1 -ω 0 2 /ω 2 -j/Q} + κ cos(ka) = 0 (2)
Here ω 0 = 2πf 0 = 1/√(LC) is the angular resonant frequency, f 0 is the corresponding temporal frequency, Q = ωL/R is the Q-factor, and κ = 2M/L is the coupling coefficient.

Assuming that k = k' -jk'', and losses are small, Equation 2 may be approximated as:

(1 -ω 0 2 /ω 2 ) + κ cos(k'a) = 0 k''a = 1/{κQ sin(k'a)} (3)
The upper equation in (3) is the dispersion relation for loss-less waves. In the axial configuration, κ is positive, the waveguide supports forward waves and propagation is obtained only over the frequency band 1/(1 + κ) (ω/ω 0 ) 2 1/(1 -κ), whose extent depends on the value of κ. The lower equation shows that losses are lowest at mid-band (k'a ≈ π/2) and are reduced by a high Q-factor and a large coupling coefficient. In the planar configuration, κ is negative and backward waves are supported.

From the point of view of propagation loss, neither configuration is entirely satisfactory, since it is more often loss per metre that is important than loss per element. Planar elements can have a large physical extent in the direction of propagation, but have a relatively small coupling coefficient since κ < 1 in this geometry. Experimental values are usually lower. Axial elements have a larger coupling coefficient, with a peak value that can approach κ = 2, but only if the period is so small that the distance propagated per element is extremely short.

We therefore introduce the modification shown in Figure 2a (which omits resistive losses) in which the capacitor and inductor are each separated into two series-connected elements. This new arrangement has the same dispersion relation as that of Figure 1a.

However, sub-division of the inductor allows adjacent resonators to be overlaid so that large, positive coupling is achieved in a planar geometry, as shown in Figure 2b. Subdivision of the capacitor allows the formation of high-value integrated parallel plate components that use a thin substrate as a dielectric interlayer as shown in Figure 2c. Both sides of the substrate carry inductor loops and capacitor plates and a cable is realised by cascading sections so that inductors from adjacent elements overlay to form air-cored transformers.

In addition to reducing loss and improving manufacturability, this arrangement should reduce the relative size of non-nearest neighbour coupling, a feature that has complicated understanding and development of magneto-inductive devices [START_REF] Syms | Higher order interactions in magneto-inductive waveguides[END_REF]. However, departures from ideal behaviour are still likely to arise from parasitic capacitances C 1 between the tracks of overlapping inductors and C 2 between the plates of adjacent capacitors. Careful choice of design dimensions is required to minimise their effect.

Cable layouts are specified using the parameters of Figure 3a, which shows one period.

Elements are defined in terms of their overall width W and half-length D P (= a). Inductors are defined in terms of their half-length D L and track width T. Capacitor plates are defined in terms of their half-length D C = (D P -D L )/2, and a gap G C between the plates is used to reduce C 1 . A gap G L is used to separate the inductors and capacitors, and a further transverse separation S L is introduced between the tracks on either side of the substrate to reduce C 2 . Periodic repetition allows a complete cable to be defined, together with inductors that can act as integrated transducers for input and output coupling as shown in Figure 3b. The overall length of a cable with N resonant elements is then (N + 1)D P .

Fabrication and experimental characterisation

Prototype thin film MI cables were fabricated in two metre lengths by the UK company Clarydon (Willenhall, West Midlands), using double-sided patterning of copper-clad polyimide. The starting material was 25 µm thick Kapton ® HN (DuPont, Circleville, OH), coated on each side with a 35 µm thick pressure-bonded layer of copper. The copper was patterned by lithography and wet chemical etching, using two consecutive exposures to a pair of one-metre-long photomasks whose layouts were defined by a Gerber file.

Registration to the Kapton sheet was achieved using mechanical alignment pins.

Dimensions for operation at MRI frequencies were estimated from earlier work. PCBs both vary linearly to good approximation. Figure 4b shows the corresponding variation of f 0 , which shows that the designs straddle the frequency range from 63.8 MHz to 127.6

MHz, corresponding to 1 H MRI at fields between 1.5 T and 3 T.

The extracted capacitance may be compared with an estimate C est = D C (W -G C )ε 0 ε r /2t obtained from a parallel plate model, where ε 0 = 8.85 x 10 -12 F/m, and ε r = 3.5 is now the relative dielectric constant and t = 25 µm is the thickness of the polyimide sheet. The extracted values are generally smaller than these estimates, suggesting experimental error in the determination of f T2 (and hence also in f 0 ) caused by proximity to the propagating band.

Cable properties were determined after attaching SMA connectors to the input and output transducers and connecting to the network analyser. The cables could be flexed gently without significant variations in transmission. However, folding the cables so resonators at different points could couple magnetically did introduce changes. Figure 5 shows the frequency variation of the S-parameters of two-metre lengths of four different cables (A, D, F and G). The remaining designs have equivalent performance at appropriate frequencies.

Figure 5a shows the frequency variation of S 21 . In each case, propagation is band-limited, with the centre frequency and bandwidth increasing from Design A to G. Out of band, there is increasing transmission at higher frequencies, which is attributed to the parasitic capacitance C 1 in the transformers. Overall transmission also increases from design to design, but relatively slowly. For Design A, for example, propagation is obtained from 44

MHz to 88 MHz, and minimum insertion loss of around 11 dB is obtained near 63.8 MHz frequency. For Design G, minimum loss has reduced to around 7.5 dB, and, this design would be suitable for operation at 127.6 MHz. Figure 5b shows the frequency variation of S 11 . In each case, impedance matching is moderate, with a minimum return of around -5 dB for Design A reducing to -7 dB for Design G. These results suggest that the majority of the insertion loss must be due to attenuation rather than coupling loss.

After measurement, lines were attached to the outside of 8 Fr catheters using heat-shrink tubing, and re-measured. The only change in performance was a slight increase in centre frequency following from the reduction in inductance L caused by the change in geometry. [START_REF] Shamonina | Magneto-inductive waves supported by metamaterial elements: components for a one-dimensional waveguide[END_REF]

Comparison with theory

To compare the experimental results with theory, a method of estimating S-parameters is required. We use a simple approach that ignores multiple reflections, but which also neglects loss in calculation of reflection coefficients and hence is valid only for intermediate attenuation. To estimate reflection losses, we assume the geometry of Figure 6a, where a semi-infinite line ending at element 0 is terminated using a resistor R L via an inductive transducer. Other resistive losses are ignored. For the final elements, Kirchhoff's laws give:

{jωL + 1/jωC}I 0 + jωM{I -1 + I L } = 0 {R L + jωL/2}I L + jωMI 0 = 0 (4)
From the lower equation in (4) the load current can be found. Substituting into the upper equation, we obtain:

{jωL + 1/jωC + Z L }I 0 + jωMI -1 = 0 (5)
Here Z L = ω 2 M 2 /{R L + jωL/2} is an effective load impedance. A solution is now attempted as a sum of counter-propagating waves, i.e. as I n = I I exp(-jnka) + I R exp(+jnka)

where I I and I R are incident and reflected wave amplitudes. This solution automatically satisfies the loss-less recurrence equations away from the termination. Substituting into Equation 5, and using these relations, we can obtain the reflection coefficient Γ = I R /I I for current waves as:

Γ = -{Z L -Z 0 }/{Z L + Z 0 *} (6)
Here Z 0 is the characteristic impedance of a MI waveguide, previously found in as [START_REF] Solymar | Waves in metamaterials[END_REF]:

Z 0 = jωM exp(-jka) (7)
and Z 0 * is the complex conjugate of Z 0 . At mid-band (ka = π/2), Z 0 is real and has the value Z 0M = ω 0 M. In principle, it should be possible to match Z 0M to a real resistive load by appropriate choice of M and by making the effective termination Z L real at f 0 , using an additional series capacitor. In this case we simply require ω 0 M = R L .

Including propagation losses arising from the imaginary part of the propagation constant, but neglecting multiple reflections, the scattering parameters of an N-element waveguide with identical terminations at either end may then be expressed in dB as:

S 11 ≈ 10 log 10 { Γ 2 } S 21 ≈ 10 log 10 {(1 -Γ 2 ) exp(-2Nk''a) (1 -Γ 2 )} (8)
Theoretical estimates obtained from Equations 3 and 6-8 were compared with experimental data as follows. The inductance L was assumed to be accurately determined.

The resonant frequency f 0 ' (an approximation to f 0 obtained by matching theory to experiment), Q-factor and coupling coefficient κ were then adjusted to fit the centre frequency, bandwidth and maximum transmission, respectively. Figure 6b

  were fabricated as panels measuring 300 mm x 2 m. Each panel contained three repeats of an array containing eight different MI cables with the parameters given in TableI. In each case, the same value of D P = 10 cm was used, so that the overall element length of 20 cm was less than the critical value given earlier. A 2 m long panel then contained 200/10 -1 = 19 resonant elements. The overall width W was taken as 4.7 mm throughout, to place the conductors on the diameter of an 8 Fr (2.7 mm dia) catheter. The lengths D L and D C of the inductors and capacitors were varied across the array to obtain a variation in the resonant frequency f 0 . The widths of all narrow features including track widths and clearance gaps (T, G C , G L , and S L ) were taken as 0.5 mm, the minimum feature size that could be patterned reliably over a 2 metre length. Figure3cshows a completed array with design A at the top and H at the bottom, from which individual guides can be separated using a scalpel. Electrical performance was measured using an Agilent E5061A Electronic Network Analyser. The equivalent circuit parameters are given in TableIand were extracted from measurements of integrated transducers. A large capacitor C T = 1 nF was first soldered across a transducer, which effectively comprised half an element, to create a new element defined mainly by L/2 and C T . The resonant frequency f T1 of this element was found by inductive probing, and used to estimate L. The capacitor was then removed, and a short circuit soldered across the two half-length capacitor plates at the substrate rear below the transducer connections, to create a further new resonant element now defined mainly by L/2 and C/2. The resonant frequency f T2 = f 0 /2 of this element was then used to estimate C. Component values extracted from either end of the same cable were consistent, suggesting good dimensional control. Figure4ashows the variation of L and C with D L ;

9 )

 9 shows a typical comparison between experiment and theory for the frequency variation of S-parameters of Designs A and G, assuming R L = 50 Ω. Generally, the agreement is excellent, although the theory clearly cannot predict the oscillations arising from multiple reflections.The fitting parameters are detailed in TableI, and the variation of f 0 ' with D L is superimposed on Figure4bfor comparison with the earlier estimate. Discrepancies between f 0 ' and f 0 confirm the small inaccuracy in experimental determination of the latter. The Q-factor is modest, rising quasi-linearly with f 0 ' from 36 in Design A to 55 in Design H, as shown in Figure7a. The coupling coefficient κ rises slowly with D L from 0.61 to 0.69, suggesting that the central sections of the inductors provide slightly more effective coupling than the ends. The combination of rising Q-factor and coupling coefficient causes a reduction in propagation loss. At mid-band, the loss per element can be found in dB from Equation3as: Loss/El =10 log 10 {exp(-2/κQ)} (This value can be converted into an equivalent loss per metre by dividing by the repeat distance D P (= a). Figure 7a also shows the variation of propagation loss with f 0 '. The loss falls from ≈ 0.4 dB/element to ≈ 0.23 dB/element (or 4 dB/m to 2.3 dB/m) over the range shown. Compared with earlier MI waveguides [14], the second figure represents a twenty-fold reduction in loss per metre, largely due to the increased size of the new elements. Finally we show in Figure 7b the variation with the inductor length D L of the mid-band impedance Z 0M . The impedance rises from ≈ 20 Ω in Design A to ≈ 70 Ω in H, due to a combination of a slow increase in M and a more rapid rise in f 0 . Since the values are close to 50 Ω, it should be relatively simple to reduce coupling losses by small changes in layout. 5. Conclusions Low-loss propagation of magneto-inductive waves has been demonstrated using thin-film cables fabricated entirely by double-sided patterning of copper-clad polyimide. The resonant elements are formed using single-turn inductors and parallel plate capacitors that use the substrate as a dielectric interlayer. Integrated coupling tranducers are also formed from single-turn inductors. Large, positive coupling between elements is obtained despite the use of a planar arrangement, and the availability of high-value integrated capacitors allows operation at low (100 MHz) frequencies. The fabrication method is intrinsically low-cost and extensible to long lengths using step-and-repeat patterning, and should allow rapid development of other thin-film magneto-inductive components such as splitters and filters. Low insertion and propagation losses have been demonstrated over two-metre lengths. Experimental measurements of S-parameter variations have been compared with the predictions of a simple theoretical model, and good agreement has been obtained. Further improvements in performance and a reduction in element size should follow from the use of multi-turn inductors. These aspects are now being investigated. Finally we note that a time-varying external magnetic field can induce voltages in the open loops. However, if the external field is slowly varying in space, the overall voltage can be minimised by replacing open loops with figure-of-eight windings, so that induced voltages in each half-winding at least partly cancel. This arrangement would avoid RF heating or damage by the transmit field in a MRI scanner, together with any substantial modification to the excitation pattern [36]. Voltages induced by faster-varying fields from local dipole distributions would not necessarily be subject to such cancellation. However, any resulting signals would be encoded in frequency space by the gradient fields, and could be separated out by scanner software. Such signals can be used for visualising the track of the cable [37].

Figure 3c (

 3c Figure 3c (Fig3c.JPG)


L Bedra

A L Thomann

N Semmar

R Dussart

J Mathias

Highly sensitive measurements of the energy transferred during plasma sputter deposition of metals

This work reports results obtained from heat flux measurements performed during the deposition of metallic thin films by low-pressure plasma sputtering. It introduces a sensitive diagnostic, which allows to perform such measurements directly during the process and to follow in real-time mechanisms involved in plasma/surface interaction. Although quantitative results are provided and discussed, the main scope of this article is a qualitative study of the sputter-deposition process via the energy flux transfers. The diagnostic developed for energy flux measurements is presented and the versatility of the experimental apparatus is described.

Results on the study of the deposition of Pt (and Fe) thin films demonstrate a good reproducibility of the measurements and the ability to separate the energetic contributions of the main plasma (∼ 300 mW/cm 2 ) from the deposition process ones (2 to 23 mW/cm 2 ). The influence of gas pressure, plasma power and target bias voltage, on the energy transferred to the silicon substrate is also studied. challenging research area [1]. The complexity of the energy transfer study is due to the fact that energetic contributions are of different kinds [2,3]: -energy transfer by collision from electrons, ions, excited neutrals, sputtered atoms, -release of potential energy from metastable atoms, neutralization of ions or adatom condensation radiation from emitting plasma and heated devices (target, reactor walls etc.)

Depending on the plasma source, the reactor geometry, the substrate bias, the main species contributing to the energy transfer are different. Whereas charged particles are the

Introduction

At present time, plasma enhanced processes, such as thin film deposition, etching, polymer functionnalisation, etc. are widely used for various industrial applications (microelectronics, protective coatings, material treatments…). To achieve the control of the process and help to the scale-up step, a better knowledge of the involved mechanisms is still necessary. Simultaneously to the plasma characterization, a good knowledge of the energy released onto the substrate is of crucial importance to control accurately the properties of the plasma modified material. Up to date, the fundamentals of these energy transfers are still a main source of energy flux in case of biased substrates [4], contribution of electrons or neutrals may become significant in other cases [2][START_REF] Ekpe | Reactive Sputter Deposition[END_REF][4][5][6]. Events occurring during plasma/surface interaction could be more complicated when chemical reactions (molecule dissociation, chemical etching, etc…) occur on the substrate surface [2,7]. Nevertheless, for non reactive sputtering, it is commonly admitted that the total energy transfer is composed of the contributions listed below [2,[START_REF] Ekpe | Reactive Sputter Deposition[END_REF]:

Sputter-deposition stage

• The adsorption enthalpy of the incoming atoms, usually referenced as condensation energy • The kinetic energy of the sputtered atoms

• The energy of the gas ions, which recombine with electrons when colliding with the negatively biased target, becoming fast neutrals. Their key role has been evidenced in magnetron sputtering [6,[8][9][10][11] Plasma contribution

• The kinetic energy of gas atoms [12] • The potential energy of metastables that can be partially released at the surface • The kinetic energy of the charged particles: ions accelerated through the plasma sheath, and electrons which may interact with the substrate (eg in RF plasmas). For ions that are neutralized at the surface, the ionization energy has to be taken into account Other transfer processes • The radiative energy coming from both excited particles of the plasma and heated devices (vessel walls, metallic target …)

To distinguish each of these energy flux contributions, specific experiments have to be made in different configurations. Results provided by literature most often come from calculations based on temperature measurements [4,12]. Even if some sophisticated thermal probes have been developed [13][14][15], the total energy flux is always estimated a posteriori from thermograms recorded during the heating and cooling steps. Mathematical treatments are then employed to estimate the heat flux, that introduce systematic deviations. Moreover, with this kind of methods, it is not possible to evidence transfer mechanisms of different kinetics such as transfer by collision (instantaneous) or transfer involving a heating step (IR emission). Moreover, detection of transient or small energetic contributions (several mW/cm²) could not be reasonably achieved.

The present work describes a study of the energy transfers onto a silicon substrate during deposition of metallic thin films by plasma sputtering. It is based on measurements performed with an energy flux diagnostic whose time resolution (1ms) is sufficient to follow the energy transfer occurring at the substrate surface in real time. Unlike Ellmer et al. [16] whose calorimetric sensor exhibits similar characteristics (i.e. sensitivity ≈ 20µV/mW/cm²), in the present energy flux diagnostic, the sensor is maintained at fixed temperature. This is favourable to repetitive heat loading and long operating time. Especially remarkable is the time rise, that is lower compared to the calorimetric sensor one (few ms). The experimental configuration has been chosen in order to separate heat fluxes coming from the argon plasma itself, and the ones due to the Sputter-Deposition Process SDP. An Inductively Coupled Plasma (ICP) reactor is used, where a metallic target can be independently DC biased. After a brief description of the experimental setup, results obtained with respect to experimental parameters are presented and discussed.

Experimental apparatus

The energy flux diagnostic is based on a commercial sensor built by Vatell Corporation [17] and composed of 1600 thermocouples/cm 2 mounted in series, and having a 6 mm diameter active surface (See Fig. 1a). Its principle is based on the Seebeck effect (thin film thermopile). The Vatell probe has been preferred to other commercial heat flux sensors because of its good sensitivity and time resolution (~1ms). This Heat Flux Microsensor (HFM) is inserted in a water-cooled copper chamber (Fig. 1a). Hence, the HFM is set at a sufficiently low temperature (278 K) to make the heat flux permanently oriented toward the probe. Moreover, the lower the HFM temperature, the more accurate the energy flux signal (better signal to noise ratio). Measurements are carried out with a Keithley ® Nanovoltmeter 2182, since the output HFM voltages are of the order of µV at the relatively low energy fluxes reached in the present conditions.

The plasma reactor is a 40 cm diameter and 20 cm height chamber, in which pressure can be set down to 10 -5 Pa. The argon (Ar) gas inlet is set to 5 sccm and the working pressure is adjusted between 0.5 and 5 Pa. The experimental apparatus can be used in two configurations:

The first one is dedicated to the calibration procedure of the energy flux diagnostic. It has been widely described in previous paper [18]. For this step, a cylindrical (copper) homemade blackbody, surrounded by thermal shields, is inserted in the reactor at 0.5 mm from the HFM. The blackbody can be heated up to 500 K with a DC power supply. The calibration is performed in vacuum, so that only radiative transfers occur between the blackbody and the HFM, satisfying thus the NIST (National Institute of Standard and Technology) procedure [19].

The second configuration, designed for the SDP study, is schemed in figure 1b). The plasma is created in argon gas. A 13.56 MHz generator is able to provide a power up to 1000 W, via a matching box (reflected power < 5W). The sputtering target and the energy flux diagnostic are placed in a TCP reactor, 10 cm away from each other.The sputtered target is a 5x5cm 2 and 0.5mm thick metallic plate (Pt or Fe). A DC generator is connected to the target.

Hence, the target voltage can be varied from -50 to -350 V. The substrate is a 0.5 mm thick and 1x1 cm 2 silicon wafer directly stuck [20] on the HFM active surface with a thermal paste, in order to reduce the thermal contact resistance. During the SDP, substrates are at floating potential.

Results and discussion

Previous studies, based on comparisons between experiments and COMSOL multiphysics simulations, have shown that the major part of the heat flux reaching the substrate is transferred to the HFM with negligible losses [START_REF] Bedra | Proceedings (CD) of the 5 th European Thermal-Sciences Conference[END_REF]. Since the HFM is water-cooled at 278 K and the substrates relatively thin, the heat flux remains directed toward the HFM.

Therefore, the energy flux density on the substrate is deduced from the HFM measurement by multiplying the value obtained from the calibration curve with the ratio between the areas of the substrate and the HFM active surface.

1. SDP contribution to the global energy transfer

A typical energy flux time evolution recorded during sputtering of Pt is presented in Fig. 2a. This experiment consists of a sequence of seven sputter-deposition steps, lasting 1 min each, with increasing negative bias voltages of the target. First of all, it is interesting to note that the background signal (heat flux density before switching on the plasma, i.e. for t < 1500 s) is not equal to zero, but of the order of 18 mW/cm 2 . This is due to radiative transfer between the reactor at room temperature and the substrate which is cooled down to 5°C. After switching off the plasma (t ≈ 3700 s), the signal reaches again this value.

As soon as the plasma is turned on (t ≈ 1500 s), the heat flux through the substrate surface increases sharply within 2s. The plasma contribution (∆ϕ plasma = 300 mW/cm 2 ) has been studied in [18] and is due to energy transfer from charged particles, especially Ar ions.

After this switching on step, the signal continues on increase until it reaches a steady state (at about 2500 s). This behaviour is attributed to the progressive heating of the reactor, inducing radiative transfer from the walls toward the substrate. This thermal contribution is detected by the HFM in addition to the plasma one.

From t = 2500 s, small signals are visible on Fig. 2b, corresponding to the 1 min lasting sputter-deposition steps. One can first observe on each signal a sharp rise followed by three kinds of evolution:

the top of the first signals (-50 and -100 V) slowly increases, -the last ones (from -200 V) decrease rather linearly, -for -150 V signal, a steady state is reached.

The slow rise is due to a radiative transfer from a heated device. As soon as the target is biased, it undergoes bombardment from the positive Ar ions. Its temperature rises (the target is not cooled) and it starts emitting in the infrared range. This radiation is detected by the HFM and partly overlaps the sputter-deposition signal.

To sustain this explanation, an experiment has been made with a 5x5cm 2 piece of Si inserted between the sputtering target and the HFM. The Si shield was set very close (0.5 mm) to the substrate-HFM system, in order to avoid any metal atom deposition on the silicon substrate. Silicon was chosen as a shield for its wide spectral transmittance (1-9 µm) [START_REF] Allmen | Ion Beam Interactions with Materials[END_REF],

which allows most of the IR radiation emitted by the target to reach the HFM. Note that the Si shield, left floating, can also be slightly heated under bombardment of low energy (e(Vp-Vf))

argon ions. When biasing the target in such a configuration, a small signal with a different shape from the one of SDP steps is observed (see Fig. 3). As a matter of fact, the sharp rise attributed to the atom deposition onto the substrate (that can be assisted by fast argon neutrals)

does not exist anymore. However, as it can be seen in Fig. 3, there is a slow rise of the signal, which is attributed to a heating process of both sputtered target and Si shield. This experiment was thus useful to demonstrate that the sharp rise of the sputtering signal is due to collision processes (momentum transfer from particles) that we are interested in. The direct link between the target heating and the further evolution of the first SDP signals in the sequence is also checked. After a while, the target temperature becomes constant, and the SDP signal reaches a steady state as observed on Fig. 3 for -150 V.

The decreasing trend of the SDP signal (from -200 V) observed on Fig. 2b can also be explained. This behaviour is attributed to the progressive coating of the upper reactor window just below the antenna by sputtered Pt atoms. This statement is supported by the fact that the signal only decreases during the sputter-deposition steps, whereas it is constant in-between (plasma contribution in Fig. 2b). If such a thin Pt layer covers the window, plasma-antenna coupling becomes less efficient (confirmed through the plasma colour change) and the electron density in the plasma is globally lowered. Consequently, the sputtering ions at the target are less numerous and the sputtering process becomes less efficient. This leads to a decrease of the energy transferred during the SDP. Moreover, after each sputtering step, the contamination layer being thicker, and the Ar ions density lower, the plasma contribution diminishes too.

From this first experiments it is seen that the contribution corresponding to the SDP ∆ϕ sput is well quantifiable and strictly distinguished from the ICP plasma signal. It is proved that the HFM sensitivity is sufficiently high to detect the small amount of energy deposited by the SDP (from 2 mW/cm² to 23 mW/cm 2 ), hardly observed by classical thermal probes. It is also of particular importance to notice the ability of the HFM diagnostic to distinguish the heat flux transferred by fast mechanisms (conduction, adsorption) from those involving a thermal step (target heating,…).

Bias voltages ranging from -50 down to -350 V were applied in order to study the effect of the target bias voltage on the energy transfer by the SDP onto the silicon substrate.

At first glance, one can see on Fig. 2b that the more negative the bias voltage, the higher the energy transfer. This will be discussed in the paragraph 3.3.

2. Reproducibility of heat flux measurements

To investigate the reproducibility of both the SDP and the heat flux density measurements, additional experiments were carried out. The signal of a sequence of 6 sputterdeposition steps of Pt was recorded for a constant target bias voltage of -200 V (Fig. 4a and4b). It is clearly shown that the corresponding heat flux density ∆ϕ sput = 8-9 mW/cm 2 remains constant from one step to another. Note that the heated target contribution was removed from the first one. This shows that the presence of the previously deposited metallic layers does not perturb the energy flux density measurements. Indeed, measurements being performed on a growing metallic layer containing some interfaces (sputtering off steps), an increasing thermal resistance should have been formed. This would have led to a decrease of the measured signal (∆ϕ plasma and ∆ϕ sput ). Possible perturbation of energy flux measurements induced by a change of the heat conduction were reported by Ellmer et al. [16] in the case of the calorimetric sensor they use. They conclude that for relatively low thicknesses of the deposited layer, this effect is negligible. The good reproducibility of the signal after each sputtering step indicates that measurements remain accurate enough during the growth of the metallic layer, in the experimental conditions used in Fig. 4.

Rather than the thickness, the interfaces created inside the layer during the plasma/surface interaction steps can influence the thermal conductivity. To check this point, we have performed two kinds of experiments where the growing regime of the Pt layer was modified.

First, we have compared a sequence of 6 Pt sputtering steps of 1 min each with a continuous sputtering process of 6 min; depositing respectively either 6 layers or one continuous layer for the same total sputtering time. Fig. 5 shows the HFM signal for the continuous sputtering step of 6min. Once again, one can see on this graph the effect of the processes described above: after the SDP contribution, a slow rise due to the radiative transfer from the heated target and a linear decrease, attributed to the growth of a Pt layer on the window. The value of ∆ϕ sput = 8-9 mW/cm 2 either calculated from the sharp rise or from the falling down of the signal, is the same for both cases: short time sputtering steps and long time continuous coating. The energy measurement is thus not affected by the layer growth mechanism.

The second conducted test consists of making several Pt sputtering steps (with increasing negative bias voltage), but by turning off the plasma between each. As shown in Fig. 6, the sputter-deposition contribution ∆ϕ sput for a given target bias are the same on both experiments (8-9 mW/cm 2 ). This validates the rather accurate reproducibility of the diagnostic. Thus, it is proved from these last experiments that, in the present conditions, the presence of a growing metallic layer on the substrate does not affect the energy flux measurements.

A comparison is made with the SDP of Fe in the same conditions than in Fig. 4 for Pt (see Fig. 7a and7b). The contribution of the SDP ∆ϕ sput = 6-7 mW/cm 2 is well reproducible step to step. However, in this case, the plasma global signal does not decrease, even after several sputtering steps. This is also visible on the top of the sputtering slots, which never decreases.

In opposite, they keep growing in a slow way due to the target IR emission and reach a steady state regime when the temperature becomes constant. The different behaviour observed on the sequence of 6 sputter-deposition steps between Pt and Fe is also a check of the reason for the decreasing tops observed on the Pt sputtering signals. The iron sputtering yield for 300 eV argon ions is lower (0.6) than the platinum one (0.8) [START_REF] Yamamura | [END_REF], thus the dielectric window under the excitation antenna is slower contaminated in the case of iron. The global Fe quantity deposited (in conditions of Fig. 5) after 6 min total sputtering time is not enough to significantly perturb the RF power/plasma coupling.

Energy transfer during DSP versus experimental parameters

All these experiments have shown that the diagnostic is suitable to study plasma/surface interaction via energy transfers, and for deposition process control. The order of magnitude of the global energy deposited onto the substrate is in good agreement with works on magnetron sputtering reported in literature [2,5,16]. An important result is that, according to the experimental configuration and to the sensitivity of the sensor, it is possible to separate the sputter-deposition contribution from those due to the plasma or from the residual heating of the reactor parts. This is an advantage compared to conventional techniques used for energy flux measurements during deposition. It is shown that in the present conditions, the energy part brought by condensing atoms and reflected neutrals is very small (≈ 5%) compared to the contribution of the argon plasma. This is in correspondence with S. Mahieu et al. work [6,11], where the contributions to the energy momentum flux are calculated from plasma characterizations and simulations.

In the following, the diagnostic is used to study the influence of experimental parameters onto the SDP contribution: bias voltage, gas pressure and plasma power. Fig. 8 shows the linear evolution of the energy brought by the SDP with respect to the Pt target bias voltage. Obviously, as the target voltage becomes more negative, the kinetic energy and the flux of the Ar + attracted by the target increases. This leads to a more efficient sputtering process (higher sputtering yield of metal atoms). The metal atoms sputtered out of the target are thus more numerous. It has been shown that, the mean kinetic energy of sputtered atoms only weakly depends on the energy of the incoming argon ions [9,24,25]. The increase of the deposition contribution is thus mainly due to a rise of the number of condensing atoms. In the same manner, the contribution of the argon ions reflected by the target gets higher. This can be predicted from simple calculations given for example in [9].

Both phenomena tend to increase the global energy transfer coming from the SDP. The behaviour observed in Fig. 8 was thus expected.

For the most negative voltage, i.e. -350 V, the energy transferred to the Si substrate by the SDP is around 25 mW.cm -2 . The target voltage corresponding to ∆ϕ sput = 0 is about 25V.

Taking into account the plasma potential (≈ 10 V in the present conditions), the corresponding energy of the sputtering argon ions can be estimated to 35 eV. It is interesting to compare this value with the sputtering threshold of Pt by Ar+ given in literature (25-30 eV) [START_REF] Yamamura | [END_REF]. The good agreement between both values indicates that the energy transfer from metal sputtered atoms is the main contribution in the SDP.

Measurements performed at various gas pressures are presented in Fig. 9a. They have been made at 3 different bias voltages (-100, -200 and -350 V) and for each of the 4 pressure values (0.5, 1, 3 and 5 Pa). As expected, the energy transferred by the plasma increases with pressure. This is because the ion density increases when the plasma gets more confined by collisions. This point is reported in [26] for instance.

Since the number of collisions of plasma particles increases with pressure, the sputtered atoms are also subjected to deviations: they are scattered away from their path to the substrate. Moreover, they lose a significant part of their kinetic energy [START_REF] Ekpe | Reactive Sputter Deposition[END_REF]9,24,27].

Consequently the energy contribution of the condensed atoms (or land reflected neutrals) ∆ϕ sput drops down (see Fig. 9b).

One can notice on Fig. 9a that the lower the pressure, the better resolved the sputtering slots. Zooms of two sputtering steps for -200 V, 0.5 Pa and 3 Pa respectively are presented in Fig. 10. It is clearly seen that the deposition signal shape changes with the pressure. Therefore, mechanisms involved in the energy transfer are varying with pressure. It has been reported in literature that the gas temperature increases with the pressure [28]. This is evidenced on Fig. 10b where the gas thermal contribution dominates the signal.

In Fig. 11, the energy flux density evolution is plotted versus the plasma power. The plasma is switched 'on' and 'off' before and after each power value. As expected, the evolution of the plasma energy contribution is proportional to the RF power. Since the electron density linearly evolves with power in an ICP plasma, the energy transferred to the surface increases. A good agreement has been found between ionic current measured with Langmuir probe (not given here) and plasma contribution to the global heat flux transfer. This suggests that the energy transferred by the plasma as a function of the power mainly depends on the ions flux evolution. This is confirmed by estimations performed in a previous work [18] in similar experimental conditions (ICP argon plasma, 0.5 Pa, substrate at floating potential). The ion energetic contribution was estimated to about 80% of the total.

As RF power increases, the energy transfer due to the SDP rises (Fig. 11b). This is due to a higher ion density in the plasma leading to an enhanced sputtering process. The number of adsorbed atoms onto the substrate becomes more significant, increasing the global energy flux transferred to the substrate.

Conclusion

This work highlights application of a sensitive energy flux sensor to a semiquantitative investigation of the energy transfers occurring during SDP. Direct energy flux measurements are performed with an original diagnostic developed at the laboratory. Results

show that such a system allows to follow the real time evolution of the energy flux transferred to the substrate. From experiments presented here, the ability of the diagnostic to monitor a deposition process is clearly established. According to the chosen experimental conditions and to the sensor sensitivity, the contribution of the SDP was successfully isolated from the Ar plasma one. Moreover, the short response time allows to get rid of the slow contributions due to IR radiations emitted from the heated parts of the chamber.

The influence of several experimental parameters (Ar pressure, target voltage and RF power) on the energy transferred to the substrate was studied. It is shown that plasma contribution increases with respect to both pressure and RF power. These general trends, already reported in the literature, were expected. For the SDP contribution, a linear rise with bias voltage and plasma power, and a decrease as a function of the pressure was qualitatively evidenced. This was explained in terms of sputtered atom and reflected neutral kinetic energy and flux variations. Another paper is in progress where measured energy transfers from the SDP will be compared to estimations from energy balances.

Figure 1 :

 1 Figure 1: a) Photos showing the heat flux micro-sensor (inch scale) and its integration in the water-cooled substrate holder, b) schematic of the ICP plasma reactor in sputter-deposition configuration.

Figure 2 :Figure 3 :

 23 Figure 2: a) Energy flux measurement during a sequence of seven sputter-deposition steps of Pt, in 0.5 Pa pressure and 400 W argon plasma. b) Zoom of Fig. 2a showing the 1 min sputterdeposition steps performed with target voltages ranging from -50 to -350V Figure 3: Energy flux measurement during sputter-deposition step performed with a Si shield located in front of the substrate. In this configuration no particles coming from the SDP are able to reach the surface. The recorded signal is thus only due to the contribution from heated devices (metal target and Si shield).

Figure 4 :

 4 Figure 4: Test of reproducibility for Pt deposition at -200V bias target, in 0.5 Pa and 400 W argon plasma. a) Energy flux measurements, b) zoom of Fig. 4a showing the 1 min sputterdeposition steps performed with a target voltages of -200 V. The SDP contribution is the same for each sputter-deposition step.

Figure 5 :

 5 Figure 5: Energy transferred during a continuous 6 min sputter-deposition of Pt at 0.5 Pa, 400W and -200 V. The sharp rise is due to transfer from sputtered metal atoms and reflected neutrals. The following slow evolution (in the circle) is characteristic of radiative transfer from the heated target. The slow global decrease is attributed to the progressive coating of the upper window by Pt atoms, which influences the RF power/plasma coupling.

Figure 6 :

 6 Figure 6: Comparison of the energy transfer during SDP of Pt when the plasma is turned off between each sputtering step or not, (0.5 Pa and 400W). The good agreement between both sets of values shows that the growing regime of the Pt layer on the substrate does not influence the measurements.

Figure 7 :

 7 Figure 7: Test of reproducibility for Fe sputter-deposition at -200 V bias target, in 0.5 Pa and 400 W argon plasma. a) Energy flux measurements, b) zoom of Fig.7ashowing the 1 min sputter-deposition steps performed with a target voltages of -200 V. As in the case of Pt deposition, the SDP contribution is the same for each sputter-deposition step. However, the shape of the sputter-deposition signals indicates that there is no modification of the RF power/plasma coupling (no decrease after several sputter-deposition steps).

Figure 8 :

 8 Figure 8: Energy flux density due to the SDP of Pt versus the target bias voltage in a 0.5 Pa and 400 W argon plasma. The increase of the SDP contribution when the target bias voltage becomes more negative was expected, and is explained by a rise the flux and energy of the Ar

Figure 9 :

 9 Figure 9: a) Energy flux measurements performed at four argon pressures, for 400 W RF power and -100 V, -200 V, -350 V target bias voltages. b) Evolution of the SDP contributions versus pressure for -200 and -350 V target bias voltages. The observed decrease is explained by the increase of the collision number between particles (sputtering ions, sputtered metal atoms, reflected neutrals) and argon atoms, which leads to scattering phenomena and reduction of the mean kinetic energy.

Figure 10 :

 10 Figure 10: Shape of the sputter-deposition signals for two argon pressures at 400W RF power: a) 0.5 Pa and b) 3 Pa. It is clearly seen that the argon pressure influences the SDP signal, and consequently the mechanisms of energy transfer. At 3 Pa a thermal contribution is visible together with the fast transfer from SDP particles.

Figure 11 :

 11 Figure 11: Energy transfer as a function of the RF plasma power (1Pa argon pressure): a) heat flux measurements, b) SDP contribution. The energy transferred during the SDP increases with the RF power because of the global rise of the ionisation degree in the plasma. The number of sputtering ions at the target becoming higher, the sputtering process is enhanced.

FiguresFig. 1

 1 Figures

  Fig.1-a

  Fig.4-a

  Fig.11-a

Confidential: not for distribution. Submitted to IOP Publishing for peer review 18 December 2009

Acknowledgements

This work is supported by the ANR (Agence Nationale pour la Recherche).