L Gutiérrez

R Mejías

D F Barber

S Veintemillas-Verdaguer

C J Serna

F J Lázaro

M P Morales

AC Magnetic susceptibility study of in vivo nanoparticle biodistribution

We analysed magnetic nanoparticle biodistribution, before and after cytokine conjugation, in a mouse model by AC susceptibility measurements of the corresponding resected tissues. Mice received repeated intravenous injections of nanoparticle suspension for two weeks and they were euthanized one hour after the last injection. In general, only 10% of the total injected nanoparticles after multiple exposures were found in tissues. The rest of the particles may probably be metabolised or excreted by the organism. Our findings indicate that the adsorption of interferon to DMSA-coated magnetic nanoparticles changes their biodistribution, reducing the presence of nanoparticles in lungs and therefore their possible toxicity. The specific targeting of the particles to tumour tissues by the use of an external magnetic field has also been studied. Magnetic nanoparticles were observed by transmission electron microscopy (TEM) in the targeted tissue and quantified by AC magnetic susceptibility.

Introduction

Nanosized materials are already providing novel tools that are contributing to improve healthcare in the 21 st century [1]. Opportunities include superior diagnostics and biosensors, improving imaging techniques and innovative therapeutics to enable tissues regeneration and repair. One of the main challenges is the design of nanosized drug delivery systems able to target specific diseases or to allow the transport of drugs across biological barriers. In this sense, magnetic nanoparticles offer the advantage of an efficient carrier for drug delivery in the presence of a magnetic field that can be combined with Magnetic Resonance Imaging (MRI) detection [2].

However, there is an urgent need to improve the understanding of toxicological implications of nanomedicine. One of the top priorities is the determination of the distribution of nanoparticulate carriers in the body following systemic administration through any route [3]. Although pictorial evidence of nanoparticle accumulation in vivo can be obtained by radiological imaging methods, the only technique that can give quantitative mass-balance information at this time is through radionuclide labelling [4,5].

Magnetic measurements are sensitive and offer substantial information in magnetic nanoparticles biodistribution studies, as they are specific for transition metals and allow characterization of a big portion of tissue samples. Recently, magnetization curves of lyophilized samples of liver, spleen and kidney, enabled quantitative estimation of the amount of magnetic material in those organs by comparison of the normalized saturation magnetization of the organs to that of the nanoparticles alone [6]. In the intravenous repeated exposure protocol, the percentage of magnetic nanoparticles uptake per organ was an average of 35% for liver, 1.5% for spleen and 0.5% for the kidney [6]. In that case, magnetisation curves failed in quantifying magnetic nanoparticles in other organs and tissues containing much lower amounts of magnetic nanoparticles since this technique it is not able to distinguish magnetic nanoparticles from other iron species present in the body.

Another approach to measure magnetic nanoparticles biodistribution is the measurement of the AC (alternating current) magnetic susceptibility. In this technique an AC magnetic field (the excitation) is applied to the sample and the resulting AC magnetisation (the response) is recorded. From the experiment, which quite often is carried out from cryogenic temperatures up to room temperature, the in-phase (χ') and the out-of-phase (χ'') susceptibility components are determined. Quantitative analysis has been done before for biological tissues that did contain both ferritin iron and iron oxide magnetic nanoparticles [7], and is based on the treatment of the temperature dependent out-of-phase susceptibility profile. Both species (magnetic nanoparticles and iron-containing ferritin cores) have a χ''(T) maximum located at different temperatures, due to their different average particle size and crystalline structure, that allows their differentiation by AC susceptibility measurements. Eventually, as highly magnetic nanoparticles (as, e.g., magnetite) may show some degree of magnetic interaction some distortion of the χ''(T) profiles may occur. However, this phenomenon is also systematically contemplated by magnetic analysis of agar diluted nanoparticle samples with different concentrations, and the resulting χ''(T) profiles, now with careful control of the particle concentration, are also incorporated into the quantitative analysis protocol as a collection of standards.

In this paper, magnetic nanoparticles designed in terms of magnetic core, coating material and functional ligands to improve their magnetic properties and tested as in vivo drug delivery system for tumour immunotherapy [8] have been used. Uniform magnetic nanoparticles 9 nm in size were coated with dimercaptosuccinic acid (DMSA) and functionalized with a cytokine. The whole compound was injected to mice and the biodistribution of the particles was studied by AC magnetic susceptibility measurements. Quantitative data of the particle concentration in different organs were obtained with the help of particulate agar dilution standards. Furthermore, the specific targeting of the injected magnetic nanoparticles to tumour sites by using a magnetic field was also studied. The study of the biodistribution of magnetic nanoparticles within the different organs of an animal model is of paramount importance for biomedical applications and the main scope of this paper.

Material and methods

Synthesis of magnetic nanoparticles

Monodisperse dimercaptosuccinic acid-coated magnetite nanoparticles (DMSA-MNP) (9.2 nmdiameter ± 13% SD) were prepared following the protocol described by Roca et al [9]. Nanoparticles were synthesized in organic medium using oleic acid as a surfactant and DMSA was used to displace oleic acid from the nanoparticle surface. The coated particles were then stable in water at pH 7 with hydrodynamic sizes <100 nm and a negative surface charge (-40 mV) over a wide pH range (4)(5)(6)(7)(8)(9)(10)(11)(12). DMSA-MNP were bound to murine recombinant interferon-γ (IFN-γ) (Peprotech) as described by Mejías et al [10] producing functionalized particles (IFN-γ-DMSA-MNP).

Agar dilutions preparation

Agar (Fluka (C 12 H 18 O 9 )x, Mw = 3000-9000) gel solutions (1% w/v) were prepared using four different dilutions (D1-D4) of the original particle suspension in MilliQ water. The mixtures of the agar powder and the particle suspensions were heated up to 55 ºC and allowed to cool down to room temperature in a warm water ultrasonic bath, what provides a homogeneous distribution of the particles in the agar gel. The iron concentration in the agar gels ranged from 2 to 0.0001 mg Fe/ml. These gels were then freeze-dried during 24 h and the resulting products were used for the magnetic measurements. Finally, the iron concentration achieved in the freeze-dried samples was D1 = 154.5, D2 = 47.9, D3 = 1.1 and D4 = 0.011 mg Fe/ g dry product.

Mouse model

To study the magnetic nanoparticles biodistribution among the different organs, twelve-weekold female C57BL/6 (Harlan Laboratories) mice received intravenous injections of DMSA-MNP (300 µg Fe/injection) twice a week for two weeks. Another batch of animals was treated in the same way but using IFN-γ-DMSA-MNP, and the same iron concentration. Some animals were also treated with 3-methylcholanthrene (MCA) in order to induce a tumour in their right leg and were afterwards exposed to a magnetic field of 0.4 T on the right flank for one hour after each particle injection. During the whole study, animals were maintained in the Centro Nacional de Biotecnología (CNB) animal facility and the study was approved by the Ethics Committee for Animal Experimentation at the CNB in compliance with European Union legislation.

One hour after the last injection mice were euthanized, perfused to remove rest of blood in the tissues, and spleen, liver, heart, brain, lungs, kidneys and the tumour tissue (in the corresponding animals) were harvested for analysis.

Magnetic characterization

The magnetic characterization was carried out in a Quantum Design MPMS-5S SQUID magnetometer with an AC susceptibility option. The measurements were performed with an AC amplitude of 0.45 mT, in the temperature range between 1.8 and 300 K and at a frequency of 1 Hz.

Transmission Electron Microscopy characterization

Transmission electron microscopy observations were performed in a 200-KeV JEOL-2000 FXII microscope. A part of the tumorous tissue was fixed, washed with buffer, dehydrated in graded series of acetone, and embedded in epoxy resin (TAAB 812 resin) following standard protocols for TEM observations. Staining with heavy metals was avoided in order to facilitate the particle observation in the tissues [11].

Results and discussion

Dipolar interactions study in magnetic nanoparticles agar dilutions

The temperature dependence of both components of the magnetic susceptibility, χ' and χ'', is shown in figures 1 and 2 for the four different dilutions of the magnetic nanoparticles in agar. All these dilutions exhibit a single peak in both the in-phase and the out-of-phase components, indicative of blocking of the particle magnetic moments. In figure 1, where the magnetic data are presented per mass of sample, the increase in the maxima height follows the increase of iron concentration of the samples. However when representing the susceptibility per mass of iron (figure 2) it becomes visible that for increasing particle concentration the maxima get lower and shift to higher temperatures as previously observed for these systems [7,[12][13][14][15][16]. This phenomenon results from the progressive increase of the interparticle dipole-dipole interaction strength. The out-of-phase susceptibility per mass of iron of the magnetic nanoparticles dilutions is of key interest, as it will be used as the calibration standard for the subsequent magnetic determination of the concentration of the same particles in tissues [7]. The pre-exponential factor ( 0 ) that appears in the Arrhenius expression for the relaxation time ( = 0 exp(E a /k B T) ) has been calculated to study the interparticle interactions of the nanoparticles dilutions, following a protocol previously described [7] (figure 3a). For increasing iron concentration, 0 values show (figure 3b) a progressive deviation from the negligible interaction regime (10 -9 -10 -12 s) [17] towards unphysically low values, as previously observed [7]. For the quantitative magnetic determination of the particles in the tissues, agar dilutions of the same particles with a similar degree of dipolar interactions would be the optimum calibration standard. for sample D1, and (b) dependence of the 0 prefactor on the particle concentration. For increasing particle concentration a progressive 0 decrease takes place, leaving only the most diluted sample within the negligible dipolar interaction range (10 -9 -10 -12 s).

Quantitative analysis of the particle biodistribution among different tissues

The use of AC magnetic susceptibility measurements as a quantitative tool for the determination of magnetic nanoparticles in biological tissues was previously described [7]. Basically, it was demonstrated that it is possible to determine the iron concentration in the form of magnetic nanoparticles of a given sample from the proportionality factor that relates its mass out-of-phase susceptibility to that of a reference sample with the same type of particles, same particle size distribution and same degree of dipolar interaction strength. The use of the out-of-phase susceptibility, as an alternative to the in-phase one, is especially practical as it is insensitive to diamagnetic and paramagnetic contributions from other species in the sample [18]. Roughly speaking, the height of the tissue samples χ'' maxima, when located at the same temperature as that of the injected particles, is a surrogate measure of the iron concentration in the form of particles within the tissue and, as in this case the particle size distribution is very narrow, the χ'' maxima height is also a surrogate measure of the number of particles in the tissue. Then, just by looking at the height of these maxima we will be able to investigate the magnetic nanoparticles biodistribution in the different tissues. It has to be pointed out, also, that this technique informs us just about the magnetite nanoparticles, independently if they are carrying the IFN-γ or not.

Previous studies on magnetic nanoparticles biodistribution have shown that particles are usually recognized and taken up by the macrophages of the mononuclear phagocyte system and subsequently accumulated in the liver, spleen and lungs [19][20][21]. The possible accumulation of particles in the lungs was of especial interest for us when studying the biodistribution of magnetic nanoparticles, as it has been previously reported that the DMSA coating targets the particles to the lungs [22]. The attachment of another molecule to the DMSA-MNP, in this case the IFN-γ to be used for tumour treatment, drastically affects both the surface charge and the hydrodynamic size of the particles which may lead to significant changes in the biodistribution [23]. For this reason, we explored the possibility of significant changes in the biodistribution when adding the IFN-γ to the DMSA-MNP. In figure 4 the out-of-phase magnetic susceptibilities of lung and liver tissues from three animals that were treated with DMSA-MNP and two animals that were treated with IFN-γ-DMSA-MNP are shown. The single maxima around 80 K indicates the presence of particles in the tissues, being the lungs the organs that have a higher concentration of particles in comparison with the liver. It can be observed that while the χ'' height of the liver tissues in both treatments remains very similar, indicating a similar iron concentration, the iron concentration in the lungs is significantly reduced when adding the IFN-γ. Then, it can be concluded that the IFN-γ attachment to the DMSA-MNP reduces almost three times the amount of particles that reach the lungs. The biodistribution of particles among other tissues (spleen, brain, heart and kidneys) was also magnetically studied. The results have been incorporated in figure 5 for both treatments (DMSA-MNP and IFN-γ-DMSA-MNP). Apart form the previously discussed cases of lungs and liver, the presence of particles is also clearly observed in the spleen. In particular, a significant difference is found when comparing the concentration of particles in spleen tissues from animals treated with IFN-γ-DMSA-MNP and with DMSA-MNP, being higher the amount of particles that arrive to the spleen if the particles carry IFN-γ. The presence of particles in the rest of the characterised tissues (brain, heart or kidneys) was, in general, negligible under the detection limits of the technique, (see data from perfused animals in figure 6). This result is the same as in previous biodistribution studies of magnetic nanoparticles with different coating and size [24]. The detection limit of the DMSA-MNP was 0.005 mg Fe / g dry tissue. This value was estimated from the iron concentration in the form of particles, whose signal would be twice as the average noise found in the measurements.

It is of especial interest to mention the effect of the presence of blood in the tissues in biodistribution studies. In our case, tissues were collected from the animals one hour after the last injection, so the presence of particles in the blood after such a short time is still a possibility. For this reason, our study was performed with animals that were perfused with phosphate buffered saline (PBS) solution in order to remove the blood from all the tissues before their characterisation. However, it is also interesting to quantify how much the magnetic susceptibility of a given tissue may be altered by the presence of blood. In figure 6, the out-ofphase susceptibility of different tissues coming from two animals, one perfused before tissue extraction and the other non-perfused, is shown. It is striking how the height of the out-of-phase susceptibility may increase, up to 8 times for the liver, if the tissues are not perfused. The presence of rests of blood in the non-perfused tissues is also responsible for the maxima observed in heart and kidney in which no signal of the particles is found in the perfused tissues. This fact, confirms that part of these particles are still circulating one hour after the injection [8]. The location in temperature of the tissue samples out-of-phase susceptibility maxima has been considered to choose the optimum agar dilution standard for magnetic quantification of the particles. It has previously been found that the degree of magnetic nanoparticles aggregation in the different tissues is manifested in the out-of-phase susceptibility as a change of shape and temperature location of the χ'' maxima as predicted by the increased dipolar interactions [7]. In this case, the χ'' profiles of the liver, spleen and lung tissues of the same animal show rather good superimposition, with small differences when the data is plotted scaled to their maxima (figure 7a) indicating a similar degree of aggregation in all tissues where particles were found.

When comparing the shape and temperature location of the out-of-phase susceptibility of a given tissue with that of the agar dilutions (figure 7b) slight differences can though be observed. The tissue χ''(T) maximum is located at slightly higher temperatures than those of the magnetic nanoparticles dilutions meaning that, in the tissues, a higher degree of aggregation was present. These differences agree with the obtained τ 0 values for several tissue samples that yielded values lower than 10 -23 s, in that a τ 0 decrease associated to the increase of particle aggregation is expected (figure 3). The iron concentration in the form of particles in the tissues was calculated (table 1) choosing as reference material for the quantification protocol the most concentrated gel (D1) as this is the one that fits better the tissue samples data. It should be taken into account that these iron concentration values correspond in this case only to iron in the form of particles, although other iron-containing species may also coexist in the tissue. Once the iron concentration was obtained, the total amount of iron in the form of the magnetic nanoparticles in each organ was calculated taking into account the weight of the whole freeze-dried organ. The average amount of iron in the form of magnetic nanoparticles in each organ was calculated with data from three different animals of each type. The total amount of iron in the form of MNP found in the animals, resulting from the addition of the quantities found in all the characterised organs are in the range between 90 and 140 µg, which is around 10% of the total injected iron (1200 µg). This value also corresponds to around 30% of the iron administered in the last injection to the animal (figure 8). Although there may be still a big percentage of particles from the last injection in the blood (figure 6), these data indicate that there is not a significant accumulation of the particles from previous injections in tissues. The injected particles are probably dissolved and assimilated by the body, especially in the form of ferritin, as observed for intramuscularly injected iron oxyhydroxide nanoparticles [25]. The "unaccounted" portion of iron in the form of magnetic nanoparticles is around 90% of the total injected during 2-week-treatment (4 injections of 300 µg Fe each). Therefore, the low amount of particles found in the tissues after the treatment supports their use in biomedical applications, as it means that these particles do not accumulate in the organism.

Targeting of magnetic nanoparticle to tumour tissues by magnetic fields

As one of the most important applications of magnetic nanoparticles in biomedicine is their use as magnetic carriers for drug delivery, the specific targeting of the IFN-γ-DMSA-MNP to tumour tissues under local magnetic field created by placing a magnet next to them was tested. The presence of magnetic in the tumour tissue was confirmed both by TEM observations and AC magnetic susceptibility measurements. Magnetic nanoparticle aggregates with sizes in the range between 120 and 300 nm were observed in the tumour tissues (figure 9). The unstained sections allowed identifying the presence of the particles although the histological localization was difficult to resolve due to the low contrast in the different cell structures. The presence of these aggregates was found by TEM in tissues treated with IFN-γ-DMSA-MNP either with or without magnetic field application. Although qualitatively it could be said that it was easier to find the particles in the tissues when the magnetic field was applied, indicating a higher particle concentration, it is really hard to quantify their amount from the TEM micrographs. AC magnetic susceptibility measurements in order to calculate the iron concentration in the tumour tissues were also performed (figure 10). In mice treated with IFN-γ-DMSA-MNP, the iron concentration in the form of magnetic nanoparticle in the tumours was in the range of 0.08 -0.1 mg Fe/g dry tissue and the mean volume size was 2408 mm 3 . The mean tumour volume of animals treated with IFN-γ-DMSA-MNP plus the external magnetic field was significantly smaller (mean volume size = 446 mm 3 ) than that of those not treated with the external magnet. As the size of the tumours decreased, a higher concentration of particles (figure 10 a) was found in the tumours, accumulating up to 10 mg Fe/g dry tissue in the form of the magnetic nanoparticles for the smallest tumour (figure 10 a). Same data as in (a) but with a different vertical scale in order to better appreciate the significant differences between control and injected animal under no magnetic field.

Conclusions

We have used AC magnetic susceptibility measurements to study the magnetic nanoparticle biodistribution in a murine model. Changes in the biodistribution of the particles have been found after their functionalization with Interferon-γ. Specific targeting to tumour sites has been achieved by the use of an external magnetic field. Our findings show that just around 10% of all the injected particles were found intact within the tissues one hour after the last injection, which means that these particles do not accumulate in the organism even after repeated injections and therefore may be easily metabolized or excreted.

Figure 1 .

 1 Figure 1. Temperature dependence of the (a) in-phase and (b) out-of-phase components of the susceptibility, per mass of sample, of the freeze-dried agar dilutions of the magnetic nanoparticles.

Figure 2 .

 2 Figure 2. Temperature dependence of the (a) in-phase and (b) out-of-phase components of the susceptibility, per mass of iron, of the freeze-dried agar dilutions of the magnetic nanoparticles.

Figure 3 .

 3 Figure 3. (a) Example of 0 determination, based on the method described by López et al [7],for sample D1, and (b) dependence of the 0 prefactor on the particle concentration. For increasing particle concentration a progressive 0 decrease takes place, leaving only the most diluted sample within the negligible dipolar interaction range (10 -9 -10 -12 s).

Figure 4 .

 4 Figure 4. Temperature dependence of the out-of-phase component of the susceptibility, per mass of sample, of lung and liver tissues from (a) three different animals treated with DMSA-MNP and (b) two different animals treated with IFN-γ-DMSA-MNP.As both plots use the same quantitative scale, it is concluded that DMSA coating targets the particles to the lungs but that this effect is reduced by the attachment of the cytokine, which alters both the size and surface charge of the injected compound.

Figure 5 .

 5 Figure 5. Temperature dependence of the out-of-phase component of the susceptibility, per mass of sample, corresponding to freeze-dried tissues from different organs: (a) mouse treated with DMSA-MNP and (b) mouse treated with IFN-γ-DMSA-MNP.

Figure 6 .

 6 Figure 6. Temperature dependence of the out-of-phase susceptibility, per mass of sample, of freeze-dried (a) liver, (b) brain, (c) heart and (d) kidney tissues from two different animals. One animal (red circles) was perfused before tissues removal. Circulatory vessels of the nonperfused one (black squares) still contained in-blood-dispersed nanoparticles.

Figure 7 .

 7 Figure 7. Temperature dependence of the out-of-phase susceptibility scaled to its maximum for (a) different tissues from the same animal where magnetic nanoparticles have been identified and (b) the agar dilutions of the magnetic nanoparticles and a liver tissue.

Figure 8 .

 8 Figure 8. Percentage of the magnetic nanoparticles from the last MNP administration found in each organ from animals treated with (a) DMSA-MNP and (b) IFN-γ-DMSA-MNP. Values have been calculated from the total amount of iron found in each whole tissue in the form of MNP and the total amount of injected iron in the last administration.

Figure 9 .

 9 Figure 9. Transmission electron micrographs of magnetic nanoparticles aggregates found in the tumour tissues from mice treated with IFN-γ-DMSA-MNP and an external magnetic field at two different magnifications (a) higher and (b) lower.

Figure 10 .

 10 Figure 10. (a) Temperature dependence of the out-of-phase susceptibility per mass of sample of three tumour tissues coming from the following animals: control, animal after IFN-γ-DMSA-MNP injection and animal after IFN-γ-DMSA-MNP injection under applied magnetic field. (b)Same data as in (a) but with a different vertical scale in order to better appreciate the significant differences between control and injected animal under no magnetic field.

Table 1 .

 1 Ranges of iron concentration (in the form of particles) in the different tissues obtained from the AC susceptibility measurements.

	Treatment	[Fe particles ] (mg Fe/g dry tissue) Liver Spleen Lung
	DMSA-MNP	0.062 -0.084	0.046 -0.061	1.22 -1.90
	IFN-γ-DMSA-MNP 0.090 -0.092	0.14 -0.36	0.40 -0.50

Acknowledgements

This work was partially supported by grants from the Spanish Ministry of Science and Innovation (MICINN) (MAT2008-01489 and CSD2007-00010 to MPM, SAF-2008-00471 to DFB), the Madrid regional government CM (S009/MAT-1726), and the ISCIII-Spanish Ministry for Health & Social Policy (ISCIII-MSPS) (PI060549 to FJL; Cooperative Research Thematic Network program (RETICS) and Research Network in Inflammation and Rheumatic Diseases (RIER) RD08/0075/0015 to DFB). LG holds a Sara Borrell post-doctoral contract (CD09/00030) from the ISCIII-MSPS and RM receives FPU pre-doctoral fellowships from the MICINN.


C Sabah
email: sabah@physik.uni-frankfurt.de

H G Roskos

Numerical and Experimental Investigation of Fishnet-based Metamaterial in a X-Band Waveguide

Keywords: Metamaterial, fishnet, negative refractive index, single and double negative, left-handed, microwave, waveguide experiment PACS: 41.20.Jb, 81.05.Xj, 78.67.Pt

HAL is

Introduction

Artificial metamaterials (MTMs) are composite structures that have been engineered to have unusual electromagnetic properties, such as simultaneous negative permittivity and permeability, which are not readily available in nature. They have attracted considerable interest due to their potential applications in several fields of science and engineering [START_REF] Tretyakov | Analytical Modeling in Applied Electromagnetics[END_REF][START_REF] Engheta | Metamaterials -Physics and Engineering Explorations[END_REF]. Such MTMs can be constructed using a dielectric host and metal inclusions. They have been intensively studied in the form of various periodical combinations [START_REF] Tretyakov | Analytical Modeling in Applied Electromagnetics[END_REF][START_REF] Engheta | Metamaterials -Physics and Engineering Explorations[END_REF]. Among them, one of the most promising structures is the so-called fishnet MTM which consists of stacked dielectric and metallic layers with two-dimensional periodic holes in the metal layers [START_REF] Zhang | Near-infrared double negative metamaterials[END_REF][START_REF] Zhang | Experimental demonstration of near-infrared negative-index metamaterials[END_REF][START_REF] Dolling | Low-loss negative-index metamaterial at telecommunication wavelengths[END_REF][START_REF] Chettiar | Dual-band negative index metamaterial: double negative at 813 nm and single negative at 772 nm[END_REF][START_REF] Kafesaki | Left-handed metamaterials: The fishnet structure and its variations[END_REF][START_REF] Alici | Characterization and tilted response of a fishnet metamaterial operating at 100 GHz[END_REF][START_REF] Alici | A planar metamaterial: Polarization independent fishnet structure[END_REF][START_REF] Valentine | Three-dimensional optical metamaterial with a negative refractive index[END_REF][START_REF] Marques | Analytical theory of wave propagation through stacked fishnet metamaterials[END_REF][START_REF] Garcia-Meca | Double-negative polarization-independent fishnet metamaterial in the visible spectrum[END_REF][START_REF] Wei | Broadband negative refraction in stacked fishnet metamaterial[END_REF][START_REF] Menzel | Validity of effective material parameters for optical fishnet metamaterials[END_REF][START_REF] Jelinek | Fishnet Metamaterials -Rules for refraction and limits of homogenization[END_REF]. Because of its superior performance, many researchers have focused on the investigation of the fishnet MTM to characterize and synthesize new combinations. The fishnet structure can be treated as an array of thin wires which are continuous along the electric field direction and short slab and/or cut wire pairs as magnetic resonators which are contiguous along the magnetic field direction. Under certain conditions, the structure can provide a negative refractive index at around the transmission peak.

In the present study, the electromagnetic response of a fishnet-based MTM is investigated, both numerically and experimentally, for X-band frequencies (8 GHz to 12 GHz). The structure is designed for the X-band rectangular waveguide (WR-90) and simulated using a full-wave electromagnetic solver based on the method of moments. The MTM layers are manufactured using low-cost printed circuit board production and the experiment is performed using a network analyzer and a WR-90 waveguide by placing the stacked layers into the waveguide. In the literature, the published fishnet MTMs are formed from continuously metallized mesh-like structures which are positioned to be perpendicular to the propagation direction of the wave. The main goal of this study is to explore the physical characteristics of the fishnet-based MTM formed by non-continuous metallization (see Figure 1: the metallic part is not touching the walls of the waveguide), and to tune the negative response of the permittivity and permeability onto each other.

Note that stacked fishnet MTMs composed of a periodic array of perforated conductor screens with continuous metallization have been studied numerically in Refs. 11 and multilayer fishnet MTMs have not been performed because of the difficulties arising for the interpretation of the data as a result of the continuous metallization. However, in our case, the proposed structure with non-continuous metallization was studied both numerically and experimentally. The key benefit of the new design with noncontinuous metallization is that it allows to take advantage of the method of images for the retrieval of the effective parameters. In this case, the effective medium theory can be applied easily and the proposed waveguide system loaded by a small metamaterial sample is adequate to carry out the extraction procedure. Both in the simulation and experiment, the reflection and transmission characteristics of the designed structure are obtained and then the effective material parameters are retrieved based on the Nicolson-Ross-Weir (NRW) procedure [START_REF] Nicolson | Measurement of the intrinsic properties of materials by time domain techniques[END_REF][START_REF] Weir | Automatic measurement of complex dielectric constant and permeability at microwave frequencies[END_REF]. The stacked structure is assumed to be effectively a homogeneous medium because the wavelength of the propagating wave through the fishnet-based MTM is much larger than the periodicity of the structure in the propagation direction.

Note that, to our knowledge, the present experiment is the first experimental verification of simulations for fishnet-based MTMs in a waveguide. The data show that we succeed to achieve simultaneously negative permittivity and permeability in a certain frequency band. It is observed that the simulation and experimental data agree with each other quite well.

Numerical Simulation and Experiment

The schematic representations of the experiment and the front view of a single layer of the MTM structure are shown in Figure 1. The FR4 substrate has a thickness of λ/60 (λ is the vacuum wavelength at the operation frequency) and precisely fits WR-90. The metallic part, which is centered on FR4 and not connected to the waveguide walls, is made of copper with a conductivity of 5.8×10 7 S/m and a thickness of 18 µm which is larger than the skin depth at 10 GHz. The metallic part has the following dimensions: w = 2λ/3, l = λ/3, d 1 = λ/40, and d 1 = 2d 1 . The periodicity along the propagation direction is equal to the total thickness of the single MTM layer (substrate and copper) which is much smaller than the operation wavelength. The substrate is chosen to be as thin as possible to minimize the dielectric loss. The aim of the optimization which led to the selected dimensions was to have a double negative window at around 10 GHz. In the sketch of the MTM, the white part represents FR4 and the black part copper.

The structure was simulated using EEsof EDA design and simulation software.

Waveguide boundary conditions were used for the side walls, and open boundaries for the waveguide ports for the excitation and detection of electromagnetic waves. Both in the simulation and the experiment, a 15-layer MTM structure was used and arranged as copper-FR4-copper-FR4-copper-.… The electromagnetic wave propagates in the z-direction (normal to the plane of the fishnet-based MTM), and the electric and magnetic fields are oriented along the x-and y-directions, respectively. In this case, one obtains a magnetic response by the substrate-separated double-strips oriented in y-direction. The electric response is dominated by the strips in x-direction (acting as a dilute Drude metal). Double negative and fishnet behavior can be achieved if a sufficient number of layers are stacked onto each other [START_REF] Zhang | Near-infrared double negative metamaterials[END_REF][START_REF] Zhang | Experimental demonstration of near-infrared negative-index metamaterials[END_REF][START_REF] Dolling | Low-loss negative-index metamaterial at telecommunication wavelengths[END_REF][START_REF] Chettiar | Dual-band negative index metamaterial: double negative at 813 nm and single negative at 772 nm[END_REF][START_REF] Kafesaki | Left-handed metamaterials: The fishnet structure and its variations[END_REF][START_REF] Alici | Characterization and tilted response of a fishnet metamaterial operating at 100 GHz[END_REF][START_REF] Alici | A planar metamaterial: Polarization independent fishnet structure[END_REF][START_REF] Valentine | Three-dimensional optical metamaterial with a negative refractive index[END_REF][START_REF] Marques | Analytical theory of wave propagation through stacked fishnet metamaterials[END_REF][START_REF] Garcia-Meca | Double-negative polarization-independent fishnet metamaterial in the visible spectrum[END_REF][START_REF] Wei | Broadband negative refraction in stacked fishnet metamaterial[END_REF][START_REF] Menzel | Validity of effective material parameters for optical fishnet metamaterials[END_REF][START_REF] Jelinek | Fishnet Metamaterials -Rules for refraction and limits of homogenization[END_REF]. Usually, the magnetic response can be attributed to the excitation of a virtual current loop between the strips perpendicular to the magnetic field. These currents should be strong enough to be able to neutralize the magnetic field and produce a resonance displaying negative effective permeability. Simulations show that in our structure, the currents on opposite metallic surfaces are anti-parallel to each other at the resonance frequency, and hence the currents in each virtual metallic loop are circulating which is shown in Figure 2. This confirms the explanation given above and gives a clear identification of the character of the resonance. As a consequence, a negative permeability arises at the resonance. Note that each metal layer contributes to current loops with regard two adjacent dielectric layers. The two current contributions on each layer are opposite to each other, hence the total current is reduced which is not shown here. Therefore, the magnetic response of the whole stack is a collective response of all layers. At a stop-band frequency, it is observed that the currents on the metallic parts are in-phase and symmetric (data not shown). Consequently, the structure behaves like an ordinary structure comprised of a combination of dielectrics and conductor elements, and no artificial magnetism is observed. Note that the effective permittivity is achieved by the interaction of the field with the metallic parts which means it is controlled by the dimensions of the strips and periodicity. In the experiment, the stacked structure is placed at the center of a WR-90 waveguide of which the input and output ports are connected to a network analyzer via two coaxial probes. After the full two-port calibration, the reflection and transmission data, both in amplitude and phase, are measured. Figure 3 shows the simulated and measured S-parameter data for the investigated structure. The step-function-like transmission spectrum with a high left-handed (LH) peak in the step, in conjunction with a dip in the phase close to the same frequency, 10 GHz, are clear indications for double negative and fishnet behavior. The experimental and the simulation results are in good agreement with each other. The residual differences are likely to result from some deviations in the experiment from the idealized conditions of the simulations, a possible candidate being the dispersion of the dielectric constant of the substrate FR4 [18]. A second candidate is the fabrication tolerances related with the printed circuit board production, notably the etching process of the metal. Small changes of the lateral dimensions by a few microns during the manufacturing process can lead to a shift of the resonance on a megahertz scale. In addition, imperfect mounting of the multi-layer sample in the center of the waveguide are to be considered.

The effective material parameters of the investigated structure are obtained based on the assumption of an effectively homogeneous medium since the propagation wavelength is much larger than the periodicity of the structure in the propagation direction. The retrieval method is applied based on the method of images by properly selecting the boundary conditions which allow to treat the structure as an infinite homogeneous material. The equivalent structure is the combination of an infinite number of the repeated samples in all spatial directions. We expect that the structure will provide an anti-resonant behavior in the permittivity which is visible in our results. This behavior can also be seen in Refs. 5, 7, 8, and 19-26. Figure 4 presents the extracted material parameters using the NRW method in the calculation [START_REF] Nicolson | Measurement of the intrinsic properties of materials by time domain techniques[END_REF][START_REF] Weir | Automatic measurement of complex dielectric constant and permeability at microwave frequencies[END_REF]. As it is seen from the figure, the structure provides simultaneously negative real parts of the permittivity and permeability in a band between 10.0 GHz and 10.7 GHz which covers the high transmission peak. However, the negative index band is larger and lies between 8.94 GHz and 10.7 GHz (see Figure 4, Zoom of Re(n)). Note that only the real part of the permittivity is negative between 8.94 GHz and 10 GHz. Although Re{ε}<0 and Re{µ}>0, the refractive index can be negative when the imaginary term is large enough [START_REF] Zhang | Experimental demonstration of near-infrared negative-index metamaterials[END_REF][START_REF] Zhou | Negative index materials using simple short wire pairs[END_REF][START_REF] Mccall | The negative index of refraction demystified[END_REF][START_REF] Depine | A new condition to identify isotropic dielectricmagnetic materials displaying negative phase velocity[END_REF]. This situation generally happens near the MTM resonance as can also be observed in the figure. Nevertheless, this type of negative refractive index does not support left-handed (LH) behavior. Thus, the negative refractive index has two regions which support either single negative (between 8.94 GHz and 10 GHz) or double negative (between 10 GHz and 10.7 GHz, LH region) characteristics. Also, the permittivity shows Drude-like behavior because of the coupling between the electric field and the copper strips as in the continuous-wires case. In addition, the permeability shows Lorentz-like behavior due to the strong resonant response to the magnetic field as in the magnetic resonators situation. Note that the anti-resonant behavior of the permittivity, the strong resonant response of the permeability, and the periodicity effects show that homogenous effective medium approximation can be applied with justification.

In order to verify the existence and validity of the negative index of refraction, a unique retrieval of effective parameters from the reflection and transmission data is obtained by enforcing the causality. The applied extraction method is based on the KK relations which have been used to calculate the index of refraction using calculated or measured data sets [START_REF] Varadan | Unique retrieval of complex permittivity and permeability of dispersive materials from reflection and transmitted fields by enforcing causality[END_REF]. Note that, for practical reasons, KK integral has to be truncated, which yields some error. Nevertheless, the evaluation of the KK equation even for the finite bandwidth can provide approximate data for the verification of the actual data. As it is seen from Figure 4, there is a reasonable agreement between the results (simulation, experiment, and KK relation) for the real part of the effective refractive indexes which validates the existence of the negativeband and the anti-resonant behavior of the structure.

Conclusion and Discussion

In this study, a fishnet-based MTM has been introduced and the electromagnetic characteristics of the structure have been investigated, both numerically and experimentally, for the microwave X-band regime. The structure is designed to have no DC conductive between its metallic parts and the waveguide walls, and to exhibit double negative behavior at around 10 GHz. The currents, from one metal surface to the consecutive one, are anti-symmetric. Thus, they form a virtual current loop and generate a magnetic response yielding a negative permeability. The electric response which provides the negative permittivity is controlled by the structural parameters. The homogenous-effective-medium theory is applied to acquire the effective material parameters of the presented MTM. The single and double negative regions with evidence for a LH transmission peak are identified using the simulated and experimental results. The structure exhibits a relatively high FOM and opens opportunities notably with regard to waveguide miniaturization and for waveguidebased applications such as waveguide antennas and imaging systems in a waveguide.

With regard to the latter, a waveguide with the proposed fishnet MTM can be designed for near-field imaging with the evanescent field from the interface, orexploiting the negative refractive index close to minus unity at around 10.5 GHz -one can envision a lensing system in a multimode waveguide at microwave frequencies [START_REF] Grbic | Near-Field Plates: Subdiffraction Focusing with Patterned Surfaces[END_REF].

Figure 1 :

 1 Figure 1: Schematic representations of the experimental set-up (left side) and a single layer of the fishnet-based MTM (right side). VNA stands for vector network analyzer.

Figure 2 :

 2 Figure 2: Current distribution of opposing metallic surfaces of the fishnet-based MTM. The left panel corresponds to the first metallic layer while the right one represents the second layer. The size of the arrows indicates the strength of the current.

Figure 3 :

 3 Figure 3: Simulated and measured S-parameters for the fishnet-based MTM.

Figure 4 :

 4 Figure 4: Effective material parameters as a function of frequency for the fishnetbased MTM.

Figure 5 :

 5 Figure 5: FOM as a function of frequency for the proposed MTM.

Acknowledgement:

C. S. acknowledges the COST Action MP0702 for the STSM grant; would like to thank to S. A. Tretyakov for being the host for the STSM, providing his facility for the experimental study, and his valuable comments; to C. R. Simovski for his helpful comments; and to O. Luukkonen, A. Karilainen, and P. Alitalo for their help during the experimental study.


Feng Chen

Robert Schafranek

Wenbin Wu

Andreas Klein
email: aklein@surface.tu-darmstadt.de

Reduction induced Fermi level pinning at the interfaces between Pb(Zr,Ti)O 3 and Pt, Cu and Ag metal electrodes

Keywords: numbers: 73.20.At, 63.35.Fx, 79.60.Jv, 77.55.+f

The interface formation between Pb(Zr,Ti)O 3 and Pt, Cu and Ag was studied using in situ photoelectron spectroscopy. A strong interface reaction and a reduction of the substrate surface is observed for all three interfaces as evidenced by the appearance of metallic Pb species. Despite the different work function of the metals, nearly identical barrier heights are found with E F -E VB = 1.6 ± 0.1 eV, 1.8 ± 0.1 eV and 1.7 ± 0.1 eV of the as-prepared interfaces with Pt, Cu and Ag, respectively. The barrier heights are characterized by a strong Fermi level pinning, which is attributed to an oxygen deficient interface induced by the chemical reduction of Pb(Zr,Ti)O 3 during metal deposition.

Introduction

Lead zirconate titanate Pb(Zr,Ti)O 3 (PZT), as one of the most commonly used ferroelectric materials, has been intensively studied duo to its potential application e.g. in dynamic random access memory (DRAM), piezoelectric sensors and actuators [START_REF] Scott | Ferroelectric memories[END_REF][START_REF] Dawber | [END_REF]3,4]. For PZT thin film, the cycling stability, imprint performance and leakage current strongly depend on the used electrode material [5,6,7,8]. Electrical fatigue causes a reduction of polarization with increasing switching numbers and is a severe limitation of device operation. The fatigue phenomenon for PZT thin film is especially pronounced with metal electrodes such as Pt. Different fatigue models and mechanisms have been reviewed by Tangantsev et al. [9] and Lou et al. [10]. Accumulation of oxygen vacancies at the ferroelectric/electrode interface and/or injection of charge carriers through the interface have been suggested to be related to the fatigue phenomenon. Both effects are directly linked to the PZT/electrode interface properties.

As probably the most crucial feature in electronic devices, the choice of electrode material determines the Fermi level position at the interface, which defines the barrier for electron (Φ B,n = E CB -E F ) and hole injection (Φ B,p = E F -E VB ). For ideal unpinned interfaces, the Schottky barrier heights should depend on the work function of the electrode material. The position of the Fermi level at PZT interfaces indeed shows a strong dependence on the work function with oxide electrodes [11]. The barrier heights at the PZT/RuO 2 and PZT/ITO interfaces (ITO = Sn-doped In 2 O 3 ) are determined by photoelectron spectroscopy as Φ B,p = 1.0 eV and ∼ 2.1eV, respectively, which is ∼ 70 % of the work function difference between RuO 2 (φ = 6.1 eV) and ITO (φ = 4.5 eV). This suggests a rather weak Fermi level pinning at the interface. Based on tight binding calculations for the quantification of the induced gap states model as outlined by Mönch [START_REF] Mönch | Electronic Properties of Semiconductor Interfaces[END_REF], a significantly stronger Fermi level pinning with only ∼ 30 % variation of barrier height with electrode work function has been derived by Robertson and Chen [START_REF] Robertson | [END_REF].

Only a few absolute numbers for barrier heights of different PZT/metal interfaces are reported in literature. Pintilie et al. derived barrier heights of Φ B,p = 1.86 eV, 2.11 eV and 2.21 eV for contacts with Pt, Cu and Ag, respectively [14]. The small variation of barrier height with metal work function [START_REF] Lide | CRC Handbook of Chemistry and Physics[END_REF] suggests a rather strong Fermi level pinning at PZT/metal interfaces, in contrast to the PZT/oxide interfaces. Chen et al. have investigated the PZT/Pt interface using in situ photoelectron spectroscopy [START_REF] Chen | [END_REF]. For the as-deposited interface prepared by magnetron sputtering of Pt onto a contamination-free PZT thin film surface, a Fermi level position of E F -E VB = 1.6 eV has been found. This value is in excellent agreement with the barrier height derived from Scott et al. (1.6 eV [17, 18]) and close to the value of Pintilie et al. (1.86 eV [14]).

The interface formation between PZT and Pt is characterized, however, by a chemical decomposition of the PZT substrate, which is evident from the observation of metallic Pb species in the photoelectron spectra [START_REF] Chen | [END_REF]19]. It has been suggested that the decomposition of the substrate is caused by the heat of condensation of the metal atoms during deposition, which can be as high as ∼ 4 eV [20]. Chemically reactive interfaces have also been observed during deposition of Cu and Au onto (Ba,Sr)TiO 3 [21]. The chemically reduced PZT substrate surface can be reversibly oxidized and reduced by post-deposition treatments under oxidizing or reducing conditions, which is accompanied by a reversible change of the barrier height from Φ B,p = 1.1 eV (oxidizing conditions) to 2.2 eV (reducing conditions) [START_REF] Chen | [END_REF]. It has particularly been observed that the changes may already occur at room temperature. The strong dependence of the barrier height on the chemical state of the interface has also been reported by other groups [22,23]. The effect is not restricted to PZT/Pt but also observed at other oxide/metal interfaces [24,25].

During the deposition of oxides on top of PZT no metallic Pb emission was detected in the Pb 4f photoelectron spectra. As these interfaces do not show a strong Fermi level pinning, it is suggested that the Fermi level pinning reported for PZT/metal interfaces [14] is related to the chemical reduction of the interface. In this study the interface formation between Pt, Cu, and Ag with PZT thin films has been investigated using in situ X-ray and ultraviolet photoelectron spectroscopy (XPS, UPS). A chemical reduction of PZT is reported for all three interfaces. In addition, the barrier height depends only weakly on the metal work function. The results therefore provide strong support that the chemical reaction at the interface is the origin of Fermi level pinning of as-deposited PZT/metal interfaces.

Experimental

The experiments were performed using the integrated surface analysis and preparation system DAISY-MAT (DAmstadt Integrated SYstem for MATerial Research), which combines a Physical Electronics PHI 5700 multitechnique surface analysis system with several deposition chambers via an ultrahigh vacuum sample transfer [START_REF] Chen | [END_REF]. At room temperature Pt, Ag and Cu, respectively, were incrementally deposited onto clean PZT substrates. After each deposition the sample was examined by XPS using a monochromatic Al K α photon source, which provides a typical resolution of ∼ 0.4 eV, as determined by the gaussian broadening of the Fermi edge of a metallic Ag reference sample. Binding energies are given with respect to the Fermi edge emission of the same reference with a typical accuracy of < 100 meV. Due to the low film thickness of the PZT films of 50 nm, no strong charging of the sample during photoemission measurement was observed. All XP spectra were recorded using a takeoff angle of 45 • . Ultraviolet photoelectron spectra were excited with He discharge lamp (hν = 21.2 eV) and recorded in normal emission with a -1.5 eV sample bias.

The PZT thin films were prepared by pulsed laser deposition using a KrF 248 nm excimer laser with a repetition rate of 10 Hz and an energy density of 1.8 J/cm 2 . Platinized Si wafers (Inostek) were used as substrates. The temperature during PZT deposition was set to 650 • C and the oxygen pressure was kept at 30 Pa. A PZT target with a Zr/Ti ratio close to the morphotropic composition (52/48) was used for deposition. The Zr/Ti ratio is maintained during deposition as verified by chemical composition analysis using XPS. In order to obtain contamination-free surfaces prior to metal deposition, the PZT thin films were heated to 400 • C in 0.5 Pa oxygen for 1 h, which has effectively been used for cleaning other oxide surfaces [24,26]. Platinum and copper were deposited onto clean PZT thin films using radio-frequency magnetron sputtering at room temperature from 2" targets with a power of 5 W, an Ar gas pressure of 0.5 Pa and a substrate to target distance of 10 cm. The deposition rates estimated from the attenuation of the substrate emission lines are ∼ 5 nm/min for Pt and ∼ 1.6 nm/min for Cu, respectively. Silver was evaporated from a temperature controlled effusion cell using an Al 2 O 3 crucible. The vacuum during metal deposition was below 10 -6 Pa. The evaporation rate is ∼ 1.5 nm/min.

Results and Discussion

Typical XPS survey spectra recorded during the course of copper deposition onto PZT are presented in Figure 1. The as-prepared film shows emissions from Pb, Zr, Ti, O and C. The C emission is attributed to adsorbed hydrocarbon species with a representative binding energy of 285 eV. No significant carbonate species are observed at higher binding energy in the C 1s spectrum. After heating the sample at 400 • C in 0.5 Pa oxygen for 1 h, no emissions related to carbon are detected. The sample remained free of (carbon) contaminations during the whole experiment.

During stepwise deposition of Cu, the substrate emission lines are attenuated and the Cu emission intensity increases. After deposition of ∼ 18 nm of Cu the Zr 3d, Ti 2p and O 1s lines are completely attenuated. In contrast, the Pb emissions can still be recorded after 36 nm of copper deposition and the Pb emission intensity does not change from 18 to 36 nm Cu film thickness. This indicates that metallic Pb is floating on the surface of the growing Cu film.

The inset shows the valence band spectra including secondary electron cutoff recorded with ultraviolet photoelectron spectroscopy using He I, corresponding to a work function of φ = E vac -E F = 4.7 ± 0.1 eV for PZT. The valence band maximum (VBM) position is derived by linear extrapolation of the leading edge of the valence band emission at E F -E VB = 2.1 ± 0.1 eV. This value is ∼ 400 meV larger than the VBM position derived from the XPS spectra (see inset in Figure 3(b)), which can be attributed to a slight charging of the film, as charging in UPS is typically stronger than in XPS. While charging affects the absolute binding energies of the VBM and the secondary electron cutoff, the shift of both values is identical if the charging is not too large. The ionization potential (I P = E vac -E VB ) and the electron affinity χ = I P -E gap ) are not affected in this case and are determined from the UP spectrum as I P = 6.8 eV and with a band gap of 3.4 eV [START_REF] Scott | Ferroelectric memories[END_REF] as χ = 3.4 eV. These values compare well with those given by Scott (χ = 3.5 ± 0.2 eV [START_REF] Scott | Ferroelectric memories[END_REF]17]). It is noted, however, that the ionization potential may depend strongly on surface orientation and surface termination [27,28] and is therefore a poor quantity for estimating Schottky barrier heights.

X-ray induced Pb 4f and O 1s photoelectron core level spectra of the PZT substrate The constant line shapes and widths of core levels attributed to the PZT substrate, which are the Zr 3d, Ti 2p and the Pb +II 4f emissions, indicate that the formed barriers have a unique value and do not vary along the surface. As the deposited films are polycrystalline in nature due to the polycrystalline substrate used, this indicates that the barrier heights do not depend on interface orientation as also demonstrated recently for the PZT/RuO 2 interface [29].

The deposition of all three metals leads to a partial decomposition of the PZT substrate, as evident from the observation of a metallic Pb component, which is indicated in Fig. 2(a-c) by dashed vertical lines. A metallic Pb component appears at a binding energy of ∼ 137 eV and is most pronounced for Cu deposition. The weakest intensity of metallic Pb is observed for Ag deposition. An interface reaction is not expected in the view of bulk thermodynamics as the metal oxides of Pt, Cu and Ag have only low heats of formation. Copper has the largest heat of formation of metal oxide for the studied contact metals. This corresponds with the largest amount of metallic Pb observed during deposition of Cu, suggesting that metal oxide formation contributes to the decomposition of the substrate. Formation of Pt-, Cu-or Ag-oxides is, however, not observed in the XP spectra.

In interface experiments using photoemission, a decomposition of the substrate has been observed even if the contact partners do not react in the bulk [30]. The frequently observed reduction of compound semiconductor substrates in the course of metal deposition has also been related to the condensation energy of the deposited species [31]. This has to be expected particularly for deposition of atomic species, as is the case for magnetron sputtering or thermal evaporation of metals. Rao et al. have explicitly calculated the binding energy of Pt on BaTiO 3 to be 4 eV [20], which exceeds the vacancy formation energy in the bulk [32]. As vacancy formation at surfaces is typically less expensive than in the bulk due to the lower coordination number, the reduction of the substrate at the surface becomes even more favourable.

Additional energy gain favoring substrate decomposition may come from the dissolution of substrate metal atoms in the growing metal film. Enthalpies of solution of Pb in Pt, Cu and Ag have been calculated as -16, +23 and +9 kJ/mol, respectively [33]. Intermetallic Pt-Pb phases like Pt 5-7 Pb [34,35] and Pt 3-4 Pb [36] are also believed to serve as nucleation seeds for PZT(111) orientation during growth of PZT on Pt. As an additional term the surface energy of the deposited materials might be lowered by segregation of the substrate species to its surface (surfactant effect).

The evolution of the intensity of the metallic Pb species is not the same for the three metals as also evident from Fig. 2. While the metallic Pb is attenuated with increasing Pt deposition, its intensity saturates in the case of Cu and Ag deposition. The behavior for Cu and Ag is explained by Pb floating on top of the growing metal film, while the metallic Pb remains at the interface or is dissolved in the growing Pt film. The different behavior of the metallic Pb species is in accordance with the different enthalpies of solution of Pb in Pt, Cu and Ag. Lead is expected to dissolve only in Pt while the positive heat of solution with Cu and Ag should result in a segregation of Pb.

The binding energy of Pt 4f and Ag films are 71.1 eV, 932.7 eV, and 368.3 eV, respectively, which are the same as the binding energies of the clean metals [START_REF] Moulder | Handbook of X-ray Photoelectron Spectroscopy[END_REF]. The binding energy of the Ag emission is slightly higher for lower film thickness, which could be related to island formation of the Ag film [START_REF] Wertheim | [END_REF]. Large binding energy shifts of metals can also be caused by alloy formation as reported e.g. for alloys of Au with In and Ga [39,40]. Alloy formation may also be the reason for the decreasing binding energy of the metallic Pb component in the case of Ag deposition. It has been argued above, however, that alloying of Pb with Ag is not likely. A third possible explanation for the binding energy shifts of the Ag and the metallic Pb emission is sample charging, which could cause larger binding energies for low metal film thickness. The charging will disappear when a metal film is deposited on the sample, as the film electrically connects the surface of the sample with the sample holder once the film is sufficiently thick, which occurs already after a few nm of deposition [41,42].

The O 1s core levels are attenuated after the final Pt and Ag deposition but not for the Cu covered sample, where a small signal around 529.7 eV binding energy remains. Such a behavior has also been observed during Cu and Au deposition onto (Ba,Sr)TiO 3 [21]. The oxygen signal after Cu deposition is still observed after complete attenuation of the Pb +II , Ti, and Zr core levels, clearly indicating that it is not related to PZT, as might have been the case e.g. for islands growth of the Cu film. The O 1s signal does not decrease after the final Cu deposition, suggesting that the remaining O 1s comes from oxygen on the surface of the Cu film. Such surface oxygen is noticed only for deposition of Cu, which also leads to the largest amount of metallic Pb. The source of oxygen is therefore attributed to the chemical reduction of the PZT substrate. The absorption of oxygen or water from the vacuum chamber as source for the appearance of an O 1s emission after Cu deposition is not likely, as Cu and Pt were deposited under comparable conditions and oxygen would also adsorb on Pt.

To determine the Schottky barrier heights, the Fermi level positions at the interfaces are required. These are derived from the core level binding energies by subtracting the binding energy difference of the PZT core levels with respect to the PZT valence band maximum of the uncovered substrates. The core level to valence band maximum binding energy difference is constant for a material and should not change during metal deposition if no strong chemical disruption of the substrate occurs [43,44,45]. The PZTrelated core level emissions, including the oxidic Pb +II 4f component, exhibit parallel shifts during metal deposition for all three interfaces as evident from Figure 3(a-c). Due to the parallel shift of these binding energies, it is safe to attribute them to emissions from structurally intact PZT substrate and hence to shifts of Fermi level position with respect to the PZT valence band maximum. The starting positions of the VBM of the cleaned PZT films are derived from the XPS valence band spectra before metal deposition, which are shown in the insets of Fig. 3. Any charging effect during photoemission of the uncovered PZT films will not affect the barrier height determination, as the deposited metal layer will create a short circuit between the surface and the sample holder. The latter defines the binding energy reference. The Fermi level equilibration (electrical contact) of the surface and the sample holder is justified by the fact that the binding energies of the core levels of the deposited metals correspond to their reference values. Therefore, the Fermi level is at zero binding energy after metal deposition. The binding energy of the valence band maximum after metal deposition, which is extracted from the binding energy before deposition plus the change of binding energy of the core levels during deposition, corresponds to E F -E VB at the interface, i.e. the hole Schottky barrier.

As also observed for the Pb 4f emission, the VBM binding energies of the three PZT thin films before metal deposition are slightly different, which may be attributed to different sample charging or to slightly different conditions of the substrate/PZT interface. The Fermi level positions at the interface with the deposited metal are derived from the plots in Fig. 3 for a metal thickness where the shifts of the core level binding energies saturate. The Fermi levels are E F -E VB = 1.6 ± 0.1 eV, 1.8 ± 0.1 eV and 1.7 ± 0.1 eV at the PZT/Pt, PZT/Cu and PZT/Ag interfaces, respectively. These values directly correspond to the Schottky barrier heights for holes, while the Schottky barrier heights for electrons are calculated using a band gap of 3.4 eV [START_REF] Scott | Ferroelectric memories[END_REF] as E CB -E F = 1.8 ± 0.1 eV, 1.6 ± 0.1 eV and 1.7 ± 0.1 eV, respectively. Considering the experimental uncertainty, the Fermi level at the interface is more or less located at the same position for all three metals. This result is in very good agreement with the similar leakage currents for these materials [14].

The energy band diagrams of the three different PZT/metal interfaces are summarized in Fig. 4. The vacuum level, which is included in Fig. 4, is derived from the work functions of 5.65 eV, 4.65 eV and 4.25 eV for Pt, Cu and Ag, and from an ionization potential of PZT of 6.8 eV, respectively. The possible band bending in the PZT substrate is not included in the graphs, as the absolute Fermi level position in the interior of the films is uncertain due to possible charging effects. Due to the low doping of the PZT films, it is also reasonable to assume that the films are fully depleted. The energetic situation at the investigated PZT/metal interfaces is, however, not affected by this uncertainty as the Fermi level of the deposited metal serves as the binding energy reference. The barrier heights at the interfaces are derived from the XPS measurements described above. The difference in contact potential for the three different metals is mainly compensated by large interface dipole potential drops. These are 0.45 ± 0.1 eV for PZT/Pt, -0.35 ± 0.1 eV for PZT/Cu and -0.84 ± 0.1 eV for PZT/Ag, respectively.

The Schottky barrier heights may be modified by post-deposition treatments, as previously demonstrated for the PZT/Pt interface [START_REF] Chen | [END_REF]22,23]. It is currently not clear if such modification is also possible for Cu and Ag contact materials, as these exhibit a different chemical structure of the interface. This is related to the different solution enthalpies of Pb in the deposited metals. While Pb can dissolve in Pt and therefore remain close to the interface, it is not dissolved in Cu and Ag and hence segregates to the surfaces of these films. The variation of barrier height observed with Pt contacts is accompanied by an increase/decrease of the metallic Pb species [START_REF] Chen | [END_REF]22,23]. This suggests that the insensitivity of the barrier height on the metal work function is related to the decomposition of the substrate. There are several processing options where the substrate decomposition may be avoided: (i) condensation of atomic species of metals might be avoided by deposition from solutions, like (electro-)chemical or metal pastes, or from gaseous compounds (metal-organic); (ii) direct contact of the deposited species with the bare PZT surface might be avoided by covering the surface with sub-nanometer thick buffer layer before metal deposition; (iii) post-deposition treatments like firing in ambient conditions as typically performed for ceramic actuators. All such treatments should lead to a different reactivity at the interface and therefore to different barrier heights and leakage currents. Fermi level pinning is a well known phenomenon for semiconductor interfaces, which is particularly pronounced for covalently bonded semiconductors like Si or III-V compounds [46]. The Fermi level pinning is related to induced gap states, which occur at semiconductor interfaces due to the wave function matching leading to an exponentially decaying wave function in the semiconductor energy gap [47,48]. For a high density of induced gap states, the Fermi level at the interface is pinned close to the charge neutrality level of the induced gap states [49], which has been derived by evaluating branch point energies or dielectric midgap energies [START_REF] Mönch | Electronic Properties of Semiconductor Interfaces[END_REF]50,51]. Charge neutrality levels for high permittivity oxides have been calculated by Robertson and Chen [START_REF] Robertson | [END_REF]. The levels for PbTiO 3 and PbZrO 3 are given as E CNL -E VB = 1.9 and 2.6 eV, respectively. The former corresponds well with the Schottky barrier heights determined for PZT in this work. The samples used in the experiments, however, have a Zr/Ti ratio of nearly 0.5. If the charge neutrality level scales linearly with the composition, an E CNL -E VB ≈ 2.35 eV is estimated based on the values of Robertson and Chen. This is significantly higher than the observed Fermi level position at the three interfaces.

Extrinsic defects can considerably affect the barrier heights [START_REF] Chen | [END_REF]24,25,52,53]. It is therefore only reasonable to compare charge neutrality levels with experimental Schottky barrier heights for interfaces with low concentrations of extrinsic defects. As the defects are related to a chemical reduction of the interface, it is likely that these are related to oxygen deficiency. Hence, the lowest defect concentrations are expected for most oxidizing conditions, which consistently leads to a downward shift of the Fermi energy at the interface [START_REF] Chen | [END_REF]24,25], corresponding to a lowering of the hole Schottky barrier. The lowest Fermi level position observed at the PZT/Pt interface is E F -E VB = 1.1 eV [START_REF] Chen | [END_REF], which is significantly lower than the charge neutrality level calculated by Robertson and Chen [START_REF] Robertson | [END_REF]. Due to the large deviation between the charge neutrality level and the Schottky barrier height for nearly defect-free interfaces, it is suggested that Fermi level pinning by induced gap states is not pronounced for PZT/metal interfaces. This is in agreement with the large variation of Schottky barrier heights of PZT with RuO 2 (φ = 6.1 eV) and Sn-doped In 2 O 3 (φ = 4.5 eV) [11], where oxygen deficiency is not expected to play a role. The observed Fermi level pinning at PZT/metal interfaces is consequently ascribed to extrinsic defects at the interface. Due to the observed chemical reduction of the PZT, oxygen vacancies are the most likely candidates for these defects.

Summary and Conclusion

The interface formation between contamination-free surfaces of PZT thin films with Pt, Cu and Ag has been studied using photoelectron spectroscopy with in situ metal deposition. The metals are deposited either by magnetron sputtering or by thermal evaporation. Metal atoms are thus the dominant gas phase species in the deposition process. Their condensation on the surface results in a chemical decomposition of the PZT substrate, as observed during deposition of all three metals. This is evident from the observation of a metallic Pb species, which is most pronounced for deposition of Cu.

The Schottky barrier heights of PZT with Ag, Cu and Pt are the same within the experimental uncertainty and are derived as E F -E VB = 1.7 ± 0.1 eV. For a band gap of 3.4 eV, this corresponds to a midgap Fermi level position and nearly identical Schottky barrier heights for electrons and holes. As Schottky emission often dominates the leakage current within PZT/metal contacts, a similar magnitude of leakage current is expected. Pintilie et al. [14] found that the leakage current is largely insensitive to the work function of the top metal electrodes, which is in very good agreement with the similarity of the Schottky barrier heights derived from the photoemission measurements presented here.

The observed Fermi level pinning at PZT/metal interfaces is attributed to oxygen vacancies at the interface, which are induced by the chemical reaction. Fermi level pinning by induced gap states, which is important for more covalently bonded semiconductors, is less important for the PZT/metal interfaces.

Figure 2 .

 2 Figure 2. X-ray photoelectron core level spectra of PZT thin films in the course of Pt (a), Cu (b) and Ag (c) deposition. The core level spectra of Ti 2p and Zr 3d are omitted. The dashed lines indicate metallic Pb. The thickness of different deposited metallic films is given in nanometers.

Figure 3 .

 3 Figure 3. Evolution of the PZT core level lines with increasing Pt (a), Cu (b) and Ag (c) thickness.The distance between core level lines and VBM has been subtracted. The Schottky barrier height for holes Φ B,p corresponding to the distance between Fermi level E F and the valence band maximum E VBM , amounts to 1.6 ± 0.1 eV for PZT/Pt interface, 1.8 ± 0.1 eV for PZT/Cu interface and 1.7 ± 0.1 eV for PZT/Ag interface as determined from the saturation of the core level binding energy shift. The PZT band gap was taken as 3.4 eV[START_REF] Scott | Ferroelectric memories[END_REF]. VBM and CBM refer to the band edges of PZT. The insets indicate the x-ray photoelectron valence band spectra of the uncovered PZT films used for each interface formation experiment.

Figure 4 .

 4 Figure 4. (Color online) band diagram of PZT/ Pt, PZT/Cu and PZT/Ag interfaces containing interface states reflected by the dipole potential δ. The electron affinity χ = 3.4 eV of the cleaned PZT thin film was derived from the UPS measurement and an energy gap of 3.4 eV [1]. Considering the Schottky barrier heights for electrons Φ B,n at the interfaces and taking the work function of 5.65 eV, 4.65 eV and 4.26 eV for Pt, Cu and Ag[14], respectively, into account, the dipole potential δ can be derived form the discontinuity of the vacuum level E VAC at the interfaces. E CB , E F and E VB refer to conduction band, Fermi level and valence band of PZT, respectively.

  Pt 4f, Cu 2p 3/2 and Ag 3d 5/2 core levels of the deposited metals recorded in the course of Pt, Cu and Ag deposition are shown in Figure2. The emissions of Zr 3d and Ti 2p are not shown here, as no changes in line shapes are observed in the course of metal deposition, as already reported in Ref.[START_REF] Chen | [END_REF] for the PZT/Pt interface. The binding energies of the Zr 3d and Ti 2p core levels shift in parallel with the oxide Pb 4f component. The Pb 4f emissions of the clean PZT substrates exhibit a single doublet structure, related to oxidized Pb in PZT (Pb +II ). Slightly different binding energies of the PZT substrate emissions may be attributed to weak sample charging or to slightly different conditions of the substrate/PZT interface. Different charging of the samples may result from different thickness of the nominally insulating films or from varying substrate conditions during growth of the PZT films.

		Cu 2p	Cutoff = 16.5 eV			2.1 eV
		Intensity
			18	16	14	8	4	0
				binding energy [eV]
	Cu 2s		Cu LMM
	Intensity [arb.units]	1.92 nm 3.36 nm 5.28 nm 18 nm 36 nm						Cu 3s	Cu 3p
		0.96 nm
		0.48 nm
		0.24 nm
		0.12 nm
		heated
		O KLL as-is		O 1s	Ti 2p	Pb 4d	Zr 3p	C 1s	Zr 3d	Pb 4f
	1200 1000 800	600	400	200	0
		binding energy [eV]

Figure 1. X-ray photoelectron survey spectra recorded during incremental deposition of Cu onto Pb(Zr,Ti)O 3 . The thickness of the Cu film after each deposition step is indicated. The inset shows an ultraviolet photoelectron spectrum of a cleaned PZT film. and

  7/2 , Cu 2p 3/2 and Ag 3d 5/2 lines for the thick Pt, Cu,

	0 12 5 67 869 7 6 7 9	34 5 34 6 74 5 84 6 734 : 94 8 34 76
		3
	0 32		!" 6) 6* 868 * 82 $% &'( & --,
	5 67 869 7 6 7 9	, , , , #
		,
	0 42 5 67 869 7 6 7 9	# # 6) 6* 868 * 8+ ./ '01( & !" , , , , , , , # -# -,
			--6) 6* 868 * 82 -

Acknowledgments

The work was supported by the German Science Foundation within the collaborative research center SFB 595 (Electrical Fatigue of Functional Material).


Alexander V Barashev

Stanislav I Golubov
email: golubovsi@ornl.gov

Response to the comments by J.H. Evans on 'On the onset of void ordering in metals under neutron or heavy-ion irradiation'

Keywords: irradiation effects, lattice defects void lattice, cascades, interstitial clusters, one-dimensional diffusion

come

Evans's criticism of the assigning of the void spatial regularity found after electron irradiation in [1] to a bubble lattice refers to the analysis of Jäger and Trinkaus [2] described in the Introduction section in [3] as a part of the problem overview. We are sorry if we made an impression that we support their view, which we do not: loop punching from bubbles would not lead to ordering, of course. We do not have any interpretation of the observation made in [1], and do not even consider it as an established result for it has never been confirmed. We think that Jäger and Trinkaus might have a similar opinion: they did not include this result into Tables 1 and2 [2] for void and bubble lattices, even though it was the only alloy of practical use.

The essence of Evans's other comments on our paper [3], as well as conclusions of his recent publications [4][5][6], is that the one-dimensionally (1-D) of the diffusing clusters of self-interstitial atoms (SIAs) have inherent difficulties in forming perfect void lattices, which 2-D diffusing SIAs do not have. However attractive the idea of 2-D diffusion could be, there is no firm evidence of its existence. In the following we focus on two main points: the dimensionality of initial void ordering and the effect of box size on MC calculations.

Dimensionality of initial void ordering. The absence of void linear alignments during early stages of ordering can be explained by the instability of such structures due to the void coalescence described by Evans in [4]. For the sake of completeness, let us recall the mechanism of coalescence. Consider a line of equally spaced voids in a close-packed direction, where one void is shifted from the middle position between two other voids, say, to the right. Then, the free volume to the left void is larger, hence, more SIAs are produced there and interact with the void. As a result of the SIA annihilation at the void surface, the void's centre of gravity should shift to the right, making a bigger distance even bigger. In other words, the linear alignments are physically unstable. In close-packed planes the void coalescence is prevented by the stabilising action of the SIA clusters moving in coplanar directions. In our paper [3] this is reflected by the fact that the most favourable conditions for destabilisation of homogeneous void arrangement correspond to formation of closepacked planes (equation ( 17)). Thus, the ordering mechanism is, indeed, linear, not planar, but the stability of ordered structures increases with increasing dimensionality, being unstable [5].

Effect of box size on MC calculations. In a partially formed void lattice, the 1-D mobile SIA clusters can be separated into two groups: a) those moving in free channels between voids with the mean free path (MFP) greater than the average distance between voids, and b) those moving between two nearest voids. The b-type SIAs lead to the void coalescence discussed above, whereas the a-type SIAs act against the latter, preventing coalescence and providing void ordering. The MFP is the characteristic distance from where on average the SIA clusters come to voids. If the simulation box is smaller than the MFP, then the relative contribution of a-type SIAs to void movement is artificially reduced: part of the a-type SIAs become unable to interact with voids, making perfection of a void lattice difficult, if possible. In a system containing randomly distributed voids of radius r and number density N, the MFP is equal to

πr 2 N ( ) -1
, which gives ~1.4 µm for r ≈ 1.5 nm and N ≈ 10 23 m -3 , as in sections 3.3 and 3.6 of Evans's paper [4]. (Note also that the MFP increases rapidly with increasing spatial correlations between voids, being infinite in a perfect void lattice with no other defects present.) Evans used a simulation box with a linear size of 215.4 nm, i.e. ~6.5 times smaller than the initial MFP, hence the failure to reproduce a perfect void lattice should not come as a surprise. Evans claims that 'the barrier for the precise alignment of voids -toward a perfect lattice -is a short range effect, and can be predicted from a trivially simple diagram [4]'. The diagram mentioned is Figure 3 in [4] illustrating coalescence of voids due to interaction with the b-type SIA, which is indeed a short-range effect. Evans also described the stabilising effect of a-type SIAs, but failed to fully appreciate its long-range character with the corresponding dramatic effect of the size of simulation box. This is why, in contrast to Evans's view, void ordering by SIA clusters with the MFP smaller and bigger than the box size should be fundamentally different.

Evans raised two other issues, to which we respond only briefly. First, he noticed that void lattices are observed in bcc metals but the enhanced swelling near grain boundaries is not, which, in his view, undermines the role of 1-D migrating SIA clusters in the formation of void lattices. We think that this is not logical: grain boundary properties, for example, can be different in bcc compared to fcc crystals. Second, Evans noticed the importance of impurities, which we did not address. In fact, it is well known that oxygen, for example, increases the stability, hence concentration, of voids, which favours void lattice formation, as observed, e.g. in [7], and predicted by our model. Other impurity effects are either too lengthy to discuss here or beyond our understanding as yet.

The issues discussed above are but technical details of void lattice formation and can be verified by wisely chosen calculations. The differences in our views on the void lattice go deeper than that. So, Evans's view is close to the general perception of the void lattice as a separate phenomenon occurring in special circumstances, which is of pure academic interest, not for structural materials under conditions of practical importance. In contrast, we argue that it is just one particular type of a bigger class of spatial correlations caused by 1-D migrating SIA clusters, which are characteristic and permanent features of the microstructure formed in both pure metals and alloys under cascade damage conditions: the absence of void lattices indicates that correlations of voids with other defects prevail. As a consequence our paper [3] becomes an important supplement to another work [8], where we show that these correlations together with the radiation-induced segregation control void swelling in structural materials at high enough irradiation doses.

Finally we mention an important related topic which is the problem of swelling saturation in void lattices, as a potential for engineering radiation-resistant materials. Golubov already argued in 1980 [9] that "spatial ordering has no influence on the growth of

Page 1 of 3 http://mc.manuscriptcentral.com/pm-pml Philosophical Magazine & Philosophical Magazine Letters

  It follows that the dimensionality of initial ordering should not follow the dimensionality of SIA migration, in contrast to Evans's belief

	1
	2
	3 4	for linear alignments.
	5
	6
	7
	8
	9
	10
	11
	12
	13
	14
	15
	16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 F o r P e e r R e v i e w O n l y
		2

Page 2 of 3 http://mc.manuscriptcentral.com/pm-pml Philosophical Magazine & Philosophical Magazine Letters

	1
	2
	3
	4
	5
	6
	7
	8
	9
	10
	11
	12
	13
	14
	15
	16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 F o r P e e r R e v i e w O n l y

http://mc.

manuscriptcentral.com/pm-pml Philosophical Magazine & Philosophical Magazine Letters

	1
	2
	3
	4
	5
	6
	7
	8
	9
	10
	11
	12
	13
	14
	15
	16
	17
	18
	19
	20
	21
	22
	23
	24
	25
	26
	27
	28
	29
	30
	31
	32
	33
	34
	35
	36
	37
	38
	39
	40
	41
	42
	43
	44
	45
	46
	47
	48
	49
	50
	51
	52
	53
	54
	55
	56
	57
	58
	59
	60

voids in molybdenum". Evans agreed with this view [6], stating that "the void lattice formation and void swelling must have separate mechanisms". There is no satisfactory explanation for the phenomenon yet. In our forthcoming publication (in collaboration with Dr. B.N. Singh, Risø National Laboratory, Denmark) we argue that it originates from the lack of dislocation climb, which also seems to be a necessary condition for the formation of a perfect void lattice. The effect is due to distinguishing features of the interaction between 1-D migrating SIA clusters and dislocations and might exist in complex alloys too.

Despite differences in our views, we would like to express our appreciation for Dr. J.H. Evans's work and thank him for initiating this discussion, which, we believe, will serve well in shaping the theoretical foundation of the observed phenomena.