Dominique Massotte

Laurence Lalanne-Tongio

Katia Befort
email: katia.befort@unistra.fr

Title of the special issue: "Addiction: a neurobiological and cognitive brain disorder" Editorial

Addiction is now recognized as a chronic neurobiological and cognitive brain disorder and is generally viewed as a switch from recreational to compulsive substance use despite aversive effects. However, addiction also emerges following misuse and/or abuse of prescription drugs after an initial therapeutic use or in patients that self-medicate. The latter aspect is at the root of the current opioid crisis that strikes North America but is also observed worldwide.

One of the major issues associated with addiction is the high prevalence of relapse that may persist for a lifetime. Several factors contribute to both the development of this brain disease and the susceptibility to relapse. They include sociocultural, psychological, genetic and neurobiological aspects, the balance of which varies depending on the substance of abuse.

In the recent years, efforts have been made to develop a translational approach in which preclinical research on rodent models would benefit to human prophylaxis and therapy. Also, the concept of addiction has been enlarged to encompass addiction to behavioural patterns such as gambling or food.

A meeting entitled « Addiction: a neurobiological and cognitive brain disorder" has been organized in Europe, within the scope and with the financial support of the international Neurex network, the most important European network in the field of neuroscience (http://www.neurex.org) (Strasbourg, March 28-29, 2017). During two days, scientists from United Kingdom, France, Italy, Belgium, and Germany gathered at the Forum de la Faculté de Médecine de Strasbourg to propose a translational perspective from molecular determinants to integrated aspects of addiction that included both preclinical and clinical data. The topics highlighted the alterations taking place during the development of addictive behaviours, their persistence in the abstinent state and their contribution to relapse. This special issue of Neuroscience & Biobehavioral Reviews entitled "Addiction: a neurobiological and cognitive brain disorder" elaborates on the various aspects covered during the meeting but is also enriched with contributions of highly renowned specialists from North America. A large part of its content is devoted to brain plasticity and neurobiological substrates critically involved in addictive behaviours through a translational perspective.

Several contributions detail the effect of drugs of abuse on neuronal plasticity, at the molecular or cellular level, in preclinical studies. Among critical players, this issue focuses on three main actors: the dopaminergic, opioid and endocannabinoid systems. All three are direct molecular targets of substance of abuse namely cocaine and psychostimulants for the dopaminergic system, cannabis and derivatives for the endocannabinoid system and opiates for the opioid system. The latter also constitutes a molecular gateway for most other drugs of abuse including alcohol, THC or nicotine. In addition, the dopaminergic system is central to the anticipation process common to all types of reward. More recently, opioid and endocannabinoid systems have both attracted renewed attention as they get activated by natural rewards such as food, sex or physical exercise that lead to endogenous opioid peptides or endocannabinoids release. Hansson et al illustrate a highly dynamic regulation of the reward system (dopaminergic and opioid) during alcohol abstinence using positron emission tomography (PET) and binding assays in preclinical studies and extend their review on human data. Chaouloff et al address the role of the endocannabinoid system in motivational behaviour, with a focus on running motivation. Marie et al focus on adaptations to opioid and psychostimulant treatments and point to critical pharmacodynamic issues in rodent models. As a whole, this special issue highlights our current view on cognitive and pharmacological clinical strategies and integrates the translational value of the knowledge gathered from preclinical models that directly shapes therapeutic approaches.

As guest-editors of the current issue, we would like to warmly thank all authors who made this adventure possible. We would also like to thank Dr Laviola for supporting this idea and more specifically the reviewers who participated in a great improvement of the final reviews proposed in this issue. Also, our deep greetings go to Ms Pascale Piguet and

Stephanie Klipfel from Neurex who were incomparable in providing support and logistic for our meeting.

Contributors

  Karila et al present an analysis of new synthetic opiates found on the market and the lack of knowledge on their mode of action having large consequences on health issues. Comer & Cahill centre their review on a new illicitly manufactured powerful opiate, Fentanyl, highlight the addictive power of such compounds and discuss whether any current treatment is efficient for fighting such effects. Moreover, beside neurotransmitter cross-talks at system and cellular levels, novel concepts are emerging that propose additional interactions at molecular level through direct physical interaction between receptors. Derouiche & Massotte review our current understanding of the functional impact resulting from such novel molecular entity. In addition, modulations at the chromatin level appear as strong actors of plastic changes occurring in addiction. Two contributions address such epigenetic adaptations in rodent models following treatments with all drugs of abuse(De Sa Nogueira et al) and in alcoholrelated animal research and human alcohol addicts (Pucci et al). The latter contribution specifically concentrated on stress effects because this environmental factor strongly impacts all three stages of the addiction cycle (intoxication/withdrawal/craving), exposing the animal to an emotional state as specifically discussed by Koob & Schulkin. Cognitive factors such as impulsivity, or loss of inhibitory controls, have recently been recognized as major key players in the vulnerability to addictive behaviours and susceptibility to relapse. This important aspect is addressed by Paasche et al within the context of time and is also examined on the emotional point of view by Hermann & Duka, with a focus on alcohol consumption. Among other factors, circadian rhythms recently attracted strong interest as illustrated by the discussion from Mendoza concerning its impact on addictive-like eating behaviours. Alteration of the habenular activity has also been proposed as a major factor contributing to the loss of control over the use of drugs of abuse and the emergence of compulsive drug seeking behaviors and the specific role of this hub brain structure involved in reward and aversion behaviors is reviewed by Mathis & Kenny. As stated earlier, in-depth knowledge of the changes underlying the different stages of addiction, and in particular cognitive deficits that may arise, is pivotal for developing novel prophylactic and therapeutic strategies. Three contributions propose reviews on therapeutic approaches with a cognitive focus. Campanella et al concentrate on new research avenues to implement event-related potentials (ERPs) in the management of alcohol disorders in humans, where the main problem for clinicians lies with the prevention of relapse. Luquiens et al discuss the matter of associating, in humans, cognitive training, identified as self-control network training, with other strategies, particularly those enhancing self-control. Finally, Sampedro-Piquero et al include a comprehensive perspective on recent studies at the preclinical and clinical levels, and propose cognitive stimulation, either by formal cognitive training or non-drug related environmental experiences, as a therapeutic perspective in drug addiction. Finally, appropriate preclinical models are instrumental to study addiction. Three contributions are addressing this fundamental aspect by examining the development of animal models of binge drinking by Jeanblanc et al, discussing the importance of adopting a dimensional framework based on domains of function by Lamontagne & Olmstead, and proposing the retina as a relevant site to investigate brain neurotransmission anomalies in cannabis users by Schwitzer et al.

-

  Hansson AC et al. Dopamine and opioid systems adaptation in alcoholism revisited: Convergent evidence from PET and post-mortem studies. -Chaouloff F et al. Exercise motivation: the key role for the endocannabinoid system -Marie N et al. Role of pharmacokinetic and pharmacodynamic parameters in neuroadaptations induced by drugs of abuse with a focus on opioids and psychostimulants. -Karila K et al. New Synthetic Opioids: Part of a new addiction landscape -Comer S & Cahill C. Fentanyl and Structurally Related Compounds: Preclinical and Clinical Pharmacology? -Derouiche L & Massotte D. G protein-coupled receptor heteromers are key players in substance use disorder -De Sa Nogueira D et al. Neuroepigenetic and addictive behaviors: where do we stand? -Pucci M et al. Environmental stressors and alcoholism development: focus on molecular targets and their epigenetic regulation -Koob GF & Schulkin J. Addiction and stress: An allostatic view -Mendoza J. Food intake and addictive-like eating behaviors: Time to think about the circadian clock(s)" -Mathis V & Kenny P. From controlled to compulsive drug-taking: the role of the habenula in addiction -Paasche C et al. Impulsivity and time perception: which relationship in addictive disorders -Herman AM & Duka T. Facets of impulsivity and alcohol use: what role do emotion play. -Jeanblanc J et al. Binge drinking, better definition required in humans to improve animal models -Lamontagne SJ & Olmstead MC. Animal Models in Addiction Research: a dimensional approach -Schwitzer T et al. Is the retina a relevant site of investigation for brain neurotransmission abnormalities in cannabis users ? Current knowledge and perspectives. -Campanella S et al Why cognitive event-related potentials (ERPs) should have a role in the management of alcohol disorders -Luquiens A et al. Cognitive training: a new avenue in gambling management? -Sampedro-Piquero P et al. Neuroplastic and cognitive impairment in substance use disorders: a therapeutic potential of cognitive stimulation.


Robert Thébaud

G Bouzerar

Bouzerar

Ch Adessi

S Thébaud

R Bouzerar

Ab initio investigation of the role of vanadium impurity states in SrTiO 3 for thermoelectricity

Keywords: thermoelectricity, thermoelectric power factor, resonant states, Seebeck coefficient, oxides, SrTiO3, ab initio electronic transport

come

Introduction

Global energy demand, due to the ceaseless increase in population and industrialization is one of the major worldwide concerns of the 21st century [START_REF] Schierning | Bring on the heat[END_REF][START_REF] To | Renewable energy road map -renewable energies in the 21st century: building a more sustainable future. Commission of the European communities[END_REF]. The unanticipated depletion of natural fossil energy resources, combined with the negative environmental impacts of pollution and global warming, has boosted the search for efficient alternative and sustainable energy harvesting methods. Thermoelectric (TE) materials are expected to play a major role in managing global energy crisis because they enable direct conversion from thermal to electrical energy, and thus provide an alternative source of power generation [START_REF] Snyder | Complex thermoelectric materials[END_REF][START_REF] Francis | Thermoelectric cooling and power generation[END_REF]. Thermoelectric generators are a convenient means of generating green energy by harnessing the waste heat, and their conversion efficiency is primarily governed by the TE figureof-merit defined as ZT = σ •S 2 κ T , where S is the Seebeck coefficient, σ the electronic conductivity and κ the total thermal conductivity (sum of electronic and lattice contributions). The current focus of TE research is directed toward the development of TE materials, which are non Email address: christophe.adessi@univ-lyon1.fr (Ch. Adessi) toxic, earth-abundant, and chemically stable at the operating temperatures. As TE generators are solid-state devices with no moving parts, they are silent, reliable and scalable, making them ideal for small, distributed power generation.

Oxide TE materials fulfill these restrictive constraints and have also the advantage of being of low cost. However, compared to traditional TE materials, they exhibit only modest TE performances due to their high thermal conductivity. Numerous studies have been done to improve their TE response by doping (significant increase of electrical conductivity). The perovskite material SrTiO 3 (STO) is particularly interesting because it has already a relatively large power factor of the order of 39 µW.cm -1 .K -2 [START_REF] Jalan | Large seebeck coefficients and thermoelectric power factor of la-doped SrTiO 3 thin films[END_REF], that is comparable to that of the best known TE materials such as Bi 2 Te 3 [START_REF] Okuda | Large thermoelectric response of metallic perovskites: Sr 1-x La x TiO 3 (0 < x < 0.1)[END_REF], However, because of its relatively high thermal conductivity of κ ≈ 11 W.m -1 .K -1 , [START_REF] Muta | Thermoelectric properties of reduced and La-doped single-crystalline SrTiO 3[END_REF] STO exhibits a relatively modest ZT of only 0.1, unlike Bi 2 Te 3 which has a κ around 1.6 W.m -1 .K -1 and a ZT ≃ 0.96 [START_REF] Park | Thermal and electrical conduction of single-crystal Bi 2 Te 3 nanostructures grown using a one step process[END_REF][START_REF] Mi-Kyung | Thermoelectric properties of Bi 2 Te 3 : Cul and the effect of its doping with Pb atoms[END_REF].

In recent years, the idea of using nanotechnology to improve the figure of merit of conventional TE materials has triggered active research. Most of the reported ZT enhancements are based on dimensionality reduction (thin films and nanowires) that leads to significant thermal conductivity reduction [START_REF] Li | Thermal conductivity of individual silicon nanowires[END_REF][START_REF] Muñoz Rojo | Thermal conductivity of Bi 2 Te 3 nanowires: how size affects phonon scattering[END_REF][START_REF] Swinkels | Diameter dependence of the thermal conductivity of InAs nanowires[END_REF].

The second strategy that could improve the ZT consists in focusing on the power factor σ .S 2 . Mahan and Sofo [START_REF] Mahan | The best thermoelectric[END_REF] suggested that the introduction of a sharp peak in the density of states could significantly boost the figure of merit. Similar arguments have also been proposed by Hicks and Dresselhaus [START_REF] Hicks | Effect of quantum-well structures on the thermoelectric figure of merit[END_REF][START_REF] Hicks | Thermoelectric figure of merit of a one-dimensional conductor[END_REF] by dimensionality reductions. Improving the power factor can be achieved by dopants that would create sharp hybridized impurity states (resonant states) inside the conduction/valence band of the host material. The procedure has been attempted by many researchers with chalcogenide compounds, for instance: Tl doped PbTe [START_REF] Heremans | Enhancement of thermoelectric efficiency in PbTe by distortion of the electronic density of states[END_REF][START_REF] Heremans | Resonant levels in bulk thermoelectric semiconductors[END_REF], Sb doped CdTe alloyed PbTe [START_REF] Tan | Enhanced density-of-states effective mass and strained endotaxial nanostructures in Sb-doped Pb 0[END_REF], Sn doped Bi 2 Te 3 [START_REF] Christopher | Resonant level formed by tin in Bi 2 Te 3 and the enhancement of room-temperature thermoelectric power[END_REF], In doped SnTe [START_REF] Zhang | High thermoelectric performance by resonant dopant indium in nanostructured SnTe[END_REF][START_REF] Tan | High thermoelectric performance SnTe-In 2 Te 3 solid solutions enabled by resonant levels and strong vacancy phonon scattering[END_REF], Mg-In [START_REF] Li | Enhanced thermoelectric performance through synergy of resonance levels and valence band convergence via Q/In (Q = Mg, Ag, Bi) co-doping[END_REF] co-doped SnTe or In doped [START_REF] Wu | Resonant levelinduced high thermoelectric response in indium-doped GeTe[END_REF] GeTe.

The physics of impurity/resonant levels may be also relevant in the case of superconductivity. For instance in heavily doped semiconductors such as B doped diamond [START_REF] Ekimov | Superconductivity in diamond[END_REF], an insulator to metal transition occurs with a superconducting behavior [START_REF] Blase | Superconducting group-IV semiconductors[END_REF] at low temperature. However, the conventional mechanism corresponds to a shift from an impurity band to a degenerate situation where the Fermi level is located in the valence band. This "resonant valence band" is then leading to a clear superconducting behavior.

In contrast to this scenario, it has recently been proposed that impurity states actually suppress the conductivity although with a strong variations of the transport distribution function leading to a boost in the Seebeck coefficient which overcompensates the conductivity reduction [START_REF] Simon Thébaud | Boosting the power factor with resonant states: A model study[END_REF]. Herein, we report on the theoretical basis of ab initio calculations the use of vanadium to dope STO which advantageously exhibits impurity states whithin the gap which promotes a boost of the Seebeck coefficient.

Theoretical background

In what follow, the TE properties are calculated using the Landauer formalism combined with ab initio calculations. In the linear response regime, the electrical conductance and the Seebeck coefficient can be written as:

G = -2e 2 h L 0 , S = -1 k B T L 1 /L 0 , with, L n = +∞ -∞ (E -E F ) n T (E) ∂ f ∂ E dE , (1)
where T is the temperature, e the magnitude of the electron charge, h the Planck's constant, k B the Boltzmann's constant, E F the Fermi level, f the Fermi distribution and T (E) the energy dependent transmission.

For a conductor of length l z , the transmission can be recast as

T (E) = λ (E) l z M(E)
, where λ (E) is the mean free path and M(E) the density of modes (DOM) [START_REF] Datta | Electronic transport in mesoscopic systems[END_REF]. For this work, we have used a constant mean free path approximation [START_REF] Kim | Influence of dimensionality on thermoelectric device performance[END_REF] i.e. λ (E) = λ 0 with λ 0 ≃ 20 Å which reproduces the room-temperature resistivity measured in 10 % La-doped STO samples [START_REF] Jalan | Large seebeck coefficients and thermoelectric power factor of la-doped SrTiO 3 thin films[END_REF][START_REF] Okuda | Large thermoelectric response of metallic perovskites: Sr 1-x La x TiO 3 (0 < x < 0.1)[END_REF][START_REF] Bouzerar | Unified modeling of the thermoelectric properties in SrTiO 3[END_REF]. The DOM can be evaluated by a direct diagonalization of the Hamiltonian of the system using the eigenvalues (see for instance Ref. [START_REF] Jeong | On landauer versus boltzmann and full band versus effective mass evaluation of thermoelectric transport coefficients[END_REF]). This DOM corresponds to a count of the bands intersecting the energy of interest. Finally, the electrical conductivity is defined as σ = l z l x ×l y G , where l x and l y are the the dimensions of the system perpendicular to the transport direction.

The ab initio calculations are performed with the DFT package SIESTA [START_REF] José | The siesta method for ab initio order-n materials simulation[END_REF]. This code is very well suited to study oxides as it is based on atomic like orbitals. We have used the Perdew, Burke & Ernzerhof [START_REF] Perdew | Generalized gradient approximation made simple[END_REF] exchange-correlation functional corresponding to a generalized gradient approximation. A Troullier-Martin norm-conserving pseudopotentials [START_REF] Troullier | Efficient pseudopotentials for plane-wave calculations[END_REF] has been used. The basis corresponds to a double-ζ -polarized basis optimized with the simplex tool of the SIESTA package. All the atomic structures were optimized up to forces less than 0.01 eV/Å and to an hydrostatic pressure less than 0.1 kbar. Finally, a Monkhorstpack of 6 × 6 × 6 k-points has been used for the self consistent calculations (80 × 80 × 80 for the transport calculations) along with a mesh cutoff of 400 Ry.

Vanadium doping

In Fig. 1 is given the band structure along with the density of states (DOS) of pristine STO and vanadium doped STO. As pointed out in Ref. [START_REF] Bouzerar | Unified modeling of the thermoelectric properties in SrTiO 3[END_REF] the lowest conduction bands of pristine STO are mainly due to the d-type orbitals of Ti (namely, it corresponds to t 2g orbitals). When doped with vanadium (in substitution of a Ti atom), the main issue is the occurrence of impurity bands at the bottom of the conduction bands. As illustrated by the projected density of states, these bands are mainly due to the d orbitals of V and, as can be seen, they are acting as resonant states. Indeed, they are in close vicinity of the t 2g bands and this is leading to a large increase of the DOS and, as pointed hereafter, of the Seebeck coefficient. However, in order to use these resonant states for TE application, the Fermi level must be in close vicinity of them. For the vanadium concentration used in Fig. 1, the Fermi level is definitely located far from the resonant region. This point raises the need to fill the conduction bands up to the resonant states either by means of a device based on a field effect or by using a co-dopant that would shift the Fermi level.

In Fig 2 is represented the electrical conductivity σ , the Seebeck coefficient S and the power factor (PF) σ .S 2 using a rigid band shift model for n-type doping. This model, which consists in moving rigidly the Fermi level, illustrates the equivalent effect of a field effect device. As a guide to the eyes, we have added at the top of the figure the corresponding equivalent doping of lanthanum in the hypothesis of a perfect electron reservoir. We have investigated the pristine case (undoped STO) and STO doped with vanadium for 2 different concentrations. It should be noted that the abscissa corresponds to the added carrier charge with respect to the neutral material. It is obtained by integrating the DOS from the Fermi level. For this reason, the conductivity for V doped STO at zero added carrier charge has a non-zero value. Conversely, for pristine STO the conductivity is exactly zero at zero added carrier charge.

For pristine STO the behavior is quite conventional. As a matter of fact, the conductivity increases with the added carrier charge and the Seebeck coefficient is negative and decreases with the added carrier. This is leading to the familiar behavior for the PF with a sharp peak 2: From top to bottom, electrical conductivity, Seebeck coefficient and power factor obtained with a rigid band shift model for pristine and V doped STO as function of the added carrier charge to the neutral material. On top is given the theoretical equivalent La codoping required to achieve the corresponding added carrier charge. linked with the two opposite trends of S and σ .

For doped STO, the behavior is completely different. The major effect occurs for the Seebeck coefficient which exhibits a sign inversion close to the resonant states. This point, as we have already pointed out in a previous work [START_REF] Simon Thébaud | Boosting the power factor with resonant states: A model study[END_REF], is opening new perspectives for obtaining both n and p-type TE materials using the same dopant. Moreover, for a concentration of 3.7%, the amplitude of the Seebeck coefficient (at the maximum of the PF) is of the same amplitude that pristine STO. One can argue that the increase of the Seebeck comes with a decrease of the conductivity, but as the PF depends on the square of the Seebeck coefficient, the resulting PF is as large as that of the pristine material. Finally, it should be noted that the range of the carrier charge, for which these large values of the PF are observed with V doped STO, is much greater than the pristine case.

Co-doping

Another way to fill the conduction band up to the resonant state could come from a second dopant which would act as an electron reservoir for STO i.e. which would lead to a significant charge transfer without modifying the band structure. Actually, La in substitution to Sr appears to be a very good candidate for electron doping in STO [START_REF] Bouzerar | Unified modeling of the thermoelectric properties in SrTiO 3[END_REF]. For instance, this reservoir behavior is also observed with yttrium and niobium doping [START_REF] Obara | Thermoelectric properties of Y-doped polycrystalline SrTiO 3[END_REF][START_REF] Ohta | High-temperature carrier transport and thermoelectric properties of heavily La-or Nb-doped SrTiO 3 single crystals[END_REF]. The whole strategy is thus to use vanadium to create resonant states and to use a co-dopant as an electron reservoir in order to fill the conduction band up to these resonant states. However, it is definitely not obvious that for STO doped with both vanadium and a co-dopant the particular behavior pointed out previously will be preserved. In Fig. 3 is given the band structure along with the DOS of co-doped STO with V and La. We have also represented the band structure of STO doped only with V (same as in Fig. 1) for comparison purposes. It can be noticed that La has not a neutral role when combined with V. The impurity bands induced by vanadium are still observed, but these bands are shifted at higher energy and are actually overlapping with the t 2g bands. Indeed, at the top of the impurity bands, we have now a clear mix with the intrinsic bands of STO. This behavior is very specific to the co-doping and for a doping with La alone, we have verified that the band structure of pristine STO is preserved i.e. that La is an electron reservoir. This mixing (or pinning) of the impurity bands with the t 2g ones has an influence on the resonant state as can be seen on the DOS. First, the resonant states are now shifted at higher energy and second, the amplitude of the DOS is reduced compared to the case where V is used alone. As presented hereafter, the amplitude of the Seebeck coefficient at the resonant states is affected too by this phenomenon. In order to have some insights on the effects associated with the co-doping, the DOM for pristine STO, V doped STO and co-doped STO with V and La are presented in Fig. 4. First of all, the sign inversion of the Seebeck coefficient pointed out previously (see Fig. 2) for V doped STO is actually directly linked with the slope inversion of the DOM. For pristine STO, the slope is strictly positive and thus the sign of the Seebeck coefficient remains constant. Conversely, for V doped STO this slope exhibits an inversion which is fully related to the resonant states induced by the vanadium. This phenomenon is observed for all doping concentrations and also when a co-dopant is introduced. however, a close examination of the expression of the Seebeck (see eq. 1) leads us to the conclusion that, in order to obtain a large Seebeck coefficient, we both need a negative slope for the DOM and a slope transition which tends as close as possible to zero. This situation is achieved for STO solely doped with V when the dopant concentration is small enough. For co-doped STO we obtain a negative slope almost equivalent but, due to the pinning of the impurity bands with the t 2g bands, the DOM does not tend to zero. For this reason, and as presented hereafter, the amplitude of the Seebeck coefficient for co-doped STO is smaller than that of STO doped with V only. In Fig. 5 is given the PF (the Seebeck and the conductivity are in inset) for co-doped STO. It corresponds to a vanadium concentration of 3.7% which has been observed to be the best choice to take benefit of the resonant states. The concentration of the co-dopant is ranging from 0 to almost 60%. We have considered three different co-dopants (La, Nb and Y) which all have been observed experimentally to be electron dopants for STO [START_REF] Obara | Thermoelectric properties of Y-doped polycrystalline SrTiO 3[END_REF][START_REF] Ohta | High-temperature carrier transport and thermoelectric properties of heavily La-or Nb-doped SrTiO 3 single crystals[END_REF]. However, as can be seen in this figure, all of them are leading to a very similar behavior.

The Seebeck coefficient is behaving in a rather close way to what we have already observed in Fig. 2, that is to say a sign which can be either positive or negative depending on the co-dopant concentration. For small codopant concentration, we have a negative sign for the Seebeck (as conventionally observed for electron doping) but for large concentration the Seebeck coefficient tends to zero and becomes positive. This behavior has a direct impact on the PF.

For low co-dopant concentration, the PF decreases when the co-dopant concentration increases. It goes to zero when the Seebeck coefficient sign reverses and finally increases and reaches a second maximum but now with a positive Seebeck coefficient for large co-dopant concentration. This observation opens the perspective to obtain both n and p type TE materials doped with exactly the same dopants. In this paradigm, the n or p nature would be chosen by modifying only the co-dopant concentration. However, due to the pinning effect mentioned previously, conventionnal dopants suvh as La, Nb or Y do not allow to obtain a signigicant PF and further investigations are required in order to improve the amplitude of the Seebeck coefficient and thus of the PF.

Conclusion

In the present work, the mechanism for SrTiO 3 doped with vanadium based on resonant states to boost the power factor has been investigated. This mechanism, conversely to the accepted picture of a boost of the density of states, is linked with a reduction of the conductivity together with a boost of the Seebeck coefficient against all odds. This result may open the perspective to use only a single dopant to obtain both n and p type semiconductor for thermoelectricity thanks to the sign inversion of the Seebeck coefficient observed in the vicinity of the resonant peak. Moreover, by using co-dopant such as La, Nb or Y, an actual sign inversion of the Seebeck coefficient is observed by modifying the co-dopant concentration of the compound. However, the power factor amplitude is actually less significant than that observed within a rigid band shift which indicates that these co-dopants are no more simple electron reservoirs in V doped SrTiO 3 .

This demonstrates the possible use of the same compound (same dopant and co-dopant) to obtain both n and p type thermoelectric materials by tuning the co-dopand concentration, which can be a true benefit for building thermoelectric devices. However, the co-doping by conventional dopants such as La, Nb or Y is not satisfactory in terms of PF amplitude. Finally, nanostructuring could be an efficient way to both tune the position of the resonant peak and eventually further enhance the n(p)-type power factor.

Figure 1 :

 1 Figure 1: Band structure and density of states for pristine SrTiO 3 and SrTi 0.875 V 0.125 O 3 along with its projected density of states for the d orbitals of V and Ti as function of the energy (centered relatively to the bottom of the conduction band of SrTi 0.875 V 0.125 O 3 and denoted E c ).

Figure

  Figure2: From top to bottom, electrical conductivity, Seebeck coefficient and power factor obtained with a rigid band shift model for pristine and V doped STO as function of the added carrier charge to the neutral material. On top is given the theoretical equivalent La codoping required to achieve the corresponding added carrier charge.

Figure 3 :

 3 Figure 3: Band structure and density of states (DOS) for SrTi 0.875 V 0.125 O 3 and Sr 0.875 La 0.125 Ti 0.875 V 0.125 O 3 along with its projected density of states for the d orbitals of V and Ti as function of the energy (centered relatively to the bottom of the conduction band).

Figure 4 :

 4 Figure 4: Density of modes (DOM) for pristine SrTiO 3 , SrTi 1-x V x O 3 (x = 12.5% and 3.7%) and Sr 0.875 La 0.125 Ti 0.875 V 0.125 O 3 as function of the added carrier charge to the materials.

Figure 5 :

 5 Figure 5: Power factor for Sr 1-y La y Ti 1-x V x O 3 , Sr 1-y Y y Ti 1-x V x O 3 and SrTi 1-x-y V x Nb y O 3 with x = 3.7% as function of the co-dopant concentration. The Seebeck coefficient and the conductivity are given in inset.


D Pithan

M.-I Fong

Richard

E V Skopin

L Rapenne

J L Deschanvres

H Renevier
email: hubert.renevier@grenoble-inp.fr

E Blanquet

G Ciatto

L Pithan

D D Fong

M.-I Richard

In situ X-ray studies of the incipient ZnO Atomic Layer Deposition on In 0.53 Ga 0.47 As

In situ x-ray studies of the incipient ZnO atomic layer

deposition on In 0.53 Ga 0.47 As

I. INTRODUCTION

For the past several years, the rapid and continuous increase in transistor density and switching speeds has led to the consideration of III-V semiconductors as replacements for silicon in Metal Oxide Semiconductor Field-Effect Transistors (MOSFETs). 1,2 In x Ga 1-x As is of particular interest due to its high charge carrier mobility, which is almost a factor of ten higher than that for Si. By varying the ratio of In to Ga in In x Ga 1-x As, 3,4 it is possible to choose the In x Ga 1-x As lattice parameter (from 0.606 nm to 0.565 nm) and the direct band gap value, from 0.354 eV (InAs) to 1.424 eV (GaAs). For this reason, this material is already widely used in infrared (IR) electronics: [START_REF] Oktyabrsky | Fundamentals of III-V semiconductor MOSFETs[END_REF] many IR receivers and emitters, high-power diode lasers, devices for high-current electronics, and mi-crowave electronics are all based on In 0.53 Ga 0.47 As/InP heterostructures (where x = 0.53 is chosen to match the InP lattice parameter).

One of the key technological problems in the development of high-performance MOSFETs concerns the quality of the metal-semiconductor contact, which must be ohmic with a specific contact resistivity less than ρ c = 10 -8 Ω.cm 2 . [START_REF] Agrawal | [END_REF] Here, pinning of the metal Fermi level is a major issue as it can lead to the formation of a Schottky barrier for charge carriers. 7,8 One possible solution is forming a metal-insulator-semiconductor structure, i.e., to insert an ultrathin, dielectric oxide between the metal and the In x Ga 1-x As semiconductor. However, the oxide must be sufficiently thin (less than 10 nm) to allow flow of the tunneling current. [START_REF] Agrawal | [END_REF] Such oxide layers can also be used as interfacial passivation layers (IPLs) [9][10][11] grown on In x Ga 1-x As under the gate dielectric.

One of the most promising materials for both depinning the metal Fermi level and creation of the IPL is ZnO. It was shown previously that the insertion of an ultrathin ZnO layer between In x Ga 1-x As and the Al metal contact decreases the contact resistance. [START_REF] Agrawal | [END_REF]12 Likewise, a ZnO IPL is known to suppress film crystallization and oxide formation, reduce interface state density, and improve the interface quality. 10,11 A highly scalable method for deposition of such a thin oxide layer is thermal Atomic Layer Deposition (ALD). 13 ALD is based on self-limiting surface chemical reactions, allowing the layer-by-layer growth of ultrathin, dense films with smooth surfaces. [START_REF] Pakkala | Handbook of Deposition Technologies for Films and Coatings[END_REF] The comparatively low substrate temperatures required for ALD make it possible to reduce the thermal budget during manufacturing of the transistor. For the ALD of ZnO, the substrate temperature can range from room temperature to a few hundred degrees Celsius. [START_REF] Tynell | [END_REF] The growth process involves the cyclical injection of time-separated gases into a chamber, within which they react with a heated substrate. 16 One ALD cycle consists of the following: the injection of precursor A and its subsequent reaction with the sample surface, followed by a purge; the injection of precursor B and its subsequent reaction with the sample surface, followed by a purge. In the case of ideal ALD, the thickness of the deposited layer is controlled only by the number of cycles. Since growth relies on chemisorption of the precursor onto the sample surface, the most important parameters for ALD are the substrate temperature, the surface functionalization, and the precursor chemistry. It is therefore expected that the initial growth behavior (ALD on the substrate) may be different from that in subsequent growth stages (ALD on the deposited material). Indeed, the presence of a ZnO transient prior to steady-state growth has been demonstrated on various substrate surfaces. For instance, Fong et al. 17 showed that ZnO films deposited on Si grow initially in the form of islands, with the onset of coalescence occurring during the fourth growth cycle. Baji et al. 18 showed that the ZnO growth behavior depends strongly on the substrate, exhibiting island-like growth on Si and layer-by-layer growth on GaN; on sapphire, the growth mode can be tuned by the deposition temperature. Consequently, to create ultrathin ZnO layers using ALD, one needs to know and understand how growth occurs at the initial stages, i.e., how thickness varies with the number of cycles, how the parameters of the process affect growth (e.g., precursor flows, substrate temperature), and how the atomic structure of the deposited material varies with film thickness.

Many in situ techniques have been used to investigate the initial stages: mass spectrometry, quartz microbalance, infrared spectrometry, surface photoabsorption, incremental dielectric reflection, surface photon interference, reflectance difference spectroscopy, optical emission spectrometry, and spectroscopic ellipsometry. 19,20 Various synchrotron techniques have also been used to study both the structure and composition of ultrathin films, exploiting the high brilliance of the beam, the possibility of changing the X-ray energy, and the availability of 2D detectors. X-ray fluorescence (XRF), X-ray diffraction (XRD), specular reflectivity (XRR), X-ray absorption fine structure spectroscopy (XAFS), and grazing incidence small angle X-ray scattering (GISAXS) are among the popular techniques used for in situ growth studies at various synchrotron centers. 17,[21][22][23] Here, we employ in situ synchrotron techniques to study the initial growth behavior of ZnO ALD on In x Ga 1-x As, as well as to characterize the resulting film morphology and crystallinity. We exploit a custombuilt thermal ALD reactor [START_REF] Skopin | Etude des premiers instants du dépôt chimique par flux alternés (ALD) de films ZnO ultra minces sur In0,53Ga0,47As[END_REF][START_REF] Boichot | [END_REF] equipped with a dedicated port for measuring X-ray fluorescence and a rotating flange for performing surface diffraction. In a previous in situ X-ray study 26 , ZnO growth on (001)In x Ga 1-x As substrates by ALD was monitored by Zn-K α X-ray Fluorescence (XRF) and X-ray Absorption Fine Structure (XAFS) at the Zn K-edge. Here, we explore the ZnO layer crystallization mechanism and mainly focus on the results of in-plane X-ray Diffraction (XRD) measurements conducted during ZnO ALD in the substrate temperature range of 120

• C to 240 • C.
The reactor was installed on the heavy-duty diffractometer of beamline ID3 27 at ESRF (Grenoble, France). ZnO ALD on In 0.53 Ga 0.47 As was monitored in situ by measuring Zn K α XRF, XRR, and in-plane reciprocal space maps (RSMs). Several samples were also selected for post-growth imaging studies by transmission electron microscopy (TEM).

II. EXPERIMENT SECTION

The In 0.53 Ga 0.47 As (001) substrates (hereafter denoted InGaAs) were provided by G.I.E III-V Lab (Palaiseau, France). More details about the substrate growth can be found in Ref. 26 . Prior to growth, the InGaAs substrates were agitated in 4M HCl solution for 5 min to remove the native oxide, rinsed in deionized water for 30 s, and then dried with argon before immediate introduction into the ALD reactor. The substrates were then annealed at 200 • C for 30 min in the reactor under a constant flow of 100 sccm nitrogen to evaporate As from the surface.

During the ALD process, we used Zn(C 2 H 5 ) 2 or diethylzinc (DEZn) as the metal precursor, water (H 2 O) as the oxidant, and nitrogen (N 2 ) as the purge gas. For each ALD cycle, the flow of DEZn was 5 sccm, and the pulse duration was 5 s, while the water flow ranged between 0.6 sccm and 6.0 sccm with a pulse length of 40 s. To clear the reactor between the DEZn and H 2 O pulses, N 2 was injected into the chamber, flowing to the pump at a rate of 1000 sccm for 45 s.

XRR and XRF data were recorded with an X-ray energy of 20 and 10 keV (above the Zn K-edge at 9.659 keV), respectively, either during each ALD cycle or after the completion of several ALD cycles (without X-rays) while purging the reactor with 100 sccm flow of nitrogen. For studies of the in-plane crystal structure, the energy was set to 20 keV in order to quickly sample a wide range of reciprocal space. In-plane diffraction measurements were obtained by measuring a series of so-called zap-scans with a 2D Maxipix T M pixel detector. The incident angle was 0.35 • , i.e., above the InGaAs and ZnO critical angle values at 20 keV (0.129 • and 0.137 • , respectively). The resulting set of detector images were analyzed using BINoculars 28 data reduction and analysis software to plot the in-plane RSMs.

The TEM observations were carried out at 200 kV with a JEOL 2010 microscope (with a resolution of ∼0.19 nm). Cross-sectioned samples were prepared by both manual and automated polishing, the latter using the MultiPrep T M system (Allied High Tech Products, Inc.). The final polishing was performed using a felt-covered disc impregnated with a silica solution until the appearance of the first extinction fringe among those of equal thickness. Ar-ion milling was then used to minimize the total thickness.

III. RESULTS

A. Substrate temperature and water pressure effects.

Figure 1 displays the equivalent film thickness, as determined by the calibrated Zn K α fluorescence signal, as a function of the number of ALD cycles for four substrate temperatures: 120 • C, 160 • C, 200 • C, and 240 • C. We denote the corresponding samples as 120, 160, 200, and 240 below. The three lower temperatures lie within the reported ALD window for the growth of ZnO on ZnO, 29,30 and the fluorescence intensity was measured during the nitrogen purge at the end of every two cycles. For the 240 • C sample, the intensity was monitored throughout the growth process -even during the precursor/oxidant chemical reactions.

After the growth of each sample (i.e., after 100 ALD cycles), the final thickness and roughness of the ZnO layer were determined by XRR, cross-sectional TEM images were used for measuring the thicknesses too (see Figure S1 in the supplementary information). The thickness value obtained for 100 cycles was then used to scale and calibrate the fluorescence intensity (denoted hereafter as Thickness(XRF)). Although such a calibration would give the true thickness if the ZnO layer density remained constant during growth, this is likely not the case before the steady growth is reached. Three different regimes of growth can be distinguished, as seen in Figure 1: transient regime (regime I and regime II) which includes an initial, slow linear growth (regime I), followed by nonlinear growth (regime II), and steady, linear growth (regime III).

The growth per cycle (GPC) calculated in growth regime III is equal to 0.17 nm.cy -1 for the three lowest temperatures, 120 • C, 160 • C, and 200 • C. The equivalent thickness curve (Thickness(XRF)) for the highest substrate temperature of 240 • C shows the same general trend. However, a higher growth rate is observed in regime I, and the GPC value in regime III is larger (0.22 nm.cy -1 ). Note that the initial growth rate (corresponding to the slope during the three first cycles) is higher than the one observed for the following cycles in growth regime I (inset of the Figure 1). Some ALD parameters can strongly influence the nucleation process. We studied the impact of water coverage, measuring the XRF intensity during the entire ALD process for three different water flows, i.e., for three different water pressures (the reactor chamber was closed during the water pulse). For a 40 s injection pulse and water flow equal to 0.6, 2.6, and 6.0 sccm, the water pressure increase in the reactor chamber was 0.07, 0.32, and 0.69 mbar, respectively. The substrate temperature was 120 • C. Figure 2 shows that the XRF intensity starts to increase approximately after 21, 28, and 36 cycles for water flows of 6.0 sccm, 2.6 sccm, and 0.6 sccm, respectively. The higher the amount of water, the larger the number of water molecules react with the sample surface, and the earlier the occurrence of the steady-state regime.

B. ZnO crystallization during growth

Reciprocal space maps were measured after different cycle numbers for three substrate temperatures: 120 • C, 160 • C, and 200 • C. During the RSM measurements, the samples were kept under a constant 100 sccm flow of nitrogen. By performing on-the-fly scanning of the sample (zap-scans), each RSM map could be acquired in approximately 15 minutes. We employ the BINoculars data reduction software 28 to plot the RSMs. Figure 3 shows a set of RSMs measured at a substrate temperature of 200 • C, with the reciprocal lattice units (r.l.u.) referenced to the InGaAs cubic lattice parameter a = 0.58687 nm.

To better observe the intensity dynamics of the ZnO diffraction peaks (or rings, as in the case of powder diffraction), the 220 InGaAs peak was subtracted from all RSM images. This was performed by selecting a background image containing the InGaAs Bragg peak and subtracting it from all subsequent images. For example, the RSM measured at 36 ALD cycles was chosen as the background image for sample 200, since ZnO diffraction peaks (rings) were absent for cycle 36. The results show that during growth, in-plane ZnO diffraction rings gradually appear, and their intensities increase with the ALD cycle number. To identify the ZnO reflections, we measured the radii of the diffraction rings, which are inversely proportional to the inter-planar distances, and referenced the distances to the ICDD database for ZnO wurtzite (PDF: 00-036-1451). In ascending radii, the three observable diffraction rings correspond to the 100, 002, and 101 ZnO diffraction peaks.

Similar RSM measurements were carried out for samples 120, 160, and 200. For sample 240, only one RSM image was measured at the end of the growth (100 ALD cycles). We note that the uniform intensity along the diffraction rings indicates the absence of in-plane texture for all samples. This was also observed for the ALD growth of ZnO on SiO 2 . [START_REF] Boichot | [END_REF] Here, no epitaxial relationship was expected since the SiO 2 was amorphous.

Given that synchrotron radiation can readily detect crystallinity from small volumes 21,27 and that we exploit the grazing incidence geometry to probe a large area of the sample and minimize the substrate signal, the initial absence of in-plane peaks is most likely explained by the synthesis of an amorphous ZnO layer on the InGaAs substrate, which then acts as a seed layer for nucleation of the wurtzite phase. To analyze the intensity variation of the weak diffraction peaks (rings) as a function of ALD cycle number, we integrated the intensity values over the azimuthal angle (i.e., over the available arc of intensity for a fixed ring radius) and extracted the intensity profile as a function of the inverse q-vector. Figure 4 shows the intensity vs. q -1 profile for substrate temperatures of 120 • C, 160 • C, 200 • C, and 240 • C at the end of growth (100 cycles).

As already reported in the case of ZnO ALD, (001)-fiber texture develops whenever the growth temperature or the thickness is increased (see for instance Boichot et al. [START_REF] Boichot | [END_REF] and references herein). To look for the appearance of (001)-fiber texture for ZnO grains as a function of growth temperature, we normalized the diffraction curves with respect to the intensity of the 100 peak. The larger the number of grains that have the (001) planes parallel to the growth surface, the larger (or smaller) the 100 (vs 002) intensity (in-plane diffraction). The 101 Bragg peak is from another family of grains. Also, the larger the number of grains that have the (001) planes parallel to the growth surface, the larger the 100 (vs 101) intensity. Figure 4 shows that when increasing the substrate temperature from 120 • C to 240 • C, the 002 and 101 diffraction intensities decrease with respect to the 100 reflection. At 240 • C, which corresponds to a temperature outside of the ALD window, the decrease of the 002 and 101 diffraction peaks intensities (with respect to the 100 peak) is much more pronounced than at the lower temperatures. This relative intensity change shows that the ZnO/InGaAs film develops (001)-fiber texture at higher temperatures, as was observed for ALD-grown ZnO/a-SiO 2 thin films. [START_REF] Boichot | [END_REF] The final film thickness for sample 240 (16 nm) is also larger than the ones grown at lower substrate temperatures (12 nm), as was shown in Figure 1.

To determine the dynamics of ZnO crystallization during growth, the three diffraction peaks were fitted using Pearson VII functions; the background was subtracted beforehand. The intensity values for each of the three profiles were then integrated. The integrated intensities as function of ALD cycle number for samples grown at 120 • C and 200 • C are shown in Figures 5(a We see in Figure 5(a) that at a temperature of 120 • C, the integrated intensities for all three diffraction peaks are close to zero for small film thickness values (0-3 nm). This means that atomic long-range order either does not exist or the proportion of crystallinity is too small to be detected. The solid lines in Figure 5 S1 in the supplementary information), and the interface remains sharp, although the presence of some amorphous material cannot be excluded. However, the interface does not look the same that for 200 • C. This may have to do with the different growth behavior observed at 240 • C by XRF (Figure 1). The crystallinity of ZnO grains is evidenced by the presence of sharp reflections in the electron diffraction pattern (see Figure S2 in the Supplementary Information). Furthermore, the 002 reflection in the diffraction pattern is more intense. The inverse Fast Fourier Transform (FFT) of the 002 reflection (Figure S2) shows the dominant growth orientation of ZnO grains is along the [001] direction, in agreement with fiber texture discussed above.

IV. DISCUSSION

A. ZnO ALD on InGaAs, transient regime

The X-ray data presented above were obtained in situ during the growth of ZnO on InGaAs. When compared to the existing literature, whether ab initio calculations or Monte Carlo simulations, they provide new insight, particularly with regard to the transient growth regime that often exists but with properties that depend on the growth parameters. This insight allows the construction of a simple growth model that we present in section IV D.

Here we describe a few prominent and systematic experimental observations on the regime.

In agreement with our previous findings, 26 the transient growth regime is comprised of two different growth modes corresponding to regimes I and II in Figure 1. The transient growth regime I (growth delay) is characterized by a significant jump of the deposition rate at cycle 1 (see inset of Figure 1 and Reference ), 26 then by a relatively low GPC (on the order of few hundredths of nm.cy -1 ), which is linear and concomitant with Zn desorption, as observed by Zn X-ray fluorescence measurements. 26 We believe this is most likely due to DEZn precursor desorption: the chemisorbed DEZn remains on the surface whereas the physisorbed DEZn molecules are removed during the purging process. At a growth temperature equal to 120 • C, we observed that regime I ends with the cessation of DEZn desorption and the formation of a poorly-ordered, ultra-thin ZnO layer. 26 As the GPC starts to increase, growth enters regime II.

The transient growth regime II is characterized by a nonlinear (S-shaped) 31 thickness-versus-cycle curve, similar to the one observed in the case of substrate-inhibited growth of type II in Reference 31 . More precisely, the GPC increases as the square of the cycle number, reaches a maximum, and then decreases to a constant value. This type of growth behavior is associated with 3D island growth. In the present case, we associate regime II with the nucleation and growth of ZnO grains (3D) on top of the poorly-ordered Zn oxide layer (2D) synthesized during regime I. The formation of ZnO grains increases the surface roughness; as a consequence, both the surface area and growth rate increase. As the surface begins to smooth, the growth rate is reduced. The transient growth regime II ends when the GPC reaches a constant level, thereby entering regime III.

The regime I growth behavior reported here and previously 26,32 is very similar to that of HfO 2 ALD on SiO 2 on silicon. Dkhissi et al. 33 showed by Density Functional Theory (DFT) calculations and kinetic Monte Carlo (kMC) simulations that the jump in growth rate during the first ALD cycle is the result of the metal precursor reaction with OH-groups already present on the SiO 2 /Si substrate surface. The degree of surface hydroxylation is determined by the substrate temperature and the chemical and physical preparation process. 34 Due to the consumption of most of the OH-groups during the first cycle and slow surface hydrolysis, they then observed a low growth rate until the coverage reached 100%. According to the authors, the rate of transition to a thin, continuous oxide film depends on the degree of surface hydrolysis during the water pulses, with the development of ionic structure occurring through densification. This accounts for the transition from molecular groups to the crystalline material and leads to an increase of the metal and oxygen coordination numbers. 33,35,36 Weckman et al. 37,38 performed extensive ab initio calculations on ZnO ALD on ZnO from DEZn and H 2 O. They showed that in addition to the standard ligand exchange reactions for DEZn, hydroxyl groups, monoethyl zinc (MEZn), and water molecules, many other processes, including densification, can occur during the precursor and oxidant reactions, eventually leading to crystalline ZnO. Gao et al. 30 gave experimental evidence of a reaction between grafted molecular ligands and the surface, as well as reactions between two grafted molecules in standing positions. Most generally, during ZnO ALD on ZnO, the Zn metallic precursor adsorbs to a surface oxygen site (e.g., water, hydroxyl group, or oxygen) and reacts with a proton of a neighboring hydroxyl group to form MEZn and release an ethane molecule. Densification increases the coordination numbers of Zn and O atoms and can occur prior to ligand exchange: i.e., Zn molecular groups (or O molecular groups) move from the oxygen sublattice (Zn sublattice) of the target ZnO wurtzite structure to the nearest neighbor vacant site of the metal (oxygen) sublattice.

In the present study, hydrolysis of the InGaAs surface is not as efficient as hydrolysis of the ZnO surface; this leads to a growth delay (regime I in Figure 1). Since the GPC behavior and surface coverage in the growth regime I are similar to those observed during HfO 2 ALD on SiO 2 , it is reasonable to propose that the growth in the regime I proceeds predominantly via densification mechanisms. By the end of regime I, at the atomic scale, the crystallographic structure can be described as embryonic wurtzite (according to XAFS spectroscopy) 26 . This experimental finding corroborates the existence of densification mechanisms in the very early stages of ZnO ALD on InGaAs.

As noted above, the amount of the water flow, i.e., the water pressure in the present case, impacts the growth delay (Figure 2), playing an important role in these mechanisms. We discuss this point further below.

B. Water pressure on transient regime I

We showed in Figure 2 that the water flow has a strong effect on the duration of regime I. We presume that increasing the water flow leads to an increase of OH-group density on the growth surface, curtailing the growth delay. [39][40][41][42] It is known that the oxidant flow can influence the initial stages of ALD by modifying the surface density of hydroxyl groups. For instance, Matero et al. 43 found that by increasing the water pulse time and flow, the growth rate initially increases before reaching a constant. They attributed this to an increase of hydroxyl group density on the surface after the water pulse. For substrate temperatures higher than 450 • C, the growth rate was found to decrease, partly due to decomposition of the surface hydroxyl groups. 44 Sweet and Parsons 45 performed in situ conductance measurements during ZnO ALD on polypropylene, nylon-6, SiO 2 , TiO 2 , and Al 2 O 3 substrates for growth temperatures between 100 • C and 175 • C. They showed that physisorbed water contributes to conduction, and that when water desorbs, the net conductance decreases. For most of the substrates, a growth delay was observed, and the conductance measurement showed water desorption during the delay. The authors suggested that the nucleation rate depends on the density of reactive hydroxyl sites on the growth surface.

In the present case, one can hypothesize that during the water pulse, the coverage of new OH-groups on the InGaAs surface increases for higher water pressures inside the reactor chamber. This could lead to an increase in the number of DEZn molecules chemisorbed or adsorbed on the InGaAs surface and a shorter growth delay. However, this assumption currently lacks theoretical support, and DFT calculations or Monte-Carlo simulations are out of scope of the present study. We do find that a long water pulse prior to the first ALD cycle does not change the growth delay. According to ab initio calculations performed by Weckman et al. for the case of ZnO ALD on ZnO, 37,38 water molecules adsorb to Zn atoms on the growth surface, with an amount dependent on the number of accessible oxygen sites near the bare Zn or MEZn sites. Interestingly, the authors showed that the adsorption energy for a water molecule on the Zn atom of MEZn is -0.4eV, while the adsorption energy for an adjacent second water molecule is -0.27eV. However, the additional water molecule decreases the ligand exchange activation energy from 1.15eV to 0.91eV. Therefore, an increase of the water pressure inside the reactor chamber can increase the number of chemisorbed water molecules (and so the water molecule cooperative effects); this, in turn, could lead to the adsorption of more DEZn molecules during the next DEZn pulse and favor ligand exchange and densification. Such effects could help to explain why the growth delay is curtailed when increasing the water pressure inside the reactor chamber (Figure 2). We note that the substrate temperature in the ALD window, 13,46 unlike the water flow, does not affect the initial growth mode.

C. Substrate temperature effect on ZnO growth

In section III B we reported that the substrate temperature is a parameter strongly affecting the texture and crystallization of the growing ZnO layer. In-plane surface diffraction shows no in-plane texture for any of the substrate temperatures used in our experiments. However, an increase of substrate temperature leads to the development of out-of-plane (001) fiber texture (see Figure 4); the effect is especially pronounced for sample 240. The appearance of (001) fiber texture was already reported for ZnO ALD on Si. When the deposition temperature is above 220 • C, the [001] growth direction is preferred. [START_REF] Tynell | [END_REF][START_REF] Boichot | [END_REF]47 The substrate temperature also affects the initial crystallization behavior. In agreement with a previous study, 26 Figure 5(a) and the post-growth TEM image in Figure 6(a) show that a poorly-ordered oxide layer forms on the InGaAs substrate at 120 • C prior to the growth of crystalline ZnO. By increasing the substrate temperature to 200 • C, it is clear from Figure 5(b) that for an equivalent layer thickness, the proportion of crystalline material is larger than that for 120 • C. In addition, the post-growth TEM image in Figure 6(c) shows that the thickness/amount of poorly-ordered materials has decreased. The ZnO layer adjacent to the InGaAs is almost fully crystalline. (Note that the total thicknesses for samples 120 and 200 are nearly the same). Similar crystalline transitions have already been reported for oxide ALD. Unlike our study, however, the results were obtained by post-growth characterization. Libera et al. 48 found that ZnO ALD on silica gel under similar conditions begins with an amorphous layer prior to crystallization. Aarik et al. 49 showed that the growth of ZrO 2 films on silicon and silica starts with the formation of an amorphous layer. An increase of deposition temperature from 180 • C to 600 • C leads to a decrease of ZrO 2 amorphous layer thickness from 50 to 5 nm. Similar results were also reported for HfO 2 films grown on silica and silicon by ALD. 50,51 In the regime of steady growth, we observe that the GPC obtained at 240 • C (0.22 nm.cy -1 ) is higher than the GPC value obtained for the three other substrate temperatures inside the ALD window (0.17 nm.cy -1 ). At high temperatures, outside of the ALD window, the thermal energy can be high enough to decompose the precursors (pyrolysis) and start additional reactions on the sample surface. 13,46 However, according to ab initio calculations, 52 the activation energy value for the pyrolysis of DEZn (or MEZn) is rather high (on the order of 2 eV or more), which precludes the reaction during ALD. Another possible mechanism that could explain the increase in GPC at high temperature stems from the results of ab initio calculations by Weckman et al. 37,52 . After a first ligand-exchange reaction between adsorbed DEZn and surface hydroxyl groups, a second slow reaction of MEZn to bare zinc atoms becomes possible. The later reaction leads to an increase of the GPC by increasing the amount of adsorbed DEZn (steric repulsion between Zn precursors is lowered) and the appearance of bare Zn sites for water molecules to adsorb to during the water pulse. This second reaction has an activation energy in the range of 0.92-1.52 eV, which is higher than the initial ligand-exchange reaction between the adsorbed DEZn and surface hydroxyl groups and is more likely at higher temperatures. At last, regarding the initial growth, we note that the growth delay is about the same for samples 120, 160, 200, and 240, unlike the effect of water flow. Why this remains uncertain, and further investigations are necessary.

D. Growth model of ZnO ALD on InGaAs

During the ALD process, the nature of the metal precursor or oxidant reaction with the surface strongly depends on the surface chemistry and functionalization. 53 In the present study, we showed that the early stages of ZnO growth on InGaAs are quite different from ZnO steady growth on ZnO. In Figure 7, we summarize and schematize the initial growth of ZnO on atomically flat InGaAs. In regime I, the metal precursor (DEZn) and oxidant (H 2 O) chemisorb at random positions to the substrate surface, surface reactions produce grafted molecules which cover gradually the substrate surface and undergo a densification mechanism.

Meanwhile, barely any growth has occurred in the direction normal to the substrate (Fig. 7(b)). By the end of the regime I, the InGaAs substrate surface is covered with an ultra-thin, poorly-ordered Zn oxide layer (Fig. 7(c)). When entering regime II, the growth rate and surface roughness increase due to 3D growth and the formation of grains. The transition from the regime I to II is clearly evidenced with the appearance on the XAFS spectra of the characteristic features of the wurtzite structure (see Figure S3 and the results of a previous study. 26,54,55 ) In regime II, the thickness curve versus cycle number (Figure 1) is reminiscent of substrate-inhibited growth of type II, 31 exhibiting the signature S-shape. After nucleation of the crystallization centers, the ZnO grains grow, and the surface roughness increases up to a maximum before decreasing after coalescence. Concomitantly, the growth rate increases non-linearly up to a maximum prior to decreasing and becoming constant after grain coalescence. 26 This behavior was initially described by a model proposed by Nilsen et al. 56,57 for simulating polycrystalline growth. According to in-plane X-ray diffraction (Figure 5), none of the films show long-range order at the start of regime II (regime IIa in Fig. 7c). Diffraction peaks are detected only when the in-plane size and the amount of crystalline material are large enough, as in regime IIb, (Figure 7(d)). The minimum thickness required for the transition from regime IIa to IIb is lower when increasing the substrate (growth) temperature. To explain layer crystallization during ALD, Hausmann and Gordon 58 proposed a growth model for HfO 2 and ZrO 2 ALD on silicon. The authors hypothesize that the growth of crystalline grains starts from a nucleus that appears at random on the surface of the amorphous layer. During the next ALD cycles, the crystallites grow in size, both in the direction perpendicular and parallel to the substrate surface, and new crystallization centers form. The crystallites eventually coalesce to yield a uniform crystalline layer. When the probability of a crystallization event is low, a poorly-ordered layer is created. The authors showed that higher deposition temperatures increase the number of nucleation events, leading to improved film crystallinity. Our experimental results generally agree with this model. Incidentally, based on the post-growth TEM image (Figure 6(d)) as well as on the diffraction intensity versus thickness trend (Figure 5(a) and (b)), it can be assumed that for sample 240 there is no evidence of growth in regime IIa. However, this issue remains open and deserves further in situ XRD and XAFS investigations during growth. Then, for all of studied samples, growth eventually enters the steady regime, i.e., the growth rate becomes constant (regime III, Figures 7(e) and 7(f)).

V. CONCLUSIONS

In summary, we conducted detailed investigations into the growth of ZnO on InGaAs by atomic layer deposition, which allowed the construction of a cycle-dependent growth model, as seen in Figure 7. While in the ALD window, growth takes place in different regimes depending on the total film thickness. Consequently, the results may be critical to those utilizing ultra-thin ZnO layers for device applications. We find that both in situ techniques during deposition and a variety of different synchrotron X-ray methods are essential for understanding the ALD process, especially at the earliest stages.

FIG. 1 .

 1 FIG. 1. Equivalent Thickness(XRF) of the deposited ZnO layers as a function of ALD cycle number for four different substrate temperatures: 120 • C (green squares), 160 • C (dark red circles), 200 • C (purple stars), and 240 • C (light blue triangles). Inset: Close-up of the Thickness(XRF) vs cycle number for the 240 • C sample for cycles 0-9.

FIG. 2 .

 2 FIG. 2. XRF curves measured continuously during in situ ALD at the same substrate temperature of 120 • C and for different water flows during the oxidant pulse: 0.6 sccm, 2.6 sccm, and 6.0 sccm. The straight line cross point with the cycle number axis gives a representative value of the onset of the steady-state growth. The value is reported in the inset as a function of water flow.

  ) and (b), respectively. The x-axis of Figure5corresponds to the equivalent thickness (nm) on bottom, which corresponds to Thickness(XRF) in Figure1, and cycle number (in some non-linear scale) on top.

FIG. 3 .

 3 FIG. 3. Reciprocal Space Maps (RSMs) or fast zap-scans measured at the end of ALD cycle number 40, 44, 48, 52, 58, 64, 70, 80, 90, and 100 (the cycle numbers are shown in the figures) for a substrate temperature of 200 • C. The RSM images are plotted in InGaAs reciprocal lattice units (r.l.u.). The images are background subtracted.

  Figures 6(a)-(d) show TEM images obtained after 100 ALD cycles for all of the samples. At 120 • C, an amorphous layer of material can be observed at the interface between the crystalline InGaAs substrate and ZnO grains. As seen in Figure 6(b)-(c), increasing the growth temperature improves the crystallinity, and the amount of amorphous material at the interface decreases. At 200 • C, one can observe that the amorphous layer thickness is drastically reduced. The TEM images obtained for the sample grown at 240 • C shows a thicker ZnO layer, approximately 16.5 nm, in agreement with XRR results (see FigureS1in the supplementary information), and the interface remains sharp, although the presence of some amorphous material cannot be excluded. However, the interface does not look the same that for 200 • C. This may have to do with the different growth behavior observed at 240 • C by XRF (Figure1). The crystallinity of ZnO grains is evidenced by the presence of sharp reflections in the electron diffraction pattern (see FigureS2in the Supplementary Information). Furthermore, the 002 reflection in the diffraction pattern is more intense. The inverse Fast Fourier Transform (FFT) of the 002 reflection (FigureS2) shows the dominant growth orientation of ZnO grains is along the [001] direction, in agreement with fiber texture discussed above.

FIG. 5 .

 5 FIG. 5. The integrated 100, 002, and 101 diffraction peak intensities (symbols) as a function of the ZnO layer thickness (bottom x-axis) and cycle number (top x-axis) for samples grown at (a) 120 • C and (b) 200 • C. Also shown are linear fits to the data.

FIG. 6 .

 6 FIG. 6. Cross-sectional TEM images of samples grown at 120 • C (a), 160 • C (b), 200 • C (c), and 240 • C (d), after 100 ALD cycles. The inset in Figure (b) shows the InGaAs diffraction plane perpendicular to the [110] zone axis.

FIG. 7 .

 7 FIG. 7. Model for ZnO growth on InGaAs for the 120 • C-200 • C substrate temperature range. We depict cross-sections for (a) the InGaAs substrate; (b) the sample in regime I, with poorly-ordered ZnO structure; (c) the sample after formation of the initial, wurtzite-like structure (regime IIa); (d) the sample after ZnO growth with a long-range order (regime IIb); (e) the sample after reaching steady growth and larger ZnO grains (regime III); (f) the sample after steady growth with a probable crystallization of amorphous ZnO (regime III).

  ACKNOWLEDGMENTSE.S. was supported by the LabEx Minos ANR-10-LABX-55-01. Financial supports for this work by ANR projects ANR-11-NANO-0014 and ANR-15-IDEX-02 are gratefully acknowledged. D.D.F. was supported by both an award from the Nanosciences Foundation and the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division. We acknowledge D. De Barros for the engineering assistance. We thank the European Synchrotron Radiation Facility (ESRF) for beamtime allocation (proposal number 82779) and facilities placed at our disposal at beamline ID3, and in particular T. Dufrane, H. Isern, and H. Lopez, for their help with the experimental setup.


Pedro A Bastos

Nelson Sadowski

Jean Vianei Leite

Jhoe Nelson

Kleyton Batistela

Gérard Hoffmann

Olivier Meunier

Chadebec

A Differential Permeability 3D Formulation for Anisotropic Vector Hysteresis Analysis

published or not. The documents may come

ODELING electrical devices possessing ferromagnetic sheets under variable magnetic fields may require, in certain cases, a high degree of accuracy. If the magnetic circuit does not have air gaps (as transformer yokes), hysteresis plays a relevant role on the device magnetic behavior. The problem becomes more complex if one wishes to consider the electrical sheets anisotropy [START_REF] Bastos | 3D modelling of a nonlinear anisotropic lamination[END_REF] and the electrical circuit coupling.

In [START_REF] Bastos | A new formulation using differential permeability based on the source-field method[END_REF], we introduced a formulation based on differential permeability coupled to the source-field method for solving non-linear problems. The source-field method has been previously developed and presented in several papers and it is also commonly called T-method [START_REF] Le Menach | Determination and utilization of the source field in 3D magnetostatic problems[END_REF]- [START_REF] Carpenter | Comparison of alternative formulations of 3-dimensional magnetic-field and eddy-current problems at power frequencies[END_REF]. When proposing [START_REF] Bastos | A new formulation using differential permeability based on the source-field method[END_REF], we pointed out that such an approach would allow solving hysteretic cases, which is now considered in this paper. The hysteresis is modeled by the Jiles-Atherton (JA) approach [START_REF] Leite | Inverse Jiles-Atherton vector hysteresis model[END_REF], [START_REF] Leite | Transformer inrush currents taking into account vector hysteresis[END_REF]. The work developed in [START_REF] Leite | Implementation of an anisotropric vector hysteresis model in a 3-D FE code[END_REF] differs from ours since it employs the magnetic vector potential and the inverse JA model. An interesting paper related to ours is proposed in [START_REF] Lin | A dynamic core loss model for soft ferromagnetic and power ferrite materials in transient finite element analysis[END_REF]; it differs from this paper using formulations often applied for losses evaluation and the vector hysteresis was not considered. Although the majority of the concepts used in this paper (anisotropy, differential permeability tensor, JA technique, electric circuit coupling, and source-field method) are well known, assembling them all in a 3-D FE program is the original contribution of this paper. To demonstrate the effectiveness of the proposed method, the TEAM Workshop Problem 32 is solved.

II. FORMULATION

With the differential permeability method, we have, for nonlinear materials

B = μ d H (1)
where μ d is the differential permeability tensor. H and B are magnetic field and induction, respectively. For the proposed vector hysteresis modeling, we utilize a time step procedure considering the differential permeability as a tensor.

As the time evolutes from tt to t, the corresponding time steps are i -1 and i . The variations of H and B are

B = B i -B i-1 and H = H i -H i-1 . ( 2
)
With the source-field method [START_REF] Bastos | A new formulation using differential permeability based on the source-field method[END_REF], [START_REF] Le Menach | Determination and utilization of the source field in 3D magnetostatic problems[END_REF], we have

H i = H i s -grad i (3)
where is the magnetic scalar potential and H s is the source field associated to the imposed current density as rot H s = J [START_REF] Bastos | A new formulation using differential permeability based on the source-field method[END_REF], [START_REF] Le Menach | Determination and utilization of the source field in 3D magnetostatic problems[END_REF]. H i-1 and B i-1 are known from the previous time step.

Considering

B i = B + B i-1 , (1)
, ( 2) and (3), we have

B i = B i-1 + μ d H i s -grad i -H i-1 . ( 4
)
The main equation on this development is

div B i = 0 ( 5 ) or div B i-1 + μ d H i s -grad i -H i-1 = 0. ( 6
)
Applying the Galerkin method on (5), we have

V N div B i dv = 0 ( 7
)
where N is the nodal shape function of a tetrahedron element and V is the domain volume. It can be written as

V N div B i dv = s(v) NB i • ds - V grad N • B i dv = 0.
The first term on the right-hand side is related to the classical boundary conditions for scalar potential [START_REF] Bastos | A new formulation using differential permeability based on the source-field method[END_REF]. The second one must be evaluated for the numerical implementation as

- V grad N • B i dv = 0 ( 8 )
or, using (4)

- V grad N • B i-1 + μ d H i s -grad i -μ d H i-1 dv = 0. ( 9
)
Let us remember that the vectors N and K, already presented in [START_REF] Bastos | A new formulation using differential permeability based on the source-field method[END_REF], are related by

H s = K I 0 (10)

A Differential Permeability 3-D Formulation for Anisotropic Vector Hysteresis Analysis

Joao Pedro A. Bastos In the previous work, we introduced a formulation joining two concepts: 1) the source-field technique and 2) the differential permeability method. It was shown that the resulting procedure produces accurate results for non-linear cases and it was favorably compared with the more classical approach considering the actual permeability. Here, we extend this formulation for vector hysteresis cases that are modeled by the Jiles-Atherton approach. It considers the magnetic anisotropy of the ferromagnetic sheets.

Index Terms-Finite element methods (FEMs), magnetic anisotropy, vector hysteresis.

I. INTRODUCTION

M

where I 0 is the current flowing in a coil conductor; K is the corresponding source field when this current is equal 1 A. Also, we will use the vector N expressed by curl H s = NI 0 .

With [START_REF] Lin | A dynamic core loss model for soft ferromagnetic and power ferrite materials in transient finite element analysis[END_REF] in the equation above, we have curl K I 0 = NI 0 and curl K = N [START_REF] Bergqvist | A simple vector generalization of the Jiles-Atherton model of hysteresis[END_REF] where K corresponds to the magnetic field created by an unitary current in a coil wire. N and K are necessary to accomplish the coupling between the electric circuit and the magnetic device. Now, let us consider the electric circuit equation

V m = R m i m + d m dt ( 12
)
where V m , R m , i m , and m are, respectively, the voltage, the resistance, the established current, and the magnetic flux linkage in a generic electric circuit m. From [START_REF] Bastos | A new formulation using differential permeability based on the source-field method[END_REF], it can be shown that the magnetic flux is given by

i = V b B i • K dv. ( 13
)
For the time step i , we have

V m i = R m i m i + d dt V b B i • K dv.
Here, we apply the derivative time discretization as

t V m i = t R m i m i + V b B i • K dv (14) t V m i = t R m i m i + V b (B i -B i-1 ) • K dv. ( 15
)
Using (4) we obtain

tV m i = t R m i m i + V b B i-1 + μ d H s i -grad i -H i-1 -B i-1 • Kdv tV m i = t R m i m i + V b μ d H s i -grad i -H i-1 • Kdv. (16)
Using a simplified notation G = grad N and also considering that the numerical integration is performed, [START_REF] Wang | 3-D FEM analysis in electromagnetic system considering vector hysteresis and anisotropy[END_REF] becomes

tV m i = t R m i m i + K T μ d K i m i -K T μ d G i -K T μ d H i-1 . ( 17
)
Using [START_REF] Lin | A dynamic core loss model for soft ferromagnetic and power ferrite materials in transient finite element analysis[END_REF], equation ( 9) is

V -grad N • B i-1 + μ d (Ki m i -grad i )-μ d H i-1 dv = 0
and, with the adopted notations

-G T B i-1 -G T μ d K i m i + G T μ d G i +G T μ d H i-1 = 0. ( 18
)
Arranging ( 17) and (18) in matrix form, we have

G T μ d G -G T μ d K -K T μ d G t R m + (K T μ d K ) i i i m = G T B i-1 -G T μ d H i-1 t V i m + K T μ d H i-1 . ( 19
)
Since we are dealing with several terms and matrix products in (19), it seems worthy to provide an implementation information related to array dimensions of terms (19). First, for a tetrahedron elements, G = grad N is a (3, 4) matrix. K is a vector depending on the number of circuits. Let us suppose that there are two circuits and then K is a (3, 2) matrix. We observe that K is related to H, which is calculated with tetrahedron edge elements [START_REF] Bastos | A new formulation using differential permeability based on the source-field method[END_REF]. Therefore, K is obtained by the product of the edge shape functions w(3, 6) by the circulation of the source field (as defined in [START_REF] Bergqvist | A simple vector generalization of the Jiles-Atherton model of hysteresis[END_REF]) along the six edges. There are two sets of such circulations since there are two circuits in this example. R is related to the circuit resistances. Supposing also two circuits, R is (2, 1) matrix. Now, let us consider the terms of (19). The term dimensions are:

1 As remark, the first four matrices above are assembled in the first line of (19), since they are related to the tetrahedra. The last two ones are assembled in the second line of (19) related to the two electric circuits.

)

III. PERMEABILITY TENSOR BY THE JA MODEL

If the magnetic flux rotates in an electrical sheet, the vector relationship between field and induction plays an important role in the device modeling. If one wants to consider the saturation effect as well as the hysteresis losses with the rotating flux, it is imperative to employ a vector hysteresis model.

Recently, several models have been proposed. Bergqvist [START_REF] Bergqvist | A simple vector generalization of the Jiles-Atherton model of hysteresis[END_REF], based on the scalar JA hysteresis model [START_REF] Jiles | Theory of ferromagnetic hysteresis[END_REF], proposed a vector model whose independent variable is the vector magnetic field. Leite et al. [START_REF] Leite | Inverse Jiles-Atherton vector hysteresis model[END_REF] proposed some modifications in the vectorized model in order to improve its numerical performance. In this last work, the model main equations are as follows:

dM = 1 -F χ • ↔ α - ↔ c • ↔ ξ • ↔ α -1 • F χ + ↔ c • ↔ ξ dH (20) F χ = χ f χ f -1 • χ f (21) ↔ χ f = ↔ k -1 • (M an -M) (22)
M an = M an (|H e |) H e |H e | . ( 23
)
where M is the total magnetization, H is the magnetic field vector, 1 is the identity matrix, χ f is an auxiliary vector, M an is the anhystereric magnetization given by the Langevin equation vector form, H e is the effective magnetic field given by H e = H+ Using (20), one can obtain the differential permeability tensor by the equation

dB = μ 0 1 + 1 -F χ • ↔ α - ↔ c • ↔ ξ • ↔ α -1 • F χ + ↔ c • ↔ ξ dH.
Some advantages of this model are its relative mathematical simplicity, easy numerical implementation, small parameters set, and numerical robustness. Furthermore, the model can represent anisotropy and reduces itself to a scalar model if the magnetic flux is unidirectional. More details about the model characteristics and implementation can be found in [START_REF] Leite | Inverse Jiles-Atherton vector hysteresis model[END_REF] and [START_REF] Bergqvist | A simple vector generalization of the Jiles-Atherton model of hysteresis[END_REF].

IV. EXAMPLE

As an example, we present the case proposed by the TEAM Problem 32 [START_REF] Bottauscio | Description of TEAM Problem: 32 A Test Case for Validation of Magnetic Field Analysis with Vector Hysteresis[END_REF]. In this case, it is necessary to utilize a vector hysteresis modeling since rotating fields are present in some regions of the structure. In Fig. 1, there is a threelimbed ferromagnetic core. The core has five Fe-Si 0.48 mm thick sheets. Therefore, the depth of the device (2.4 mm in Oy-direction) is much smaller than Ozx dimensions. It creates an additional difficulty, since the mesh may have a poor quality factor unless it is very fine (which would affect the computational time). This case could be calculated as a 2-D case, although our calculations were performed with the 3-D formulation here proposed. This problem has four different variations but we are interested on the CASE3 (as denoted in [START_REF] Bottauscio | Description of TEAM Problem: 32 A Test Case for Validation of Magnetic Field Analysis with Vector Hysteresis[END_REF]), which is appropriated for checking vector hysteresis modeling. Two windings having 90 turns each are placed on the external limbs and the voltage sources are shifted 90°. Each coil has a total resistance (external resistances are connected to the windings) of 11.42 . The peak voltage is, for both, 14.5 V and the frequency is 10 Hz. The full description of the problem can be found in [START_REF] Bottauscio | Description of TEAM Problem: 32 A Test Case for Validation of Magnetic Field Analysis with Vector Hysteresis[END_REF].

We provided the experimental hysteresis data in the vertical and horizontal directions. For their simulation, they used Preisach modeling [START_REF] Mayergoyz | Mathematical Models of Hysteresis[END_REF]. Using an optimizing procedure, we found the JA parameters presented in Table I. The corresponding B(H ) curve for the rolling (vertical) direction is shown in Fig. 2. There is a very good agreement between experimental and simulated hysteresis loops. The same agreement is also found for the transverse direction. The magnetic field in Oy-direction is negligible and, for this direction, we use parameters identical to Ox ones.

Because many calculation attempts were necessary and each simulation needed several hours, we chose a relatively coarse mesh with 9450 tetrahedron elements and 2288 nodes. As a graphical result, the following Fig. 3 shows the magnetic induction at four different time steps. Fig. 3(a) shows the whole structure. The other figures present the magnetic induction vector around the point P shown in Fig. 1. The rotational behavior of fields is easily observed. Fig. 4 shows the experimental and measured currents on the two windings and the results present excellent agreement.

For local quantities, we present the magnetic induction on the point P in Fig. 1. In Fig. 5(a), the Oz-direction induction values from the experimental bench and from the simulation are presented. In the Fig. 5(b), we have similar results for the Ox-direction. And the B-loci obtained from the previous Fig. 5(a) and (b) is shown in the Fig. 5(c). We also included results obtained from our 2-D FE system intended to solve vector hysteresis cases [START_REF] Leite | Finite element three-phase transformer modeling taking into account a vector hysteresis model[END_REF]. There are some differences among these results. When performing comparisons, it must noticed that the measured inductions are obtained through pick-up coils. These coils are 7.3 mm large in Ox-and Oz-directions, which represents a relatively large dimension. Therefore, measurements are obtained from magnetic fluxes, which are integral quantities and certainly smooth the measured values.

When considering convergence, two aspects must be seen: 1) for solving the linear system, the ICCG method is used; it normally converges well even though, in few time steps, the convergence is not reached; it is certainly related to the poor quality mesh, as already commented; 2) for the non-linearity related to B(H) material characteristics, at some time steps, the convergence is critical. To mitigate such difficulties, it is possible to apply some numerical techniques as variable time steps and under relaxation. The choice of the time step and the mesh coarseness play a considerable role on the convergence and the result accuracy. For one cycle 1200 time steps were applied.

Solutions for this TEAM problem have been seldom reported. In [START_REF] Wang | 3-D FEM analysis in electromagnetic system considering vector hysteresis and anisotropy[END_REF] results are shown. In this paper, we use current-driven windings (no coupling with the voltage sources) and the vector hysteresis phenomenon is considered only on parts of the yoke. In our simulation, the vector JA anisotropic model is used on the whole structure and the device is voltage fed. The numerical simulation is then simplified but it must be mentioned that, as in our simulation, their results present good accuracy. Considering the above analysis and in spite of some result differences, we estimate that our formulation is consistent.

V. CONCLUSION In this paper, we presented a formulation for solving vector hysteresis cases considering the coupling with electrical circuits. The inherent convergence difficulties were also discussed and the strategies to overcome them were applied with efficiency. The TEAM Workshop 32 was used for testing the proposed method and the results show a good agreement between measured and computed results.

  for G T μ d G:[START_REF] Biro | Computation of 3-D magnetostatic fields using a reduced scalar potential[END_REF][START_REF] Le Menach | Determination and utilization of the source field in 3D magnetostatic problems[END_REF] .[START_REF] Le Menach | Determination and utilization of the source field in 3D magnetostatic problems[END_REF][START_REF] Le Menach | Determination and utilization of the source field in 3D magnetostatic problems[END_REF] .[START_REF] Le Menach | Determination and utilization of the source field in 3D magnetostatic problems[END_REF][START_REF] Biro | Computation of 3-D magnetostatic fields using a reduced scalar potential[END_REF] → (4, 4); 2) for G T μ d K : (4, 3) . (3, 3) . (3, 2) → (4, 2); 3) for G T B i-1 : (4, 3). (3, 1) → (4, 1); 4) for G T μ d H i-1 : (4, 3) . (3, 3) . (3, 1) → (4, 1); 5) for K T μ d K : (2, 3) . (3, 3) . (3, 2) → (2, 2); 6) for K T μ d H i-1 : (2, 3) .[START_REF] Le Menach | Determination and utilization of the source field in 3D magnetostatic problems[END_REF][START_REF] Le Menach | Determination and utilization of the source field in 3D magnetostatic problems[END_REF] . (3, 1) → (2, 1).

↔α

  • M, and ↔ ξ is a matrix containing the derivatives of M an with respect to H e [7]. The tensors ↔ α, ↔ c, and ↔ k are related to material parameters. Two additional tensors not shown in equations above ( ↔ M S and ↔ a) with parameters related to the Langevin function are also necessary [7]. μ d can be obtained from (20) with the aid of the constitutive law dB = μ 0 (dH + dM).

Fig. 1 .

 1 Fig. 1. Device structure (dimensions in mm).

Fig. 3 .

 3 Fig. 3. Inductions in the structure. (a) t = 0.018 s. (b) t = 0.018 s. (c) t = 0.036 s. (d) t = 0.062 s. (e) t = 0.086 s.

Fig. 4 .

 4 Fig. 4. Current at the windings.

Fig. 5 .

 5 Fig. 5. Inductions at the point P. (a) O z magnetic induction at point P. (b) O x magnetic induction at point P. (c) B-loci at point P.

  1 , Nelson Sadowski 1 , Jean Vianei Leite 1 , Nelson Jhoe Batistela 1 , Kleyton Hoffmann 1 , Gérard Meunier 2 , and Olivier Chadebec 2

	1 GRUCAD/EEL/CTC, Universidade Federal de Santa Catarina, Florianópolis 88040-900, Brazil
	2 G2Elab, UMR CNRS 5269, Grenoble INP, Universit Joseph Fourier, Saint Martin d'Hères 38400, France

TABLE I PARAMETERS

 I OF THE JA MODEL Fig. 2. Experimental and calculated B(H ) curves for vertical direction.