J.-L Maurice
email: jean-luc.maurice@thalesgroup.com

D Imhoff

J.-P Contour

C Colliex

Interfaces in {100} epitaxial heterostructures of perovskite oxides

Keywords: perovskites, EELS, epitaxy, interfaces, oxide thin films

The exact perovskite structure has simple cubic symmetry and composition ABO 3 , where A is a relatively large cation and B a smaller one. The choices of A and B cations and the substitutions possible on either site generate a large variety of materials sharing the same base, with relatively small distortions of the size and shape of the cube. As in addition, these oxides often admit oxygen non stoichiometry with or without order to the amount of several per cent, they finally form a vast set of technologically relevant materials: conducting, insulating, ferroelectric, magnetic, superconducting,…. Heteroepitaxy of perovskite oxides allows one to construct atomically sharp interfaces between these materials and therefore to envisage a set of useful heterojunctions. The epitaxy has side effects that may also prove useful: (1) it forces a chemical neighbouring that would not occur naturally, creating a two-dimensional third material, and (2) it imposes a lateral strain.

Both of these effects allow one to explore novel, sometimes unforeseen, properties with a strong two-dimensional character. This paper first reviews some of the knowledge that has been accumulated on {100} surfaces and interfaces of perovskites, with an emphasis on properties that could be used in future all-oxide microelectronics. It then exposes the case of the interface between the half-metal La 2/3 Sr 1/3 MnO 3 and the insulator SrTiO 3 , which plays a key role in the magnetoresistance of magnetic tunnel junctions. It particularly presents thorough electron energy loss spectroscopy measurements that uncover the atomic scale structural and electronic properties of these objects.

what is probably the biggest challenge it has ever met with since Moore predicted its fate in 1965 [1]. Due to the scaling down of circuits, silicon's natural oxide SiO 2 will no longer fulfil the role of gate dielectric for transistors: if the trend of Moore's law is maintained, this oxide will shortly reach a thickness where electron tunnel trespassing becomes significant. This situation creates a unique opportunity for other candidate materials to replace not only the oxide, but also the whole technology and the material it is based on. Perovskite epitaxial heterostructures, which exhibit a wide variety of useful physical properties, are among these.

The perovskite family includes insulators with a high dielectric constant (e.g. SrTiO 3 ) that can be candidates for use as new gate dielectrics [2,3]. However, perovskite oxides span a vast range of physical properties: from insulating to semiconducting, conducting and superconducting, or in other respects from ferroelectric or piezoelectric to ferromagnetic, etc., depending on their exact composition. The replacement in standard MOS design of silicon itself by a semiconducting perovskite is under investigation [4]. This multiplicity is obtained within a same simple crystal structure never far from simple cubic. To describe the versatility of the family, Smyth [5] has introduced the concept of 'Perovskite space'. Thanks to the small structural changes from one compound to the other, they can form atomically sharp interfaces in epitaxy. New devices can thus be conceived based on their use in both passive and active parts [6][7][8].

Of course, as active regions will always include interfaces, one will want the latter as perfect as possible. However 'perfect' it may be, an interface at an atomic scale is an assembly of atoms for which several of the nearest neighbours are 'wrong', so that the physical properties there cannot be those of either of the two crystals in contact. This interface specificity is particularly important in heterostructures where a given crystal site can hold atoms of different valencies, as in the case of diamond and sphalerite semiconductors [9,10] or indeed perovskites. This gives rise to electrostatic frustrations -in insulating or semiconducting systems -or more generally to an interface-specific density of states that may widely differ from that of either of the two crystals in contact, as if the interface were a third material [11]. In other respects, electrostatic frustration at interfaces is also well known at grain boundaries of semiconductors [12] or insulators. The interest for this problem in heteroepitaxial perovskite structures is more recent, owing to the more recent development of the atomic-level control of growth for these materials.

The second point that makes heteroepitaxy of perovskites an interesting fundamental study is the interplay in these materials between the distortions and the electronic structure, through the Jahn-Teller effect [13,14]. The epitaxial strain must also be considered as a useful tuning parameter for the electronic, magnetic or ferroelectric properties [15].

The aim of the present paper is to shed some light on these yet little investigated interfacespecific properties. As an example, we present the La 2/3 Sr 1/3 MnO 3 /SrTiO 3 (001) interface.

La 2/3 Sr 1/3 MnO 3 (LSMO) is a ferromagnetic metal where only spin up electrons are present at the Fermi level ('half metal') [16][17][18] and SrTiO 3 (STO) is an insulator. Magnetic tunnel junctions made of the stacking LSMO/STO/LSMO, where the LSMO layers are ~20-nm thick and the tunnel STO barrier is ~2-nm thick, have exhibited tunnel magnetoresistance (TMR) ratios of about 2000% [18]. This magnetoresistance decreases with temperature much faster than the magnetisation of the two LSMO films. This has been attributed to the interfaces. After an atomic-scale analysis using electron energy loss spectroscopy (EELS), we propose here to explain how.

In section two, we give general information on the perovskite structure, its defects and the relationships between structure and properties; in section three, we describe how one can grow a perovskite layer epitaxialy on another perovskite and we introduce the importance of the choice of the terminating atomic layer on which to start the growth. In section four, we present our example of interface-specific properties in perovskites, which is that of the LSMO/STO (001) interface. We conclude in section five. §2. GENERAL INFORMATION ON PEROVSKITE OXIDES

Cubic structure

The perovskite structure has general formula ABX 3 , where A is a relatively large cation, B a smaller cation, and X an anion, oxygen in the type compound CaTiO 3 and in this paper.

Geometrically, the base perovskite unit cell is a cube which can be described in two ways: either with A ions at the corners and oxygen ions at the centre of the faces forming an octahedral cage around the B ion in the middle of the cube, or with B ions at the corners and the A ion at the centre of the cube (figure 1). The latter has the advantage of exhibiting the skeleton of corner-sharing oxygen octahedra. The space group of this base structure is Pm3m. In <100> directions, it is a stacking of {200} planes of alternating compositions AO and BO 2 , which indicates that two types of {100} surfaces can be found.

Intrinsic distortions

Depending on the size ratio of the ions, the oxygen octahedra are most often distorted, rotated or tilted over a small range; the results of these distortions can still be described by a pseudo cubic shape but adopt an orthorhombic (case of CaTiO 3 ) or rhombohedral symmetry (figure 2) [19].

The key parameter that causes these symmetry changes is not directly the ionic charge but the ionic radius [20].

Distortions and electronic structure

Jahn and Teller [21] have shown that distorting a highly symmetric atomic arrangement may minimise equilibrium electron energy. The effect that bears their names is particularly active in perovskites on the oxygen octahedra around B-ions (see e.g. ref. 14). An interesting point is the coupling by Jahn-Teller effect of the electronic structure with distortions due to epitaxial strain, in what would be electronic relaxation of strain. The cases where the centre of the oxygen cage is occupied by a 3d transition metal have especially been studied: for example copper in hightemperature superconducting cuprates (see e.g. ref. 13), or manganese in colossal-magnetoresistance manganites [22]. Figure 3 summarises the relationships between the d electron energy levels of a 3d transition metal at site B, and distortion of the octahedron in the z direction, a symmetry change typical of the epitaxial strain.

Ionic charge

The sum of the valencies of ions A and B must be six, with that of B greater or equal than that of A. One has to keep in mind, however, that the picture of six electrons localised on the oxygen ions and six holes on the cations is an oversimplification; the actual localised charge is fractional [23]. In keeping with the pseudo cubic arrangement, the choices for A and B ions are large, as are the possibilities of substitutions on either site and as is the range of oxygen departure from stoichiometry: this is why perovskite oxides span the vast range of physical properties we have A graph of some of these properties as a function of composition and point-defect content has been given by Smyth [5]. §3. HETEROEPITAXY OF PEROVSKITES

Growth technique

The deposition techniques for perovskites have undergone a tremendous progress during the development of high temperature superconductors. Physical as well as chemical deposition methods were tested. These techniques have been reviewed by Scheel et al. [24] for the case of YBa 2 Cu 3 O 7- X . A trend towards atomic layer epitaxy, which is necessary for the control of interfaces, has manifested itself since the beginning of the 1990s [25]. Although classical molecular beam epitaxy has been utilised [26], atomic layer control can be achieved by an a priori less precise technique which is pulsed laser deposition (PLD) [25,[27][28][29][30]. The reader can find general information on most of the available techniques in the review papers assembled in the MRS Bulletin of Sept. 1994.

We use PLD to prepare LSMO/STO/LSMO junctions such as the one presented in section 4.

Our growth conditions have been described elsewhere [31]. Two points worth mentioning are (1) that the targets are stoichiometric (so that controlling the surface termination of a growing film is not directly possible) and (2) that, in the particular case of the LSMO/STO/LSMO stack, the oxygen partial pressure is maintained during the whole growth at the relatively high value of ~0.3 torr (~40 Pa).

Substrate surface

In order to obtain eventually an atomically sharp interface, it is necessary to start from a perfectly flat surface. More precisely, with a view to using the specific properties of a given stacking sequence, the {100} starting surface must be everywhere of a given type, either AO or BO 2 . The unavoidable surface steps associated with miscut must have all the same height of a full unit cell. A surface step of half a unit cell changes the nature of the surface from AO to BO 2 (or vice versa) and is undesirable. Of course in reality, reconstructions occur that move the atomic positions [32,33].

Here, we only consider the type of sequence that a given surface will provoke, which is given by the chemical composition of the last {200} plane.

The chemical type of the surface can be characterised using different geometries of Rutherford scattering, e.g. low energy ion scattering spectroscopy (LEISS) or coaxial-impact- collision ion-scattering spectroscopy (CAICISS). (These techniques suppose a given atomic order at the surface, usually that of the bulk.) At a microscopic scale, a given type of surface may be recognised by measuring the friction force of a tip (friction force microscopy, FFM) [34]. However, correlating FFM measurements with macroscopic data is not straightforward, so that it is still necessary to perform one's own calibrations to ascertain whether AO or BO 2 is the toughest. In the case of the STO (001) surface, Tanaka et al., by monitoring the last single layer deposited in their layer-by-layer deposition equipment, have found the SrO termination harder [28]. Iwahori et al. have obtained the same result by comparing FFM and CAICISS data [35].

The domains of equilibrium (oxygen partial pressure, temperature) of a given termination -AO or BO 2 -are usually not known. In the case of SrTiO 3 (001), it is generally admitted that an anneal around 900°C, whether in ultra high vacuum [36] or under oxygen flow [33], produces a pure TiO 2 surface. Obtaining this surface can also be done by etching in buffered NH 4 F-HF [37].

The problem rests with the obviously less stable SrO-terminated surface. Nakamura et al. have observed by LEISS that the surface of a homoepitaxial STO film, grown by PLD on a substrate treated with the Kawasaki method [37], was SrO terminated in the conditions they used [38]. Other authors have used SrO [27,39] or Sr [28] targets to achieve SrO termination of their STO substrates or growing films. A drawback of these techniques, especially in the case of SrO target, is that one does not control whether the (002) atomic plane below the SrO surface plane is TiO 2 as it should, or if it is another SrO plane as in a Ruddlesden-Popper phase (see next section).

In our example of the LSMO/STO/LSMO tunnel junction detailed in section 4, the termination of the starting LSMO surface was one of the questions to be answered, knowing that we had no control on the substrate surface termination. The growth of LSMO onto TiO 2 -terminated STO is well documented. Yoshimoto et al. [40] on the one hand, Izumi et al. [41] independently, found by CAICISS that LSMO grown at low pressure on this surface was MnO 2 -terminated. The more recent work of Kumigashira et al. [42], performed by angularly resolved XPS, confirmed this result and also showed that, on SrO-terminated STO conversely, LSMO was La(Sr)O-terminated.

Quite unfortunately, our case of relatively high pressure growth is poorly documented. Yoshimoto et al. mention preliminary experiments where the effect of oxygen pressure would be to stabilise the La(Sr)O (001) surface [40]. The experimental investigation of any novel phenomena related to a given sequence at the interface poses the difficult problem of preparing surfaces that are unambiguously either AO or BO 2 : this is probably one of the major challenges in these studies.

Perovskite defects that can be found at epitaxial interfaces

Quite generally, performing the growth of single crystal films without defects is a challenge.

A first source of defects is the mismatch between the crystal parameters of the film and of the substrate and, as growth is generally performed at high temperature, its differential evolution with temperature.

Perovskite oxides respond very differently to epitaxial strain, depending on their plastic and elastic properties: for example SrTiO 3 is ductile at room temperature [43], whereas La 2/3 Sr 1/3 MnO 3 relaxes by fracture when grown at 850°C [44]. In all cases, the solution is to prepare layers thinner than the critical thickness t c (at which a first relaxing defect is introduced, see e.g. ref. 45). The actual critical thickness in standard growth conditions is usually neatly higher than the one that can be calculated at equilibrium, which is of the order of 10 nm for a misfit of 1% in the case of STO [45]. The actual critical thickness in the case of the growth of LSMO on STO (001), where the parameter misfit is ~0.8%, is ~150 nm [44].

It is quite important to note that the strain field of misfit dislocations extends over distances typically of the order of their period, at least several nm. This field has an important effect in such materials where bond length and angle are in close relationships with ionic charges, magnetisation or polarisability. Chu et al. have recently shown that distortions by this field in PZT (Pb(Zr 0.52 Ti 0.48 )O 3 ) ferroelectric nanodots had the effect of cancelling the polarisation in the regions considered [46].

In addition to a specific value of the crystal parameter, most perovskites have a specific noncubic symmetry so that a given pseudo cubic orientation corresponds to several orientations of the true rhombohedral or orthorhombic phase, which make as many variants in the film, separated by twin boundaries. However, twinning disorientations are small and twin boundaries moreover adapt them over a significant spatial extension [47], so that their effect close to the interface is probably small compared to the epitaxial strain. The manganite La 2/3 Sr 1/3 MnO 3 that is the object of section 4 is rhombohedral (figure 2) -and twinned in epitaxial films (see ref. [44] for details). Another defect which is specific to perovskites originates in the deposition of 'wrong' ions in the first layer (A instead of B or inversely). It leads to a fault in the perovskite stacking sequence at the interface. It can be either an A f O layer on an AO-terminated surface, or a B f O 2 layer on a BO 2 -terminated surface (where the index f indicates that the ion of type A or B belongs to the growing film). We are not aware of occurrences of the latter, while the former exists as stacking fault in bulk perovskites. The additional AO plane is then laterally shifted by ½<110> (where the indices refer to the perovskite cube). Structurally, it is equivalent to the replacement in the perovskite <100> sequence of an AO atomic plane by half a rock-salt unit cell of the compound AO; the new sequence actually forms stable phases when repeated, as described by Ruddlesden and Popper [48,49]. As mentioned in the previous section, the occurrence of such a fault would not be surprising when depositing the rock-salt compound AO on an ABO 3 perovskite substrate. §4. THE LSMO/STO/LSMO (001) INTERFACES

Generalities

Tunnel magnetoresistance (TMR) of a magnetic tunnel junction depends on the polarisation of tunnelling electrons [50]. These particles essentially originate from the very last layer of conductive material, at each interface of the two sides of the barrier. It is therefore of prime importance to know how the interfaces modify the bulk propereties.

In the case of magnetic perovskites such as manganites, magnetism and transport are related to the mixed-valency of B ions (Mn 3+/4+ in LSMO), which in turn depends on the valencies of the surrounding A ions (2/3 La 3+ and 1/3 Sr 2+ in LSMO). Ion B may be directly at the interface (type II in our previous work [51]) or 'protected' by an AO layer of its own material (type I in ref. 51). If the manganite is deposited first, type I corresponds to the configuration of figure 4a, and type II to that of figure 4b. In a sketchy approach, type I, where B (Mn) ions have bulk environment, will be less detrimental to the magnetic properties of the last layer than type II, where the environment of B ions at the interface is 'wrong' for half of it [52]. We shall see below that the two types actually correspond to opposite charge transfers, which will both modify the materials properties. In order to introduce the electrostatic side of the problem, let us briefly consider a case that has been the object of several works: that of the (001) interface between the insulating perovskites La 3+ Al 3+ O 3 (LAO) and Sr 2+ Ti 4+ O 3 [27,39]. When looking at the stacking in the [001] direction, LAO is an alternating pile-up of La turn this would inject 1/3 electron per unit cell in the former case, and 1/3 hole in the latter.

However as both Ti and Mn are mixed-valency ions, the actual charge at the interface would depend on whether these carriers be mobile or trapped by the cations, thus moving their valencies. Now introducing the fact that LSMO precisely carries charges by changing the valency of Mn ions, we can give more precision to the picture. In the interface of type I, the valency of Ti ions at the interface would be shifted towards 3+, or the released electrons would travel into LSMO and shift the valency of Mn ions over a screening length, on average also towards 3+. In the interface of type II on the contrary, the Mn ions at the interface would see their valency shifted on average towards 4+.

Tunnel magnetoresistance

Tunnel magnetoresistance across a manganite/STO/manganite trilayer was first demonstrated by Sun et al. [16]. Our work originated in electron transport experiments carried out by Viret et al. [17] on devices based on two electrodes of LSMO. The tunnel barrier was a two to three-nm thick insulating layer that could be made of either PrBa 2 (CuGa) 3 O 7 , CeO 2 or SrTiO 3 .

These structures were grown epitaxially by PLD. The highest magnetoresistance was obtained with STO as barrier material, but a sharp decrease was observed above 150 K (while the Curie temperature of the LSMO layers was above 350 K), which was attributed to oxygen vacancies in the vicinity of the interfaces [17]. Some progress has been made since then, but the electron polarisation still decreases faster at the interfaces than in the bulk with temperature [18,53].

Transmission electron microscopy

In order to understand the origin of this decrease well below Curie point, we have carried out a set of structural measurements by high resolution transmission electron microscopy (HRTEM) on the one hand, and of chemical and electronic measurements by electron energy loss spectroscopy (EELS) with the subnanometre probe of a scanning transmission electron microscope (STEM) on the other hand. We have first analysed the structure and composition of the very junction measured by Viret et al. [17]. Then, in order to study the residual Mn and La EELS signals collected after the apex of the interfaces into the barrier down to zero intensity, we have prepared the same system in identical conditions, where the STO barrier was 5.5 nm thick (figure 5).

Most of the results of our microscopic investigations have already been published in papers

where the reader can find all the technical details concerning our experimental conditions [47,51,52,54]. In the present paper, these results are revisited, and with the support of quite recent publications [55], some routes can be eliminated as possible explanations for the observed behaviour.

Electron energy loss spectroscopy

We focus here on EELS core edges. In such signals, the energy lost by incident electrons is transferred to core-level electrons that jump to energy levels in the conduction band above the Fermi level. As core levels are very narrow in energy, EELS core edges give in a first order approximation an image of the density of states immediately above the Fermi level, i.e. the density of empty states in the conduction band. In this study, several different edges were recorded and will be discussed in detail, and we will see how this simple approach has to be accepted or modified as a function of the electron levels involved in the transition.

In order to correlate unambiguously the recorded EELS spectra with their exact location of origin in the sample, the spectrum-imaging mode [56] has been used in a VG STEM microscope.

This instrument is equipped with a cold field emission source, delivering a minimum probe size of 0.5 nm, with a digitally controlled scanning unit, which can raster the incident probe over the investigated area (1D or 2D patterns and a position displacement step down to 0.2 nm) and a parallel EELS spectrometer including a new generation of CCD detector. For each probe position, EELS spectra are acquired over an energy-loss spectral domain incorporating all edges of interest, within typical recording times from tens to hundreds milliseconds for each core-loss spectrum with sufficiently high signal-to-noise ratio to be sensitive to weak changes of fine structures. These huge data sets are analysed and processed a posteriori, using the software that has been developed in our group for elemental mapping, energy loss deconvolution and multivariate statistical analysis.

Selected results extracted from these measurements are presented and discussed below. Figure 6a shows a sequence of spectra corresponding to the transition at the interface between the bottom LSMO layer and the insulating layer. Details of the evolution of the fine structures on the three most important signals O-K, Mn-L 2,3 and Ti-L 2,3 are extracted for more specific analysis (figures 6b, c and d).

As a general observation, there is no significant difference in any monitored EELS spectral feature between the top and bottom interfaces. This will be considered in section 4.3.3.

A second result is that, when going from the bulk of the LSMO film to the interface, the chemical shift of the Mn-L 2,3 edge is small and towards lower energy losses (see figure 9). When compared to the reference work of Abbate et al. [57], this result means that the MnO 2 planes are reduced, or electron-doped, in the vicinity of the interface. In our previous publications [51,52,54], we had explored several explanation of this electron doping. We had considerered segregation between the La and Sr cations of LSMO (so that there be a higher La/Sr ratio in the vicinity of the interface) and finally excluded it in regard to our recorded elemental profiles [54]. We had also discussed the presence oxygen vacancies in the vicinity of the interface, as proposed by Viret et al. [17]. We were not able to precisely define the main origin of electron doping.

We can now propose a new interpretation scheme following which the electron doping of LSMO at the interface with STO is essentially due to the fact that the stacking sequence is La 0.7 Sr 0.3 O//TiO 2 (type I), for which electrostatic equilibrium imposes the presence of extra electrons at the interface (see section 4.1.1). This result is opposite to the hole-doped (type II) configuration assumed by Yamada et al. [58] in a recent study of the same interface. This discrepancy might be related to different growth conditions. Let us now examine all the above mentioned possibilities versus our detailed EELS measurements.

La/Sr ratio at the STO/LSMO interface

Figure 7a shows an EELS map exhibiting the ratio of the La-4d and Sr-4p signals over a square area incorporating the two LSMO films on both sides of the STO tunnel junction. It does not show any significant variations over the analysed area in the bulk of the LSMO films. This is quite obvious when we plot profiles across this region, integrated over a few profiles perpendicular to the junction (see figure 7b). Both La/Sr and Mn curves have the half of their maximum value at the same probe positions and the distance between these half maximum value positions corresponds to 5.5 nm, within an accuracy better than 0.5 nm, i.e. the width of the insulating STO layer deduced from HRTEM (figure 5) or annular dark field images. It clearly indicates that there is no increase of the La/Sr ratio in the vicinity of the interface.

Oxygen concentration at the STO/LSMO interface

The departures of oxygen concentration from stoichiometry are much more difficult to assess. However, they can be searched for in the evolution of different signals when the beam is scanned across the interfaces. It can be directly on the O-K edge or indirectly in the associated transition metal L lines. Let us consider first the family of four spectra exhibiting the detailed profile of the oxygen K-edge, recorded on both reference materials LSMO and STO and at the apex of the two interfaces (bottom and top along the growth direction of the multilayer) (figure 8a). These last two are in excellent agreement, and they can be simulated as a linear combination of the two Muller et al. [55] have studied the evolution of the oxygen K edge for various oxygen deficient strontium titanate foils (SrTiO 3-δ with δ varying from 0 to 0.25). The spectra that they have recorded are shown in figure 8b for comparison with our spectra. The presence of oxygen vacancies in the STO layer when approaching the interfaces should appear through a broadening of the first line towards higher energy loss values and a vanishing of the second peak around 536 eV, which is contrary to the behaviour we observe. This effect constitutes a first hint of the absence of oxygen vacancies at the interfaces. However, one must recognize that it is difficult to extract definitive conclusions when considering only the O-K edge, because it is the dominant element present everywhere and weak variations in signal shape could be obscured by the general change of the O-K ELNES signal when evolving from the STO environment to the LSMO one.

An alternative solution, still in the STO layer, is to look for changes of the Ti L 23 lines when approaching the interface, while this signal drops to zero (no Ti present in the LSMO layers). Two spectra recorded at the top and bottom interfaces are superposed in figure 8c, after proper rescaling, on a spectrum corresponding to the centre of the STO tunnel barrier. No significant change can again be detected, while Muller et al. [55] have shown that the presence of oxygen vacancies should give a significant one: the four Ti L 23 lines, clearly resolved in vacancy-free STO and in our measurements, should broaden, mix and shift as the oxygen vacancy level (δ) increases (figure 8d).

The typical splitting of Ti-2p in four lines correspond to the superposition (figure 6d) of intra-atomic effects giving rise to two major lines corresponding to the excitation of the Ti 2p 1/2 (L 2 ) and 2p 3/2 (L 3 ), and of the crystal field effect inducing the extra splitting into t 2g and e g states (see figure 3). The presence of oxygen vacancies should indeed change these shapes for several reasons: shift of the average valency of Ti ions from 4+ to 3+, introduction of extra Jahn-Teller contributions to the splitting of the lines either directly or through the induced crystal structure distortions (figure 3). More generally, electron doping of STO would bring a change characteristic of the presence of Ti 3+ in the Ti-2p edge [59] None of these effects occur here. On the contrary, the stability of the detailed shape of the STO Ti L 2,3 signal, from the centre of barrier to the interfaces, is quite remarkable on the spectra shown in figure 8c, where the energy resolution has been improved down to 0.4 eV using the deconvolution methods developed by Gloter et al. [60]. The clear conclusion at this stage is thus that the concentration of oxygen vacancies in the whole STO layer, up to both interfaces, is close to zero. This statement is consistent with the high-pressure growth conditions (section 3.1).

Applying the same methodology to the manganese L 2,3 signal for tracking the possible presence of oxygen vacancies on the LSMO side of the interfaces is less favourable for several reasons associated with the fact that the 3d band is not empty in LSMO. Simple arguments on the nature and distribution of empty d states can no longer be used, because as shown by Kurata and Colliex [61] the white line profiles such as the Mn L 3 one are strongly influenced by intra-atomic correlation effects due to the coupling between the p hole and the d orbitals. We shall see below, however, that oxygen vacancies are not necessary to shift Mn valency and drop the electron polarisation at the interfaces.

The Mn-2p signal at the interface

Let us now focus on the evolution of the Mn-2p 3/2 (L 3 ) line at the interface. Figure 9 exacerbates the separation into two peaks as the displayed spectra correspond to a second derivative mode. Practically in the bulk of the film, the major peak lies at 642 eV and the secondary peak, which is nearly invisible in the bulk LSMO phase in normal mode, points out about 1.8 eV below.

When approaching the interfaces with STO, the peak splitting decreases by 0.2 eV and the secondary peak is sharper and its intensity increases. This is valid for both the top and bottom interfaces as they appear here as in other measurements quite symmetrical and equivalent.

In our previous paper dedicated to EELS [54], we have thoroughly discussed this evolution, notably with reference to the work of Abbate et al. [57]. We can now complete our comparisons.

Abbate et al. have recorded reference spectra of Mn-2p in the series La 1-x Sr x MnO 3 using X-ray absorption, with x varying from 0 to 0.9, i.e. Mn valency varying from 3+ to almost 4+ [57]. They paid a special attention to the two extreme compositions still compatible with the perovskite structure, namely La 0.1 Sr 0.9 MnO 3 and LaMnO 3 , for which they fitted the experimental spectra with multiplet calculations. Two peaks are present in these calculated and experimental Mn-L 3 lines, very much like in the present EELS spectra. In the series of spectra they have recorded, as the valency of Mn ion goes from 3+ to 4+, the Mn-L 3 signal undergoes essentially two monotonic changes: (1) the maximum of the Mn L 3 peak shifts by 1 eV towards higher energies, and (2) the splitting between the two peaks also increases from 1.5 to 2.4 eV [57]. As in our case the maximum shifts towards lower energies and the peak splitting decreases, we conclude that the Mn 3+ /Mn 4+ ratio increases at the interface, or else, that the last MnO 2 plane in LSMO is electron donated. The apparent increase of the pre-peak intensity in figure 9 is not associated with an increase of the splitting between the two peaks. In our previous work [54], we had proposed that it could be of essentially structural origin, due to the effect of the epitaxial strain on the distortion of MnO 6 octahedra. Actually two effects, the increased Mn 3+ /Mn 4+ ratio and the topology, should reinforce the Jahn-Teller splitting at the interface. In absence of proof, we maintain our earlier proposal that the origin of the enhancement of the low energy peak could be Jahn-Teller effect.

Regarding now the symmetry of the top and bottom interfaces, it implies that the first LSMO film ends up by an AO plane (viz. La 0.7 Sr 0.3 O), and that the thin STO layer ends up on the contrary with a BO 2 plane (viz. TiO 2 ). We have attributed this reversal to the fact that in the growth conditions used, these surfaces would be thermodynamically stable in respectively LSMO and STO. This is actually confirmed by the preliminary experiment of Yoshimoto et al. [40], in the case of LSMO, while TiO 2 is very likely the most stable in STO (see section 3.2).

Discussion

To summarise, we have shown with a careful analysis of EELS experiments that the Mn ions at the LSMO/STO interface present a modified d-band compared to the bulk of LSMO films. The EELS Mn-L 3 line exhibits a negative energy shift and a decreased splitting between its two main features, which we have attributed to an increased ratio of Mn 3+ or electron doping. Conversely, we have associated the greater sharpness of the minor peak with the interfacial distortion. The only sequence compatible with the increased ratio of Mn 3+ is MnO 2 /La 0.7 Sr 0.3 O//TiO 2 /SrO (type I). We attribute the shift towards 3+ to a transfer of electrons from the TiO 2 plane of STO, in contact with the La 0.7 Sr 0.3 O plane, towards the MnO 2 plane of LSMO.

The LSMO/STO interface has been compared, regarding its ferromagnetism, to interfaces of LSMO with other oxides. Yamada et al. [58] have used the sensitivity to surface magnetism of second harmonic generation to probe the interface magnetism of LSMO/STO, LSMO/LAO, and LSMO/two unit-cell LMO(LaMnO 3 )/STO. They have found that the interface magnetisation was the lowest for LSMO/STO, with the fastest decrease with temperature. They interpreted their results on the assumption that the LSMO/STO interface was a hole donator in their case. 49 in [22]). With such a view, both our approach and that of Yamada et al. [58] explain the decrease of magnetism at the interface. Such a conclusion is however no surprise when considering that the double exchange between Mn ions, at the basis of magnetism in LSMO, must be frustrated at an interface, be it of type I or II.

On the other hand, Garcia et al. [53] have measured the tunnel magnetoresistance of junctions made of LSMO/STO/LSMO, LSMO/LAO/LSMO, and LSMO/TiO 2 /LSMO. In that case again, although the low-temperature TMR was higher for the STO barrier, its decrease as the temperature increased was faster than for the LAO one. These junctions were made by one of us in the conditions used for the samples presented here, so that one can assume the same La 0.7 Sr 0. The goal of the present paper was to exhibit some of the latest advances in the preparation and characterisation of perovskite epitaxial heterostructures. These materials present a very large set of potentialities. Perovskite heterojunctions have been realised to obtain magnetoresistive devices [16][17][18], MOS structures [4], or 2-dimensional conduction at the interface between two insulators [39]. The effects of heteroepitaxial interfaces on ferroelectricity or bi-ferroicity of perovskites are starting to be explored [15]. Although the heteroepitaxy of perovskites is now a mature subject as it started in the late 1980s with the high temperature superconductors, the atomic-level control of it is only beginning. It appears as a wide field of research, with potential applications in very different areas of the microelectronics world, from ferroelectric memories to the devices that will replace An additional removal of degeneracy may occur due a lowering of symmetry associated with the Jahn-Teller effect (JT), the epitaxial strain, or to the presence of an oxygen vacancy. (The top interface however exhibits very similar features [54].) The spatial distance between spectra is 0.47 nm. An energy deconvolution technique has been used to improve energy resolution [60].

  Silicon metal oxide semiconductor (MOS) technology has to face in the forthcoming years

  with a weighting factor depending on the exact probe position. Non negative least square fit and multivariate statistical analysis reveal no new interface signal different from the mixing between LSMO and STO.

3 O

 3 termination of LSMO in all junctions. Thus the LSMO/LAO interface would correspond to the sequence MnO 2 /La 0.7 Sr 0.3 O // AlO 2 /LaO, for which electrostatic equilibrium would impose extra holes. The latter could therefore be less detrimental to the magnetism of LSMO than the electrons donated by LSMO/STO. Finally, Ab-initio calculations of the different types of interface configurations would be very helpful to fully understand the physics of these systems. §5. CONCLUSIONS AND PERSPECTIVES

Figure 1 .

 1 Figure 1. The perovskite unit cell ABO 3 , seen with A ions at the corners (a), or B ions at the corners (b). The ion sizes are smaller than in reality but have the right ratios. Oxygen ions that form the octahedra are not drawn in (b) for clarity.

Figure 2 .

 2 Figure 2. The rhombohedral unit cell of the manganite La 2/3 Sr 1/3 MnO 3 (a) still leads to a pseudo-cubic stacking of the oxygen octahedra (b). The crystallographic directions indicated refer to the pseudo cube (where the 'cubic' angle is 90.26°).

Figure 3 .

 3 Figure 3. Effect of varying the environment of a 3d transition metal at site B on its 3d electron states: the crystal field (CF) of the oxygen octahedron performs a first removal of degeneracy.

Figure 4 .

 4 Figure 4. The two types of interfaces obtained when growing a perovskite A f B f O 3 on the AO or BO 2 {200} surface of a perovskite ABO 3 . Depending on the valency of the cations, they may have opposite electronic properties (see text).

Figure 5 .

 5 Figure 5. HRTEM image of the sample analysed in figures 6 to 9.

Figure 6 .

 6 Figure 6. (a) Variations of electron energy loss fine structure (ELNES) across the LSMO/STO/LSMO stack shown in figure 5, using the spectrum-line technique. The evolutions of the O-1s, Mn-2p and Ti-2p edges across the "bottom" interface (where STO is grown on top of LSMO) is detailed in (b) to (d) respectively, after background subtraction.

Figure 7 .

 7 Figure 7. (a) Chemical map of the La to Sr ratio over the LSMO/STO/LSMO junction shown in figure 5. The values were extracted from the La-4d and Sr-4p spectrum images. (b) Profiles averaged parallel to the interfaces of the La/Sr atomic ratio (full line) and of the absolute Mn concentration (full circles). Acquisition time: 10 ms per spectrum. The fact that the two profiles coincide indicates the absence of any significant cation segregation.

Figure 8 .

 8 Figure 8. Comparisons of ELNES of O-1s (K-edge) and Ti-2p (L 2,3 edge) in the present case (a, c) and in recordings performed by Muller et al. [55] in SrTiO 3-δ samples with varying oxygen vacancy concentration δ/3 (b, d). (a) Comparison between the O-K signals in the bulk of the STO barrier and LSMO films and at the apex of the interfaces: interface signals are averages of the bulk ones. (b) Comparison of the Ti-L 2,3 signal from the centre of the barrier with those at the interfaces, after re-scaling for clarity: there are no significant differences. Note the sharpness of the peaks in (a) and (c) when compared to the broadening that should occur in the presence of oxygen vacancies in (b) and (d) (graphs b and d reprinted by kind permission of David Muller).

Figure 9 .

 9 Figure 9. Evolution of the ELNES of Mn-2p (L 2,3 ) edge across the LSMO/STO/LSMO stack of figure5, displayed in second derivative mode to exacerbate the fine structure. Spectra recorded when the centre of the electron probe is 0.9 nm within the barrier (where no Mn is present) best image interface-specific features. The vertical lines highlight a small amplitude shift towards lower energies when going from LSMO to the interfaces.

  Fig. 1

  Fig.3

Fig. 5

 5 Fig.5

  Fig.6

  Fig.7

9 Relative

 9 Fig. 8

  3+ O 2-and Al 3+ O 2- 2 planes, which carry respectively an electric charge of + |e| and -|e| per unit cell area, where |e| is the positive elementary charge. Whilst on the other hand, STO in this direction is a stacking of Sr 2+ O 2-and Ti 4+ O 2- 2 planes that are both neutral. Because the (002) planes are not electrostatically equivalent in LAO and STO, the (001) interface must carry a 'frustration' charge depending on the exact stacking sequence. To keep the configuration of figure 4, let LAO be the substrate; the two following cases can occur: (type I) the -ones have a charge of +2/3 |e| per unit cell. In such a case, the charge at the interface would be +|e|/3 per unit cell in the case of type I (MnO 2 /La 2/3 Sr 2/3 O//TiO 2 /SrO), or -|e|/3 in the case of type II (La 2/3 Sr 2/3 O/MnO 2 //SrO/TiO 2 ), and in

			3+ O 2-2 planes have an average electrostatic charge of -2/3 |e|
	per unit cell area and the La 3+	2/3 Sr 2+	1/3 O 2

starting surface is LaO-terminated as in figure

4a

, or (type II) the starting surface is AlO 2 -terminated as in figure

4b

. In a strictly ionic view with fixed valencies, the former corresponds to doping the structure with half an electron per unit surface cell, and the latter with half a hole. In order to experimentally study these two interfaces, Ohtomo and Hwang have prepared an STO (001) substrate with either TiO 2 -termination or SrO-termination, for respectively the interfaces of type I and II, and deposited LAO on it. If they did not obtain a doping effect with type II, they indeed obtained a tremendous (actually greater than 1/2 per unit cell) n-doping with type I interface (sequence: AlO 2 /LaO//TiO 2 /SrO), with quite high mobilities at low temperature

[39]

.

Although one of the films is conducting in our LSMO/STO interfaces, it is quite useful to submit them to the same analysis, just by replacing LAO by LSMO. Nominally in LSMO, in the absence of oxygen vacancies, the Mn 3.

  note that both possible types of interface -type I (electron donating like here), or type II (hole donating, like in the work of Yamada et al.[58]) -tend to create layers of properties equivalent to those of La 1-x Sr x MnO 3 with x ≠ 0.33. As x departs from 0.33 towards smaller values like here (electron doping), or towards higher values (hole doping), La 1-x Sr x MnO 3 has no longer the ferromagnetic properties of LSMO (see e.g. figure

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  CMOS technology. The greatest challenge at this beginning is for thin-film growers. A {100} perovskite surface has two variants: this makes it so interesting, but controlling surface termination means controlling the deposition of half a unit cell. This is, to our mind, where the biggest effort is needed. Then come the means of characterising the heterostructures obtained. We hope to have shown here, that in this regard EELS, performed with a subnanometre probe, is a unique tool that allow one to know altogether the nature, the valency, and somehow the site symmetry of the ions present at the interface.

	25/06/2010 Maurice et al. : Interfaces in perovskites
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ACKNOWLEDGEMENTS

The authors wish to thank M. Bibes (Institut d'Electronique Fondamentale, Orsay, France), A. Barthélémy and A. Fert (UMP CNRS/Thales), for fruitful discussions, A. Gloter (LPS Orsay) for critical reading of the manuscript, and É. Jacquet (UMP CNRS/Thales) for the PLD growth.


Dalil Brouri

Jean-Yves Laval

Marcin Zak

Claude Delamarre

Jean-Yves Laval

Espci Lps

J-Y Laval

Atomic structure, strain and chemical composition at the nanometric scale in Ge/Si quantum effect devices

Keywords: quantum dots, deformation, HRTEM

The miniaturization of IV-IV devices increases tremendously the role of stressinduced effects on the applied properties [1]. Mechanical stresses act in an ambivalent way: they may often constitute a technological lock but they can also open new fields of application as it is the case with quantum structures. Several stages in the processing of these devices can deeply modify the electronic properties but, up to now, the exact part played by local mechanical stress is not known. In particular, interdiffusion and segregation of species can interfere with mechanical effects. Therefore, to understand and optimise the properties of these components, one needs to gain combined information on the atomic structure, stress field and chemistry with a lateral resolution down to the smallest dimension of the components i.e. 1nm. This can be carried out only by High Resolution Transmission Electron Microscopy (HRTEM) and analytical TEM with a field emission gun (FEG). We combined X-ray nanoanalysis and high resolution observations with image processing in order to extract local deformations in silicon germanium quantum dots. Germanium quantum dots were grown at the Institut d'Electronique Fondamentale, Orsay [2,3]. The growth process was carried out by Ultra High Vacuum Chemical Vapour Deposition (UHV-CVD) on {100} silicon substrates. The pressure of the chamber was around 10 -10 Torr. The precursor gases were silane and germane diluted in hydrogen. We have investigated two kinds of Si-Ge heterostructures:

EXPERIMENTAL CONDITIONS

-Single Ge islands randomly distributed on the substrate. Sample A1 was grown at 700 °C with four monolayers (4 ML) of Ge deposited and sample A2 was grown at 800 °C with five to six ML of Ge deposited (1 ML = 0.1457 nm).

-Stacking islands (sample B1 and B2): In sample B1, dots were grown by selective epitaxial growth (SEG) on a patterned silicon {100} substrate at 650°C. The motif is a succession of lines and vias and we specifically observed islands in 0.4µm wide lines along <100>. Six ML's were deposited for the first layer and four ML's from the second to the seventh leading to a stacking of seven Ge dots separated by 9 nm thick Si layers. In sample B2, five Ge layers were self-assembled on the entire surface with constant Ge quantities separated by Si spacer layers of 22 nm. The islands obtained are randomly distributed on the surface and selfassembled vertically.

Thin-films with {110} cross-sections were prepared for HREM observations and nanoanalysis in TEM by mechanical polishing (tripode technique) perpendicular to the epilayer. The observations were carried out with a JEOL 2010 FEG electron microscope operating at 200kV equipped with a field emission gun and a PGT X-ray selective energy analyser. HREM images were obtained along <110> directions with an objective aperture corresponding to a cut-off of 29 nm -1. This aperture gives a point resolution of 0.19 nm and an information limit of 0.10 nm. Focal series were carried out to obtain the optimal defocus corresponding to a large area of dotted contrast. Simulations of the HREM images were performed with the JEMS software and showed that under such conditions large uniform areas with stable white dots (intensity maxima in images) could be obtained for a wide range of foil thickness and defocus values. We obtained experimentally and by simulations an optimal contrast for a defocus close to 1.2 times the Scherzer defocus in agreement with previous results [4]. The images were digitized with a sampling of 4 pixels/Å and 8 bit dynamics. Parts of images corresponding to 50 nm per 50 nm were processed. Image processing was achieved with routines written in Optimas v 4.0, Analytical Language for Images (ALI) and Spyglass Transform on a Pentium based computer following an algorithm which includes Wiener Fourier filtering with local noise estimation and high-low frequency removal. This procedure conserves information on lattice positions and improves signal to noise ratio. The stress field was obtained in two ways: (a) Intensity maxima localisation and (b) the "Geometric phase method", as described below: a-In order to obtain deformations from HREM images, we need a sub-pixel resolution in the localization of intensity maxima. This is obtained by the procedure proposed by Rosenauer et al [5] with a fit of four parabolas around each pixel of maximum intensity [6]. The processed area should contain a non-deformed zone where the lattice parameters were calculated by a Newton optimisation method on 5000 atomic columns. The template and deformed lattice were built up with a common origin and the displacement field was calculated at each experimental lattice point. A continuous field was then obtained by projection on a rectangular grid via interpolation and averaging with nearest neighbours [7]. Experimental strain maps were deduced by derivation. b-The "geometric phase" approach combines real and reciprocal space. Displacements are measured by calculating the local Fourier components of the lattice fringes. The phase of each of the Fourier components is simply related to the displacement. By calculating two-phase images for two different reciprocal vectors the displacement field is obtained [START_REF] Hÿtch | BAYLE Electron Microscopy 2A[END_REF]. To avoid artefacts in the calculations only images giving the same strains with these two methods are taken into account.

The conditions, for which the maxima of intensities represent effectively the {110} projection of the atomic structure and preserves exactly the interatomic distances, have been described previously [7,[START_REF] Kret | [END_REF]. On the other hand, as far as the "geometric phase method" is concerned, Plamann et al [10] have shown that for centro-symmetrical structures, astigmatism and changes in thickness do not influence the values of displacements. Furthermore, experimental strain field maps obtained via the 2 methods were compared with those obtained by finite elements calculations in GaAS/Ga 1-x In x As systems [11] using a continuous elasticity isotropic model. This enabled us to draw maps representing the indium composition. Effectively, these maps were in good agreement with X-ray nanoanalysis [12]. Consequently, these two methods can be applied to the determination of displacement, strain, stress and concentration in Si/Si 1-x Ge x systems. X-ray nanoanalysis was performed in EDX-TEM mode with a 1 nm probe. The Cliff-Lorimer factors were refined by measuring the Ge concentration on a calibrating sample. This consists of an heterostructure containing 3 germanium layers with germanium concentration of 11, 13 and 16 at% measured by Rutherford Back Scattering. The thicknesses of the layers were 120nm, 120nm, 50nm respectively and 50 nm for the silicon spacer. The calibrating sample was prepared under the same experimental conditions as used for the A 1 , A 2 , B 1 and B 2 samples. Excellent agreement was obtained on two of the layers and a mismatch of 1.5 at % for the third one. This could be due to border effects on the sample.

GERMANIUM CONCENTRATION

In order to analyse silicon and germanium interdiffusion in the quantum dots, the concentration of species were measured. For this purpose quantitative X-ray measurements were performed on a large number of quantum dots (about 30 for single islands and more than 10 for stacking islands). The quantum dots were probed along and normal to the growth direction at several points and the results are reported on representative islands.

A. SINGLE ISLANDS:

We observed hemispherical islands (Fig. 1) with a 100 nm width and a 20 nm height for sample A1 and 250 nm by 45 nm for sample A2. X-ray nanoanalysis measurements were performed and are reported on the TEM images (Fig. 1 and2). Diffusion of silicon inside islands is found and there is not a very significant variation in the composition. The Ge concentration is approximately 50-55 at % in sample A1 and 40 at % in A2. However, in addition to hemispheric form we found, in sample A2, islands with a shape intermediate between a dome and a pyramid (Fig. 2). As we can see in the TEM image, it has a truncated pyramid base of 300 nm, is longer than the "dome" islands, and 40 nm high surrounded with a 20 nm high dome. The composition is in the same range (a few % less) with a maximum Ge concentration around 40 %. Observations of cross sections along {110} were achieved on sample B1. We observed isolated islands (Fig. 3a) and two adjacent islands (Fig. 3b). The Ge layers are perfectly ordered vertically as was observed previously by Xie et al. [13] in GaAs/InAs quantum dots and in SiGe [14,15]. However there are anomalies in the shape and dimension for the first three layers. We can see that the spacer Si layer disappears between the three first layers whereas it is well established for the last layers (4,5,6,7). The nanoanalysis of heterostructure B1 (selective epitaxial grown islands) is reported in Fig. 4. There is an interdiffusion zone in the first three layers and the Ge concentration does not exceed 28 %. The concentration is maximum (40 %) in the 4 th layer and decreases smoothly down to 35% in the last layer. After the third layer the silicon layer is clearly distinguishable and there is no Ge interdiffusion between layers. The impacts of the nanoanalysis electron probe are visible in the different layers. In sample B2 the growth of quantum dots occurs on the whole surface of the substrate. The islands are 4-6 nm high with a spacer layer of 22 nm. As the Ge content was maintained constant, we observed an increase in island length from 100 nm in the first layer to 130 nm for the fifth one. Such an increase was reported in similar compounds by Le Thanh et al [16] and is a limitation for applications. Nanoanalysis measurements are reported in Fig. 5. We present data in the middle of the islands and laterally for each layer. The Ge concentration increases smoothly from 15 % in the first layer to 38 % in the fifth and the lateral concentration follows the same evolution with lower values (from 9 % to 26 %). It appears that although the islands are vertically stacked, there is dispersion in dimension and composition.

B. STACKING ISLANDS:

STRAIN CALCULATIONS FROM HIGH RESOLUTION IMAGES

HREM images of the islands were analysed to extract local deformations and composition by image processing. The procedure aimed to obtain optimal HREM images but this could be achieved only in the case of stacking islands (B1). For single islands, it was not possible to obtain very thin areas (< 20 nm) for high resolution images because the islands are not covered as in stacking islands and are affected by polishing. In Fig. 6 is shown an HREM image with a stacking of seven dots. Only half of the structure is represented. The two methods, localization of intensity maxima and the "geometric phase method" were used for the calculation of strains. Processed areas are represented by white squares. The strains ε X along <110> (x-axis) perpendicular to the growth direction (z-axis) are negligible for each processed area as shown in the cartography (Fig. 7). Strain maps along the growth direction ε Z are displayed in Fig. 8. A variation of 0.030 to 0.070 is observed in Ge whereas the strains are negligible in the Si layers. Except in the first three layers there is no diffusion between Ge layers. Since strains are negligible along the x-direction, stresses are created only in this direction and totally relaxed along z. Hence Elasticity equations in the Si 1-x Ge x reference give: Hence relative to the pure silicon reference these equations become:

σ ν ε σ ν ε ε ⋅ ⋅ = ∆ ⋅ - = ⋅ - - = = E a a E Z y x
0 ' ' = = y x ε ε a a Z ∆ ⋅ - + = ν ν ε 1 1 ' Now x a a ⋅ = ∆ 042 . 0
where x corresponds to the Ge concentration in Si 1-x Ge x . Since Poisson's coefficient is in the interval [0.27, 0.28], the Ge concentration deduced from the strain ε z ', can be written:

' 57 . 13 z x ε ⋅ ≈
From the strain maps, the Ge concentration was calculated for each layer and the result is reported in Fig. 9. The Ge concentration could be calculated only in the central part (white squares in Fig. 6) of the heterostructure which exhibits quite a regular contrast. This concentration is then found to be constant. It was shown by X-ray nanoanalysis that the Ge concentration decreases slightly towards the edges of the islands.

DISCUSSION

Diffusion of silicon inside the islands along the growth direction is found in both single uncovered and stacking islands but there is no diffusion of germanium inside the silicon spacers in stacked quantum dots. In uncovered islands, the Ge concentration was found to be nearly constant and decreases with the island's dimensions (50-55 at% for ~100nm length to 40 % for ~250nm length). However, in stacking islands, X-ray nanoanalysis measurements show also that there is Ge segregation inside the islands. The Ge concentration decreases by 10 % from the centre to the side in each layer. In stacking islands both diffusion and inter-diffusion were found. By X-ray nanoanalysis it was shown that in both selfassembled and SEG islands, Ge concentration increases for the first layers and then decreases slightly. Inter-diffusion is present only in SEG structures where the Si layer between islands becomes a few nm thick.

The germanium concentration in SiGe stacking islands measured by X-ray nanoanalysis was compared to calculations from HREM images. Except in the first two layers where interdiffusion occurs, the results are comparable using the two methods. There is good agreement for layers 3, 4, 7 but there is a 10 % difference between the two results for the fifth and sixth layers. This mismatch can be attributed to a topography effect that we found in the calibration sample and/or artefacts in the HREM image processing. Effectively, it should be noted that the calculations were carried out on areas of 50 nm by 50 nm, so it was not always possible to process simultaneously the islands and substrate. In this case, the silicon layers were taken as the template. This approximation was tested for the first layers where it was possible to carry out and compare the procedure with the substrate as well as with the Si layers. Selective epitaxial growth is assumed to give islands with uniform size and shape but, as found by electron microscopy, it is not the case for the first two layers due to interdiffusion. The growth conditions need then to be modified to optimise the structure. In this way, an interesting hypothesis was introduced by Le Than et al [16]. They attributed the increase in island length to a decrease in critical thickness induced by the stress field. Therefore Ge concentrations in the layers were adjusted to obtain "identical" islands (six ML's in the first and four in the others). However, this did not seem to be sufficient. Interdiffusion in the first germanium layers could be limited by increasing the thickness of the Si spacer layers but this could have influenced the critical thickness by stress field variations. Thus, we calculated the stress field from the strain maps. It was found to be negligible along the growth direction whereas values ranging from 2 -7 GPa were found perpendicular to this direction. These rather high stresses could effectively induce size variations in the stacking islands.

CONCLUSION

We investigated single islands and stacking islands (self-assembled and selective epitaxial grown) quantum dots. The germanium concentration was measured by X-ray nanoanalysis and calculated by image processing on {110} HREM images. We obtained fair agreement between the two methods. We mostly observed diffusion of silicon towards the germanium layers and interdiffusion is usually small between the heterolayers. However, strong interdiffusion was found in the first layers of the stacking islands. On the single islands, which were uncovered, a quasi uniform concentration was measured whereas in the stacking islands an increase in Ge concentration was observed towards the center of the islands. Changes in the shape and dimensions of the islands were found by HREM observations and give useful information on how to improve the properties of these quantum dots.

The juxtapostion of concentration maps obtained directly by X-ray nanoanalysis in FEG-TEM and by extrapolation of HREM experimental strain maps using elastic constants appears to be very efficient. With this approach, one can investigate the experimental factors that could give rise to artefacts. This leads to more precise measurements and an improvement in the reliability of the data. Finally, the combination of the two methods gives a better understanding of the atomic phenomena occurring during the growth of Si/Ge nanostructures which is key for optimising silicon germanium quantum devices.

  Atomic structure, strain and chemical composition at the nanometric scale in Ge/Si quantum effect devices

  σ x = σ y = σ and σ Z = 0 where σ x , σ y and σ Z correspond to the stresses along [100], [010] and [001] respectively.

  ε x , ε y and ε Z are the corresponding strains, a is the pure Si lattice parameter and E and ν are Young's modulus and Poisson's coefficient. The difference in lattice parameter between the alloy and pure silicon is given by

Fig. 2 : 9 Fig. 3

 293 Fig.1TEM image and X-ray nanoanalysis on single island quantum dot A1 (a) and A2 (b). Islands have mostly a dome-like shape and the Ge concentration is found to be about 50-55 at. % for A1 and 40 at% for A2

Fig. 4 X

 4 Fig. 4 X-ray nanoanalysis carried out on sample B1 for six layers. The local points in the layers are due to electron impacts and the large dark area at the bottom of the image is due to contamination as the image is obtained after analysis.

Fig. 5 X

 5 Fig.5X-ray nanoanalysis measurements on stacking islands quantum dots (B2). The island length increases from the first layer to the last layer and concentration is largest in the fifth layer (38 at%)

11 Fig. 9

 119 Fig. 9 Average germanium concentration in the centre of stacking islands obtained from the strain map. Averaged areas are shown with white rectangles.

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ACKNOWLEDGEMENTS

We are very grateful to D. Bouchier and Lam H Nguyen (Institut d'Electronique Fondamentale-Orsay) for the UHV CVD growth of the SiGe quantum dots.


E Barthel

A Perriot

A Chateauminois

C Frétigny

Elastic contact to nearly incompressible coatings -Stiffness enhancement and elastic pile-up

Keywords: thin-film mechanics, coatings, contact mechanics, elasticity, indentation testing, nanoindentation layer, thin film, coating, contact, elasticity, indentation, incompressibility

We have recently proposed an efficient computation method for the frictionless linear elastic axisymmetric contact of coated bodies [A. Perriot and E. Barthel, J. Mat. Res. 19 (

I. INTRODUCTION

Understanding the elastic contact to a coated substrate is a prerequisite to the analysis of more complex thin film behaviour. It is also an interesting problem because of two difficulties:

1. the coupling by the elastic field of planar parallel interfaces, which determines the response function;

2. the mixed boundary conditions usually involved in contact problems.

The problem has been dealt with in numerous publications, for example [1][2][3][4][5]. In a recent contribution, we have proposed a numerically efficient approach [6]. We first summarize this technique, insisting on the structure of the elastic response function on the one hand and on the treatment of the mixed boundary conditions on the other hand.

We also apply the resulting algorithm to the specific case of nearly incompressible or incompressible layer material. Compared to compressible layer material, the stiffness increases much more rapidly. At the same time, the dependance of the penetration upon contact radius is also strongly affected. More generally, the deviation of the penetration vs. contact radius relation from the homogeneous substrate solution could limit the direct applicability of an Oliver-Pharr approach to instrumented nanoindentation data treatment for coated substrates.

II. CONTACT TO A COATED SUBSTRATE

The present method is based on the elastic response function of a coated substrate calculated by Li and Chou [7]. The expression of the response function is complex but is characteristic of coupled planar parallel interfaces. We will first highlight these main features.

A. Response functions of coupled interfaces

The coupling of parallel planar interfaces through the layer of material 1 (thickness t) is schematized on Figure 1. In-plane symmetry suggests Fourier transform in the x, y plane (wave vector k). If the fields obey an equation of the

w 2 0 - d 2 dz 2 n D(k, z) = 0 for z < -t (1) w 2 1 - d 2 dz 2 n D(k, z) = A(k)δ(z -z ) for -t < z < 0 (2) w 2 2 - d 2 dz 2 n D(k, z) = 0 for 0 < z (3)
with adequate boundary conditions on the interfaces and at z = ±∞. A(k) is an excitation located on the plane z = z . For a harmonic field n = 1, and n = 2 for a biharmonic field. This general structure will be specified below along with the parameters w i .

Electromagnetic coupling between planar interfaces

The interaction of the electromagnetic field radiated by polarisable bodies at close distance results in the van der Waals interaction. Assuming that two such media with dielectric constants i and parallel interfaces are separated by a distance t, the field fluctuations [8] with wave vector k in the x, y plane and angular velocity ω n obey Eqs 1-3 with

w i = i ω 2 n + k 2 (4)
The response function can be calculated. For instance, the response at z = 0 to an excitation with wave vector k located at z = 0 (local response) is

D(0, 0) = - 2π w 1 1 D ( 5
)
with

D = 1 -exp(-2w 1 t)∆ 01 ∆ 12 (6)
and

∆ ij = w i -w j w i + w j (7)
This form of the response function is characteristic of coupled parallel interfaces. Indeed the denominator D is the determinant resulting from the solution of the linear system Eqs. 1-3. It couples the exponential field propagation factor in medium 1 (i.e. exp(-2w 1 t)) with the polarisability mismatch coefficients ∆ ij . These antisymmetric mismatch coefficients result from the boundary conditions at the interfaces, and appear quite generally in interfacial problems such as electrostatic image potential, Fresnel reflection coefficients or Dundurs elastic mismatch parameters. The response function D can be used to calculate van der Waals interactions. Indeed the secular equation D = 0 determines the coupled surface plasmons eigenfrequency from which the variation of the energy of the system with the distance t can be calculated.

Response function of a coated substrate

Similarly for our contact problem, we assume a coated elastic half-space under an axisymmetric frictionless loading (Fig. 2). The layer, of thickness t, and the half-space are elastic, isotropic and homogeneous, while their adhesion is supposed to be perfect. Let E 0 and ν 0 (resp. E 1 and ν 1 ) be the elastic modulus and the Poisson ratio of the half-space (resp. of the layer).

Due to axisymmetry, we use f the 0 th -order Hankel transform of f defined as:

f (k) = 0 ∞ dr r J 0 (kr) f (r)
instead of the Fourier transform. Here J 0 (x) is the 0 th -order Bessel function of the first kind which displays a cosine-like oscillatory behaviour suitable for the present geometry. Then, for a coated substrate, we fall under the framework of Eqs. 1-3 for linear elasticity. As is usual in 2-D elasticity problems, the fields obey a bilaplacian equation so that n = 2. We consider a static problem so that w i = k. Under these hypotheses, Li and Chou obtained a relation [7] between the applied normal surface stress q(k) (taken positive when compressive) and the displacement u z (k, z) (positive is inwards).

More specifically for z = 0 (with u z (k, 0) ≡ u(k)):

ku(k) = C(kt)q(k) (8)
where the response function is:

C(kt) = 2 E * 1 1 + 4b kt e -2kt -ab e -4kt
1 -(a + b + 4b(kt)

2 )e -2kt + ab e -4kt (9)

a = αγ0-γ1 1+αγ 0 , b = α-1 α+γ 1 , α = E 1 (1+ν 0 ) E 0 (1+ν 1 ) , γ 1 = 3 -4ν 1 and γ 0 = 3 -4ν 0 E * 1
being the reduced modulus of the layer defined as

E 1 /(1 -ν 1 2
). The structure of the response function is again characterized by the exponential field propagation factors and antisymmetric elastic mismatch factors for the field transmission at the interfaces. However, compared to electromagnetic response, the form is complexified by the bilaplacian-type field and the shear-free boundary conditions at the surface.

B. Boundary conditions

Contact problems such as indentation are characterized by mixed boundary conditions (Fig. 2): the normal surface displacement u is specified in the contact zone -by the penetration and shape of the indenter -while the normal applied stress q is given outside -usually zero -. Now Eq. ( 8) can only be used to calculate the surface displacement everywhere on the surface provided the normal surface stress is known everywhere on the surface. The response function Eq. 9 is therefore useless as such [7]. However, this problem can be circumvented by a mathematical trick (or change of basis, or use of auxiliary functions).

The method, which appears explicitly in the later papers by Sneddon [4,9], has proved fruitful for the description of complex contacts. For example we have been able to propose an exact solution to the long standing question of the adhesive contact of viscoelastic spheres in this way [10].

Algebraically the method relies on the relation

J 0 (kr) = r 0 cos(kt)dt √ r 2 -t 2 (10)
that is to say the Bessel function J 0 is the cosine transform of the function

Θ(r -t) √ r 2 -t 2 (11)
where Θ, the Heaviside step function, anticipates our mixed boundary conditions. The trick can also be viewed as transforming back by a cosine transform the variables which were transformed forward with a Hankel transform. We do not fall back in proper real space, but in a space where our boundary conditions assume a suitable form, due to Eq. 10.

Explicitly we introduce the auxiliary fields g and θ defined as [10]:

g(s) = 0 ∞ dk q(k) cos(ks) (12) θ(s) = 0 ∞ dk ku(k) cos(ks) (13)
Let us now apply the cosine transform to Eq. ( 8). Then: As a result of the boundary condition q(s) = 0 for s > a, g(t) = 0 for t > a where a is the contact radius. Then the upper bound in the spatial integral Eq. 14 is actually a, not infinity. The equilibrium equation 14 has now the form

θ(s) = 2 π 0 ∞ g(r) 0 ∞ dk C(
θ(s) = 2 π a 0 g(r)K(r, s)dr (16)
and a simple algorithm can then be devised. Indeed the function θ is known inside the contact zone for an arbitrary indenter shape h(r): from Eqs. 10 and 13 one obtains (s < a)

θ(s) = d ds 0 s dr rh(r) √ s 2 -r 2 (17)
This can be calculated analytically for most simple indenter shapes. In addition, the kernel K in Eq. 16, as defined by Eq. 14, can be calculated from the response function C(kt) by fast Fourier transform (FFT). Thus, discretizing Eq. 14, g(s) for s < a can be calculated numerically as the solution to a linear system. From g(s), s < a, force, penetration and contact stiffness can be computed [6].

Some of the results obtained with this algorithm have been presented earlier. In this paper, we want to insist on a specific case: when the layer is incompressible or nearly incompressible.

III. INCOMPRESSIBLE AND NEARLY INCOMPRESSIBLE COATINGS -EFFECTIVE CONTACT STIFFNESS

In our previous paper [6], we calculated the contact force P , the contact stiffness S and the penetration δ as a function of contact radius a for a large range of modulus mismatch and a single value of Poisson ratio ν = 0.25 for both substrate and film. These results provided a detailed description of the transition between the film dominated regime and the substrate dominated regime.

It is well known, however, that confinement of the layer at large contact radius values a/t 1 will result in specific phenomena for nearly incompressible materials [11]. Indeed, for such materials, volumetric deformations are penalized so that shear deformations predominate. In the present case, such deformations are hampered by the confinement. The response is therefore dependent upon the axial compression modulus in the absence of lateral strain -the so-called oedometric modulus of the layer [12] -

E o = E(1 -ν) (1 -2ν)(1 + ν) ( 18
)
Especially relevant is the case of a compliant layer deposited on a more rigid substrate. This could be a polymer film on a glass substrate for instance. Using our previous normalization scheme [6], we have calculated the response of the elastic frictionless contact of a sphere on a coated substrate for a film/substrate reduced modulus mismatch equal to 0.1. The numerics were carried out with the Igor data treatment software (Wavemetrics) on a standard 1.60 GHz processor. To probe the relevant part of the response function, a variable cut-off depth B = 3000a/t was used. The other parameters for the numerics are N 1 = 2 20 points for the cosine transform and the contact radius a was discretized over N 2 = 500 points. The resulting computation time for a given contact radius is of the order of 1 second. The results at large Poisson ratios were checked by increasing the computation parameters N 1 and N 2 without significant variations in the results. Fig. 3 displays the normalised contact stiffness, or effective reduced modulus, as a function of the normalized contact radius for Poisson ratios comprised between 0.1 and 0.5. The usual transition between film modulus (0.1) and substrate modulus, which is the normalizing parameter, i.e. 1, is readily obtained. The results are almost insensitive to the Poisson ratio ν for ν < 0.25. Sizeable deviation is recorded for 0.4 < ν < 0.5. In this range, we observe that the transition occurs earlier and is increasingly steep as the layer becomes less compressible. However, the system does finally reach the bare substrate reduced modulus.

For incompressible coating materials, this earlier saturation of the reduced modulus is essentially due to the elastic compliance of the substrate itself and is better evidenced from the surface and interface normal displacements. These displacements as computed by inverse Hankel transform from the discrete g functions obtained at various a/t ratios are displayed on Fig. 4. At low penetrations (a/t = 0.1), the substrate remains undeformed and the compressible and incompressible systems are undistinguishable. At larger contact radii (a/t = 1), the substrate starts to deform and the coating material is increasingly confined. For the incompressible material, an elastic pile-up of the coating material forms around the contact zone, while a global elastic sink-in results from the deformation of the substrate and increases with increasing contact radius. Generally speaking, these results illustrate the impact of the incompressibility on the partitioning of the elastic displacements between substrate and coating. Most noteworthy, at contact radius a/t = 8, for an incompressible layer, the surface displacement is almost completely due to substrate deformation; yet a roughly equal contribution from layer and substrate is calculated for a compressible coating material under the same conditions of confinement.

IV. SURFACE DEFLEXION AND INSTRUMENTED INDENTATION DATA ANALYSIS

With instrumented indentation, in the absence of direct measurement of the contact area, the Oliver & Pharr method is used to infer the contact radius from measured variables, i.e. force, penetration and contact stiffness [13]. One usually uses

h c = δ -ε P S ( 19
)
where S is the contact stiffness, P the force, δ the penetration and h c the contact depth. The form of the equation and the value of the constant ε are such that eq. 19 is exact for a purely elastic system. It has been experimentally demonstrated that eq. 19 is very useful also for elasto-plastic materials, mostly when plastic pile-up is minimal.

For the analysis of instrumented indentation on coated substrates, the same equation is used. However, Eq. 19 is no longer valid. Similarly, the usual relation between penetration and contact radius such as

δ = π 2 a tan β (20)
for a cone of half-included angle β breaks down. It is replaced by a more complex relation which involves the mechanical parameters of the system. This explicits the fact that Eq. 20 is a mechanical relation even though the mechanical parameters have accidentally dropped out for a homogeneous substrate. For coated substrates, some examples are plotted on Fig. 5. A salient feature is that small contact radii are more easily reached ( i.e. with smaller penetrations) for incompressible layers than compressible layers. This is due to the elastic pile-up effect. However, for a/t 4.5 a cross-over takes place. Larger radii are achieved by larger penetrations for incompressible layers because of the increased effective stiffness.

If we keep the form of Eq. 19 for coated substrates, we may attempt a more accurate approach by calculating the value of ε for a given coating configuration. Some results are displayed on Fig. 6. Note that in the transition region, ε drops to significantly lower values and that again the approach to incompressibility results in considerable variations. Values for ε as low as 0.2 may affect the data treatment in cases where the elastic contribution is significant (large S, ie sizeable elastic recovery). Due to the ease of calculation involved here, adequate ε values are readily calculated self-consistently during actual data treatment.

Finally, it is important to observe that failure to reach a correct evaluation of the contact radius is a double source of errors. A direct error incurs on the evaluation of the effective reduced modulus E * through

E * = √ πS 2β √ A ( 21
)
where β is the non-axisymmetry correction factor and A the contact area. A second error affects the evaluation of the layer reduced modulus from the effective reduced modulus because the model for the latter, such as discussed in section III, will be evaluated at an incorrect value of the contact radius. In the case of compliant films, these errors add up. An evaluation for ν = 0.2 and a modulus mismatch of 100 results in an error of up to 60 % at a/t 3.

V. CONCLUSION

Summarizing our approach to the elastic contact of coated substrates [6], we have shown that the form of the response function calculated by Li and Chou [7] is characteristic of the coupling of parallel planar interfaces through the elastic field. Using a new basis of functions well suited to the mixed boundary conditions, we obtain an integral relation that is easily solved numerically and provides force, penetration and contact stiffness as a function of the contact radius, for arbitrary moduli ratios and arbitrary axisymmetric indenter shape.

The stiffness of incompressible layers increases much more steeply with contact radius than more compressible coatings as soon as the layer is confined in the contact. Indeed volumetric deformation is strongly penalized while significant shear is prevented by the confined geometry. This is accompanied by sizeable elastic pile-up which significantly reduce the penetration needed to reach a given contact radius. For large contact radii, the stiffness of the layer dominates and the surface deformation is almost completely due to the elastic yielding of the substrate. Again, this phenomenon occurs at lower contact radii for nearly incompressible layers because of the enhanced stiffness.

The deviation from the homogeneous material penetration vs. contact radius relation presumably bears upon the validity of the Oliver and Pharr approach to instrumented indentation. A possible improvement for soft and quite elastic layers could be obtained by calculating more accurate values of with the present method. Fig. 3: Effective reduced modulus S/2a as a function of normalized contact radius a/t for a layer/substrate reduced modulus mismatch of 0.1 (E substrate = 1, E f ilm = 0.1) and different layer Poisson ratios. The substrate Poisson ration is 0.2. Fig. 4: Computed normal displacement u of surface (plain) and interface (dashed) for the contact of a sphere to a coated substrate (E substrate /E f ilm = 10). Radii are normalized to contact radius a, displacements to a 2 /R. The coating Poisson ratio is ν = 0.2 on the left, 0.5 on the right. Calculation parameters as in Fig. 3. The curves are offset by unit increments for clarity.

1 ¡ ¢ £ , ν ¤ ¥ ¦ § ¢ © § ¢ £ , ¤ ¥ ¤

  then the response function D obeys, in the notation of Fig.1,

7 CAPTIONSFig. 1 :

 71 Fig.1: Geometry of the coupling between parallel planar interfaces. The layer thickness is t.

Fig. 2 :

 2 Fig. 2: Schematic representation of the indentation of a coated elastic half-space.

Fig. 5 :

 5 Fig.5: Computed penetration as a function of normalized contact radius for a sphere on a coated substrate (E substrate /E f ilm = 10, ν substrate = 0.2) for various film Poisson ratio. The penetration is normalized to a 2 /R.

Fig. 6 : 5 .

 65 Fig.6: Computed values for the "constant" in Eq. 19 as a function of normalized contact radius and film Poisson ratio. Same parameters as in Fig.5.

FIG. 2 :

 2 FIG. 2:

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ACKNOWLEDGMENTS

The authors thank the Saint-Gobain group for its interest in fundamental thin film problems.