Acta Materialia 99 (2015) 1–6
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Direct observation of NiSi lateral growth at the epitaxial h-Ni2Si/Si(1 0 0) interface M. El Kousseiﬁ a, K. Hoummada a, T. Epicier b, D. Mangelinck a,⇑ a b
IM2NP, Aix Marseille Université-CNRS, UMR 7334, Faculté de Saint Jérôme, 13397 Marseille, France MATEIS, Université de Lyon, UMR 5510, INSA de Lyon, Bât. B. Pascal, 69621 Villeurbanne Cedex, France
a r t i c l e
i n f o
Article history: Received 14 April 2015 Revised 22 July 2015 Accepted 23 July 2015
Keywords: Ni silicide Lateral growth Interface Precipitate shape Model
a b s t r a c t The ﬁrst stages of NiSi phase formation at the expense of h-Ni2Si and a Si substrate are investigated by transmission electron microscopy (TEM). These measurements show the presence of a low density of NiSi particles at the h-Ni2Si/Si(1 0 0) interface and allow their complete shape to be determined. This stage corresponds to the lateral growth of NiSi at the epitaxial h-Ni2Si/Si(1 0 0) interface. The shape of these particles is in agreement with the predicted models, and the shapes were ﬁtted by an analytical expression derived from the model developed by Klinger et al. Ó 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
1. Introduction Ni-based self-aligned silicide is widely used as a contact and interconnection in ultra-large-scale integrated circuits . It is obtained by a solid state reaction between a Ni thin ﬁlm and the Si substrate. This reaction leads to the formation of d-Ni2Si and NiSi in the ﬁrst phase and the nucleation of the NiSi2 phase at higher temperatures. Previously, interest increased signiﬁcantly in low resistivity NiSi because of its foreseeable use as a contact to the source, drain and gates of CMOS devices. However, NiSi suffers from severe agglomeration above 650 °C, and it transforms into the more resistive NiSi2 phase above 800 °C. It has been demonstrated that the addition of a small amount of an alloying element to Ni ﬁlm, such as Pt, Pd, Mo or Re, reduces the agglomeration of NiSi and prevents its transformation into NiSi2 [2,3]. Therefore, the addition of 5 at.% Pt on the Ni ﬁlm was ﬁrst used to replace pure Ni, and the Pt content was increased from 5 at.% to 10 at.% in the microelectronics industry to enhance the stability of the monosilicide. For 30-nm-thick Ni (13 at.% Pt) ﬁlms, h-Ni2Si was observed to be the ﬁrst phase to grow . Another study conducted by Panciera et al.  conﬁrmed this result for thinner (10 nm) ﬁlms with a lower Pt concentration (10 at.% Pt) and showed the epitaxy of h-Ni2Si on (1 0 0)Si. Dekeyser et al. also found similar results for 4-nm ﬁlms of pure Ni . These contrast ⇑ Corresponding author. E-mail address: [email protected]
(D. Mangelinck). http://dx.doi.org/10.1016/j.actamat.2015.07.062 1359-6454/Ó 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
with a pure Ni–Si system where the diffusion-controlled growth of d-Ni2Si as the ﬁrst phase and the formation of NiSi at the expense of d-Ni2Si were observed [see Ref.  and other references therein]. It was also found that h-Ni2Si grows as a transient phase in coexistence with d-Ni2Si [3,8], although this phase is metastable below 825 °C. h-Ni2Si grows as the ﬁrst phase instead of d-Ni2Si for the Ni (10 at.% Pt) alloy ﬁlms currently used in microelectronic devices, and NiSi grows at the expense of the h-Ni2Si silicide. As a result, the formation of NiSi may change. Relatively little information is available on the growth of NiSi for the Ni (10 at.% Pt)/Si reaction; the presence of h-Ni2Si has been shown to inﬂuence the formation of NiSi [8–12]. Therefore, a better understanding of the mechanisms responsible for NiSi growth is needed for better control of NiSi contact quality. Differential scanning calorimetry (DSC) showed that the formation of a single product phase occurs in a two-step growth process for silicides [13–15] and other compounds [16,17]. Apart from DSC measurements, Lucadamo et al.  presented evidence for a two-stage reaction mechanism in Nb/Al multilayer thin-ﬁlms by TEM and in situ X-ray diffraction (XRD) experiments using high-intensity synchrotron radiation. Delattre et al. also found CoSi2 islands with irregular shapes at the CoSi/Si interface . The Al9Co2 phase was also identiﬁed  as the ﬁrst reaction product using atom probe tomography (APT): instead of a continuous layer, globular nuclei were observed at the beginning of the Al/Co reaction, and they quickly grew to a thickness of approximately
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10 nm before a dense layer developed. Also using APT, Hoummada et al.  found a Ni2Si particle with a shape in accordance with nucleation followed by lateral growth formation after the deposition of a Ni ﬁlm on a Si substrate. However, in both cases [19,20], the limitation of the APT ﬁeld view does not allow the total particle to be analyzed. To explain the two-step growth, a model was developed by Coffey et al. : the ﬁrst step is the nucleation and the two-dimensional in-plane growth of the initial interface up to the coalescence of the product phase, and the second step is the thickening of the product layer by growth, perpendicular to the interface plane. Other models were proposed to simulate mainly the lateral growth along the interfaces during the solid state reaction [13,20,22] and/or during the peritectoid reaction  (a + b ? x) at low temperature. These models are based on different approximations and different phenomena. However, all of the models consider the diffusion along the interfaces and they conclude that the product phase should reach a stationary thickness that depends on the kinetics parameters, in accordance with the experimental results [14–17,19]. The models also led to a relatively similar particle shape. However, the experimental studies on the ﬁrst stages of the phase formation along the interfaces have never shown the full particle shape during its lateral growth, so they cannot be compared to the models. In this paper, the ﬁrst stages of the NiSi phase formation at the expense of the h-Ni2Si phase have been investigated by transmission electron microscopy (TEM). These analyses observed the NiSi lateral growth step at the h-Ni2Si/Si interface and determined the full shape of the particle. A model developed by Klinger et al. was modiﬁed to ﬁt the shape of the particles, and good agreement was obtained with the TEM images.
Si Ni 2
Pr ot ec
Ten-nanometer-thick Ni (10 at.% Pt) ﬁlms were deposited by magnetron sputtering on (1 0 0)Si substrates. The (1 0 0)Si substrates were cleaned with diluted HF prior to loading into the sputtering chamber. The deposition was performed in a sputtering deposition setup with a base pressure of 1.3 108 mbar using a 99.99% pure Ar gas ﬂow and a 99.99% Ni(Pt) target. The wafer was rotated during the deposition to improve the homogeneity of the layer. Then, the reaction between the Ni(Pt) ﬁlm and the substrate was followed by in situ XRD. For XRD measurements, the samples were loaded into the XRD chamber, which was equipped with a heating stage and maintained under an ambient vacuum of approximately 105 mbar. In situ XRD analyses were performed after increasing the temperature from room temperature to 150 °C at a rate of 30 °C/min. The temperature was then increased by 5 °C steps and kept constant during the XRD measurements, which typically lasted for 6 min. Isothermal measurements were also performed. TEM measurements (TITAN microscope equipped with an image Cs-corrector and operated at 300 kV) were performed by cross-sectional views on samples prepared by a focused ion beam dual beam instrument (FIB, FEI Helios600 NanoLab) along the direction (1 1 0) of Si after deposition of a protection layer.
beginning of the NiSi formation and to select a sample corresponding to the ﬁrst stages of the NiSi formation for the present TEM study and APT analysis. An APT analysis was conducted later, however, to analyze the chemical composition of the h-Ni2Si phase. The sample for TEM was annealed by in situ XRD using the same conditions as the sample used in Fig. 1 up to the temperature of 250 °C (black line in Fig. 1): it was then hold at 250 °C and the annealing was stopped after the ﬁrst appearance of the characteristic peak of
2. Experimental Setup
Fig. 1. In situ XRD diffraction measurements during annealing of 11 nm Ni (10 at.% PT) deposited on a Si(1 0 0) substrate. The black line shows the annealing performed on the sample to analyze the beginning of NiSi formation.
tio la ye r
Fig. 1 shows the three-dimensional view of the in situ XRD measurement for the reaction of 11 nm of Ni (10 at.% Pt) with (1 0 0)Si. The peaks at 44° and 56° correspond to the Ni(Pt) ﬁlm and NiSi, respectively. During the Ni(Pt) consumption, no XRD peaks were detected because of the formation of the h-Ni2Si phase in epitaxy with the Si substrate . In situ XRD was used to determine the
Fig. 2. Conventional TEM micrographs of the 250 °C annealed Ni (10 at.% Pt) sample observed in the cross-section along a h1 1 0i Si direction: (a) low magniﬁcation overview; (b) high magniﬁcation micrograph.
M. El Kousseiﬁ et al. / Acta Materialia 99 (2015) 1–6
NiSi at 2h = 56°. The TEM cross-sectional views presented in Fig. 2 show the different sample layers, and a continuous thin layer of Ni silicide that was identiﬁed as the h-Ni2Si phase is observed on the Si substrate. At the h-Ni2Si/Si interface, some particles appeared with an elliptical shape; they are marked with numbers in Fig. 2(a), and a zoomed image of one sample is shown in Fig. 2(b). In Fig. 2(a), four particles are present at the h-Ni2Si/Si interface; they correspond to the NiSi phase that forms isolated particles instead of a continuous thin layer. From the TEM observations, the distance that separates the particles varies between 0.8 and 1.2 lm, and the average distance between the particles is estimated to be approximately 1.1 lm. The density of the NiSi particles is low, approximately 1 nucleus/lm2. The morphological features (the complete shape and size of the particles) can be obtained from TEM measurements. The particle shown in Fig. 2(b) at relatively high magniﬁcation exhibits an elliptical shape as observed in all of the NiSi particles. The length of these particles varied between 130 and 380 nm, and the thicknesses of their middle varied from 13 to 17 nm, respectively. The three-dimensional NiSi particle shape can thus been deduced from these measurement and is approximately cylindrical with a diameter much larger than its height and with edges in an asymmetrical lens shape.
4. Discussion As previously discussed, the ﬁrst stages of formation during reactive diffusion are associated with nucleation and lateral growth. The NiSi particle size observed in this study is very large compared to the typical critical nucleus size needed for nucleation. Indeed, the formation of a critical nucleus requires ﬂuctuations in composition [24,25], and this should limit the critical size to within a few nm3. In this case, the interface energies and the driving force are unknown, and it is impossible to calculate the critical size for nucleation. However, an estimate may be made using typical Gibbs’ free energies (a few ten of kJ/mol) and typical interface energies (a few hundreds of mJ/m2). The situation observed in Fig. 2(b) is certainly not the ﬁrst stage of nucleation but a later stage of growth. Moreover, the TEM micrographs show that the aspect ratio of the nuclei is relatively large (between 10 and 20), and the particle did not consume the entire thickness of the h-Ni2Si phase, which indicates a fast lateral growth compared to the normal growth of the NiSi nuclei. Several experimental studies [14–19] reported the presence of a discontinuous phase as the ﬁrst results of the reaction between the two other phases. However, the entire particle shape has not been reported; thus, it is not possible to compare these experimental results with existing models [13,20,22,23]. The TEM results provide a direct observation of the particle shapes, which are similar to that proposed in these models. They also highlight that the formation of the NiSi phase begins by the nucleation and lateral growth at the h-Ni2Si/Si interface during the reaction of Ni (10 at.% Pt) ﬁlms with Si. Indeed, even the very simple shape (cylindrical particles) assumed in the Coffey model  is similar to the shape observed in this study because NiSi particles can be approximately assimilated to cylinders. However, the TEM results provide more information on the shape, which can then be more quantitatively compared to the following models. The models of Lucenko  and Vovk  need numerical calculation and require several unknown parameters. The Klinger model  leads to an analytical solution that is easy to handle, so it was chosen to ﬁt the particle shapes in this study. However, Fig. 3 shows that the position of the NiSi particle is not symmetrical with respect to the h-Ni2Si/Si interface. The NiSi particles are more developed on the side of the h-Ni2Si phase
Fig. 3. HR-TEM image of a NiSi particle obtained on a 250 °C annealed Ni (10 at.% Pt) sample observed in the cross-section along a h1 1 0i Si direction. The superimposed yellow lines correspond to the ﬁt deduced from the modiﬁed Klinger model (see text for details). (For interpretation of the references to colour in this ﬁgure legend, the reader is referred to the web version of this article.)
compared to the side of the Si substrate. This asymmetrical shape is explained by matter conservation during the reaction (h-Ni2Si + Si ? 2NiSi), taking into account the atomic volume of the different phases. The ratio between the consumed thicknesses of Si(HSi) and h-Ni2Si (HhNi2 Si ) obtained by TEM (0.36 on average from several particles such as those in Fig. 2(b)) is close to the expected value (the theoretical value depends on the composition of h-Ni2Si, as explained later). In the Klinger model, it is assumed that all of the phases have identical atomic volumes. This is not the case for the Ni/Si or Ni(Pt)/Si systems, however, because the atomic volume of Si (20 Å3) is approximately twice the volume of the silicides (11 Å3). The model was thus modiﬁed to consider the different atomic volumes for the three phases. The main assumptions of the Klinger model are as follows: (1) the asymmetrical position of the particle with respect to the h-Ni2Si/Si interface results from matter conservation during the reaction between h-Ni2Si and Si, (2) the mechanical equilibrium of the interfacial energies is responsible for the particle shape and (3) the Ni and Si interdiffusion along the interfaces drives the kinetics of the fast lateral growth. The Ni and Si elements are thus considered to diffuse in opposite directions along the Si/NiSi and h-Ni2Si/NiSi interfaces, as shown in Fig. 3. The diffusing element ﬂux along the interface occurs in response to the driving force due to the gradient of the chemical potential difference that depends on the curvature gradient. Moreover, to calculate the steady state shape of the moving interface and its velocity, the ﬂux is considered together with a local mass conservation condition across the moving interface and the boundaries. From the parameters shown in Fig. 3, the main formulas used from the Klinger model are modiﬁed to consider the difference in atomic phase volume. Going forward, phases h-Ni2Si, NiSi and Si (diamond structure) are referred to as h, g, and D, respectively. First, the condition at the triple junction between the three phases is expressed; this condition is the continuity of ﬂuxes equivalent to a global mass condition:
HDg ¼ mD H and H#g ¼ mh H mD ¼
xh xg XD and mh ¼ 1 ma xh xD Xg
H is the thickness of the particle and HDg and H#g are the thicknesses of g on the D and h side, respectively, as shown in Fig. 3. The thickness ratios (mh and mD) are calculated from the phase
M. El Kousseiﬁ et al. / Acta Materialia 99 (2015) 1–6
concentrations and atomic volumes. Parameters x/ and X/ are the mole fraction and atomic volumes for the / phase (/ = h, g, D), respectively. Note that, even if the total volume is roughly conserved, HDg and H#g are different from the thicknesses of D and h consumed by the formation of the g particle (HD and Hh ) since the atomic volumes of the different phases are not equal. This is particularly true for D since HD 53 HDg due to the larger atomic volume of Si. Secondly, because the triple junction is bound to move along the Si/h-Ni2Si interface, a mechanical equilibrium condition is imposed, which involves the projected surface tensions along the Si/h-Ni2Si interface (Fig. 3). It is written as:
cDg cos aD þ chg cos ag ¼ cDh
cDg ; chg and cDh are the interface energies shown in Fig. 3, and aD, (ah) are the angles between cDh (chg ) and the Si/h-Ni2Si interface. Thirdly, the chemical equilibrium at the triple junction is written using a variation of the chemical potential with the curvature: DG0 ¼ mD XDg K Dg cDg þ mh Xhg K hg chg
where K Dg is the interface curvature between D and g, and K hg is the interface curvature between h and g. Following Chuang and Rice  and Klinger et al. , the differential equation governing the shape of the moving h/g interface is:
ðch cg Þ V ¼
Lhg Xhg chg @ 2 a 2 xh xg @l
where a is a local angle between the h/D and h/g interfaces, as shown in Fig. 3. V is the interface velocity, l is the curvilinear coordinate along the moving interface, and c is the concentration equal to x/X. Lhg represents the atomic mobility along the h/g interface. This differential equation has an approximate solution very close to the exact solution  that can be expressed as:
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ! pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ pﬃﬃﬃ 2 þ 4 þ y2 2 pﬃﬃﬃ x ¼ 4 þ y 2 log ð1 þ 2Þy
The best particle shape ﬁt from Eq. (6) is superimposed on the TEM images of Figs. 2(b), 3 and 4. Although it is not always easy to deﬁne the interfaces, the simulations ﬁt reasonably well within the particle limits in each case with the same parameters used for all ﬁts. Table 1 gives the values of the parameters used to ﬁt the shape of the precipitates. In order to minimize the ﬁtting parameters, most of the parameters were kept constant for the ﬁt: i.e., only the interfacial energies were varied in order to ﬁt the shape of the precipitates. The range of their variation (dc) is indicated in Table 1. Among the ﬁxed parameters, the composition and the atomic volume of NiSi and Si are known, but they do not have unique values for h-Ni2Si because this phase is not stoichiometric. However, an atom probe measurement (not shown here) of this sample showed that the composition of h-Ni2Si is approximately constant and is equal to 40 at.% Si. An average value of the atomic volume for h-Ni2Si was determined using mass conservation and the thickness measured by TEM analysis. From the asymmetrical shape of NiSi, it was found that the formation of 1.33 nm of NiSi led to the consumption of 1 nm h-Ni2Si phase and 0.39 nm of Si; this corresponds to an average atomic volume of 11 Å3. For these values, there is only a small volumetric change during the formation of the NiSi phase from the h-Ni2Si and Si. This relative non-variation of volume can also be observed in the TEM images, where there is no apparent deformation at the sample surface (there is an absence of typical ‘lobes’ of diffraction contrast). However a small volumetric change may be still present and should results in stresses during the reaction. The driving force was taken to be 5 kJ/mol from the energy of formation used in Table 1; the energy of formation for h-Ni2Si was estimated to 45 kJ/mol, because the effect of Pt on the energy of h-Ni2Si is unknown, but it should be substantial . For the diffusion, the mobility for both Si and Ni at the interface was chosen to be 1022 at/(s J): these values allow to obtain a speed for lateral growth in accordance with the experimental precipitates diameter (d) if the following approximation, d Vt, is used with t being the time of heat treatment and with V given byEq. (6). These mobilities have dimensions of at/(s J) instead of at/(m s J) because the ﬂux is a surface (or interface) ﬂux with dimensions of at/(m s).
where x and y are the normalized coordinates x ¼ kX and y ¼ kY with:
Vðch cg Þðxh xg Þ Lhg Xhg chg
The total thickness and the speed of lateral growth can then be expressed by:
2Dc M 2 DG0 M 1 ¼ DG 0
sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ M1 2DcM 22
M 2 ¼ r h mD XDg cDg
M 1 ¼ m2D cDg rh ¼
2=3 DcxD 2=3 1=3 Dcxh þ ð1 r h Þmh Xhg chg L Dg Lhg
2=3 DcxD 2=3 1=3 Dcxh þ m2h chg L Dg L hg
xh xg xh xD
DcxD ¼ ðcD cg ÞðxD xg Þ=XDg
Fig. 4. HR-TEM image of another NiSi particle obtained on a 250 °C annealed Ni (10 at.% Pt) sample observed in cross-section along a h1 1 0i Si direction with the ﬁt indicated by yellow lines. The curvature of the h-Ni2Si/Si interface in front of the particles is highlighted by the white line. (For interpretation of the references to colour in this ﬁgure legend, the reader is referred to the web version of this article.)
M. El Kousseiﬁ et al. / Acta Materialia 99 (2015) 1–6 Table 1 Values of the parameters used to ﬁt the shape of the precipitates: only the interfacial energies were varied and the range of their variation is indicated in the column labeled dc.
NiSi h-Ni2Si Si NiSi/Si NiSi/h-Ni2Si Si/h-Ni2Si
L (at/s J)
0.5 0.4 1 – – –
0.12 0.11 0.20 0.15 0.11 –
43 45 0 – – –
– – – 3 1.5 0.1
– – – 2.5–3.1 1–1.8 0.03–0.4
– – – 1022 1022 –
By setting the mobility for both Si and Ni equal at the two moving interfaces and by considering ﬁxed values for the concentration, the atomic volume and the energy of the three phases, Eqs. (6) and (8) show that the total thickness and the shape of the precipitate will mainly depend on the interfacial energies. As the epitaxial h-Ni2Si/Si interface is either coherent or semi coherent with a low energy , the h-Ni2Si/Si interface energy was kept at least 10 times lower than the ones for the incoherent NiSi/Si and NiSi/h-Ni2Si interfaces. The values for the interface energies that reproduces the best both the thickness and the shape of precipitates are reported in Table 1. The ranges for the interface energies were obtained by keeping two of these energies constants and by changing the value of the last one until the thickness and the shape of the precipitates are not ﬁtted anymore. This procedure leads to energies for the NiSi/Si and NiSi/h-Ni2Si interface in the range of 1 J/m2 in accordance with values commonly reported in the literature for incoherent interfaces. However, the variations of the interface energies are relatively large because of the difﬁculty in properly imaging the wetting angles. Indeed, as the TEM images are a 2D view of a 3D object, the image only corresponds to part of the particle lens shape. Moreover, the 2D image obtained in TEM is a projection of a 3D volume: it is thus difﬁcult to visualize clearly the precipitates especially at their edges because the projection will lead to some overlapping between the different phases (h-Ni2Si, NiSi and Si). This may also mask the contrast linked to possible stress in the vicinity of the precipitates. Geometrical Phases Analysis was tried to evidence the stress but no pertinent result were obtained most probably because of a too thick sample or the 3D organization of the microstructure, with possible overlapping between the three phases. Another more fundamental problem may be that the mechanical equilibrium is not established during the lateral growth. Consequently, the measured angles would not correspond to equilibrium. A possible indication of this non-equilibrium is the curvature of the h-Ni2Si/Si interface in front of the particles that is highlighted by the white dashed line in Fig. 4. This deformation might also be due to the difference between HD and HDg ðHD 53 HDg Þ linked to the difference in atomic volumes. This can lead locally to large stresses even if the global volume is conserved. Whatsoever, it is clear that the simulation ﬁts well with the overall measured shape of different particles, and this fact validates the main assumption of the Klinger model. The presence of a low density of NiSi particles at the h-Ni2Si/Si interface may be related to the difﬁculty of this NiSi phase to nucleate. The nucleation barrier for NiSi is proportional to the cube of the change in interface energy (Dc chg þ cDg chD ) over the square of the driving force (DG ð1 xh ÞGg Gh ), and it might be relatively high because of the low driving force . Additionally, the change in interface energy is not favorable for nucleation because of the low energy of the epitaxial h-Ni2Si/Si interface . Due to this high nucleation barrier, nucleation should occur on the grain boundary/interface contact because the grain boundaries in the h-Ni2Si phase should lower the nucleation barrier. The
nucleation sites are expected to occur at the intersection of the interface and the grain boundaries of the h-Ni2Si phase. However, no grain boundary was observed during TEM or APT analyses, indicating that the grain size of h-Ni2Si is very large, which is consistent with the epitaxial relationship. Accordingly, there should be a low number of available nucleation sites. The difﬁculty in nucleating on a coherent interface and the low number of nucleation sites should cause the density of NiSi nuclei to be very low in the presence of h-Ni2Si. In these conditions, the lateral growth regime should occur on a longer time scale; these results may explain why this stage is observable by TEM. Even it may be difﬁcult to observe, lateral growth should still play some role for the high heating rates used in microelectronics industry because the nucleation is expected to be heterogeneous and thus to occur on nucleation sites whose nature and number should not depend too much on temperature. Moreover, previous works [14,15] have shown that the lateral growth has a lower activation energy than the normal growth and should thus be less sensitive to change in temperatures than the normal growth. Finally the precipitates thickness corresponds to a large proportion of the total thickness for NiSi and depends mainly on the ratio between the driving force and the change in interface energy (Eq. (8)) that should not also be very sensitive to temperature change. 5. Conclusions The complete shape of NiSi particles formed at the epitaxial h-Ni2Si/Si interface by nucleation and lateral growth was demonstrated and successfully observed by TEM analyses. The elliptical shape of NiSi particles is similar to model predictions, and the shapes are well-ﬁtted by a model adapted from that proposed by Klinger et al. . The good agreement between this model and the experimental results validates the main assumptions of this study, that is, conservation of mass, the diffusion along the interfaces that is driven by the curvature gradient and the mechanical equilibrium at the triple junction (the latter is only partially veriﬁed in this work). Acknowledgements The authors acknowledge ﬁnancial support from the CNRS-CEA ‘‘METSA’’ French network (FR CNRS 3507) for the TEM experiments at CLYM (www.clym.fr), which is also acknowledged for access to the microscopes. Marion Descoins and Maxime Bertoglio are greatly acknowledged for technical support. Magali Gregoire from STMicroelectronics is acknowledged for providing the samples. Discussions with Federico Panciera were very fruitful. References  C. Lavoie, F.M. d’Heurle, C. Detavernier, C. Cabral Jr., Towards implementation of a nickel silicide process for CMOS technologies, Microelectron. Eng. 70 (2–4) (2003) 144–157.  D. Mangelinck, J.Y. Dai, J. Pan, S.K. Lahiri, Enhancement of thermal stability of NiSi ﬁlms on (1 0 0)Si and (1 1 1)Si by Pt addition, Appl. Phys. Lett. 75 (1999) 1736.  C. Lavoie, F.M. d’Heurle, C. Detavernier, C. Cabral Jr., Towards implementation of a nickel silicide process for CMOS technologies, Microelectron. Eng. 70 (2003) 144.  M. Putero, L. Ehouarne, E. Ziegler, D. Mangelinck, First silicide formed by reaction of Ni(13%Pt) ﬁlms with Si(1 0 0): nature and kinetics by in-situ X-ray reﬂectivity and diffraction, Scripta Mater. 63 (2010) 24.  F. Panciera, D. Mangelinck, K. Hoummada, M. Texier, M. Bertoglio, A. De Luca, M. Gregoire, M. Juhel, Direct epitaxial growth of h-Ni2Si by reaction of a thin Ni(10 at.% Pt) ﬁlm with Si(1 0 0) substrate, Scripta Mater. 78–79 (2014) 9.  K. De Keyser, C. Van Bockstael, C. Detavernier, R.L. Van Meirhaeghe, J. JordanSweet, C. Lavoie, Epitaxial formation of a metastable hexagonal nickel–silicide, Electrochem. Solid-State Lett. 11 (2008) H266.
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