Direct Observation of the Thickness-Induced Crystallization and Stress

Research Article www.acsami.org

Direct Observation of the Thickness-Induced Crystallization and Stress Build-Up during Sputter-Deposition of Nanoscale Silicide Films Bar̈ bel Krause,*,† Gregory Abadias,§ Anny Michel,§ Peter Wochner,∥ Shyjumon Ibrahimkutty,∥ and Tilo Baumbach†,‡ †

Institut für Photonenforschung und Synchrotronstrahlung (IPS), and ‡Laboratorium für Applikationen der Synchrotronstrahlung (LAS), Karlsruher Institut für Technologie, Karlsruhe 76131, Germany § Institut PPrime, Université de Poitiers, Poitiers 86000, France ∥ Max-Planck-Institute for Solid State Physics, Stuttgart 70569, Germany

ABSTRACT: The kinetics of phase transitions during formation of small-scale systems are essential for many applications. However, their experimental observation remains challenging, making it difficult to elucidate the underlying fundamental mechanisms. Here, we combine in situ and real-time synchrotron X-ray diffraction (XRD) and X-ray reflectivity (XRR) experiments with substrate curvature measurements during deposition of nanoscale Mo and Mo1−xSix films on amorphous Si (aSi). The simultaneous measurements provide direct evidence of a spontaneous, thickness-dependent amorphous-to-crystalline (a−c) phase transition, associated with tensile stress build-up and surface roughening. This phase transformation is thermodynamically driven, the metastable amorphous layer being initially stabilized by the contributions of surface and interface energies. A quantitative analysis of the XRD data, complemented by simulations of the transformation kinetics, unveils an interface-controlled crystallization process. This a−c phase transition is also dominating the stress evolution. While stress buildup can significantly limit the performance of devices based on nanostructures and thin films, it can also trigger the formation of these structures. The simultaneous in situ access to the stress signal itself, and to its microstructural origins during structure formation, opens new design routes for tailoring nanoscale devices. KEYWORDS: in situ, stress, crystallization kinetics, MoSi, sputter deposition, silicide, solid-phase crystallization materials5,11 but also for alloys, 8,14−16 and even pure metals.17−19 In this case, the amorphous layers are typically only stable at extremely low temperatures. A remarkable exception are amorphous Mo and W layers, which can be stabilized at room temperature in silicon-based multilayer stacks.20,21 Mo/Si multilayers are of special interest for Braggmirror applications in the X-ray and EUV regime, including the optics for EUV lithography and free electron lasers.21−23 These applications require an extremely low interface roughness. The a−c transition, however, leads to an undesired roughness

1. INTRODUCTION Phase transitions belong to the intrinsic material properties, which are significantly affected by the object size and dimensionality.1,2 The kinetics of these phase transitions are very difficult to access, especially when they are taking place during formation and processing of thin films and nanostructures.3,4 A special case, the solid-phase crystallization (SPC), is a widely used approach to produce poly-silicon layers for thin film transistors and solar cells.5,6 The kinetically hindered exothermic transition from a metastable amorphous layer to a polycrystalline film can be triggered by annealing,7,8 catalytic processes,9,10 or by locally injected energy.11−14 Interestingly, amorphous-to-crystalline (a−c) transitions were observed not only for single-element semiconductor © 2016 American Chemical Society

Received: September 29, 2016 Accepted: November 22, 2016 Published: November 22, 2016 34888

DOI: 10.1021/acsami.6b12413 ACS Appl. Mater. Interfaces 2016, 8, 34888−34895

Research Article

ACS Applied Materials & Interfaces increase.21 Thus, the control of the crystallization process is of paramount importance for the device efficiency. The temporal development of a−c phase transitions driven by annealing or catalytic reactions was revealed by timeresolved laser reflectivity24 and transmission electron microscopy (TEM).10,25 However, it remains challenging to access the kinetics of phase transition during thin film deposition. On the basis of postgrowth observations,21 the crystallization of Mo/Si at a thickness of ∼2−3 nm21,23,26−28 was initially attributed to a composition gradient at the interface. More recent in situ and in real-time measurements using spectroscopic ellipsometry26 or multiple-beam optical stress (MOSS) measurements28,29 suggested a different scenario: the characteristic transient signal at the critical thickness for the a−c transition of Mo was explained by a volume contraction, resulting in a higher density and local stresses. A model based on equilibrium thermodynamic considerations was proposed, assuming that below the critical thickness the amorphous phase is stabilized by the energetic contributions of surface and interface.17,26,28 Despite their high sensitivity to microstructural modifications, in situ MOSS and laser reflectivity measurements do not provide any direct information on the time-dependent atomic ordering during crystallization. In this work, we want to address this question by combining in situ and real-time X-ray reflectivity (XRR), X-ray diffraction (XRD), and optical stress measurements during thin film deposition of Mo1−xSix alloys on a-Si, as schematically shown in Figure 1. The measurements

silicon(100) substrates, covered by native oxide, were mounted on a specially designed substrate holder, which permitted unconstrained bending of the substrate, UHV transfer of the sample, and did not shadow the incoming and scattered X-ray beams. No external heating or cooling was applied during deposition. The Si buffer and cap layers with a nominal thickness of 4.5 nm were deposited at the RF magnetron power 60 W. For the codeposition of alloys, Mo was deposited at a DC power of 20 W, while the RF power of Si was varied between 0 and 60 W. Depending on the RF power, the Mo1−xSix deposition time of 900 s resulted in a composition-dependent layer thickness of 28−37 nm. The flux of the sputter gas Ar was 1.8 sccm, corresponding to a pressure of 0.5 Pa. The chemical composition of the layers was estimated from the in situ XRR oscillations and cross-checked by X-ray photoelectron specroscopy (XPS) measurements on reference samples. For this, the growth chamber was docked to a UHV cluster system. After deposition, the samples were transferred under UHV conditions to the XPS analysis chamber. 2.2. In Situ X-ray Measurements. The synchrotron radiation experiments were performed at the MPI beamline of the synchrotron ANKA (Karlsruhe),32 using an X-ray energy of 12 keV (wavelength λ = 1.03 Å). The deposition chamber was mounted vertically on a Huber 4 + 2 circle diffractometer. The X-ray beam with an incident angle αi = 1.6° was focused to a spot size of about 0.3 × 0.2 mm (horizontal × vertical) at the sample position. During deposition, the reflected beam was monitored using a scintillation detector. Simultaneously, a section of the diffraction rings was recorded by a Pilatus detector mounted on the same detector arm but with an angular offset of 24°. Both data were aquired with an integration time of 1 s. Under the here-used growth conditions, the free sample curvature, required for the MOSS measurements, did only slightly influence the resolution of the XRR signal. The intensity of the reflected beam oscillates with the film thickness. The oscillation period τ gives direct access to the growth rate:31 F=

π π ≈ for αi ≫ αc |kz|τ k sin(αi)τ

(1)

kz is the z-component of the wave vector k = 2π/λ, and αc is the critical angle for total external reflection. Our experiments were performed at αi = 1.6°, which is much larger than αc(Mo) = 0.29° and αc(Si) = 0.15°. Therefore, the thickness

Dτ =

π |k z |

(2)

deposited during one oscillation depends only weakly on the material. Assuming bulk densities, at an X-ray energy of 12 keV, one oscillation period corresponds to 1.87 nm for deposition of Si, and 1.91 nm for deposition of Mo. The in situ XRR data were fitted on the basis of a layer growth model, taking into account the fit results of a postgrowth angular XRR measurement. The densities of the individual layers, including the silicide interface layer, were assumed to be constant, while the roughness and the layer thickness were varied. The formation of the MoSi/Si (Si/MoSi) interface was modeled assuming that for a certain time span the deposited Mo (Si) is completely transformed into MoSi2, reducing simultaneously the thickness of the previously deposited Si (MoSi) layer. The 2D detector (Pilatus 100-k, Dectris) with 195 × 487 pixels (pixel size 172 μm) was mounted at a distance of 480 mm to the sample position. During deposition, it covered the angular range 2θ = 22−32°, including the Mo(110) peak at 26.77°. The images were background-subtracted, and radial scans in an angular distance of about 13° to the surface normal were extracted. For this, the positions of each pixel were converted into reciprocal space coordinates, and for each data point the intensity was integrated over Δqz = 0.005 Å−1. 2.3. In Situ Stress Measurements. The real-time stress evolution during deposition was followed in situ using a multiple beam optical stress sensor (MOSS) developed by kSA. A 3 × 3 laser beam array was reflected by the sample and recorded with a high-resolution CCD

Figure 1. Schematic of the measurement geometry used for the simultaneous in situ XRR, XRD, and MOSS experiments during codeposition of Mo−Si alloy thin films.

give insight into the time-dependent thickness, density, and roughness development during deposition, and reveal simultaneously the development of the local atomic order.30,31 Thus, they give direct evidence of a thickness- and compositiondependent a−c transition in the Mo−Si system. These observations are linked to the simultaneously recorded stress development.29 The experimental results are summarized in a model for the kinetics of the composition- and thicknessdependent a−c transition in Mo1−xSix alloys.

2. EXPERIMENTAL SECTION 2.1. Sputter Deposition. The Si/MoSi/Si sandwich structures were deposited in a modular UHV magnetron sputtering chamber designed for in situ X-ray experiments.30 Two magnetron sources with a target diameter of 2 in. were mounted at an angle of 19° to the substrate surface normal. The target−substrate distance was 129 mm for molybdenum and 162 mm for silicon. The 7 × 12 × 0.1 mm3 34889


Research Article

ACS Applied Materials & Interfaces camera.29 During deposition, the stress of the film changes continuously, resulting in a time-dependent curvature of the substrate. This bending changes the angular divergence of the laser beam array. The Stoney equation was employed to calculate the average force per unit length, or equivalently the σ(t) × h(t) product, where σ is the average stress, and h is the film thickness. The curvature sensitivity was better than 2 × 10−4 m−1.

during deposition of a Si/Mo/Si sandwich structure. t is the deposition time scaled to the onset of the Mo deposition. The deposition periods for the Si buffer and cap layer are indicated. During deposition of the amorphous Si (a-Si) buffer layer, the film force decreases only slightly, and the diffraction signal does not change at all. Only the XRR intensity oscillations reveal the growing film: from the observed period, a Si deposition rate of 0.0125 nm/s could be determined. However, all three signals show a much stronger response to the onset of Mo deposition: after a sudden tensile stress increase, which can be explained by the silicide formation at the interface,23 the film force reaches a plateau in the region 60 ≲ t ≲ 90 s (see inset in Figure 2a). Simultaneously, a broad diffraction peak develops with continuously increasing intensity, and the oscillation period of the XRR signal decreases by about a factor 2, corresponding to the deposition rate F = 0.0307 nm/s for Mo. The amplitude of the XRR oscillations increases rapidly, partially due to the large electron density contrast between Mo and Si, but also due to a smoothening of the film (see Figure 4c). The low stress signal, the broad diffraction peak, and the smoothening observed for t < tc ≈ 90 s are characteristic for the formation of an amorphous Mo layer. At t > tc, the situation changes drastically: the film force increases rapidly with the amount of deposited material (Figure 2a), accompanied by the sudden formation of a narrow Mo(110) Bragg peak (Figure 2b) and the increasing surface roughness revealed by the damping of the XRR oscillations (Figure 2c). In agreement with earlier reports,21,28 these observations indicate the onset of Mo crystallization at a critical thickness hc ≈ 2.8 nm, after the initial formation of an amorphous layer. The transition is accompanied by a tensile stress increase of +3.5 GPa, consistent with a volume contraction of −2.5%. Similar values are commonly reported during densification of metals. 3.2. Composition Dependence of the Crystallization Process. Interestingly, this crystallization phenomenon was not only observed for the deposition of pure Mo, but also for Mo1−xSix alloys with various Si content x. Some examples for the composition-dependent in situ XRD measurements are shown in Figure 3a−d. The transition from broad to narrow peak was found for Si contents up to 20 at. %. With increasing x, the a−c transition occurs at later deposition times, corresponding to critical thicknesses hc ranging from ∼2.8 nm for pure Mo to ∼11.3 nm for 20 at. % Si. For x ≳ 25 at. % Si, only a broad intensity distribution was found (Figure 3a), linearly increasing with the deposition time. This confirms that the crystallization process only happens at low Si content, as proposed by Fillon et al.28 The question, however, remains how exactly this crystallization process takes place. To understand the dynamic pathway of the observed thickness-induced a−c phase transformation, the XRD signal was quantitatively analyzed and modeled. Figure 3e displays radial scans (●) extracted few seconds after the visible onset (t = tc) of the amorphous-to-crystalline transition. The scans show characteristic oscillations related to the crystallite size. The central maximum narrows with increasing Si content, indicating an increasing vertical crystallite size Dc at the onset of crystal growth. The evolution of Dc as a function of the Si content was determined from a fit of the radial scans (red lines in Figure 3e). The measured intensity

3. RESULTS AND DISCUSSION 3.1. Fast Crystallization and Stress Evolution. Combined XRR, XRD, and MOSS measurements were performed during codeposition of magnetron-sputtered Mo1−xSix alloys in a wide composition range. As an example, Figure 2 shows simultaneously performed real-time measurements of (a) the film force per unit length, (b) the XRD signal, and (c) the XRR

Figure 2. Simultaneous in situ (a) stress, (b) XRD, and (c) XRR measurements during deposition of a pure Mo layer. The deposition periods of the Si buffer, the Mo layer, and the Si cap layer are indicated. The deposition time t is normalized to the onset of Mo deposition. The amorphous-to-crystalline transition at tc ≈ 90 s [indicated in (a)] induces characteristic changes in all signals: a sudden increase in the force per unit length shown in the inset of (a), a simultaneous narrowing of the diffraction signal along the surface normal, and a damping of the XRR signal, which is related to a roughness increase. 34890


Research Article

ACS Applied Materials & Interfaces

which are smeared out completely by t ≈ 400 s. These streaks were surprisingly well reproduced assuming simply a coherent crystal growth in vertical direction after the sudden crystallization, with a time-dependent vertical crystallite size D(t) = Dc + F(t − tc) (blue lines in Figure 3b−d). The calculated blue lines at q1 ± n*2π/D(t), with n = 1, 2, etc., correspond to the minima of the size oscillations. Such coherent growth is consistent with the columnar growth typically observed for sputtered Mo films.33,34 The discrepancy between Dc and hc is much larger than expected from the volume decrease of about 2.5% due to the crystallization, and can be explained by the formation of an interface layer consisting mainly of MoSi2.23,35 3.3. Temporal Evolution. A closer inspection of the timedependent stress development, shown in Figure 4a for a wide composition range, indicates that the crystallization process is additionally governed by a second, much larger time-scale: up to the onset of the amorphous-to-crystalline transition, the

Figure 3. (a−d) Time-dependent development of radial scans along the surface normal, measured during deposition of Mo1−xSix layers with different composition. (e) Radial scan (dots) extracted shortly after the onset of the transition. The data were fitted (red lines) assuming coherent crystallites with the vertical size D. The blue lines in (b−d) are calculated assuming that these crystallites grow coherently during further deposition. (f) Vertical size Dc of the crystallites (extrapolated to the onset of the transition estimated from the integrated XRD signal), as compared to the Mo1−xSix thickness expected from the deposition rate.

⎛ Dc(q − q ) ⎞ 2 2 z 1 ⎟⎟ e−(qz − q1) σD I(qz) = a1 sinc⎜⎜ 2π ⎝ ⎠ 2a w2 + 2 π 4(qz − q2)2 + w22

(3)

was described as the sum of the contributions from the crystalline and amorphous phases. The first term represents the coherent scattering of a crystal with the Bragg position q1 and the average size Dc. The size distribution σD of the coherent crystals results in a damping of the oscillations and was taken into account by a Debye−Waller factor. The second term corresponds to the contribution of the coexisting amorphous phase, described by a Lorentzian at the position q2 and with the fwhm w2. The parameters a1 and a2 depend on the amount and the texture of the crystallized material. The results (○) are reported in Figure 3f and compared to the deposited thickness hc (●), calculated from deposition rate and deposition time at the onset of crystallization as detected by XRD. With increasing Si content, Dc increases from 2.5 to 8.6 nm, and is always smaller than hc. The error bar of Dc indicates the thickness distribution used for the fit. These suddenly forming large crystallites are a direct proof for an extremely fast crystallization process, transforming the already deposited amorphous material nearly over the entire film thickness. The width of the Bragg peak and the size oscillations narrow with increasing deposition time, forming curved streaks in the diffraction maps,

Figure 4. Amorphous-to-crystalline transition is not only observed for pure Mo, but also for Mo1−xSix alloys with x ≤ 20 at. %. Both the onset and the duration of transition, indicated by colored areas for x = 11 at. % (red line) and x = 20 at. % (blue line), increase with x. This is revealed by (a) the time-dependent force per unit length during deposition. (b) A direct fingerprint for the phase transition, however, is the integrated intensity of the Mo(110) peak, which could be simulated using interface-driven lateral crystallization model (broad gray lines). (c) The crystallization is accompanied by a sudden roughness increase, which continues during later growth. 34891


Research Article

ACS Applied Materials & Interfaces stress-curve seems to be independent of composition and is characterized by a steady-state stress regime (−150 MPa) after the initial tensile rise at the MoSi/Si interface. Above the critical thickness hc, a sudden tensile stress develops. The transition itself, that is, the sudden increase of the film force, is highlighted for x = 11 at. % Si (pink background) and x = 20 at. % (blue background). The later value is close to the critical composition above which only amorphous alloys with a steady-state compressive stress are expected. From Figure 4a it is obvious that the stress transition is not a step function, but results in a smeared-out, s-shaped increase of the film force. Both the height and the width of the s-shaped stress variation increase with increasing Si content. The height can be explained by the amount of material that is transformed. At higher Si content, the transition takes place later; that is, a thicker layer crystallizes, leading to a higher amount of tensile stress generated by the volume change. The scattered intensity, integrated in the qz direction and plotted in Figure 4b, is a simple measure of the crystallinity of the sample. For the amorphous alloys with Si content larger than 20 at. % (here shown only for 25 at. %), the integrated intensity increases linearly with time. For lower Si content, this behavior is followed by a characteristic s-shaped increase at the a−c transition, which resembles the composition-dependent stress signal. The later XRD intensity increase is again linear. From the in situ XRR measurements, the time-dependent surface roughness of the film was determined. The results are plotted in Figure 4c. For all samples, an initial smoothening of the amorphous film is observed, while the roughness increases continuously after the onset of the crystallization. The a−c phase transition is expected to affect the surface roughness.15,36 The continuous roughening during further deposition, however, can only be explained by growth processes including the formation of V-shaped columns or facets. 3.4. Simulation of the Bragg Intensity. For all samples, the temporal evolution of the integrated intensity could be satisfactorily reprocuded on the basis of a simple 3D growth scenario, adapted from ref 37. The fit results are shown as thick gray lines in Figure 4b. The phase transformation of the already deposited amorphous layer starts at tc. It is described as nucleation and subsequent interface-controlled lateral expansion of crystalline regions. A number of randomly distributed pre-existing nuclei is assumed, corresponding to a site-saturated nucleus density (caused, e.g., by nucleation at specific defects). Even if the initial nucleus formation is not directly accessible with the current experimental setup, the (110) texture of all crystalline films indicates that the nucleation of the crystalline phase takes place at the surface or the interface.16 The density of the pre-existing nuclei was derived from the grain size measurements reported in ref 28. Because of the continuous transfer of atoms through the amorphous/crystalline interface, the crystallized volume increases with a growth front velocity v. The continuous deposition of new material is taken into account, assuming that it is instantly transformed to the phase on which it is deposited. Figure 5 vizualizes the growth scenario and its numerical implementation. The orange cylinders with the radius R(t) = v(t − tc) and the height Dc + F(t − tc) represent the crystallite evolution at different time steps, and the blue regions correspond to the amorphous film. Lighter hues indicate later time steps. The crystallization front moves in the radial direction up to when it meets a neighboring crystallite, resulting in a Voronoi tesselation of the film.

Figure 5. Schematic of the crystallization process. At tc, a random distribution of nuclei is assumed. The laterally expanding crystallites at different times after the onset of crystallization are indicated by orange cylinders, and the amorphous regions are shown in blue. Lighter hues correspond to later times. The crystallites consist of many mosaic blocks, shown as stacks of differently tilted lattice planes, which are coherent in the vertical direction. The crystallite height increases with the deposition rate, while the lateral expansion is determined by the interface velocity v.

The above-described growth model was then used to calculate the time-dependent area, A(t), covered by crystalline material. From this, the Bragg intensity was calculated assuming fully coherent mosaic blocks in the vertical direction (indicated in Figure 5 by the black lattice planes). Because of the local stresses induced by the a−c transformation, the lateral coherence length of the mosaic blocks is much smaller than the lateral crystallite size. Therefore, the measured integrated intensity: I(t ) = c1[1 − A(t )]Ft + c 2A(t )[Dc + F(t − tc)]2

(4)

is directly related to the area covered by the crystallites. The first term of eq 4 corresponds to the scattering of the remaining amorphous material, and the second term to the scattering of the crystallized area at time t. The simulated temporal evolution of the integrated intensity was optimized simultaneously for the different Si contents. The main fit parameter of our model was the growth front velocity v = 13 nm/s. The transition time tc, the deposition rate F, and crystallite height Dc at the onset of crystallization were only marginally changed as compared to the values determined from the integrated XRD signal and the XRR measurements. Because Dc ≲ 10 nm, the crystallite expansion in the vertical direction takes place within less than 1 s and cannot be resolved in our experiment. The lateral crystallization, however, can be resolved because the distance between the nuclei is much larger, varying between 50 nm and more than 1 μm.28 For t < tc, A(t) = 0, only the linearly increasing amount of amorphous material (described by the first term) contributes to the measured intensity. The weight factor c1 is identical for all samples, reflecting the negligible influence of the Si content on the scattering of the amorphous phase. For t > tc, the crystalline area (described by the second term in eq 4) increases according to the above-described model, while the amorphous contribution decreases. c2 takes into account the interplay between measurement and texture direction. The parameter varied only by ±3% for different Si contents. This indicates that the texture did not change significantly after the onset of crystallization and was similar for all samples, as confirmed by reciprocal space maps after deposition. With increasing island distance, the complete crystallization needs more time, explaining the broadening of the s-shaped diffraction signal. The lateral crystallization model explains also 34892


Research Article

ACS Applied Materials & Interfaces why the stress curve and the X-ray intensity show such a similar behavior. The stress signal is dominated by the volume contraction, which is proportional to A(t)*[Dc + F(t − tc)]. 3.5. Kinetics of the Phase Transformation. The a−c phase transformation is driven by the Gibbs free energy release ΔGa→c(x) during crystallization. The kinetics of the process are governed by the activation energy WN for nucleation, and the activation energy WG for the transfer of atoms through the amorphous/crystalline interface. As observed by Fillon et al.,28 the grain size varies significantly with the Si content, indicating that the nucleation barrier increases with x because the incorporation of Si in the bcc Mo lattice is energetically unfavorable. For interface-controlled growth, the growth front velocity at the temperature T is ⎛ W (x ) ⎞⎡ ⎛ ΔGa → c(x) ⎞⎤ v(T , x) = v0 exp⎜ − G ⎟⎢1 − exp⎜ ⎟⎥ ⎝ kBT ⎠⎢⎣ ⎝ kBT ⎠⎥⎦

Figure 6. Schematic of the composition-dependent Gibbs free energy difference between amorphous (blue line a) and crystalline bulk phase (black line c1). For x < xc, the crystalline phase is stable. For thin films, the energetic contribution Δγ of the interfaces results in a thicknessdependent relative shift between both curves (indicated by the gray lines c2 and c3), stabilizing the amorphous phase for h < hc(x).

(5)

where kB is the Boltzmann constant and v0 is a constant prefactor.37 The integrated XRD intensity was successfully reproduced assuming a constant growth front velocity v, which suggests that in our case eq 5 simplifies to ⎛ W ⎞ v(T ) = v0 exp⎜ − G ⎟ ⎝ kBT ⎠

surface energy between the a-Si/vacuum interface (γa‑Si ≈ 1 J/ m2)40 and the Mo(110)/vacuum interface (γMo = 3.5 J/m2).38 Δh is higher than the expected interface thickness of 0.5−1 nm21,23,41 and includes probably the neglected composition dependence of Δγa→c. Another reason might be the limited sensitivity of XRD to extremely small crystalline clusters. This is supported by the MOSS signal. The onset of curvature change of the stress signal always slightly precedes the slope change of the XRD signal.

(6)

WG is independent of x, probably because it is dominated by the local bond rearrangement of the Mo atoms, and the driving force fulfills |ΔGa→c(x)| ≫ kBT in the time scale relevant for the XRD measurements. Following Fillon et al.,28 the change in the Gibbs free energy for the a−c transformation of Mo1−xSix alloys can be written as ΔGa → c(x) = Δga → c(x) +

4. CONCLUSIONS We could demonstrate the feasibility of combined stress, diffraction, and reflectivity measurements during nanoscale structure formation. Employing this approach, the origin of the stress transition in Mo1−xSix thin alloy films, that is, the spontaneous crystallization, was evidenced. The results show that the thickness- and composition-dependent a−c transition of Mo1−xSix with x ≲ 20 at. % is dominated by a lateral crystallization process, similarly to the explosive crystallization of Si and Ge. The understanding of the phase formation leads to new insights into the roughness formation, which is a main aspect of the reflectance optimization of EUV mirrors. The roughness increases at the onset of phase transformation, but seems to be dominated by growth effects and not by the phase transformation itself. Interestingly, such a thickness-dependent a−c transition was also proposed for W/Si. W and Mo belong to the group of bcc metals with a glass-forming ability at extremely high cooling rates. This was demonstrated for nanometer-sized levitating spheres and nanobridges.19,42 Assuming that the glass-forming ability and the formation of a stable amorphous layer in thin films are related, the lateral crystallization process might also be relevant for other glass-forming bcc metal/silicon alloys and the only glass forming fcc metal, Ni.19

Δγa → c (7)

h

where ⎛ x(1 − x) ⎞ Δga → c(x) = gaMo ⎜1 − ⎟ →c xc(1 − xc) ⎠ ⎝

(8)

gMo a→c,

is the composition-dependent bulk contribution. For the value for pure Mo, different calculated values including −32 kJ/ mol38 and −37 kJ/mol39 are reported (∼0.3−0.4 eV/atom). xc is the maximum composition for crystalline bulk alloys, and γa→c contains the contributions of the surface and the interface. For bulk material, only the first term of eq 7 contributes. Δga→c(x) is negative for x < xc; that is, the crystalline phase is favored. Otherwise, the amorphous phase is stable. In case of a growing thin film, the energetic balance changes with the film thickness h, as schematically shown in Figure 6. Please note that for simplicity of the drawing, only the relative shift between the Gibbs free energy of the amorphous and the crystalline phase is visualized. For h < hc, ΔGa→c(x0) > 0 stabilizes the amorphous phase. For h > hc(x0), ΔGa→c(x0) < 0, and the crystalline phase becomes thermodynamically stable. The critical thickness hc(x0) for the a−c transition at the composition x0 is reached when the curves intersect exactly at x0. hc increases with increasing x, as illustrated in Figure 6, and diverges at xc. Taking into account the expected formation of an amorphous interface layer,23 we assumed h = hexp − Δh. With gMo a→c = −32 kJ/mol (−37 kJ/mol), the values Δh = 1.81 ± 0.05 nm and Δγa→c = 3.1 J/m2 (3.7 J/m2) were obtained from a fit of the experimental data. Δγa→c is close to the change in

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Bärbel Krause: 0000-0001-6288-0283 Notes

The authors declare no competing financial interest. 34893


Research Article

ACS Applied Materials & Interfaces

■

(16) Rodriguez, A.; Rodriguez, T.; Olivares, J.; Sangrador, J.; Martin, P.; Martinez, O.; Jiminez, J.; Ballesteros, C. Nucleation Site Location and its Influence on the Microstructure of Solid-Phase Crystallized SiGe Films. J. Appl. Phys. 2001, 90, 2544−2552. (17) Suits, J. C. Question of Superconducting Iron. Phys. Rev. 1963, 131, 588−591. (18) Wright, J. Amorphous Transition Metal Films. IEEE Trans. Magn. 1976, 12, 95−102. (19) Greer, A. L. New Horizons for Glass Formation and Stability. Nat. Mater. 2015, 14, 542−526. (20) Windt, D. L.; Christensen, F. E.; Craig, W. W.; Hailey, C.; Harrison, F. A.; Jimenez-Garate, M.; Kalyanaraman, R.; Mao, P. H. Growth, Structure, and Performance of Depth-Graded W/Si Multilayers for Hard X-ray Optics. J. Appl. Phys. 2000, 88, 460−470. (21) Bajt, S.; Stearns, D. G.; Kearney, P. A. Investigation of the Amorphous-to-Crystalline Transition in Mo/Si Multilayers. J. Appl. Phys. 2001, 90, 1017−1025. (22) Khorsand, A.; Sobierajski, R.; Louis, E.; Bruijn, S.; van Hattum, E.; van de Kruijs, R.; Jurek, M.; Klinger, D.; Pelka, J.; Juha, L.; Burian, T.; Chalupsky, J.; Cihelka, J.; Hajkova, V.; Vysin, L.; Jastrow, U.; Stojanovic, N.; Toleikis, S.; Wabnitz, H.; Tiedtke, K.; SokolowskiTinten, K.; Shymanovich, U.; Krzywinski, J.; Hau-Riege, S.; London, R.; Gleeson, A.; Gullikson, E.; Bijkerk, F. Single Shot Damage Mechanism of Mo/Si Multilayer Optics under Intense Pulsed XUVExposure. Opt. Express 2010, 18, 700−712. (23) Louis, E.; Yakshin, A.; Tsarfati, T.; Bijkerk, F. Nanometer Interface and Materials Control for Multilayer EUV-Optical Applications. Prog. Surf. Sci. 2011, 86, 255−294. (24) Johnson, B. C.; Gortmaker, P.; McCallum, J. C. Intrinsic and Dopant-Enhanced Solid-Phase Epitaxy in Amorphous Germanium. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 77, 214109. (25) Nikolova, L.; LaGrange, T.; Stern, M. J.; MacLeod, J. M.; Reed, B. W.; Ibrahim, H.; Campbell, G. H.; Rosei, F.; Siwick, B. J. Complex Crystallization Dynamics in Amorphous Germanium Observed with Dynamic Transmission Electron Microscopy. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87, 064105. (26) Schubert, E.; Mändl, S.; Neumann, H.; Rauschenbach, B. RealTime In Situ Spectroscopic Ellipsometry Investigation of the Amorphous to Crystalline Phase Transition in Mo Single Layers. Appl. Phys. A: Mater. Sci. Process. 2005, 80, 47−50. (27) Largeron, C.; Quesnel, E.; Thibault, J. Interface Growth Mechanism in Ion Beam Sputtering-Deposited Mo/Si Multilayers. Philos. Mag. 2006, 86, 2865−2879. (28) Fillon, A.; Abadias, G.; Michel, A.; Jaouen, C.; Villechaise, P. Influence of Phase Transformation on Stress Evolution during Growth of Metal Thin Films on Silicon. Phys. Rev. Lett. 2010, 104, 096101. (29) Fillon, A.; Abadias, G.; Michel, A.; Jaouen, C. Stress and microstructure evolution during growth of magnetron-sputtered lowmobility metal films: Influence of the nucleation conditions. Thin Solid Films 2010, 519, 1655−1661. (30) Krause, B.; Darma, S.; Kaufholz, M.; Gräfe, H.-H.; Ulrich, S.; Mantilla, M.; Weigel, R.; Rembold, S.; Baumbach, T. Modular Deposition Chamber for In Situ X-ray Experiments during RF and DC Magnetron Sputtering. J. Synchrotron Radiat. 2012, 19, 216−222. (31) Kaufholz, M.; Krause, B.; Kotapati, S.; Köhl, M.; Mantilla, M. F.; Stüber, M.; Ulrich, S.; Schneider, R.; Gerthsen, D.; Baumbach, T. Monitoring the Thin Film Formation during Sputter Deposition of Vanadium Carbide. J. Synchrotron Radiat. 2015, 22, 76−85. (32) Stierle, A.; Steinhäuser, A.; Rühm, A.; Renner, F. U.; Weigel, R.; Kasper, N.; Dosch, H. Dedicated Max-Planck Beamline for the In Situ Investigation of Interfaces and Thin Films. Rev. Sci. Instrum. 2004, 75, 5302−5307. (33) Chen, L.; Lu, T.-M.; Wang, G.-C. Biaxially Textured Mo Films with Diverse Morphologies by Substrate-Flipping Rotation. Nanotechnology 2011, 22, 505701. (34) Magnfält, D.; Fillon, A.; Boyd, R. D.; Helmersson, U.; Sarakinos, K.; Abadias, G. Compressive Intrinsic Stress Originates in the Grain Boundaries of Dense Refractory Polycrystalline Thin Films. J. Appl. Phys. 2016, 119, 055305.

ACKNOWLEDGMENTS We thank the synchrotron radiation source ANKA for the provision of beamtime. We acknowledge the help of M. Kristen during chamber installation at the beamline, the technical support in the ANKA UHV Analysis Laboratory by H. Gräfe and A. Weißhardt, and the general support of the ANKA staff. The research was financially supported by the French Ministry of Foreign Affairs and International Development (MAEDI), the Ministry of Education and Research (MENESR), and the PROCOPE project no. 57050352 of the German Academic Exchange Service (DAAD).

■

REFERENCES

(1) Tolbert, S. H.; Alivisatos, A. P. Size Dependence of a First Order Solid-Solid Phase Transition: The Wurtzite to Rock Salt Transformation in CdSe Nanocrystals. Science 1994, 265, 373−376. (2) Bardhan, R.; Hedges, L. O.; Pint, C. L.; Javey, A.; Whitelam, S.; Urban, J. J. Uncovering the Intrinsic Size Dependence of Hydriding Phase Transformations in Nanocrystals. Nat. Mater. 2013, 12, 905− 912. (3) Renaud, G.; Lazzari, R.; Revenant, C.; Barbier, A.; Noblet, M.; Ulrich, O.; Leroy, F.; Jupille, J.; Borensztein, Y.; Henry, C. R.; Deville, J.-P.; Scheurer, F.; Mane-Mane, J.; Fruchart, O. Real-Time Monitoring of Growing Nanoparticles. Science 2003, 300, 1416−1419. (4) Hejral, U.; Müller, P.; Balmes, O.; Pontoni, D.; Stierle, A. Tracking the Shape-Dependent Sintering of Platinum-Rhodium Model Catalysts under Operando Conditions. Nat. Commun. 2016, 7, 10964. (5) Spinella, C.; Lombardo, S.; Priolo, F. Crystal Grain Nucleation in Amorphous Silicon. J. Appl. Phys. 1998, 84, 5383−5414. (6) Dross, F.; Baert, K.; Bearda, T.; Deckers, J.; Depauw, V.; El Daif, O.; Gordon, I.; Gougam, A.; Govaerts, J.; Granata, S.; Labie, R.; Loozen, X.; Martini, R.; Masolin, A.; O’Sullivan, B.; Qiu, Y.; Vaes, J.; Van Gestel, D.; Van Hoeymissen, J.; Vanleenhove, A.; Van Nieuwenhuysen, K.; Venkatachalam, S.; Meuris, M.; Poortmans, J. Crystalline Thin-Foil Silicon Solar Cells: Where Crystalline Quality Meets Thin-Film Processing. Prog. Photovoltaics 2012, 20, 770−784. (7) Malek, J. Kinetic Analysis of Crystallization Processes in Amorphous Materials. Thermochim. Acta 2000, 355, 239−253. (8) Liu, F.; Sommer, F.; Mittemeijer, E. Parameter Determination of an Analytical Model for Phase Transformation Kinetics: Application to Crystallization of Amorphous Mg-Ni Alloys. J. Mater. Res. 2004, 19, 2586−2596. (9) Hayzelden, C.; Batstone, J. L. Silicide Formation and SilicideMediated Crystallization of Nickel-Implanted Amorphous Silicon Thin Films. J. Appl. Phys. 1993, 73, 8279−8289. (10) Radnoczi, G. Z.; Dodony, E.; Battistig, G.; Vouroutzis, N.; Kavouras, P.; Stoemenos, J.; Frangis, N.; Kovacs, A.; Pecz, B. Structural Characterization of Nanostructures Grown by Ni Metal Induced Lateral Crystallization of Amorphous-Si. J. Appl. Phys. 2016, 119, 065303. (11) Mineo, A.; Matsuda, A.; Kurosu, T.; Kikuchi, M. Velocity of Propagation in the Shock-Crystallization of Sputtered Amorphous Germanium. Solid State Commun. 1973, 13, 329−331. (12) Sharma, R. K.; Bansal, S. K.; Nath, R.; Mehra, R. M.; Bahadur, K.; Mall, R. P.; Chaudhary, K. L.; Garg, C. L. Electron Beam Induced Explosive Crystallization of Unsupported Amorphous Germanium Thin Films. J. Appl. Phys. 1984, 55, 387−394. (13) Miyao, M.; Tsunoda, I.; Sadoh, T.; Kenjo, A. Ion-beam Stimulated Solid-Phase Crystallization of Amorphous Si on SiO2. Thin Solid Films 2001, 383, 104−106. (14) Matsumura, R.; Chikita, H.; Kai, Y.; Sadoh, T.; Ikenoue, H.; Miyao, M. Low-Temperature (Similar to 180 °C) Position-Controlled Lateral Solid-Phase Crystallization of GeSn with Laser-Anneal Seeding. Appl. Phys. Lett. 2015, 107, 262106. (15) Wickersham, C.; Bajor, G.; Greene, J. Impulse Stimulated Explosive Crystallization of Sputter Deposited Amorphous (In,Ga)Sb Films. Solid State Commun. 1978, 27, 17−20. 34894


Research Article

ACS Applied Materials & Interfaces (35) Rovezzi, M.; D’Acapito, F.; Patelli, A.; Rigato, V.; Salmaso, G.; Bontempi, E.; Davoli, I. Characterization of Thermally Treated Mo/Si Multilayer Mirrors with Standing Wave-Assisted EXAFS. Nucl. Instrum. Methods Phys. Res., Sect. B 2006, 246, 127−130. (36) Gilmer, G.; Leamy, H. In Laser and Electron Beam Processing of Materials; White, C., Peercy, P., Eds.; Academic Press: New York, 1980; pp 227−233. (37) Liu, F.; Sommer, F.; Bos, C.; Mittemeijer, E. J. Analysis of Solid State Phase Transformation Kinetics: Models and Recipes. Int. Mater. Rev. 2007, 52, 193−212. (38) Jiang, Q.; Lu, H. Size Dependent Interface Energy and its Applications. Surf. Sci. Rep. 2008, 63, 427−464. (39) Springer Materials, Landolt-Börnstein, new series IV/19A, 2016. (40) Hara, S.; Izumi, S.; Kumagai, T.; Sakai, S. Energy, Stress and Structure of Well-Relaxed Amorphous Silicon: A Combination Approach of Ab Initio and Classical Molecular Dynamics. Surf. Sci. 2005, 585, 17−24. (41) Maury, H.; André, J.-M.; Guen, K. L.; Mahne, N.; Giglia, A.; Nannarone, S.; Bridou, F.; Delmotte, F.; Jonnard, P. Analysis of Periodic Mo/Si Multilayers: Influence of the Mo Thickness. Surf. Sci. 2009, 603, 407−411. (42) Zhong, L.; Wang, J.; Sheng, H.; Zhang, Z.; Mao, S. Formation of Monatomic Metallic Glasses through Ultrafast Liquid Quenching. Nature 2014, 512, 177−180.

34895


Direct Observation of the Thickness-Induced Crystallization and Stress

Recommend Documents