# Volmer-Weber growth stages of polycrystalline metal films probed by in situ and real-time optical diagnostics

Grégory Abadias, Lionel Simonot, Jérôme Colin, Anny Michel, S. Camelio, David Babonneau

► To cite this version:

Grégory Abadias, Lionel Simonot, Jérôme Colin, Anny Michel, S. Camelio, et al. Volmer-Weber growth stages of polycrystalline metal films probed by in situ and real-time optical diagnostics. Applied Physics Letters, 2015, 107 (18), pp.183105. 10.1063/1.4935034. hal-04978476

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Volmer-Weber growth stages of polycrystalline metal films probed by in situ
and real-time optical diagnostics

G. Abadias*, L. Simonot, J.J. Colin, A. Michel, S. Camelio, D. Babonneau

Institut Pprime, Département Physique et Mécanique des Matériaux, UPR 3346 CNRS,
Université de Poitiers, SP2MI, 11 Bvd M. et P. Curie, BP 30179, F86962 Chasseneuil-
Futuroscope cedex, France

Abstract

The Volmer-Weber growth of high-mobility metal films is associated with the development of a complex compressive-tensile-compressive stress behavior as the film deposition proceeds through nucleation of islands, coalescence and formation of a continuous layer. The tensile force maximum has been attributed to the end of the islands coalescence stage, based on *ex situ* morphological observations. However, microstructural rearrangements are likely occurring in such films during post-deposition, somewhat biasing interpretations solely based on *ex situ* analysis. Here, by combining two simultaneous *in situ* and real-time optical sensing techniques, based on surface differential reflectance spectroscopy (SDRS) and change in wafer curvature (MOSS), we provide direct evidence that film continuity does coincide with tensile stress maximum during sputter deposition of a series of metal (Ag, Au and Pd) films on amorphous SiOₓ. Stress relaxation after growth interruption was testified from MOSS, whose magnitude scaled with adatom mobility, while no change in SDRS signal could be revealed, ruling out possible changes of the surface roughness at the micron scale.
Polycrystalline metallic films growing in a Volmer-Weber (VW) mode, as typically encountered during condensation of metal vapors on insulating substrates, are technologically important in a variety of applications, such as catalysis, plasmonics or optics¹⁻⁴ for which nanoparticle synthesis is a requisite. The growth proceeds with the nucleation of isolated, single-crystal 3D islands which further grow to impinge each other before coalescing to form a continuous, polycrystalline film. These distinct stages are mediated by kinetically-driven processes affecting surface morphology, grain size and texture, but also the intrinsic stress state. Recent findings based on *in situ* stress measurements⁵⁻¹³ point out a non-monotonous stress evolution with increasing film thickness, which can be outlined by a compressive-tensile-compressive (CTC) sequence associated to the pre-coalescence, coalescence and post-coalescence stages.¹⁴⁻¹⁸

Despite many models⁷⁻⁹,¹¹,¹⁹⁻²¹ proposed in the last years for explaining the origin of compressive stress in the post-coalescence regime and its relaxation upon growth interruption for VW growing films, this issue is still under controversial discussion. Nevertheless, there exists a number of several findings which converge to evidence i) the critical role played by grain boundary in the stress mechanisms and ii) that surface processes are concerned with the reversible stress relaxation which occurs at short time scales (hundreds of seconds) when deposition is stopped. Moreover, there is an established consensus that tensile stress is generated during the island coalescence stage, as grain boundaries are continuously formed, a process driven by the reduction in interfacial/surface energies²². The magnitude of the tensile rise has been shown to depend (inversely) on the island size²³ and dihedral angles at grain boundary,²⁴ as supported by experiments, analytical modelling¹⁵,²⁵ and finite element calculations.¹⁶,²³,²⁶ As compressive and tensile stress sources
are operating (competing) simultaneously in this regime, this often causes the appearance of
a tensile peak. Although the location of the tensile peak is implicitly claimed to correspond to
the onset of continuous film formation, to date there is no direct and unequivocal
experimental proof of this statement. Also, under conditions of high atomic mobility,
abnormal grain growth<sup>27</sup> may occur during and after film deposition, affecting grain size
distribution and interpretations based on post-growth microstructural characterizations.
Therefore, one way to circumvent these limitations and obtain reliable information on the
different growth regimes connected with the CTC behavior is to take advantage of *in situ*
diagnostics.

In this work, we combine simultaneously two *in situ* and real-time optical diagnostics with
submonolayer sensitivity, based on surface differential reflectance spectroscopy (SDRS) and
multiple-beam optical stress sensor (MOSS) to characterize and directly connect the growth
mode and stress behavior of a series of metal films of different mobility deposited by
magnetron sputtering. We demonstrate that the tensile peak, observed at a nominal film
thickness *h*<sub>peak</sub>~5.8, ~10.3 and ~16.0 nm, for Pd, Au and Ag, respectively, actually matches
the end of the coalescence stage, providing unambiguous support to previous analytical
models and simulations.

Ag, Au and Pd films were sputter-deposited at room temperature under Ar plasma
discharges on Si wafers (100 ± 1 µm thick) covered with native oxide. Two *in situ* and real-time
optical systems, MOSS and SDRS, were combined and implemented simultaneously during
thin film growth. The MOSS system from k-Space Associates, with curvature resolution of 2.10<sup>-4</sup> m<sup>-1</sup>, uses an incident array of 3x3 parallel beams at incidence close to the substrate normal.<sup>28</sup>
The film force per unit width, F/w, a quantity equivalent to the stress-thickness product (σ×h),
was deduced from the change in curvature using the modified Stoney equation.<sup>29</sup> The
sensitivity of the experiment was about 0.1 N.m⁻¹. The optical properties of the films during
the metal deposition were measured in the 350-950 nm spectral range with a SDRS setup
described in details in Ref. 30. The incident angle was 70°, close to the Si Brewster angle, and
the polarization direction was parallel to the incident plane in order to obtain a greater
sensitivity during the very first deposition stages. The measurements were performed by
recording one spectrum per second. Details on the deposition conditions and determination
of film thickness are provided in the supplemental material.³¹ Post-deposition structural and
morphological characterizations were carried out using atomic force microscopy (AFM) and
transmission electron microscopy (TEM).³¹

Figure 1 shows a representative plot of the film force per unit width, *F*/*w*, versus film thickness *h* recorded during sputter-deposition of the Au film. When deposition starts the force tends to go slightly compressive, followed above *h*~1.5 nm by the gradual development of tensile stresses. Above *h*~10.3 nm, the incremental stress (given by the derivative of the *F*/*w*=$f(h)$ curve with respect to *h*) turns negative, corresponding to the build-up of compressive stress which reaches a steady-state regime of $\sigma_{ss} = -240$ MPa above *h*~30 nm. This CTC behavior is in agreement with data reported in the literature for evaporated Au films on mica³² and silicon nitride³³ substrates. As pointed out by Koch³⁴, the similarity in the film force curve evolution with film thickness observed for a variety of metal films independently of the deposition process attests of its intrinsic nature, and that atomistic processes are essentially governed by the high mobility character of the deposited adatoms. The tensile peak obtained under the present deposition conditions occurs at *h*<sub>peak</sub>= 10.3 nm, lower than the values of ~12.5 and ~15.5 nm observed by Leib et al.<sup>33</sup> and Winau et al.,³² respectively, for evaporated films under similar growth rate (0.1 nm/s). As the incoming flux involves particles with a larger angular distribution and considerably larger kinetic energy in sputter-deposition than in
thermal evaporation, more nucleation sites are expected to be created, decreasing thereby
the average island size as well as the nominal deposited thickness at which they start to
coalesce. Recently, Magnfält et al.³⁵ reported a monotonous decrease of $h_{peak}$ from 21 to 14
nm when increasing the pulsing frequency during growth of Ag films using a pulsed magnetron
sputtering technique. They showed that these findings were not the result of a change in
energetic particle bombardment during growth but either due to the increase of island density
in the early growth stage and/or a delay in the coalescence of isolated clusters at later stages.

Another characteristic feature of the film force curve shown in fig. 1 is the reversible³⁶ evolution towards tension upon growth interruption: a rapid tensile rise is observed in the first few hundred seconds, which gradually levels off with time. The time-dependence stress relaxation can be fit to an exponential decay function $y = y_0 - y_1e^{-t/\tau}$. The obtained time constant in the case of Au is τ~200 s, which is of the same order of magnitude as the fast, reversible morphological change identified by Yu et al.¹⁹,²⁰ from in situ MOSS and AFM image analysis.

To further characterize the different stages observed by MOSS, representative SDRS
signals, extracted at increasing Au film thickness corresponding to labels A, B, C and D in fig.
1, are shown in fig. 2. We represent in this figure the spectro-temporal variations of $\Delta R/R_0=(R$
$-R_0)/R_0$, where R is the film reflectance at time t and R₀ that of the Si substrate being used as
a reference (at time t = 0). SDRS measurements were compared with optical simulations
assuming an ideal 2D (homogeneous and continuous) growth mode, at constant growth rate
and using the complex refractive index of the bulk metal ("multimedia view").³¹ For a small
amount of deposited metal (h=3.4 nm), isolated islands are formed following the VW growth
mode. The metallic islands exhibit a localized surface plasmon resonance (LSPR), which
induces absorption of light at wavelengths located in the visible range. This absorption band
appears as a broad maximum in the SDRS signal (see fig. 2a). Its characteristics (position, amplitude, width) depend on the complex refractive indices of both the metal islands and the substrate, but also on the size, shape and spatial arrangement of the islands.37 As the film deposition proceeds, the LSPR peak becomes greater and broader with an obvious red-shift (fig. 2b) as a consequence of coalescence events occurring during the growth of the metal islands. It has been shown for similar systems obtained by physical vapor deposition that the increase of the metal amount results in both a progressive decrease of the areal density of islands and an increase of their average diameter.37,38 Meanwhile, the average height also increases but at a lower rate than the average diameter37 because the vertical growth is driven mainly by direct deposition of atoms from the incident flux on the top of the islands, while their lateral growth is governed by adatom surface diffusion on the substrate and mostly by coalescence. The average height-to-diameter ratio of the islands therefore decreases (i.e., islands flatten), leading to the observed red-shift of the LSPR. For longer metal deposition times, the absorption band becomes less and less conspicuous (see fig. 2c for h=8.4 nm). Percolation prevails in this regime so that the metal islands cannot be individualized any longer, and above a certain thickness the metal film grows with the same optical response as a continuous film (see fig. 2d for h=10.9 nm). The reflectance subsequently evolves until a certain thickness beyond which the metallic layer becomes opaque to visible wavelengths. Both *ex situ* TEM31 and AFM (insets of fig.2) observations qualitatively support the interpretation of SDRS signals.

It is noteworthy that the nominal film thickness at which the film optically behaves as a fully continuous layer (fig. 2d), $h_{cont}$, coincides with the position $h_{peak}$ of the tensile peak maximum observed in fig. 1. To ascertain that this experimental finding is an intrinsic feature of VW growth, we have examined additional data obtained on metallic films with lower (Pd)
and higher (Ag) adatom mobility. Fig. 3a shows the comparative evolution of the film force recorded from MOSS. The characteristic CTC behavior is observed for Ag and Pd, attesting of a VW growth. However, the magnitude of the tensile stress developing during the coalescence stage is respectively lower and larger, as compared to Au. This is a direct consequence of the difference in island size. As reported in an earlier study¹³ the average diameter of islands decreases from *L* ~ 23.3 nm for Ag to *L* ~ 9.2 nm for Pd for a nominal deposited thickness *h*~3 nm. As the stress generated during grain boundary formation varies inversely with *L* (as *L*⁻¹/² in the Hoffman model²²), this explains the increase of the tensile coalescence stress with decreasing adatom mobility. This is also reflected in the position of the tensile peak maximum, occurring at *h*<sub>peak</sub>= 5.8 and 16.0 nm for Pd and Ag, respectively, since a higher island density causes earlier impingement and coalescence of islands, as well as earlier onset of continuous film formation. Similar findings were reported by Seel et al.¹⁶ for evaporated Ag films, for which the adatom mobility was varied by changing the deposition temperature.

The measured SDRS signals (red full line) and the corresponding simulated spectra (black
dotted lines) recorded during the growth of Ag, Au, and Pd films up to h=25 nm are provided
as supplemental video files (see fig. 2 and fig. S1 from ref. 32). A first way to quantitatively
determine the value hcont from these SDRS data consists in calculating the normalized
quadratic difference A between the measured and simulated data over the whole spectral
range 350-950 nm. Alternatively, the ratio B between the slopes of the measured and
simulated curves in the infrared range (730-950 nm) can be determined. In this range,
corresponding to energies below interband transitions, the dielectric function of bulk metals
can be usually modelled using a Drude approach characterized by the plasma frequency and
the damping constant related to the free electron lifetime. This latter is supposed to vary
(increase) with grain size. In the early stages of deposition, the measured slopes in the infrared
are negative due to the presence of a LSPR in the visible range, yielding negative *B* values (see fig. 3b). With increasing thickness, values of *B* increase, become positive and eventually reach an asymptotic value in the continuous growth regime (*B*=1 in the ideal case). At the same time, the quantity *A* approaches zero. The values of *h*<sub>peak</sub>, determined from MOSS, versus *h*<sub>cont</sub>, deduced from SDRS using the procedure described above are shown in the inset of fig.3b. Although the determination of *h*<sub>cont</sub> is associated with a large uncertainty (± 1 nm) whatever method is used, *A*→0 or *B*→1, we can see that within the uncertainty of data measurements and analysis, *h*<sub>peak</sub> = *h*<sub>cont</sub>, supporting the important conclusion that the observed tensile peak observed in the film force evolution during VW growth does coincide with the onset of an optically continuous metallic film.

Moreover, in fig. 3b, it is worth noting that the thickness at which $B=0$ can be obtained with a rather good precision (± 0.2 nm). At this thickness, the measured slope in the infrared is equal to zero due to a very broad resonance. It may be related to the so called elongation transition,<sup>39,40</sup> occurring shortly before percolation, where the substrate surface is largely covered by isolated and elongated structures. The percolation thickness, $h_{\text{perc}}$, was therefore obtained from $B=0$ intercept. For Au, the value $h_{\text{perc}}=5.8$ nm is in reasonable agreement with the visual inspection of AFM image taken at $h=5.9$ nm (inset of fig. 2b). For Pd, a much lower value of 1.6 nm is obtained. An independent measurement using *in situ* electrical resistivity<sup>41</sup> yielded a value of 1.6 nm for the percolation threshold in Pd films, validating our experimental procedure. For Ag, a larger value $h_{\text{perc}} \sim 7.5$ nm is found, at the origin of the later completion of the coalescence stage and formation of larger islands.

In the continuous growth regime, the metallic films develop compressive stresses, with a steady-state magnitude $\sigma_{ss}$ ranging from -50 MPa (Ag film) to -280 MPa (Pd film). Upon growth interruption, a rapid tensile rise occurs, as already noticed and discussed for the case of Au.
However, there exists a striking difference in the magnitude of the stress relaxation between the three metals, see fig. 4, where the time-dependence of the stress evolution after deposition was halted is normalized to the quantity $\Delta\sigma_{tot} = \sigma_{max} - \sigma_{end}$. Here, $\sigma_{max}$ and $\sigma_{end}$ refer to the maximum tensile stress (at $h_{peak}$) and stress at the point of interruption, respectively. The magnitude of the relative relaxation decreases significantly with decreasing material mobility, from approx. 85% (Ag) down to 8% (Pd) after 800 s. This supports the idea that the fast and reversible surface processes (with time constants $\tau$ of ~3×10$^2$s) are mediated by the atomic mobility of the metal atoms involved in surface diffusion mechanisms, in agreement with proposed models of emptying excess trapped atoms from grain boundary$^{7,11}$ or a deepening of grain boundary grooves as the surface morphology approaches its equilibrium shape.$^{20}$ It must be pointed out that no perceptible change in the SRDS signal could be detected after growth interruption. This may be related to the lack of sensitivity of the technique when probing an optically continuous film. Nevertheless, it rules out possible morphological changes that would occur at micrometric length scale.

In summary, by combining simultaneously two *in situ* and real-time optical diagnostics we were able to provide direct experimental evidence that the point at which the film stress reaches a maximum tensile value does coincide with the end of the coalescence stage and the formation of a continuous film. This behavior has been demonstrated for metals with different mobility, testifying that it is an intrinsic characteristic of metallic films growing in a VW mode.

## Acknowledgments

The authors wish to acknowledge Dr. Philippe Guérin for his technical support and maintenance of the deposition system.
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**Figure captions**

**Figure 1:** Evolution of the film force per unit width, *F*/*w*, during and after sputter-deposition of Au film on SiOx. The dashed line is a fit of the relaxation part after growth interruption (see text).

**Figure 2:** Measured SDRS signals (red full line) and the corresponding simulated spectra assuming a continuous 2D film growth (black dotted lines) for different thicknesses of Au film deposited on SiOx, extracted from video file ("Multimedia view"). (a) *h*=3.4 nm, (b) *h*=5.9 nm, (c) *h*=8.4 nm, (d) *h*=10.9 nm. The insets show the corresponding *ex situ* AFM surface morphology (250 × 250 nm² image, vertical scale is 10 nm).

**Figure 3:** a) Evolution of the film force *F*/*w* and b) *A* and *B* quantities extracted from SDRS data treatment (see text) during growth of Ag, Au, Pd films. The percolation thickness, *h*<sub>perc</sub>, film continuity thickness, *h*<sub>cont</sub>, and thickness at which the tensile peak is reached, *h*<sub>peak</sub>, are shown by arrows in the case of Ag. The inset in b) shows the evolution of *h*<sub>cont</sub> vs. *h*<sub>peak</sub> for the three studied metals.

**Figure 4:** Magnitude of the tensile stress rise after growth interruption, normalized to the quantity Δ*σ*<sub>tot</sub>, for the three studied metal films.
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