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# Solid -state dewetting in Pd/a-Ge bilayers

Bärbel Krause, Gregory Abadias, David Babonneau

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Bärbel Krause, Gregory Abadias, David Babonneau. Solid -state dewetting in Pd/a-Ge bilayers. Scripta Materialia, 2026, 276, pp.117188. 10.1016/j.scriptamat.2026.117188. hal-05497956

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# Solid-state dewetting in Pd/a-Ge bilayers

Bärbel Krause ID a,*, Gregory Abadias ID b, David Babonneau ID b

## ARTICLE INFO

### Keywords:

Dewetting

Real-time curvature measurement

Germanides

Sputter deposition

Solid-state reaction

Local epitaxy

## ABSTRACT

The post-growth morphology and the chemical composition of sputter-deposited Pd/a-Ge films were studied by in situ atomic force microscopy and X-ray photoelectron spectroscopy under UHV conditions. The polycrystalline films consist of locally epitaxial Pd/Pd₂Ge grains on an amorphous germanium buffer layer. We found that the films show a thickness-dependent tendency for solid-state dewetting, which occurs at the interface between the Pd and Pd₂Ge layers and for Pd thicknesses below 6 nm. The post-growth dewetting is correlated with the real-time stress evolution during deposition. Real-time x-ray reflectivity measurements confirm that the dewetting is kinetically hindered during deposition, while individual grains dissolve after deposition, leaving deep holes. The room-temperature dewetting of Pd/a-Ge combines characteristic features of epitaxial and polycrystalline dewetting mechanisms. We propose that it is driven by the misfit strain between Pd and Pd₂Ge, while the stability of individual grains is determined by the local grain boundary configuration.

Thin films and multilayers are used for many applications, including quantum computing, sensors, solar cells, and protection layers. Independent of the application, the long-term stability and the interface quality are key figures determining the practical use of the layer systems. Thin film degradation via dewetting was therefore extensively studied for various thin film systems. In many cases, the dewetting processes can be described by continuum approaches [1–3]. The thermal dewetting of polycrystalline metal thin films, however, is strongly affected by the grain structure, i.e. the specific orientation and local environment of each grain. It was shown that the dewetting of polycrystalline films takes place by local grain dissolution and growth of (mainly, but not only) neighboring grains [4–6].

Dewetting as stress relaxation mechanism was extensively studied for epitaxial bilayer systems [7–9]. The solid-state-dewetting of polycrystalline bilayer systems, i.e. the impact of grain boundaries in addition to the stresses induced by the interface, is less well understood [10]. In the following, we will report on the solid-state dewetting in ultra-thin, polycrystalline bilayer films. Specifically, we will demonstrate the correlation between stress evolution during deposition and a thickness-dependent tendency for post-growth dewetting at the polycrystalline but locally coherent Pd(111)/Pd₂Ge(111) interface which forms during deposition of Pd on amorphous Germanium (a-Ge) [11]. For this, we combine the results of *in situ* surface characterization studies of as-deposited bilayers (using the UHV cluster available at the KIT Light Source) with real-time information obtained during deposition, per-

formed at the beamline SIXS of the Synchrotron Soleil (France). All samples were deposited using the same growth chamber.

Pd/a-Ge bilayers were deposited by magnetron sputtering without intentional substrate heating on 1 mm thick Silicon wafers covered by native oxide. For Ge deposition, an RF power of 30 W and a target-substrate distance of 129 mm were used. Pd was deposited by DC sputtering at 20 W and a target-substrate distance of 325 mm. The base pressure of the chamber was $2 \times 10^{-6}$ Pa, the Ar pressure during deposition 0.37 Pa. The resulting deposition rates were $0.020 \pm 0.001$ nm/s for Pd, and $0.0495 \pm 0.0020$ nm/s for Ge. Under these conditions, the heating of the substrate due to the deposition itself is of the order of few degrees only, and we will refer to the substrate temperature as 'room temperature'. The surface after deposition was studied for a sample series with a 6.8 nm-thick Ge layer and a Pd thickness, $h_{Pd}$, varying between 1.2 and 9 nm. In the following, we will refer to a specific sample using the $h_{Pd}$ value and (if needed) a consecutive number for repeated depositions with the same $h_{Pd}$. The as-deposited sample surface was characterized *in situ* by non-contact Atomic Force Microscopy (AFM) and X-ray Photoelectron Spectroscopy (XPS) measurements. Height distributions and roughness values ($\sigma_{post}$, extracted by a Gaussian fit from the height distribution) were determined from AFM images with the size $1000 \times 1000$ nm² and $400 \times 400$ data points. For the roughness, an error of 10% was assumed. To highlight special features of the morphology, zoomed-in images with the size $500 \times 500$ nm² were recorded. The AFM images were plotted using the free software WSxM [12]. The

<footnote>a Institut für Photonenforschung und Synchrotronstrahlung (IPS), Karlsruher Institut für Technologie, Karlsruhe, D-76021, Germany</footnote>

<footnote>b Institut PPrime, Département Physique et Mécanique des Matériaux, UPR 3346 CNRS, Université de Poitiers, TSA 41123, Poitiers Cedex 9, 986073, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: baerbel.krause@kit.edu (B. Krause).</footnote>
<figure><img src="image_4.png" /><figcaption>Fig. 1. (a) Real-time stress evolution during deposition of Pd on amorphous germanium. For clarity, the curves corresponding to 3 different samples are vertically shifted. (b) Real-time (lines) and post-growth (black circles) roughness at different $h_{Pd}$.</figcaption></figure>

image analysis was performed with Matlab. Complementary information about the real-time evolution of the roughness, $\sigma^{\text{depo}}$, was obtained with a precision of ±0.01 – 0.02 nm from X-ray reflectivity (XRR) measurements during Pd/a-Ge deposition on 100 µm thin silicon substrates covered by native oxide. Simultaneously, the stress state during deposition was monitored by optical curvature measurements. The force per unit width (F/w), which is equivalent to the stress × thickness product, was calculated from the thickness and the elastic properties of the substrate using the Stoney equation. The slope of F/w corresponds to the incremental stress, $s_i$, which represents the stress change per deposited volume. Further information about the deposition conditions and the sample characterization, including a detailed example for the extraction of roughness values from real-time XRR, can be found in [11].

Fig. 1 relates the stress evolution during deposition to the thickness-dependent morphology during and after deposition, using the roughness as indicator for morphology changes. Fig. 1(a) presents repeated measurements of the real-time F/w curves during Pd deposition on a-Ge. In all cases, Pd₂Ge forms up to the F/w peak at $h_{Pd} = 2$ nm (region I) and is then covered by Pd. The characteristic tensile peak originates from the crystallization of an initially amorphous Pd₂Ge layer. During fur-

ther Pd deposition, an F/w plateau is observed (region II with $s_i \approx 0$), followed by compressive growth ($s_i < 0$) in region III with $h_{Pd} \ge 6.0$ nm. The stress evolution close to the interface ($h_{Pd} < 3$ nm) is highly reproducible. It is related to the interface formation and was discussed elsewhere [11]. During further deposition, the data are qualitatively similar, but the length of the plateau and the slope in the compressive region vary from sample to sample.

The F/w evolution is correlated with the roughness evolution shown in Fig. 1(b). For two of the stress curves, the simultaneously measured roughness, $\sigma^{\text{depo}}$, is shown as line in the respective color. In the regions I and II, $\sigma^{\text{depo}}$ is close to the substrate roughness ($\approx 0.33$ nm). In region III, $\sigma^{\text{depo}}$ increases slowly but does not exceed 0.6 nm. The post-growth roughness, $\sigma^{\text{post}}$, is shown as dots. Close to the interface (region I) and during later growth (region III), $\sigma^{\text{post}}$ agrees with $\sigma^{\text{depo}}$. In the plateau region, however, $\sigma^{\text{post}}$ increases with increasing $h_{Pd}$. The maximum roughness of 1 nm is obtained after deposition of $h_{Pd} \approx 5$ nm. This coincides with the maximum extent of the F/w plateau. The difference between $\sigma^{\text{depo}}$ and $\sigma^{\text{post}}$ can only be explained by post-growth morphology changes occurring in region II.
<figure><img src="image_5.png" /><figcaption>Fig. 2. (a) Examples for the morphology of Pd/a-Ge samples in the intermediate thickness region (image size 500 × 500 nm², for the corresponding 1 × 1 µm² images see supplementary material, Fig. S1). All images use the same color scale but have different zmax. The samples show characteristic holes, often surrounded by ridges (dashed circles). (b) Height distribution of 1 × 1 µm² AFM images with different hPd. For clarity, the curves are vertically shifted. The stars mark the expected position, z*, of the surface in region II and III, assuming dewetting at the Pd/Pd₂Ge interface. The dots were calculated assuming dewetting at the Pd₂Ge/a-Ge interface. The Pd₂Ge interlayer forms reactively and is completed at hPd = 2.0 nm, corresponding to a Pd₂Ge thickness of 3.0 nm. The threshold images in (c) enhance the structure evolution. Red regions with z < 〈z〉 - 1.5σpost correspond to deep holes. The blue, interconnected regions are elevated with z > 〈z〉. Fig. S2 (supplementary material) shows the same images with a constant threshold of ±0.4 nm. (d) AFM line scans crossing deep holes after deposition of different amounts of Pd.</figcaption></figure>

Fig. 2(a) shows AFM images typical for region II, revealing the origin of the roughness increase. Compared to the surfaces in region I (germanide formation) and III (thick Pd layers), which are characterized by densely packed clusters with a typical size of 20–30 nm [11], the surface in region II is less homogeneous: The cluster size varies from 10 to 50 nm, and deep holes with a typical diameter around 40 nm are visible, often surrounded by ridges (e.g., encircled regions). The corrugation increases with hPd. This morphology is known from thermal dewetting of polycrystalline thin films. Selected line scans in Fig. 2(d) visualize the difference between average surface height and local hole depth for hPd = 3.4 nm and hPd = 4.8 nm (1).

The height distributions extracted from the AFM images are shown in Fig. 2(b). They allow for comparing the average surface height, 〈z〉, and the depth of the holes. z = 0 is given by the lowest point within the scanned region. The surfaces in region I and III, which are not affected by the dewetting process, have a Gaussian height distribution. Without hole formation, 〈z〉 is comparably low (1 nm during Pd₂Ge deposition in region I, and 2 nm during later growth in region III). In region II, the height distribution shifts continuously to higher values and becomes increasingly asymmetric. Surprisingly, the height profiles of two repeated depositions, hPd = 4.8 nm (1) and (2), are different. 4.8 nm (2) is the only height profile with two maxima. The corresponding AFM image and the XPS spectra of 4.8 nm (1) and (2) are shown in Fig. 3. In agreement with the different morphologies, the Pd 3d 5/2 spectrum of 4.8 nm (1) shows the characteristic asymmetric spectrum of metallic Pd, while the spectrum of 4.8 nm (2) is broadened due to coexisting Pd-Ge and Pd-Pd components (Fig. 3(b)). We attribute the first maximum of the height distribution to uncovered Pd₂Ge areas (explaining the Pd-Ge component of the XPS signal), and the higher maximum to areas covered by metallic Pd (in agreement with the Pd-Pd component of the XPS signal). It seems that the different XPS signals of the samples 4.8 nm (1) and (2) reflect a different degree of solid-state dewetting at the Pd/Pd₂Ge interface. To verify this assumption, we have compared the measured height distributions with the expected Pd layer thickness. For each sample, the lowest data point within the measured region determines the shift of the peak

position. Assuming that the holes in the dewetting region reach down to the Pd/Pd₂Ge interface, we have calculated the surface height, z*, expected for a homogeneous Pd layer:

$$z^* = z_{ref} + h_{Pd} - h_{Pd}^0 \quad (1)$$

For hPd ≤ hPd0 = 2.0 nm, Pd is converted to Pd₂Ge. The morphology during Pd₂Ge formation does not change significantly, as confirmed by the height distributions at hPd = 1.2 nm and hPd = 1.8 nm. Therefore, we use zref = 〈z(hPd = 1.8 nm)〉 as reference for the Pd/Pd₂Ge interface. z* is shown as stars in Fig. 2(b). The maximum of the measured height distributions is close to the height expected for a homogeneous Pd layer on the Pd₂Ge interlayer, confirming that at least some of the holes reach down to (or close to) the Pd/Pd₂Ge interface. An alternative calculation was performed, assuming dewetting at the Pd₂Ge/a-Ge interface (dots). Compared to the stars, these values are increased by 3.0 nm, i.e. the Pd₂Ge thickness. This scenario can be excluded since the calculated values differ by several nm from the maximum of the height distribution. Small deviations between expected and calculated values, as e.g. found for hPd = 3.4 nm and hPd = 4.0 nm, are attributed to the small number of deep holes in the measured area, resulting in statistical errors.

The holes are better visible in the threshold images extracted from the 500 × 500 nm² AFM images (Fig. 2(c)), where areas with z < 〈z〉 - 1.5σpost are shown in red. The meander-like structures formed by areas with z above (blue areas) and below (grey + red areas) the average surface height are typical for the dewetting region. With increasing hPd, the number of holes decreases, and the typical length scales (hole diameter, meander diameter) increase.

Our results reveal a thickness-dependent tendency for solid-state dewetting of ultrathin Pd layers deposited at room temperature on a-Ge. The post-growth dewetting occurs only for hPd values in the plateau region of the real-time F/w curve, i.e., post-growth dewetting is only observed in a thickness region where the incremental stress during deposition is near 0. The surface roughness is a clear indicator of the morphology change. As shown in Fig. 1(b), the dewetting during deposition is kinetically hindered. The roughness increase occurs only af-
<figure><img src="image_6.png" /><figcaption>**Fig. 3.** (a) AFM image of the sample (2) with $h_{Pd} = 4.8$ nm (image size $1000 \times 1000$ nm$^2$). (b) XPS spectra of the samples (1) and (2) with $h_{Pd} = 4.8$ nm (black and red symbols). The Shirley background and the fitted Pd-Pd and Pd-Ge components are shown as gray, red and black lines. The expected peak positions for the Pd-Pd and the Pd-Ge bond are indicated by solid and dashed vertical lines, respectively.</figcaption></figure>

ter growth interruption. It originates from the local dissolution of Pd grains, leaving holes that reach down to the $Pd_2Ge$ interlayer. As expected for solid-state dewetting, the density of holes decreases with increasing Pd thickness [1]. When $h_{Pd}$ exceeds the $F/w$ plateau region, the Pd film remains stable. This is in agreement with previous studies of solid-state dewetting. Various polycrystalline, thin metal films of 10–40 nm thickness were reported to be stable at room temperature, but dewetting could be induced by a temperature increase of the order of 100 K [4,5,10]. Sputter-deposited, ultrathin Ag layers on silicon covered by native oxide, e.g., were found to be continuous after deposition, but dewetted at elevated temperatures. The homologous temperature, $T/T_m$, i.e. the temperature normalized to the melting point $T_m$ of a material, is a measure for self-diffusion. The room-temperature values for Pd and Ag are 0.15 and 0.22 [13]. Thus, solid-state dewetting of a continuous film at room temperature should be less likely for Pd than for Ag. Furthermore, it was found that a Ge buffer layer facilitates the formation of continuous Ag layers at few nm thickness [14]. Pd interacts much stronger than Ag with Ge, forming even compounds and locally

epitaxial bilayer grains. Therefore, the observed dewetting of Pd at room temperature seems to be surprising.

In the following, we will discuss our findings in the context of the dewetting models summarized in Fig. 4. Fig. 4(a) visualizes the post-growth dewetting of epitaxial, Fig. 4(b) the post-growth dewetting of polycrystalline thin films. The solid-state dewetting after Pd deposition on a-Ge occurs at the coherent Pd/$Pd_2Ge$ interface, combining therefore characteristics of epitaxial and polycrystalline solid-state dewetting, as schematically shown in Fig. 4(c). Based on our experimental observations, we consider the post-growth dewetting without wetting layer (Volmer-Weber growth). Without deposited flux $F$, and assuming a sufficiently high mobility of the atoms, dewetting can occur at $h_c = 0$ nm. Dewetting during deposition occurs for layers above a flux and temperature-dependent critical thickness, $h > h_c(F, T)$. As shown in Fig. 4, post-growth dewetting is possible for $h < h_c(F, T)$.

Dewetting is driven by the reduction of the Gibbs free energy, $\Delta G$, with
<figure><img src="image_7.png" /><figcaption>Fig. 4. Post-growth solid-state dewetting for (a) epitaxial, (b) polycrystalline, and (c) locally epitaxial thin films. The critical thickness, $h_c$, for dewetting during deposition depends on the flux F and the temperature T. In case of epitaxial thin films, it is also affected by the lattice strain, $\epsilon$. Due to the locally different grain boundaries (dashed yellow/red lines), the critical thickness of polycrystalline films is position-dependent (x being the position). Thus, grain 1 dissolves after deposition while grain 2 with different grain boundary orientations remains unchanged. For locally epitaxial films, both contributions, x and $\epsilon$, are relevant.</figcaption></figure>

$$ \Delta G = \Delta G_{s/l} + \Delta G_{GB} + \Delta G_{el} \quad (2) $$

The geometry changes during the dewetting process affect the surface and interface contributions, summarized in $\Delta G_{s/l}$, and reduce the total grain boundary energy, $\Delta G_{GB}$. In case of epitaxial films (Fig. 4(a)), the reduction of the elastic energy $\Delta G_{el}$ due to the lattice mismatch is dominant. The elastic energy increases with increasing film thickness and can be reduced by different mechanisms, including grain rotation, dislocation formation, twinning, and dewetting [1,7,15]. Dewetting is favored at low film thicknesses and large lattice mismatch, i.e. the critical thickness for dewetting in epitaxial systems, $h_c(F, T, \epsilon)$, depends on the lattice strain, $\epsilon$. Dewetting (i.e., quantum dot formation) during and after deposition can occur for nm-scale semiconductor layers with a lattice mismatch $\ge 2\%$ [7]. As previously reported, we found strong indications

for local epitaxial growth of Pd on a Pd$_2$Ge template [11]. For the coherent growth of Pd(111) on Pd$_2$Ge(111) with the proposed in plane orientation Pd$_2$Ge[110] || Pd[110], the lattice mismatch is comparatively large (5.6% with respect to Pd along Pd[110]). Thus, the reduction of the elastic energy can explain the dewetting at the Pd/Pd$_2$Ge interface. Recent simulations based on continuum models propose that strain accelerates the dewetting process [16]. The observed dewetting of only few nm thin Pd layers on Pd$_2$Ge already at room temperature, which is also the deposition temperature, is in agreement with this conclusion.

In case of polycrystalline films, the grain boundary energy is assumed to be most relevant. It depends on the grain size and increases with the angle between adjacent grains, leading to a position-dependent critical thickness, $h_c(F, T, x)$. The dewetting of a polycrystalline film is visualized in Fig. 4(b). Grain boundaries act as surface diffusion barriers [17], imped-
ing the inter-grain diffusion required for dissolution of grains. Annealing enhances the inter-grain diffusion, enabling the dissolution of unfavorable grains with large-angle grain boundaries. The material is added to more favorable grains, which leads to a characteristic inhomogeneous morphology [2,18]. For Pd/a-Ge, we have found typical signs for grain dissolution. We suggest therefore that both contributions (grain boundary and misfit strain) contribute to the dewetting process. Thus, the critical thickness, $h_c(F, T, x, e)$, depends on lattice mismatch and position. Close to the interface, we assume a Pd grain density given by the $Pd_2Ge$ template, as shown in Fig. 4(c). $\Delta G_{GB}$ and $\Delta G_{el}$ increase with the film thickness, i.e. the driving force for dewetting increases. $\Delta G_{el}$ as a volume effect drives the dewetting process, but the local grain boundary energy, $\Delta G_{GB}(x)$, determines the probability for dissolution of a specific grain. The dewetting is observed only in region II, indicating that other relaxation or growth mechanisms dominate the later growth stages.

Interestingly, the post-growth dewetting occurs in a thickness region where the $F/w$ signal during deposition is nearly constant. For epitaxially strained films with $h < h_c(F, T, e)$, a constant slope during deposition would be expected, with negative slope for $a_F > a_S$ and positive slope for $a_F < a_S$, $a_F$ and $s_S$ being the lattice parameters of film and substrate. However, in case of polycrystalline thin films, lattice mismatch is only one of many contributions to the total stress [19]. The $F/w$ plateau might be related to superposed effects, e.g. a tensile incremental stress due to the local epitaxy, and a compressive incremental stress due to point defects. Competing mechanisms of stress build-up and relaxation, sensitive to tiny changes in the growth conditions and local defect density, would explain the slightly different lengths of the $F/w$ plateau during repeated depositions. Eventually we find that the $F/w$ plateau is clearly correlated with the occurrence of post-growth dewetting, but its origin remains ambiguous due to the complexity of the system.

We have shown that dewetting processes in locally epitaxial systems can occur within few nm of the interface, in analogy to the quantum dot formation in epitaxial systems. The discrepancy between post-growth and real-time roughness evolution indicates a kinetically hindered dewetting process. Solid-state dewetting in polycrystalline layers is strongly affected by the local microstructure, and its control is therefore even more challenging than the control of epitaxial quantum dot formation.

### CRediT authorship contribution statement

**Bärbel Krause:** Writing – original draft, Investigation, Formal analysis, Conceptualization; **Gregory Abadias:** Writing – review & editing, Investigation, Formal analysis; **David Babonneau:** Writing – review & editing.

### Data availability

Data will be made available on request.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgements

We acknowledge the synchrotron radiation source SOLEIL for the provision of beam-time within the standard proposal 20191667. We would like to thank the team of the beamline SIXS, Alessandro Coati, Yves Garreau, Andrea Resta, Alina Vlad, and Benjamin Voisin, for assistance in using beamline, and acknowledge the general support of the synchrotron staff. We are grateful for the support at the UHV Analysis Laboratory (KIT/IPS), provided by Annette Weißhardt. This work pertains to the French Government programs "Investissements d'Avenir"

(EUR INTREE, reference ANR-18-EURE-0010) and LABEX INTERACT-IFS (reference ANR-11-LABX-0017-01).

## Appendix A. Supporting material

The threshold analysis of selected $1 \times 1$ µm$^2$ AFM images is presented in Fig. S1 of the supporting material. An alternative threshold-analysis of the $500 \times 500$ nm$^2$ images, using a fixed threshold of $\pm 0.4$ nm, is presented in Fig. S2.

### Supplementary material

Supplementary material associated with this article can be found, in the online version, at 10.1016/j scriptamat.2026.117188

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