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Complex dewetting scenarios of ultrathin silicon films for large-scale nanoarchitectures

Si-based nanoarchitectures are formed with unprecedented precision and reproducibility via templated dewetting of thin SOI.


Fabrication and characterization
The investigated samples were UT-SOI substrates: single-crystal (001) Si films, 12 nm thick on a 25 nm thick buried oxide (BOX) SiO2 layer on a Si (001) bulk wafer. E-beam lithography (EBL) and reactive ion etching (RIE) are performed following a well-established procedure (fig. S1a): a resist is spin-coated on the sample surface and irradiated with electrons to define the patches to be etched on the sample. The resist and RIE parameters are reported in (74). The resist is then developed via chemical attack, removing the e-beam-written parts and exposing the UT-SOI surface. The RIE process is used to remove the exposed UT-SOI surface. The etching depth was about 15 nm thus etching the UT-SOI up to the underlying BOX. The sample surface is then exposed to O2 plasma in order to remove the residual resist. Additional chemical cleaning is performed in N2 atmosphere before dewetting, by dipping the sample in a 5% HF solution for 20 seconds. In the ultra-high vacuum of a molecular beam reactor the samples are annealed at high temperature. All the investigated samples are cleaned with an annealing flash at 600°C for 30 minutes in order to eliminate any trace of native oxide from the sample surface. Two different samples were annealed with different procedures: sample A, 720 for 3 hours; Sample B, 740°C for 15 minutes. The samples are characterized with different imaging techniques: atomic force microscopy (AFM, the AFM images were processed using WSxM software), scanning electron microscopy (SEM) and optical dark-field microscopy (DF, see the three panel of fig. S1b). DF microscope images are obtained by shining white light with a ~70 degrees angle with respect to the sample surface (see the right panel of fig. S1b). The light diffusion is collected by a high numerical aperture (NA=0.75) 100X magnification objective lens providing a lateral resolution of about 400 nm. Images are registered with a C-MOS camera. As the overall collection angle in the NA of the objective lens is smaller than 70 degrees, the direct reflection from the sample is completely rejected and the flat surface appears completely black. Note that the silicon and titania islands are de facto dielectric Mie resonators, thus the collected signal is the resonant scattering from these nano-antennas. This is reflected in the different scattering colors visible in the DF images. Figure S2 illustrates the AFM and SEM characterizations of more complex dewetted patterned substrates. Further characterization of the level of ordering can be obtained via 2D Fourier transform (FT) of the DF images shown in Figure 3 in the main text (see fig. S3a). Sharp features of the FT are visible both at the center and on the sides of the images accounting for a good reproducibility of the final outcome over many repetitions. It is not easy to quantify the level of disorder over many repetitions of such complex patterns. A possible way is measuring the sizes of the dewetted particles in each individual patch from DF images providing a qualitative picture of their statistical distributions. This analysis is presented in the supplemental information fig. S3b. Starting from the DF images shown in Figure 3 in the main text and producing a binary black and white images (see the insets on each panel of fig. S3b), we can plot the statistical distribution of the islands over 144 repetitions of the same pattern. Note that, as the lateral resolution of the DF microscope is limited by the numerical aperture (NA) of the objective lens, this procedure may overestimate the real size of the islands (lateral resolution LR~0.6 λ/NA, where NA=0.75 is the numerical aperture of the 100X magnification objective lens and λ is the wavelength of the scattered light, thus LR~400 nm). Qualitatively, the main features are summarized as follows: for simple patches (few holes) the fluctuations of the islands' size distribution are in the ~% range. For more complex architectures the islands' size distributions broaden even if in some cases bimodal and trimodal distributions of size are still well visible. In fine, for strongly disconnected patterns the statistical distributions are almost completely blurred.

Simulations
A 3D model accounting for surface diffusion limited kinetics during dewetting phenomena is considered. In particular, a Phase-Field approach is selected in order to deal with 3D geometries and with complex evolutions involving topological changes. The Phase-Field (PF) model adopted in this work consists of calculating the evolution of an order parameter φ describing the phases of the system, namely the solid (φ = 1) and the vacuum phase (φ = 0), with a continuous variation in between (41,75). This model is based on the Ginzburg-Landau energy functional:

Equation 1
= ∫ ( ϵ 2 |∇φ| 2 + 1 ϵ (φ)) Ω ϵ corresponds to the thickness of the transition region between the phases while (φ) = 18φ 2 (1 − φ) 2 is a double-well potential ensuring the energy minima for the bulk phases. The surface energy density is here considered isotropic and it is set to γ = 1 (generalization to anisotropic surface energies can be found in Refs. (45, 46) ). The evolution law to reproduce surface diffusion is given by the degenerate Cahn-Hilliard equation where (φ) = 2 (φ) is the mobility restricted to the interface while μ is the chemical potential given by / φ. Notice that, in Eq. 2, the mobility function is a fourth order polynomial in φ. This, at variance with previous reports of phase field modelling of solid state dewetting, ensure a better description of surface diffusion at long timescales (87, 88).
When considering isotropic γ, μ is computed by the following equation: The use of the stability function (φ) = 30φ 2 (1 − φ) 2 (40, 48) leads to higher order convergence allowing to take into account larger interface thickness and time stepping. The chemical potential from Eq. (3) directly corresponds to the diffuse interface representation of the local curvature at the interface (shown in Fig. 2 in the main text).
In fig. S5 an illustration of the phase field description of the thin-film during dewetting is shown together with the adapted mesh. In all the simulations we set ϵ = 0.2.

Supplementary Information Videos
Along with the relevant snapshots of the simulations reported in Figure 3 and 4 in the main text, we provide here also the complete morphological evolutions by means of the Supplementary Materials Videos as listed in the proper section. They report the evolution of the square patches, with and without patterning, from a top-view. The frames shown therein are taken every 500 iterations of the numerical method. Notice that we adopted an adaptive time step so that the time scale is nonlinear. In particular, more iterations per unit time are required when topological changes occur. With this choice, we illustrate better the crucial phases such as holes formation and breakups, as they occur on a much faster time scale than the global evolution. However, the difference in the velocity of different stages is still qualitatively described.

Nanoimprinting
A scheme of the soft nanoimprinting (Soft-NIL) of xerogels is shown in the fig. S7. Silicon substrates, with the dewetted nano-architectures, are first treated in a solution of 0.05M SiCl2(Me)2 in ethanol to make the surface hydrophobic. A mixture of PDMS reactants (90w% RTV141A; 10w% RTV141B from BLUESIL) is then poured onto the substrate, degassed and annealed at 120°C for 1h. The PDMS mold (negative print of the initial substrate) is then peeled off the substrate surface. Before nanoimprinting, molds are placed under vacuum (p<1 mbar) for at least 5 mins. Titania films were prepared from solutions containing molar ratios of 1TiCl4 (Aldrich)/40EtOH (absolute)/7H2O (milli Q)/0.0005 PEO-PPO-PEO Pluronic F127 (Aldrich). Silica films were prepared from solutions with molar ratios of 1 TEOS (Aldrich)/ 20 EtOH (absolute) / 5 H2O (milli Q)/ 0.0002 PEO-PPO-PEO Pluronic F127 (Aldrich). Replicas are made from sol-gel thin layers coated on silicon or glass substrates using a dip-coater (ACEdip from Solgelway) in a controlled atmosphere (Relative Humidity = 20%) at a constant withdrawal speed between 1 and 6 mm/sec in order to obtain the desired thickness. Just after dip-coating, the PDMS mold is placed onto the freshly made xerogel at ambient temperature, without additional pressure, for 1 min then transferred in a 70°C stove for 5 mins in order to consolidate the xerogel. Once cooled down, the PDMS mold is easily peeled off without degrading the replica. Finally the replica is annealed at 400°C for 30 mins to complete condensation and -in the case of titaniacrystallization into anatase nanocristals. The characterizations of nanoimprinted SiO2 patterns on a Si substrate are shown in fig. S8.