*3.2. Compliance Substrates: Pillar Growth*

The pillar technology is intended to doctor the thermal strain of the deposited SiC film by growing a suspended (thick) layer on top micrometric Si pillars, which eventually bend to accommodate the larger thermal retraction in the cooling down of the SiC film with respect to the Si substrate. The pillars are patterned in arrays in the Si substrate by a dry etching process [42,43] (Figure 3). The <111> orientation is the most critical one for stress accumulation with film thickness on flat substrates (less than 1 µm without cracks) and also provides a better quality of the deposited material on pillars. Therefore, the shape of the pillars (hexagonal in cross-section) and the arrangement of the arrays (still hexagonal in the pattern), which are suitably rotated with respect to the wafer flat to reduce the slanted 111 facet extension, have been optimized for the <111> growth orientation, wherein the pillar technology could provide the most important contribution.

**Figure 3.** Pattern (left) and shape of the pillars (right). Both pillars and the pattern have a hexagonal structure.

Understanding and controlling the 3D crystal growth and subsequent coalesce dynamics are the keys to optimizing the patterning and obtaining high-quality 3C-SiC suspended layers on the underlying Si pillars. To this goal, an extensive theory-experiment analysis of the evolution of the crystal growth has been performed and detailed in Reference [44]. First, the faceted growth of the individual SiC crystals has been characterized, as illustrated in Figure 4, by comparing the profiles of samples grown at different times with phase-field simulations based on the kinetic growth model of Reference [15]. The unknown facet-dependent growth rates to be set in the model have been extrapolated by fitting the simulation profiles to the experimental ones, resulting in a good match between Figure 4a and b. Once calibrated, the simulations allow us to investigate all intermediate stages of the growth (c), as well as the subsequent dynamics of merging between neighboring crystals.

**Figure 4.** (**a**) SEM (1-10) cross-section view of the upper part of a SiC crystal after 3 µm (red) and 6 µm (blue) deposition on top of a 2 µm-wide Si pillar (gray), which is 8 µm tall. (**b**) Phase-field simulation profiles for the same conditions of (**a**) reproduced every 1 µm deposition. (**c**) 3D view of the evolution sequence obtained from simulations (see Reference [44]).

As illustrated in Figure 5, two limiting cases have been studied, corresponding to a 90◦ rotation of the hexagonal pillar pattern. In case (a), pillar rows are along the [11-2] directions so that coalescence occurs with a six-fold symmetry by bridging the large {111}-C terminated facets with the smaller {100} ones, leaving six identical holes to fill at the latest stages. In the same way, in case (b), pillar rows are aligned along the [1-10] direction such that coalescence occurs at facet edges, resulting in a three-fold symmetry arrangement with a larger hole in between {111}-C facets and smaller ones at the crossing of {100} facets. As made evident by simulations, this latter arrangement is the most convenient, returning a smoother surface profile after the deposition of about 12 µm.

**Figure 5.** Comparative analysis of the coalescence of SiC crystals grown on Si pillars for the two different patterns with pillar rows along (**a**) the [11-2] and (**b**) [1-10] directions from both experiments and simulations. SEM views are reported for samples obtained after 12 µm SiC deposition on 5 µm large prismatic Si pillars, spaced by 2 µm gaps. The magnified views highlight the different patterns of holes left by partial coalescence. Simulation snapshots are shown for both the 3 and 12 µm deposition. The colored regions show the variations in height by the colormap. A smoother profile is achieved in case (**b**) (see Reference [44]).

The strain relaxation in the 3C-SiC epilayer is enabled by the tilting of the pillars underneath. As reported in Reference [45] for the case of Ge grown on Si pillars, the deformation can be described as a rigid-body rotation of each pillar. It is possible to conclude that the capability to rotate strongly depends on the aspect ratio of prismatic (or paralepidid) pillars. Indeed, as shown in Figure 6a for the pillar at the periphery of the array exhibiting the maximum deformation, the rotation mechanisms and consequently the stress relaxation are larger for a smaller pillar width. Another important parameter that controls the relaxation in the 3C-SiC epilayer is the height of the pillars. Indeed, as observed in Figure 6b for different patch sizes, the higher the pillar, the better is the strain relaxation. The stress (and strain) relaxation at the center of the array decreases when the patch size is increased, at a fixed pillar aspect ratio, asymptotically matching the reference case without any pillar when the patch size tends to be infinite. The relaxation of the elastic energy in the epilayer can be enhanced also by changing the pillar spacing or, more importantly, the pillar shape. Indeed, if compared to the standard parallelepiped pillars, Tshaped ones (Figure 6c) offer a higher capability to rotate, being thinner in the intermediate section of the pillar. This results in a lower residual stress or equivalent strain, as shown in Figure 6a. The T-shape (Figure 6c) case is comparable to the one with parallelepiped pillars, characterized by a base of half-size and a larger pillar spacing, with the advantage that the T-shape ones have a larger top surface for each pillar, above which the SiC can be grown. According to the approach discussed in Reference [46], in Figure 6b, the relation between the width and height of the pillars is plotted to guarantee a curvature radius of the sample that is larger than 10 m. The curvature radius is calculated from the average residual strain in the epilayer according to the Timoshenko formula for planar bilayers [47].

**Figure 6.** (**a**) Color maps of the xx component of the stress tensor (σxx) for three 3C-SiC epilayers grown on array of pillars with different geometries. Top: parallelepiped pillars, spaced by 2 µm and with a base width of 5 µm. Center: parallelepiped pillars, spaced by 4.5 µm and with a base width of 2.5 µm. Bottom: T-shape pillars, spaced by 2 µm and with a maximum base width of 5 µm. (**b**) Plot of the height of the pillars as a function of the width of the pillars that is needed to guarantee a curvature radius of the sample that is larger than 10 m (acceptable for post-processing of 4′ wafers). A (111) Si substrate is considered. (**c**) SEM image of the T-shape pillars (adapted from Reference [46]).
