# Growth and Coalescence of 3C-SiC on Si(111) Micro-Pillars by a Phase-Field Approach

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental

#### 2.2. Phase-Field Model of Kinetic Growth

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Representation of the crystal structure in the phase-field model for a realistic, faceted morphology. The $\phi $ function is shown in a {$11\overline{2}$} cross section. The inset shows the adaptively refined mesh along with the contour line of the crystal surface ($\phi $ = 0.5). Colour map of (

**b**) the adatom lifetime $\tau \left(\widehat{\mathbf{n}}\right)$ and of (

**c**) the chemical potential $\mu $ on the crystal surface, with the white arrows showing the diffusion direction of the material along the surface. A schematic representation of the flux distribution is also reported.

**Figure 2.**SEM views of SiC crystals grown on Si pillars after (

**a**) 3 $\mathsf{\mu}$m and (

**b**) 6 $\mathsf{\mu}$m of deposition. Si pillars consist of 8 $\mathsf{\mu}$m tall hexagonal prisms with {110} sidewalls and 2 $\mathsf{\mu}$m large {111} top facet and they are arranged in an hexagonal pattern with 3 $\mathsf{\mu}$m spacing. The main crystal facets are marked by symbols.

**Figure 3.**(

**a**) Superposition of SEM cross-sections along the [$11\overline{2}$] showing the upper part of the hexagonal, 2-$\mathsf{\mu}$m-wide and 8-$\mathsf{\mu}$m-tall, initial Si pillar (gray) and the 3C-SiC crystal grown on top after 3 $\mathsf{\mu}$m (red) and 6 $\mathsf{\mu}$m (blue) of deposition. (

**b**) Cross-section along the same direction for the simulated crystal: the black dashed lines are taken for each $\mathsf{\mu}$m of deposition, the red (blue) profile corresponds to 3$\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}$m (6 $\mathsf{\mu}$m) of deposition. (

**c**) Simulated growth sequence in perspective view.

**Figure 4.**Simulations of crystal morphology evolution for different Si pillar shapes: (

**a**) cylindrical, (

**b**–

**d**) prismatic with triangular base and (

**e**) with squared base. Top views are reported after 1.5 and 4.5 $\mathsf{\mu}$m of SiC deposition along with lateral views obtained by superposition of the corresponding stages: 1.5 $\mathsf{\mu}$m in red and 4.5 $\mathsf{\mu}$m in blue (the dashed white lines show the profile of the initial pillar in side view). In all cases, 7 $\mathsf{\mu}$m tall Si pillars are considered with the same area of the top base, equal to 5 $\mathsf{\mu}$m${}^{2}$.

**Figure 5.**Top view of coalescence experiments for the deposition of 12 $\mathsf{\mu}$m and simulations for two deposition stages. Two hexagonal patterns, sketched in the blue insets, are considered: (

**a**) pillar rows along [11$\overline{2}$] and (

**b**) pillar rows along [1$\overline{1}$0]. The surface height, refered to the (111) crystal top, is shown by the color maps. The Si pillar base is 5 $\mathsf{\mu}$m and the gap between pillars is 2 $\mathsf{\mu}$m.

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**MDPI and ACS Style**

Masullo, M.; Bergamaschini, R.; Albani, M.; Kreiliger, T.; Mauceri, M.; Crippa, D.; La Via, F.; Montalenti, F.; von Känel, H.; Miglio, L.
Growth and Coalescence of 3C-SiC on Si(111) Micro-Pillars by a Phase-Field Approach. *Materials* **2019**, *12*, 3223.
https://doi.org/10.3390/ma12193223

**AMA Style**

Masullo M, Bergamaschini R, Albani M, Kreiliger T, Mauceri M, Crippa D, La Via F, Montalenti F, von Känel H, Miglio L.
Growth and Coalescence of 3C-SiC on Si(111) Micro-Pillars by a Phase-Field Approach. *Materials*. 2019; 12(19):3223.
https://doi.org/10.3390/ma12193223

**Chicago/Turabian Style**

Masullo, Marco, Roberto Bergamaschini, Marco Albani, Thomas Kreiliger, Marco Mauceri, Danilo Crippa, Francesco La Via, Francesco Montalenti, Hans von Känel, and Leo Miglio.
2019. "Growth and Coalescence of 3C-SiC on Si(111) Micro-Pillars by a Phase-Field Approach" *Materials* 12, no. 19: 3223.
https://doi.org/10.3390/ma12193223