[Paper Review] Effects of thermal, elastic, and surface properties on the stability of SiC polytypes

Senja Ramakers, Anika Marusczyk+5 more|arXiv (Cornell University)|Jan 14, 2022

Advanced ceramic materials synthesis129 references25 citations

TL;DR

This study uses multi-method density functional theory (DFT) to investigate the thermodynamic stability of SiC polytypes (3C, 2H, 4H, 6H), comparing bulk, thermal, elastic, and surface properties. It finds that surface energy—particularly for Si-terminated (0001) surfaces—dominates 3C-SiC nucleation, while bulk stability slightly favors 4H/6H; thus, both surface and bulk effects are essential for accurate growth modeling.

ABSTRACT

SiC polytypes have been studied for decades, both experimentally and with atomistic simulations, yet no consensus has been reached on the factors that determine their stability and growth. Proposed governing factors are temperature-dependent differences in the bulk energy, biaxial strain induced through point defects, and surface properties. In this work, we investigate the thermodynamic stability of the 3C, 2H, 4H, and 6H polytypes with density functional theory (DFT) calculations. The small differences of the bulk energies between the polytypes can lead to intricate changes in their energetic ordering depending on the computational method. Therefore, we employ and compare various DFT-codes: VASP, CP2K, and FHI-aims; exchange-correlation functionals: LDA, PBE, PBEsol, PW91, HSE06, SCAN, and RTPSS; and nine different van der Waals (vdW) corrections. At $T=0$~K, 4H-SiC is marginally more stable than 3C-SiC, and the stability further increases with temperature by including entropic effects from lattice vibrations. Neither the most advanced vdW corrections nor strain on the lattice have a significant effect on the relative polytype stability. We further investigate the energies of the (0001) polytype surfaces that are commonly exposed during epitaxial growth. For Si-terminated surfaces, we find 3C-SiC to be significantly more stable than 4H-SiC. We conclude that the difference in surface energy is likely the driving force for 3C-nucleation, whereas the difference in the bulk thermodynamic stability slightly favors the 4H and 6H polytypes. In order to describe the polytype stability during crystal growth correctly, it is thus crucial to take into account both of these effects.

Motivation & Objective

• To resolve the long-standing discrepancy between experimental observations (3C-SiC nucleation) and theoretical predictions (4H/6H more stable at 0 K).
• To benchmark the performance of multiple DFT codes (VASP, CP2K, FHI-aims), exchange-correlation functionals, and van der Waals corrections on SiC polytype stability.
• To evaluate the influence of thermal, elastic, and surface effects on the relative stability of 3C, 2H, 4H, and 6H SiC polytypes.
• To determine whether surface energy or bulk thermodynamics is the dominant factor in polytype selection during epitaxial growth.

Proposed method

• Employed three DFT codes—VASP, CP2K, and FHI-aims—using different exchange-correlation functionals (LDA, PBE, PBEsol, PW91, HSE06, SCAN, RTPSS) and basis sets to ensure methodological robustness.
• Applied nine van der Waals correction schemes to assess dispersion effects on polytype stability.
• Calculated zero-temperature bulk energies and used phonon calculations to include entropic contributions from lattice vibrations at finite temperature.
• Computed surface energies for (0001) surfaces of all polytypes, focusing on Si-terminated and C-terminated terminations relevant to epitaxial growth.
• Performed systematic comparison across DFT implementations and functionals to assess consistency and sensitivity of results.
• Used the phonon density of states and Helmholtz free energy to evaluate temperature-dependent stability trends.

Experimental results

Research questions

• RQ1 Which DFT method and functional combination yields the most reliable prediction of SiC polytype stability?
• RQ2 How do thermal contributions from lattice vibrations affect the relative stability ordering of 3C, 4H, and 6H SiC at finite temperatures?
• RQ3 To what extent do van der Waals corrections and biaxial strain from point defects alter the relative stability of SiC polytypes?
• RQ4 What is the role of surface energy—particularly for Si-terminated (0001) surfaces—in determining the nucleation preference for 3C-SiC over 4H-SiC?
• RQ5 Can the experimentally observed 3C-SiC nucleation be explained by bulk thermodynamics alone, or is surface energy the dominant factor?

Key findings

• At T = 0 K, 4H-SiC is marginally more stable than 3C-SiC, with a bulk energy difference of a few meV/SiC, depending on the DFT method.
• Including entropic contributions from lattice vibrations increases the stability of 4H-SiC relative to 3C-SiC, reinforcing its thermodynamic preference at high temperatures.
• Neither advanced van der Waals corrections nor strain induced by point defects significantly alters the relative stability ordering of the polytypes.
• Si-terminated (0001) surfaces of 3C-SiC are significantly more stable than those of 4H-SiC, with a surface energy difference favoring 3C nucleation.
• The surface energy difference is large enough to dominate over the small bulk energy differences, explaining the experimentally observed tendency for 3C nucleation.
• The combined analysis shows that both surface energy and bulk thermodynamics must be considered to correctly model polytype stability during SiC epitaxial growth.