Soft modes at the stacking faults in SiC crystals: First-principles calculations

We use first-principles calculations based on density functional theory to determine and understand the driving force of the observed stacking fault expansion in SiC. We verify the suggestion based on recent experiments that the free energy difference between the faulted and the perfect structures is responsible for this expansion and show that its origin lies in a large entropy associated with soft vibrational modes of the faulted SiC structure that involve shearing of SiC on a long length scale. As a consequence, velocity of sound is expected to reduce noticeably in SiC with stacking faults, measurement of which should validate the soft-mode mechanism. Such mode-softening is absent in related group IV semiconductors, such as Si, Ge, and C.

Figure 1

Contour plot of generalized stacking fault $\text{energy}\left(\gamma \right)$ surface for slip on the glide plane of $4H\text{−}\mathrm{Si}\mathrm{C}$. For isovalues of energies equispaced between the minimum and maximum, contours are labeled with integers from 1 (lowest energy) to 10 (highest energy).

Figure 2

(Color online) Stacking fault energy $\left({\gamma }_{\mathit{isf}}\right)$ of $4H$ and $6H$ polytypes of SiC as a function of temperature. Inset shows a comparison of our calculated estimate of specific heat with experimental values as a function of temperature.

Figure 3

(Color online) (a) Phonon density of states of perfect and faulted $4H\text{−}\mathrm{Si}\mathrm{C}$ (top) and $6H\text{−}\mathrm{Si}\mathrm{C}$ (bottom); arrows indicate the soft modes in faulted structures. (b) Soft phonon mode of frequency $107{\mathrm{cm}}^{-1}$ in faulted $4H\text{−}\mathrm{Si}\mathrm{C}$.