(390d) The Impact of Configurational Entropy on Point Defect Thermodynamics and Diffusion in Crystalline Silicon

It has long been suggested that the familiar intrinsic point defects (vacancies and self-interstitials) encountered in crystals at low temperatures transform into extended domains characterized by a missing or excess atom compared to the same-sized region in the perfect crystal so that such “extended defects” may be viewed as droplet-like regions of enhanced or diminished density [1]. Yet the implications of such a transformation, or whether it even occurs in crystalline Si, remain uncertain. For example, the apparent non-Arrhenius dependence of the Si self-diffusion coefficient observed in experiments has been attributed by some to a transition between point and extended defect states at an intermediate temperature [2]. Yet, other researchers have argued that there is no need to invoke such a transition in defect structure to explain such observations [3,4], and have suggested that uncontrolled experimental conditions, e.g., interactions with unintentional impurities [4], are responsible for the observed behavior. The existence of extended defects thus remains unresolved.

To address this fundamental problem, here we consider a comprehensive thermodynamic analysis of the thermodynamics of vacancy and self-interstitial formation over a broad temperature range based on thermodynamic integration with a particular focus on entropic contributions. In cooled liquids, it is well known that the form of the intermolecular potential can greatly influence the configurational entropy and, correspondingly, we analyze several empirical Si potentials to determine how the potential influences both the temperature dependence of the configurational entropy as well as the enthalpy and total entropy of defect formation. We indeed find that the configurational entropy associated with point defects increases significantly upon heating, consistent with the existence of extended defects. Moreover, each type of defect species gives a significantly different contribution to the configurational entropy at elevated temperature and to a qualitive difference in the temperature dependence of the entropy of defect formation in the extended defect regime. Finally, we discuss the consequences of these thermodynamic changes of defect formation on the temperature dependence of diffusion in heated crystals. We show that large configurational entropy leads to a change in the diffusion barrier of these defects and provide a hypothesis for why this change has been difficult to isolate in experimental measurements of self-diffusion.

[1] A. Seeger and K. P. Chik, Phys. Status Solidi B Basic Res. 29, 455 (1968).

[2] R. Kube et al., Phys. Rev. B Condens. Matter 88, 085206 (2013).

[3] G. D. Watkins, J. Appl. Phys. 103, 106106 (2008).

[4] T. Südkamp and H. Bracht, Phys. Rev. B Condens. Matter 94, 125208 (2016).