Mg diffusion in Si on a thermodynamic basis

Abstract

In the present work, magnesium diffusion in silicon studied recently in the temperature range 600-1200 °C (Astrov et al. in Phys Status Solidi A 214:1700192, 2017; Shuman et al. in Semiconductors 51:5, 2017) is investigated on the basis of the cBΩ thermodynamic model, which connects point defect parameters with the macroscopic elastic and expansion properties. The calculated activation Gibbs free energy, activation enthalpy, activation entropy, activation volume and activation specific heat of Mg diffusion exhibit non-linear temperature dependence, due to the anharmonic behavior of the isothermal bulk modulus of Si. The calculated activation enthalpy of diffusion (1.67-2.12 eV) is in agreement with the reported experimental value (1.83 ± 0.02 eV) of Mg diffusion in Si, whereas the calculated activation volume (60% of the mean atomic volume) is compatible with the reported interstitial diffusion of Mg impurities.

An Overview of the Experimental Studies on the Electrical Conductivity of Major Minerals in the Upper Mantle and Transition Zone

“…The significance of the model lies in its applicability to the case of ionic conduction in minerals observed at high-T or proton conduction at lower T, where the self-diffusion coefficients, and consequently the electrical conductivity calculated through the Nernst-Einstein relation, can be estimated over a broad temperature and pressure range, if the thermo-elastic properties of the mineral under investigation (i.e., B, ∂/∂T] P , ∂/∂P] T and β) are known in these P-T conditions. In addition, the important point defect parameter of activation volume can be calculated as a function of T and P, giving further insights to the investigation of the related conduction mechanism, as it has been pointed out previously [118][119][120].…”

First-principles adaptive-boost accelerated molecular dynamics simulation with effective boost potential construction methods: a study of Li diffusion in Si crystal

“…This positive temperature dependency of activation enthalpy has been also predicted in the similar system, such as Mg interstitial diffusion in Si crystal. 25) Figure 11 also shows experimental values of diffusivity. The average activation enthalpies were estimated as 0.660, 22) 0.720, 23) and 0.659 24) for temperature ranges 298-1623K, 273-1150 K, and 633-1150 K, respectively.…”

Magnesium‐Related Donors in Silicon: State of the Art

“…[29][30][31] was interpreted in ref. [39] on the basis of a thermodynamic analysis of processes that determine the mobility of magnesium atoms in the silicon lattice.…”