Pressure effects on self-diffusion in silicon

Abstract

The effects of hydrostatic pressure on the energetics of self-diffusion in silicon are investigated via parameter-free total-energy calculations. The three microscopic mechanisms, vacancy, interstitial, and concerted exchange, which have very similar activation energies in Si, exhibit different pressure dependences.The results suggest that a set of experiments carried out at different pressures can unravel their relative contributions by a comparison to the present results. In addition, it is shown that in contrast to the (111) surface, the nearest neighbors of the Si vacancy relax inwards, rather than outwards.Self-diffusion in silicon has been the subject of extensive experimental and theoretical studies. Various microscopic mechanisms have been considered, but no consensus has yet been achieved regarding their relative importance. Experimentally, the measured activation enthalpy varies from 4.1 to 5.1 eV (Ref. 1) depending on the measurement technique and temperature range. Due to the nature of the bonding in silicon, it was initially thought that native defects mediate self-diffusion. In addition, it was shown experimentally that the concentration of native defects is small, and therefore the contributions of complex defects, e.g. , divacancies, are negligible.Theoretical studies " obtained very similar activation enthalpies for the vacancy and interstitial mechanisms, as well as proposed a new one, namely that of concerted exchange. All three mechanisms have activation energies in the experimentally observed range. Therefore, due to both experimental uncertainties and theoretical approximations, it has not been possible to determine the relative contributions of these mechanisms to the self-diffusion process. In this paper we present the results of parameter-free totalenergy calculations of the effects of hydrostatic pressure on the energetics of these mechanisms. Although the three mechanisms have very similar activation enthalpies at zero pressure, the response to external pressure of each mechanism is qualitatively different, making the determination of their relative contributions possible. The use of pressure as a probe to investigate diffusive processes in solids is not new. Several results for metals and ionic compounds were reported over twenty years ago. In semiconductors, however, the 6rst results of pressure effects on self-diffusion in germanium' and silicon, and on diffusion of As in silicon, have appeared only recently.In the high-temperature regime the self-diffusion coef6cient can be written as Dsa Doexp( -hH, d/kT), where hH, d denotes the activation enthalpy. The prefactor Do in (1) is proportional to exp(hS, d/k ), where AS,4 is the activation entropy. For diffusion involving defects, the activation enthalpy is the sum of the formation enthalpy dHf and the migration enthalpy hM .We will now analyze the process whereby a native defeet is created in a crystal and the effect of an external pressure on its formation energy. When a vacancy is created in a dislocation-free crystal, one atom leav...

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