Dynamics of Hydrogen in Silicon at Finite Temperatures from First Principles

Abstract

Hydrogen defects in silicon still hold unsolved problems, whose disclosure is fundamental for future advances in Si technologies. Among the open issues is the mechanism for the condensation of atomic hydrogen into molecules in Si quenched from above T≈700 °C to room temperature. Based on first‐principles calculations, the thermodynamics of hydrogen monomers and dimers is investigated at finite temperatures within the harmonic approximation. Free energies of formation indicate that the population of normalH− cannot be neglected when compared to that of normalH+ at high temperatures. The results allow us to propose that molecular formation occurs during cooling processes, in the temperature window T≈700−500 K, above which the molecules collide with Si—Si bonds and dissociate, and below which the fraction of normalH− becomes negligible. The formation of normalH− and most notably of a fast‐diffusing neutral species can also provide an explanation for the apparent accelerated diffusivity of atomic hydrogen at elevated temperatures in comparison to the figures extrapolated from measurements carried out at cryogenic temperatures. Finally, it is shown that the observed diffusivity of molecules is better described upon the assumption that they are nearly free rotors, all along the migration path, including at the transition state.

Crucial role of vibrational entropy in the Si(111)-7$\times$7 surface structure stability

“…1. These findings are corroborated by the results of Estreicher et al [28] and by convergence tests reported by Gomes et al [37], who found no significant improvement in the calculated specific heat of Si when moving from a 64-atom cell to a 216-atom cell.…”

“…The vibrational free energy of 5 × 5 and 7 × 7 reconstructed Si(111) surfaces was obtained within the quasiharmonic approximation, according to the usual procedure employed for defects and surfaces in semiconductors and metals [27,28,35,36]. This approach is applicable to silicon up to few hundred Kelvin [28,37], and in particular to Si(111) DAS surfaces, which form unique and stable minimum energy structures. For surfaces with structural degrees of freedom, e.g.…”

The Impact of Different Hydrogen Configurations on Light- and Elevated-Temperature- Induced Degradation

“…This implies that the specific kinetics of the hydrogen inand out-diffusion might differ between p-and n-type wafers. Possible causes could, for example, be the charge state of atomic hydrogen and related diffusivities, or the trapping-kinetics of atomic hydrogen with the dopants, which all differ between Band P-doped silicon [38], [51], [70], [71].…”

Theory of shallow and deep boron defects in 4H-SiC

“…The vibrational mode frequencies of 4H-SiC cells containing boron defects were evaluated in 𝑁 = 72-atom cells (3×3×1 primitive cells). We considered the participation of all atoms in the dynamical matrix, whose elements were found from the force derivatives with respect to the atomic positions [61].…”

“…In Ref. [61], we demonstrated that these calculations cannot be improved by enlarging the supercells. Also important, is the fact that the constant volume calculations match well the constant pressure measurements across a wide range of temperatures.…”