Pressure-enhanced crystallization kinetics of amorphous Si and Ge: Implications for point-defect mechanisms

Abstract

The effects of hydrostatic pressure on the solid-phase epitaxial growth (SPEG) rate v of intrinsic Ge(100) and undoped and doped Si(100) into their respective self-implanted amorphous phases are reported. Samples were annealed in a high-temperature, high-pressure diamond anvil cell. Cryogenically loaded fluid Ar, used as the pressure transmission medium, ensured a clean and hydrostatic environment. v was determined by in situ time-resolved visible (for Si) or infrared (for Ge) interferometry. v increased exponentially with pressure, characterized by a negative activation volume of −0.46Ω in Ge, where Ω is the atomic volume, and −0.28Ω in Si. The activation volume in Si is independent of both dopant concentration and dopant type. Structural relaxation of the amorphous phases has no significant effect on v. These and other results are inconsistent with all bulk point-defect mechanisms, but consistent with all interface point-defect mechanisms, proposed to date. A kinetic analysis of the Spaepen–Turnbull interfacial dangling bond mechanism is presented, assuming thermal generation of dangling bonds at ledges along the interface, independent migration of the dangling bonds along the ledges to reconstruct the network from the amorphous to the crystalline structure, and unimolecular annihilation kinetics at dangling bond ‘‘traps.’’ The model yields v = 2 sin(θ)vsnr exp[(ΔSf + ΔSm)/k] exp− [(ΔHf + ΔHm)/kT], where ΔSf and ΔHf are the standard entropy and enthalpy of formation of a pair of dangling bonds, ΔSm and ΔHm are the entropy and enthalpy of motion of a dangling bond at the interface, vs is the speed of sound, θ is the misorientation from {111}, and nr is the net number of hops made by a dangling bond before it is annihilated. It accounts semiquantitatively for the measured prefactor, orientation dependence, activation energy, and activation volume of v, and the pressure of a ‘‘free-energy catastrophe’’ beyond which the exponential pressure enhancement of SPEG cannot continue uninterrupted due to a vanishing barrier to dangling bond migration. The enhancement of v by doping can be accounted for by an increased number of charged dangling bonds, with no change in the number of neutrals, at the interface. Quantitative models for the doping dependence of v are critically reviewed. At low concentrations the data can be accounted for by either the fractional ionization or the generalized Fermi-level-shifting models; methods to further test these models are enumerated. Ion irradiation may affect v by altering the populatio