Self-diffusion in germanium isotope multilayers at low temperatures

Self-diffusion in intrinsic single crystalline germanium was investigated between 429 and 596 ° C using G 70 e / G nat e isotope multilayer structures. The diffusivities were determined by neutron reflectometry from the decay of the first and third order Bragg peak. At high temperatures the diffusivities are in excellent agreement with literature data obtained by ion beam sputtering techniques, while considerably smaller diffusion lengths between 0.6 and 4.1 nm were measured. At lower temperatures the accessible range of diffusivities could be expanded to D ≈ 1 × 10 − 25 m 2 s − 1 , which is three orders of magnitude lower than the values measured by sputtering techniques. Taking into account available data on Ge self-diffusion, the temperature dependence is accurately described over nine orders of magnitude by a single Arrhenius equation. A diffusion activation enthalpy of 3.13 ± 0.03 eV and a pre-exponential factor of 2.54 × 10 − 3 m 2 s − 1 for temperatures between 429 and 904 ° C are obtained. Single vacancies are considered to prevail self-diffusion in Ge over the whole temperature range.