Unified framework of radiation damage and mechanical stress evolution during ion-induced amorphization of germanium

Abstract

Abstract

Mechanical stress evolution during ion irradiation provides novel insights into radiation damage mechanisms in crystalline materials. In this work, we study the stress, damage, and swelling of single-crystalline germanium under 1–6 MeV I, Au, and Ag ion irradiation at room and low temperatures using in situ stress-bending measurements, Rutherford backscattering analysis in channeling mode (RBS/C) damage analysis, and surface profilometry. We extend an established defect model based on binary collision simulations and critical defect density to incorporate stress formation and other observables. Using a model with just five free parameters, we accurately describe the evolution of damage, stress, and surface swelling across various temperatures. Our model precisely determines the critical defect density required for amorphization, which is temperature-dependent but otherwise consistent across diverse ions and energies (∼11% at 297 K, ∼8% at 126 K). This parameter allows for the prediction of damage formation, stress evolution, and amorphization behavior in germanium using binary collision simulation codes. It can be converted to other amorphization thresholds: displacements per atom (∼0.38) and critical damage energy density (∼5.8eV/atom), which compare well to established literature values at room temperature. We additionally report that the damage cross sections calculated with the binary collision model the stopping and range of ions in matter are systematically lower than the ones measured with RBS/C by factors of 3–21, dependent on energy, ion species, and temperature.