Direct measurement and modelling of internal strains in ion-implanted diamond

We present a phenomenological model and finite element simulations to describe the depth variation of mass density and strain of ion-implanted single-crystal diamond. Several experiments are employed to validate the approach: firstly, samples implanted with 180 keV B ions at relatively low fluences are characterized using high-resolution x-ray diffraction; secondly, the mass density variation of a sample implanted with 500 keV He ions, well above its amorphization threshold, is characterized with electron energy loss spectroscopy. At high damage densities, the experimental depth profiles of strain and density display a saturation effect with increasing damage and a shift of the damage density peak towards greater depth values with respect to those predicted by TRIM simulations, which are well accounted for in the model presented here. The model is then further validated by comparing transmission electron microscopy-measured and simulated thickness values of a buried amorphous carbon layer formed at different depths by implantation of 500 keV He ions through a variable-thickness mask to simulate the simultaneous implantation of ions at different energies.