A continuum particle model for micro-scratch simulations of crystalline silicon

In order to suffice the stringent surface requirements imposed on silicon wafers, thorough investigation of the fabrication methods is necessary. Typically, the processing conditions for slicing and grinding operations are determined via scratch experiments, where the information is mostly derived from the wear scars at the scratched surface. In order to cultivate an improved understanding of the subsurface deformations caused by silicon micro-scratching, numerical simulations are instrumental. For this purpose, a continuum particle-based micro-scale formulation is here proposed that addresses two challenges: (i) the need for a numerical methodology enabling mechanical continuum-discontinuum transitions and (ii) a constitutive model that accounts for the mechanics resulting from the underlying phase transformations. In this paper, both aspects are covered in order to simulate the basics of silicon micro-scratching. First, an extension of the recently introduced Continuum Bond Method (CBM), a continuum-based particle methodology, is presented along with its implementation details in LAMMPS. Then, the finite strain extension of an infinitesimal continuum inelastic model for silicon taken from literature is discussed which captures the mechanical effects of the underlying silicon phase transitions. The cubic diamond Si-I material serves as the parent phase which transforms to a tetragonal Si-II structure upon compression. Subsequent decompression of the Si-II phase initiates the transformation to an amorphous phase. In the constitutive model, an isotropic approach is adopted, whereby the inelastic transformation strains (both volumetric and deviatoric) follow from stress-based criteria. These two models are integrated and the continuum behavior of a silicon scratch is investigated in the context of experimental observations from literature.