Analytical modeling of grinding-induced subsurface damage in monocrystalline silicon

Monocrystalline silicon is a predominant type of semiconductors. However, subsurface damage (SSD) of silicon has been widely reported during the mechanical grinding process. Although relevant efforts have been reported, most theoretical studies only qualitatively explained the SSD formation mechanism rather than quantitatively evaluate SSD values, while most experimental measurement techniques unavoidably damaged (even destroyed) the ground surfaces and therefore could only be ultilised ex-situ. To fill this gap, this paper suggests an analytical model of grinding-induced SSD in silicon, where the explicit relationship between SSD and the ground surface roughness Rz is analytically established considering the (i) ductile-regime effect, (ii) crystallographic orientation effect, and (iii) material property degradation due to high grinding temperature. Based on the model, grinding-induced SSD could be nondestructively, quickly and conveniently evaluated, in-situ or ex-situ, by measuring Rz values based on a handheld profilometer. Grinding trials indicated the model could accurately evaluate SSD depths along both the 〈100〉 and 〈110〉 crystallographic orientations in both dry and wet silicon grinding processes. Further discussion on how the model could guide and monitor the industrial silicon grinding is also presented. The proposed model therefore is anticipated to be meaningful to facilitate design, manufacture, and applications of monocrystalline silicon.