Contents lists available at ScienceDirect Materials & Design journal homepage: www.elsevier.com/locate/matdes Analytical modeling of grinding-induced subsurface damage in monocrystalline silicon Hao Nan Li ⁎ , Tian Biao Yu, Li Da Zhu, Wan Shan Wang School of Mechanical Engineering and Automation, Northeastern University, Shenyang Zip 110819, PR China ARTICLE INFO Keywords: Monocrystalline silicon Grinding Subsurface damage ABSTRACT 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. 1. Introduction Monocrystalline silicon is a predominant type of semiconductor materials, and is considered as the building block of many electronic devices [1,2], such as large-scale integrated circuits (IC), high-effi- ciency solar cells, microelectromechanical systems (MEMS) and high- performance semiconductor equipment. During industrial manufactur- ing of silicon, grinding is commonly utilised as the last “rough” machining process prior to high-precision lapping because grinding can achieve high material removal rates with relatively low cost [3,4]. However, substantial experimental observations [5–7] indicated that grinding process easily led to significant subsurface damage (SSD) including micro-cracks, dislocation, and stacking faults, even under a smooth ground surface. This SSD was reported to be not only harmful to mechanical properties and service life of silicon products, but also influential to functional performances of semiconductors or electronic components [8]. To this end, a multitude of efforts focusing on the understanding or characterisation of the grinding-induced SSD in monocrystalline silicon have been made. In the early-stage research, the formation mechanism of SSD has been explored by performing indentation tests or scratch trials. Cheong and Zhang [9] observed the nano-indentation events and found that the SSD of silicon was formed accompanying with the phase transforma- tion, where the diamond cubic silicon (Si-I) was transformed into the metallic state (Si-II). Zarudi et al. [10] further improved Cheong and Zhang's study [9] by performing the cyclic indentation tests so as to imitate the similar cyclic loads of the cutter-specimen interaction in machining processes. Another two new crystalline phases including the body centered-cubic silicon (Si-III) and the rhombohedral silicon (Si- XII) were found several microns beneath the surface, and therefore these two phases were believed related with SSD in silicon machining. Besides, Zarudi et al. [11] assumed the temperature rise induced by the indenter-workpiece friction might also contribute to the SSD formation, but the cryogenic scratching test of silicon specimens showed the very limited effect of the low temperature on the reduction of SSD depths. Instead of using a geometrically well-defined indenter, the second- stage research started to perform real machining trials. Yan et al. [12] conducted straightforward diamond machining experiments on silicon specimens by using cutting tools with different rake angles, and the results indicated that in grinding, where the abrasive negative rake angle was usually large (around −60°), the SSD depths were mono- tonously increased with the increasing depths of cut. Therefore a good http://dx.doi.org/10.1016/j.matdes.2017.05.068 Received 23 December 2016; Received in revised form 22 May 2017; Accepted 24 May 2017 ⁎ Corresponding author. E-mail address: lhnlwfb@163.com (H.N. Li). Materials & Design 130 (2017) 250–262 Available online 24 May 2017 0264-1275/ © 2017 Elsevier Ltd. All rights reserved. MARK