Simplified calculation of indentation contact deformation of monocrystalline silicon

GE Mengran; WANG Quanjing; ZHANG Zhenzhong

doi:10.37188/OPE.20223011.1317

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Simplified calculation of indentation contact deformation of monocrystalline silicon

Micro\/Nano Technology and Fine Mechanics | 更新时间：2026-09-11

- Simplified calculation of indentation contact deformation of monocrystalline silicon
- Optics and Precision Engineering Vol. 30, Issue 11, Pages: 1317-1324(2022)
- 作者机构：
  
  山东建筑大学机电工程学院，山东济南 250101
- 作者简介：
- 基金信息：
- DOI：10.37188/OPE.20223011.1317
  CLC： TH161.13
- Received：23 November 2021，
  
  Revised：2021-12-30，
  
  Published：10 June 2022
- 稿件说明：
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葛梦然,王全景,张振中.单晶硅压痕接触变形的简化计算[J].光学精密工程,2022,30(11):1317-1324.

GE Mengran,WANG Quanjing,ZHANG Zhenzhong.Simplified calculation of indentation contact deformation of monocrystalline silicon[J].Optics and Precision Engineering,2022,30(11):1317-1324.
葛梦然,王全景,张振中.单晶硅压痕接触变形的简化计算[J].光学精密工程,2022,30(11):1317-1324. DOI： 10.37188/OPE.20223011.1317.

GE Mengran,WANG Quanjing,ZHANG Zhenzhong.Simplified calculation of indentation contact deformation of monocrystalline silicon[J].Optics and Precision Engineering,2022,30(11):1317-1324. DOI： 10.37188/OPE.20223011.1317.

摘要

单晶硅、光学玻璃等脆性材料磨粒加工获得高质量加工表面的关键是单颗磨粒的实际刻划深度小于材料脆塑转变的临界切削深度，但单颗磨粒刻划加工的实际划痕深度的计算需要考虑单晶硅与磨粒压痕接触弹性变形的影响。由于金刚石磨粒切削刃与玻氏压头尖端具有结构相似性，对单晶硅与玻氏压头的压痕接触变形进行了理论分析和实验研究。基于纳米压痕实验原理，建立了玻氏压头加载压入单晶硅的位移深度和压痕深度的计算公式。将玻氏压头与单晶硅试件的接触等效为球体与平面的接触，建立了接触弹性变形的简化计算公式。对单晶硅进行了纳米压痕实验，得到单晶硅的纳米硬度为12.22 GPa，等效弹性模量为173.09 GPa，实测了玻氏压头与单晶硅纳米压痕接触的弹性接触刚度和压头的位移深度、压痕深度，接触弹性变形量超过了压头位移深度的50%。该结果为单晶硅的金刚线精密切片和精密磨削工艺参数的优化奠定了理论基础。

Abstract

In abrasive machining for brittle materials such as monocrystalline silicon and optical glass， the key to obtaining a high-quality machined surface is that the single abrasive grit's actual scratching depth should be less than the critical cutting depth of ductile-to-brittle. However， when calculating the actual scratching depth of the single abrasive grit， the influence of indentation contact elastic deformation between monocrystalline silicon and abrasive grit must be considered. Owing to the structural similarity between the diamond abrasive cutting edge and the tip of the Berkovich indenter， the indentation contact deformation between monocrystalline silicon and the Berkovich indenter is theoretically analyzed and experimentally investigated in this study. Based on the nano-indentation experiment principle， the calculation equations of indenter displacement depth of Berkovich indenter loading press into monocrystalline silicon and indentation depth on monocrystalline silicon after unloading are established. A simplified calculation equation of contact elastic deformation between the Berkovich indenter and the monocrystalline silicon specimen is established by transforming the contact between them into the contact between sphere and plane. Nano-indentation experiments are carried out on the monocrystalline silicon. The measured nano-hardness of monocrystalline silicon is 12.22 GPa， and the effective elastic modulus is 173.09 GPa. The experiments were used to obtain the elastic contact stiffness， indenter displacement depth， and indentation depth of the nano-indentation contact between the monocrystalline silicon and the Berkovich indenter. The contact elastic deformation exceeds 50% of the indenter displacement depth. This study's findings are helpful for optimizing the process parameters for diamond wire saw precision slicing and the precision grinding of monocrystalline silicon.

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