Finite element modeling of high-pressure deformation and phase transformation of silicon beneath a sharp indenter
Finite element modeling of high-pressure deformation and phase transformation of silicon beneath a sharp indenter
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DOI：
10.1088/0268-1242/24/2/025014
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发表时间：
2009-02
影响因子：
1.9
通讯作者：
Tadao Kiriyama;H. Harada;Jiwang Yan
中科院分区：
文献类型：
--
作者：
Tadao Kiriyama;H. Harada;Jiwang Yan
单晶硅对锋利压头的机械响应建模是优化晶圆制造工艺的重要步骤。本文采用有限元方法对压头加载和卸载过程中硅的变形进行了分析，并对应力场和高压相分布的变化进行了动态模拟。我们发现纳米压痕中硅的变形可以简单地用两个因素来表征：一是各高压相的弹性应变，二是各相变的等效弹性应变。加载时，压痕能主要被相变吸收，并以高压相的弹性应变形式积累。压头下方高压相的分布模式与压痕载荷无关，相变区域的深度约为压痕深度的两倍。卸载时，除β-Sn相外的高压相发生逆相变。 β-Sn相不会转变回金刚石相，而是转变为其他非平衡相，这成为残余应变的主要原因。在卸载过程中，非平衡相从金刚石相区域向压头尖端扩展，而非平衡相和金刚石相之间的边界保持不变。卸载机制与最大压痕负载的变化以及弹出事件的存在/不存在无关。
Modeling of the mechanical response of single crystalline silicon to a sharp indenter is an essential step for the optimization of wafer manufacturing processes. In this paper, deformation of silicon during indenter loading and unloading was analyzed by the finite element method, and the changes of stress field and high-pressure phase distribution were dynamically simulated. We found that the deformation of silicon in nanoindentation can be simply characterized by two factors: one is the elastic strain of each high-pressure phase and the other is the equivalent elastic strain of each phase transformation. In loading, indentation energy is absorbed mostly by phase transformation, and accumulated as the elastic strain of the high-pressure phases. The distribution pattern of the high-pressure phases beneath the indenter is independent of the indentation load, and the depth of the phase-transformed region is approximately twice the indentation depth. In unloading, high-pressure phases except the β-Sn phase undergo reverse phase transformations. The β-Sn phase does not transform back to the diamond phase but changes to other non-equilibrium phases, which becomes the dominant reason for residual strain. During unloading, the non-equilibrium phase expands from the diamond phase region toward the indenter tip, while the boundary between the non-equilibrium phase and the diamond phase remains unchanged. The unloading mechanism is independent of the change in the maximum indentation load and the presence/absence of pop-out events.