Abstract
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.
| Original language | English |
|---|---|
| Article number | 025014 |
| Journal | Semiconductor Science and Technology |
| Volume | 24 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2009 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Electrical and Electronic Engineering
- Electronic, Optical and Magnetic Materials
- Materials Chemistry
- Condensed Matter Physics
Cite this
Finite element modeling of high-pressure deformation and phase transformation of silicon beneath a sharp indenter. / Kiriyama, Tadao; Harada, Hirofumi; Yan, Jiwang.
In: Semiconductor Science and Technology, Vol. 24, No. 2, 025014, 2009.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Finite element modeling of high-pressure deformation and phase transformation of silicon beneath a sharp indenter
AU - Kiriyama, Tadao
AU - Harada, Hirofumi
AU - Yan, Jiwang
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
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U2 - 10.1088/0268-1242/24/2/025014
DO - 10.1088/0268-1242/24/2/025014
M3 - Article
AN - SCOPUS:64249139595
VL - 24
JO - Semiconductor Science and Technology
JF - Semiconductor Science and Technology
SN - 0268-1242
IS - 2
M1 - 025014
ER -