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# Split singularities and dislocation injection in strained silicon

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By Martijn Feron, Zhen Zhang and Zhigang Suo

The mobility of charge carriers in silicon can be significantly increased when silicon is subject to a field of strain.In a microelectronic device, however, the strain field may be intensified at a sharp feature, such as an edge or a corner, injecting dislocations into silicon and ultimately failing the device. The strain field at an edge is singular, and is often a linear superposition of two modes of different exponents. We characterize the relative contribution of the two modes by a mode angle, and determine the critical slip systems as the amplitude of the load increases. We calculate the critical residual stress in a thin-film stripe bonded on a silicon substrate.

The related work: node/434

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## Comments

## Few remarks and questions

It is a very interesting topic. I investigated cracks in three-dimensional domains and corner singularities in the past. It is an important issue. However, I have few questions:

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Yuval

## Mode III and Dundurs Beta

Dear Yuval Freed,

Thank you very much for your interest in this topic, I am pleased to answer your questions.

1. We do not consider the mode III stress intensity factor, since we analyze the "infinite stripe" problem, and therefore the mode III is not of interest.

2. By stating Dundurs beta = 0, we basically assume Poisson's ratio to be equal for both materials, i.e. 0,5. This would mean incompressible material behaviour, which is physically not applicable. However, our goal was to present a framework and method, which could be applied over a wide range of material and geometric properties. Poisson's ratio could be altered and analysis repeated for other values, in order to study the effect of beta effects.

Best regards,

Martijn Feron

## 3D singularity and oscillatory singularity

Dear Yuval,

Thank you very much for your interest and great comment.

## i need your emeil adreess

i need your emeil adreess

## subdivision method to solve integral with weak singularity

i need this papers about the use of subdivision method to solve integral with weak singularity in bem

- J O Lachat & J O watson " effective numerical treatment of boundary inegral equation " a new formulation for three dimenssional elasostatics Int .Jr.Numer.methods .Eng.211-228(1958)