T. Vodenitcharova

A mechanics prediction of the behaviour of mono-crystalline silicon under nano-indentation

Abstract This paper uses a new constitutive model developed recently by the authors to analyse the multi-phase transformations in mono-crystalline silicon when subjected to nano-indentation. The finite element method is employed to the integration of the stress–strain relationship. A very good agreement is reached with the experimental measurements, with an accurate prediction of the observed pop-in and pop-out and detailed phase transformation events in loading and unloading. It was found that due to the change of microstructures, the material in the deformation zone could experience a local unloading during indentation loading or undergo a local loading during indentation unloading. The phase transformation events during indentation are closely related to the variation of both the deviatoric and hydrostatic stress components.

The Effect of Thermal Shocks on the Stresses in a Sapphire Wafer

Sapphire wafers can experience temperature variations during processing in a furnace, which in turn can cause large deformation and stresses in the wafers. This paper aims to reveal the mechanism of stress development and evolution in sapphire wafers during thermal shocks, as well as the dependence of the stresses on some process parameters. Finite-element stress analysis was conducted on a single sapphire wafer subjected to thermal shocks. The results show that the thermal gradient in the radial direction induces high stresses even in mechanically unrestrained wafers. The largest stress components occur at the wafer edge as the largest normal stresses are circumferential; whereas the maximum tensile stress is realized upon cooling, the highest value of the maximum shear stress and the minimum compressive stress eventuate in the heating-up phase. The normal stresses have a parabolic distribution in the radial direction. It was found that holding the furnace temperature leads to a more uniform temperature distribution across the wafer but brings about higher tensile stresses in the cooling phase

Transient thermal analysis of sapphire wafers subjected to thermal shocks

Rapid heating and cooling are commonly encountered events in integrated circuit processing, which produce thermal shocks and consequent thermal stresses in wafers. The present paper studies the heat transfer in sapphire wafers during a thermal shock as well as the dependence of the wafer temperature on various process parameters. A three-dimensional finite-element model of a single sapphire wafer was developed to analyze the transient heat conduction in conjunction with the heat radiation and heat convection on the wafer surfaces. A silicon wafer was also investigated, for comparison. It was found that the rapid thermal loading leads to a parabolic radial temperature distribution, which induces thermal stresses even if the wafer is not mechanically restrained. The study predicted that for sapphire wafers the maximum furnace temperature of 800 degC should be held for two hours in order to get a uniform temperature throughout the wafer