O. W. Dillon

Dislocation dynamics during the growth of silicon ribbon

The thermal viscoplastic stresses and the dislocation densities in silicon ribbon are computed for an axially changing thermal profile by using an iterative finite difference method. A material constitutive equation (Haasen–Sumino model) which involves an internal variable (mobile dislocation density) is used. The results are interpreted as showing that there is a maximum width of silicon ribbon that can be grown when viscoplasticity and dislocations are considered. This maximum width limitation does not exist if the material behavior is elastic.

Dislocation dynamics of web type silicon ribbon

Silicon ribbon grown by the dendritic web process passes through a rapidly changing thermal profile in the growth direction. This rapidly changing profile induces stresses which produce changes in the dislocation density in the ribbon. A viscoplastic material response function (Haasen-Sumino model) is used herein to calculate the stresses and the dislocation density at each point in the silicon ribbon. The residual stresses are also calculated.

The Constitutive Equation for Silicon and Its Use in Crystal Growth Modeling

A stress analysis that describes the crystal growing process requires a material model that is valid over a wide temperature range and includes dislocation motion and mutliplication. The stresses developed in the growing process could induce residual stresses, changes in dislocation density and buckling into the growing crystals. The dislocation density is introduced as an internal variable in the constitutive model. The stress-strain and dislocation density-strain characteristics of silicon crystals are discussed as a function of temperature, strain rate, and initial dislocation density

The effects of temperature on the machining of metals

The machining behaviors of metals at various workpiece temperatures are studied by the milling operation. Cutting power was recorded; tool life, chip size, surface finish and the microstructures of chips were examined.

Dislocation dynamics and the viscoplastic buckling of dendritic web type silicon ribbon

The effect of dendrites (reinforced edges) on the residual stresses, dislocation densities and buckling behavior during growth of web type silicon ribbon is studied. A viscoplastic material response function (Haasen-Sumino model) is used to calculate the stresses and the dislocation density at each point in the silicon ribbon. In addition, the role of dendrites on the viscoplastic buckling behavior of the ribbon is investigated. The critical thicknesses, the corresponding deflection shapes and lateral deflection speeds are calculated. These results are then compared with similar data obtained for flat plates.

Dislocation motion and multiplication during the growth of silicon ribbon

Abstract The production and motion of dislocations during the growth of silicon ribbon by the dentritic web process is treated. Thermal elastic stresses are calculated from a temperature distribution defined along the growth direction of the ribbon. Dislocation motion and multiplication in the ribbon due to thermal stresses are monitored taking the ribbon crystallography into consideration and employing the Hassen-Sumino deformation model. The dislocation density and distribution obtained from the crystallographic considerations are compared with experimental observations of the defect configuration in silicon ribbon and similar computational results obtained assuming isotropic deformation conditions.

Thermal buckling of silicon sheet

Results of buckling analyses for three closely related thermal profiles are discussed. They come from the same basic furnace design but reflect changes that occur in the thermal profile when different pull speeds are used to produce wider or thicker ribbon. It is shown that the three profiles differ near the solid-melt interface. Details of the calculation procedure for the in-plane stresses are also given. The shapes associated with the first three modes for each profile are shown. The shape of the first mode for each thermal profile is different. This is primarily due to differing geometry associated with the different pull speeds.<<ETX>>

Dislocation Dynamics During the Czochralski Growth of Silicon

The thermal stresses induced by temperature variations that exist during steady-state Czochralski growth produce plastic deformations in the crystal by dislocation motion and generation. The temperature variations in the crystal are calculated numerically by the finite element method (FEM). Employing the Haasen-Sumino viscoplastic response function for silicon and the calculated temperature profile, the thermal stresses, the dislocation densities, and the residual stresses in the crystal are also calculated. Only low dislocation densities are of interest and hence the associated viscoplastic deformations are found to be small. The assumption is made that there is a very low dislocation density along the solid-melt interface. The Haasen-Sumino material model is modified to include a back-stress to account for the locking effects due to the impurity concentration in the crystal. This analysis provides guidance for growing large diameter crystal of materials with known constitutive relations which have a low dislocation density and low thermal stresses.

Constitutive Law for Calculating Plastic Deformations During CZ Silicon Crystal Growth

During the growth of CZ silicon crystals, dislocation motion and generation are induced by the thermal stresses which arise from rapid cooling from the solidification temperature. These defects limit the fraction of acceptable silicon device chips obtained from a crystal. Current semiconductor technology is restrained by the lack of a predictive material model that can reliably calculate the dislocation motion and multiplication in CZ material at temperature close to the melting point. The concepts of Haasen and Sumino are modified to predict axial tensile results in CZ silicon up to 1300 °C. This modified formulation is the basis of the constitutive model presented.