Determination of axisymmetric elastic constants in anisotropic silicon for a thyristor tablet

Abstract

The stress distribution in a thyristor tablet due to thermal shrinkage is considered. The thyristor tablet consists of two cylindrical layers, anisotropic silicon (the semiconductor) and molybdenum (the substrate). Using the software package ‘ANSYS’ stresses are calculated for 4 different cases namely, I) the axisymmetric case, II) the 3-dimensional isotropic silicon, III) the 3-dimensional anisotropic (100) silicon and IV) the 3-dimensional anisotropic (111) silicon. Good agreement is found between cases I and II which serves as a check for the accuracy of the numerical calculations. Comparing cases III and IV one finds that for (111) Si the Van Mises stress lies up to 15% above the value of (100) Si. Although a 4-fold axis in the stress distribution is observed for (100) Si and a 3-fold axis for (111) Si, for practical purposes one can neglect this anisotropy for Si and perform an axisymmetric calculation, since the dependence of the stresses on the azimutal angle is rather weak. Finally, the elastic constants (or more precisely, the material property matrices) for (100) and (111) Si, respectively, as they should be used in an axisymmetric (but not isotropic) analysis, are presented.