Finite Cylinders of Si1 − x Ge x Alloy Under the Double-Punch Test and Effect on Three Valence-Bands

Abstract

An analytical solution for the stress and strain fields within a finite circular solid cylinder of Si1 − xGex alloy under the double-punch test is presented. The method of solution uses the displacement function approach, together with proposing a new expression for the displacement function so that all of the boundary conditions are satisfied exactly. The present solution covers the solution by Wei and Chau [1] for isotropic cylinders under the double-punch test when the isotropic limit case is considered. Numerical results show that strain and stress distributions within the cylinder are not uniform, and strain or stress concentrations are usually developed near the end surfaces, but the strain and stress distributions within the central part are relatively uniform. Moreover, according to quantum mechanics and the energy band theory, the effects of strain on three valence bands, namely the heavy hole (HH) band, the light hole (LH) band and the split-off (SO) band of Si1 − xGex alloy and the corresponding conductivity masses are analyzed. It was found that the quantum behavior of the three valence bands, such as the energy distribution, the shape of constant energy surfaces, the magnitude and the distribution pattern of the conductivity masses can be modified considerably by the external force applied in the double-punch test, depending on the proportion between silicon and Germanium in Si1 − xGex alloy.