Finite Cylinders of Si_{1 − 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 Si_{1 − x}Ge_x 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 Si_{1 − x}Ge_x 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 Si_{1 − x}Ge_x alloy.

Keywords:

• Si_{1 − x} Ge _x alloy
• double-punch test
• analytical solution
• inhomogeneous strain
• quantum valence-bands
• effect on electronic structure

ACKNOWLEDGEMENTS

This research is supported by the National Natural Science Foundation of China (grant no.10672023 and 10872033).