Analytical solutions for finite cylinders compressed between platens and the strain effect on the valence-band structure of Si_1-xGe_x alloy

This paper presents an analytical solution for inhomogeneous strain and stress distributions within finite circular cylinders of Si_1-xGe_x alloy under compression test with end friction. The method follows Lekhnitskii's stress function approach, but a new expression for the stress function is proposed so that all of the governing equations and boundary conditions are satisfied exactly. Numerical results show that the axial, radial, circumferential and shear strains are all inhomogeneous within finite cylinders, and local strain concentrations near two end surfaces were usually developed as long as friction exists between end surfaces and loading platens. Moreover, by using envelope-function method, the effect of strain on the valence-band structure of Si_1-xGe_x alloy is also studied. It was found that strain can induce band splitting, alteration of the shape of constant energy surfaces of the heavy-hole and the light-hole bands of Si_1-xGe_x alloy.