A k·p analytical model for valence band of biaxial strained Ge on（001） Si_1-xGe_x

In this paper,the dispersion relationship is derived by using the k·p method with the help of the perturbation theory,and we obtain the analytical expression in connection with the deformation potential.The calculation of the valence band of the biaxial strained Ge/(001)Si1-xGex is then performed.The results show that the first valence band edge moves up as Ge fraction x decreases,while the second valence band edge moves down.The band structures in the strained Ge/(001)Si 0.4 Ge 0.6 exhibit significant changes with x decreasing in the relaxed Ge along the 0,0,k] and the k,0,0] directions.Furthermore,we employ a pseudo-potential total energy package(CASTEP) approach to calculate the band structure with the Ge fraction ranging from x = 0.6 to 1.Our analytical results of the splitting energy accord with the CASTEP-extracted results.The quantitative results obtained in this work can provide some theoretical references to the understanding of the strained Ge materials and the conduction channel design related to stress and orientation in the strained Ge pMOSFET.