Strained Si, Ge and SiGe alloys modeling with full-zone k.p method optimized from first principle calculation
The electronic energy band structure of strained and unstrained Si, Ge and SiGe alloys is examined in this work using thirty-level k.p analysis. The energy bands are at first obtained with ab initio calculations based on the Local-Density-Approximation of Density-Functional Theory, including a GW correction and relativistic effects. The so-calculated band structure is then used to extract the unknown k.p fitting parameters with a conjugate-gradient optimization procedure. In a similar manner, the results of ab initio calculations for strained materials are used to fit the unknown deformation potentials that are included in the present k.p Hamiltonian following the Pikus and Bir correction scheme. We show that the present k.p model is an efficient numerical method, as far as computational time is concerned, that reproduces accurately the overall band structure, as well as the bulk effective density of states and the carrier effective masses, for both strained and unstrained materials. As an application, the present thirty-level k.p model is used to describe the band offsets and the variations of the carrier effective masses in a strained material, a Si(1-x)Gex/Si(1-y)Gey layer system.