Strained Si, Ge, and Si1-xGex alloys modeled with a first-principles-optimized full-zone k•p method

The electronic energy band structure of strained and unstrained Si, Ge, and SiGe alloys is examined in this work using a 30-level k center dot 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 center dot 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 center dot p Hamiltonian following the Pikus-Bir correction scheme. We show that the present k center dot p model is an efficient numerical method, as far as computational time is concerned, which 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 30-level k center dot p model is used to describe the band offsets and the variations of the carrier effective masses in the strained Si1-xGex/Si1-yGey system.