Analytic Solution for In-Plane Valence Subbands of Strained SiGe Superlattice

Effective mass theory is used to calculate the in-plane valence subbands of strained SiGe superlattice within the 6 x 6 Luttinger model and under a correct boundary condition. The envelope wavefunctions are given analytically as a linear combination of bulk wavefuctions. The boundary conditions imposed on the envelope functions yield a 24 x 24 matrix, and from the zeros of its determinant the inplane energy dispersion E is obtained as a function of inplane wavevector k_||. We discuss the mixing among the heavy-hole, light-hole and spin-split-off states at finite k_|| and the dependence of the dispersion on the spin-split-off band and strain.