A Tetrahedron Method for Doubly Constrained Brillouin Zone Integrals Application to Silicon Optic Phonon Decay

Abstract Integrals over the Brillouin zone with two delta‐functions are considered. Such integrals are constrained to the intersection of two different constant energy surfaces. Following the discussion by Lehmann and Taut for the case of one delta‐function, the tetrahedron method is shown to yield simple analytic results when the energies and weight functions are linearly interpolated throughout a small tetrahedron. The method is illustrated with a calculation of the density of available two‐phonon decay channels of the Q = O optic phonon of Si.