We report in this work the calculation of the anisotropic hyperfine constants for the ${\mathrm{Si}}^{29}$ lattice nuclei surrounding the shallow donor impurities P, As, Sb in silicon. We have used a Slater-Koster linear combination of atomic orbitals representation of the Bloch functions of the silicon lattice. These Bloch functions are used in the Brillouin-zone expansion of the impurity wave function. With these calculations we are able to further substantiate our earlier matchings of the ${\mathrm{Si}}^{29}$ lattice sites and the electron-nuclear-double-resonance shells measured by Hale and Mieher. The formalism developed is sufficiently general so that it might be used in future calculations of other electronic defects.

• Received 12 August 1974

DOI:https://doi.org/10.1103/PhysRevB.11.849