Lattice strain from substitutional Ga and from holes in heavily doped Si:Ga

The average lattice strain per Ga atom with respect to pure silicon, total="a/aNGa =+(0.9±0.1)×10-24 cm3, for heavily doped Si was measured by high-resolution x-ray diffraction. This strain includes effects of both substitutional Ga atoms in the lattice and doping-related holes in the valence band. The local size-effect lattice strain around substitutional Ga atoms, which is not expected to be affected significantly by valence-band holes, was determined from the Ga-to-Si nearest-neighbor distance measured using extended x-ray-absorption fine structure (EXAFS). This distance, rNN=2.41±0.02, is 0.06 larger than the usual Si-to-Si nearest-neighbor distance and was used to calculate the size-effect contribution per Ga atom to the average lattice strain, size=(1.2±0.3)×10-24 cm3. This value was subtracted from the overall lattice strain total to determine the lattice strain per valence-band hole, h=-(0.3±0.3)×10-24 cm3, and the hydrostatic deformation potential for the valence-band edge in silicon, av=-0.5±0.5 eV. These results were obtained from Si samples prepared by liquid-phase epitaxy. They were characterized by Rutherford backscattering, ion channeling, electron microscopy, and resistivity measurements, as well as by x-ray diffraction and EXAFS. The samples were of excellent crystal quality, with uniform Ga concentrations of 1.0 and 1.5×1020 cm-3, with substitutional fractions greater than 95% and similar electrical resistivities of 2×10-3 cm. © 1992 The American Physical Society.