Determination of the lattice contraction of boron-doped silicon

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Abstract
We report a study of the change in lattice constant when single-crystal silicon is substitutionally doped with boron. The measurements were made using 10-μm-thick epilayers with boron concentrations (NB) in the range 1.7×1019–1.2×1020 cm−3. The influence of elastic strain in the epilayers and their substrates was eliminated by including Bragg reflections from planes that were inclined to the (100) surface. We obtained a value for the lattice contraction coefficient β=(5.19±0.09)×10−24 cm3, where the range is ± one standard error. Specimens with NB≊2×1019 cm−3 were strained to give coherent interfaces with their substrates. Evidence for relaxation (presumably by misfit dislocations at the interface) was observed with NB≊5×1019 cm−3 (corresponding to a lattice mismatch of approximately 2.5×10−4), but this occurred in a patchy fashion and remained incomplete while NB was increased to 1.2×1020 cm−3 (corresponding to a mismatch of 6.5×10−4). This partial relaxation occurred at somewhat smaller mismatches than would be expected from reported studies of silicon-germanium alloy epilayers on silicon substrates. Our technique for analyzing a set of Bragg reflections to separate the effects of elastic strain and lattice mismatch appears to be novel and has general applicability to the study of epilayer/substrate combinations.