Theoretical explanation for doping dependence of lattice constants in Ge:B films: Revealing nanoscale impurity types from macroscopic perspective

Lattice parameters of boron doped germanium (Ge:B) films have been measured and reported across the entire currently attainable concentration range up to ∼1 × 1022 cm−3. Previously speculated deviation from Vegard’s law for the Ge:B system has been verified, and in-depth investigations have revealed that the lattice constants for Ge:B are collectively determined by a series of mechanisms. At low doping levels, where all B atoms maintain substitutional status, Vegard’s law and an additional electronic effect are the main causes for lattice change. At high doping levels, ab initio calculations suggest a preponderance of substitutional B-interstitial B pairs over isolated interstitial B atoms. Further simulation revealed that those Bs–Bi pairs contribute little toward both lattice parameter change and carrier concentration, which conveyed strong theoretical explanation for experimental observations in both the current work and literature. The findings of this work have not only elucidated the long-obscure lattice constant perspective in Ge:B system but also provided an important paradigm for lattice study in various doping and low-solubility-alloy systems.