Effect of Point Defects on Electronic Structure of Monolayer GeS

Using density functional theory calculations, atomic and electronic structure of defects in monolayer GeS were investigated by focusing on the effects of vacancies and substitutional atoms. We chose group IV or chalcogen elements as substitutional ones, which substitute for Ge or S in GeS. It was found that the bandgap of GeS with substitutional atoms is close to that of pristine GeS, while the bandgap of GeS with Ge or S vacancies was smaller than that of pristine GeS. In terms of formation energy, monolayer GeS with Ge vacancies is more stable than that with S vacancies, and notably GeS with Ge substituted with Sn is most favorable within the range of chemical potential considered. Defects affect the piezoelectric properties depending on vacancies or substitutional atoms. Especially, GeS with substitutional atoms has almost the same piezoelectric stress coefficients eij as pristine GeS while having lower piezoelectric strain coefficients dij  but still much higher than other 2D materials. It is therefore concluded that Sn can effectively heal Ge vacancy in GeS, keeping high piezoelectric strain coefficients.