Engineering vacancies in 2D WSe₂ using impurity doping.

Manipulation of defects such as chalcogen vacancies in 2D transition-metal dichalcogenides by impurity doping opens new ways of tuning the optical, electronic and transport properties, and is of great interest for technological applications. Our experimental collaborators can tune the density of Se vacancies in WSe₂ monolayers, by substitutional impurity doping of 3-d transition metal atoms with varying valency (Ti, V, Cr, Mn and Co) at a dilute dopant density of ~0.04 at.%. We use density functional theory to study the thermodynamic stability of vacancies in presence of the dopants – and focus on the details of the underlying dopant-vacancy interaction, and clustering of multiple vacancy around dopants. We find that isolated Se vacancies are charge neutral, and typically show an attractive binding to all the dopants we consider. We find that Ti and V dopants prefer to pair with a Se divacancy and host a -1 charge, while Cr, Mn, and Co dopants prefer to pair with Se monovacancy and host a -1 charge. We further develop a tractable model based on electrostatic interactions between the induced Bader charges due to the dopants and vacancies. We can explain the experimental trends in vacancy densities and average dopant-vacancy distance, using a Boltzmann-averaged distribution based on electrostatic binding energies calculated from our electrostatic model, with Bader charges obtained from our DFT calculations.