Tutorial

The properties of many materials can be strongly affected by the introduction of impurity atoms. For example, the doping of semiconductor materials lies at the foundation electronics industry.

The amount of impurities sufficient to significantly alter the property of materials is in general in the ppm. Intrinsic defects, which are ubiquitous in every material, also generally appear in this concentration range.

For such small concentrations, it can be assumed that each defect will not feel the presence of other defects. Despite the truth of this claim should be carefully assessed on a case-by-case basis - defect complexes do occurr and concentrations of intrinsic defects might be considerable, as in the case of nonstoichiometric compounds - defect mutual independence, that is considering the dilute limit, is generelly assumed since it allows to easily obtains relevant properties of defective systems, such as defect and carrier concentrations.

Spinney implements the formulism devised for point defects in the dilute limit, it is also assumed that first-principles calculations of point defects are performed within the supercell formalism [PTA+92], which is currently the most widely employed.

This tutorial will review the most common steps involved in the study of point defects in solids using first-principles simulations and will show how Spinney can be used to assist with the investigation.

Contents

• The defect formation energy in the supercell approach
  • In-depth Tutorial
  • Quickstart Guide
  • Manage a defective system with the class DefectiveSystem
• Correction schemes for electrostatic finite-size effects
  • Theoretical introduction
  • Implementation in Spinney
• Thermodynamic limits for the chemical potentials
  • Limiting values of the chemical potentials
  • Plotting the feasible region
  • Beyond binary compounds
  • Including temperature and pressure effects through the gas-phase chemical potentials
• Charge Transition Levels
  • Using the class Diagram
  • Using the class DefectiveSystem
• Equilibrium defect concentrations in the dilute limit
  • Calculate equilibrium defect concentrations with Spinney
  • Using the class DefectiveSystem