ME Seminar Series: Ab Initio Modelling of Defects at Semiconductor Surfaces: Doping as a Thermodynamic Factor
Doping, either intentional or unintentional, can affect charge state, concentration, and distribution of defects in a material. Although different aspects of this influence had been discussed in literature, their relative significance and completeness are still debatable. Experiments measuring defect concentrations as a function of thermodynamic variables (T, p, doping) are scarce. On the other hand, previous theoretical approaches have aimed at a description of isolated defects, or, more recently, dopant-defect complexes. In this work, we demonstrate that these approaches missed an important part of the free energy that can greatly influence defect concentrations. Dopants introduce charge carriers, either holes (p-type) or electrons (n-type). The charge carriers can occupy defect electronic levels, leading to charging of both the dopants and the defects. Due to the long-range nature of the Coulomb interaction, the electrostatic energy of this charge separation strongly depends on the concentration and distribution of defects and dopants. Thus, in addition to the local contributions to the free energy of defect formation, such as breaking or making bonds and local lattice distortions, there is a global contribution due to the overall electrostatic energy of the system. We show that this global contribution can be significant at realistic conditions.