Marker-Method Calculations for Electrical Levels Using Gaussian-Orbital Basis Sets

The introduction of defect-related states in the bandgap of semiconductors can be both advantageous and deleterious to conduction, and it is therefore of great importance to have quantitative computational methods for determining the location of electrical levels. In particular, where the defect levels are deep in the bandgap, the states involved are typically highly localized and the application of real-space, localized basis sets have clear advantages. In this chapter the use of such basis sets both for cluster and supercell geometries is discussed. Agreement with experiment is often hampered by problems such as the underestimate of bandgaps when using density-functional theory. We show that these can be somewhat mitigated by the use of "markers", either experimental or theoretical, to largely eliminate such systematic errors.