From density functional theory to defect level in silicon: Does the “band gap problem” matter?
Modeling the electrical effects of radiation damage in semiconductor devices requires a
detailed description of the properties of point defects generated during and subsequent to
irradiation. Such modeling requires physical parameters, such as defect electronic levels,
to describe carrier recombination. Density functional theory (DFT) is the method of
choice for first-principles simulations of defects. However, DFT typically hugely
underestimates the fundamental band gap in semiconductors, and the band gap is the
energy scale of interest for defect levels. Moreover, boundary conditions in the supercell
approximation used in DFT calculations of defects also can inject large errors and
uncertainties. I describe a new, more rigorous methodology for supercell calculations,
implemented in the SeqQuest DFT code, that incorporates a proper treatment of
electrostatic boundary conditions, locates a fixed chemical potential for the net defect
electron charge, includes the bulk dielectric response, and creates a robust computational
model of isolated defects. Using this methodology, the computed DFT defect level
spectrum for a wide variety of Si defects spans the experimental Si gap, i.e., exhibits no
band gap problem, and the DFT results agree remarkably well with experiment for those
values that are experimentally known. The new scheme adds rigor to computing defect
properties, and has important implications for density functional theory development.