## From density functional theory to defect level in silicon: Does the “band gap problem” matter?

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#### Abstract

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.

#### Bio

Dr. Schultz is currently a Principal Member of Technical Staff at Sandia National Laboratories in the Multiscale Dynamic Materials Methods Department. His research has been focussed on development and application of atomistic materials simulations methods enabled by high-performance computing, particularly first principles density functional theory methods for extended (bulk and surface) systems. He is the principle architect of the QUEST suite of Gaussian-based density functional theory codes developed at Sandia, and is involved in multiscale methods development intended to invest higher-scale methods (e.g., classical interatomic potentials) with quantum accuracy. His applications interests span the chemical and electronic properties of defect in bulk oxides and semiconductors, amorphous materials, surface chemistry and catalysis, and structural energetics of bulk crystal phases and surface relaxation.
Dr. Schultz first got his Ph.D. in physics from the University of Pennsylvania, followed by a post-doctoral fellowship at Sandia, and then a stint in a metallurgy group at the GE Corporate Research and Development Center in Schenectady, before arriving at Sandia in 1992, where he has remained since. His focus remained on computational materials methods applied to different problems, with an emphasis on solving engineering-driven materials problems. He joined the Executive Editorial Board for Modelling and Simulation in Materials Science and Engineering in 2008.

#### Credits

Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under Contract DE-AC04-94AL85000. Abstract (SAND2007-5831)

#### Sponsored by

Network for Computational Nanotechnology (NCN)
Center for the Prediction of Reliability, Integrity and Survivability of Microdevices (PRISM)

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Armstrong 1109, Purdue University, West Lafayette