Characterisation and Control of Defects in Semiconductors by Filip Tuomisto;

Author:Filip Tuomisto; [Неизв.]
Language: eng
Format: epub
ISBN: 9781785616556
Publisher: Institution of Engineering & Technology
Published: 2019-12-15T21:00:00+00:00

1Please note that absolute S/W values are difficult to compare between experiment and theory. Instead, one should rather look at trends among a set of samples or defects considered.

Chapter 7

First principles methods for defects: state-of-the-art and emerging approaches

Elif Ertekin1 and Hannes Raebiger2

1Department of Mechanical Science and Engineering, University of Illinois at Urbana–Champaign, Champaign, IL, USA

2Department of Physics, Yokohama National University, Yokohama, Japan

Electronic structure theory [1,2] is a powerful tool to predict properties of defects from first principles. In principle, one needs to solve the many-particle Schrödinger equation for bulk and defect-containing materials to obtain total energies, which can then be associated with macroscopic observables via thermodynamics. In practice, the Schrödinger equation is solved at different levels of approximation, which lead to a variety of uncertainties often making it difficult to assess the degree of accuracy attainable. This chapter describes typical approaches and levels of approximation and the common sources of uncertainties encountered. On one hand, it provides a generalized framework for carrying out defect calculations. On the other hand, it is intended as a guide to experimentalists how to read theory papers, assess conclusions, and interact with theorists. Some of the common terms used throughout this chapter are briefly described in Table 7.1.

Table 7.1 Common nomenclature and simple explanations

TermHandwaving explanation

Defect level Spectral levels induced by a defect, often within the band gap. In this chapter, defect level refers to a defect-induced one-electron quasiparticle level (see below, and Section 7.1). Easily confused with thermodynamic charge transition level

Quasiparticle energy Single electron spectral energies. The energy required to add/remove an electron from a specific level (or orbital) at fixed atomic coordinates

Charge transition level Thermodynamic activation energy for ionization of a defect. Sometimes also called a zero-phonon line. A difference from quasiparticle levels is that in a thermodynamic excitation, atomic coordinates in general are not fixed

Total energy The ground state energy of an interacting many-electron system. This is the eigenvalue of many-electron Schrödinger equation (7.11), or evaluated, e.g., from (7.13) or (7.16)

Self-interaction When the Coulomb repulsion potential energy of all electrons is calculated based on the charge density (classically), it contains a spurious term of an electron repelling itself. This is called self-interaction, which in wave-function-based methods is easily accounted for, but not so in charge-density-based methods

Finite size effect An error introduced when describing a macroscopic system (∼1023 atoms, practically infinite) within an atomic scale, finite, model (much less than 1023 atoms)

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