There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Electronic excitations lie at the origin of most of the commonly measured spectra. However, the first-principles computation of excited states requires a larger effort than ground-state calculations, which can be very efficiently carried out within density-functional theory. On the other hand, two theoretical and computational tools have come to prominence for the description of electronic excitations. One of them, many-body perturbation theory, is based on a set of Green’s-function equations, starting with a one-electron propagator and considering the electron-hole Green’s function for the response. Key ingredients are the electron’s self-energy S and the electron-hole interaction. A good approximation for S is obtained with Hedin’s GW approach, using density-functional theory as a zero-order solution. First-principles GW calculations for real systems have been successfully carried out since the 1980s. Similarly, the electron-hole interaction is well described by the Bethe-Salpeter equation, via a functional derivative of S. An alternative approach to calculating electronic excitations is the time-dependent density-functional theory (TDDFT), which offers the important practical advantage of a dependence on density rather than on multivariable Green’s functions. This approach leads to a screening equation similar to the Bethe-Salpeter one, but with a two-point, rather than a four-point, interaction kernel. At present, the simple adiabatic local-density approximation has given promising results for finite systems, but has significant deficiencies in the description of absorption spectra in solids, leading to wrong excitation energies, the absence of bound excitonic states, and appreciable distortions of the spectral line shapes. The search for improved TDDFT potentials and kernels is hence a subject of increasing interest. It can be addressed within the framework of many-body perturbation theory: in fact, both the Green’s functions and the TDDFT approaches profit from mutual insight. This review compares the theoretical and practical aspects of the two approaches and their specific numerical implementations, and presents an overview of accomplishments and work in progress.

/pdf/electronic-excitations-density-functional-versus-many-body-2tgqd9dfpy.pdf

Electronic excitations: density-functional versus many-body Green's-function approaches

The unique electrical, mechanical and physical properties of two-dimensional materials make them attractive candidates in flexible nanoelectronic systems. Here Akinwande et al. review the literature on two-dimensional materials in flexible nanoelectronics, and highlight barriers to their full implementation.

/pdf/two-dimensional-flexible-nanoelectronics-4fvhvf1sg7.pdf

Two-dimensional flexible nanoelectronics.

This review provides a perspective on the use of orbital-dependent functionals, which is currently considered one of the most promising avenues in modern density-functional theory. The focus here is on four major themes: the motivation for orbital-dependent functionals in terms of limitations of semilocal functionals; the optimized effective potential as a rigorous approach to incorporating orbital-dependent functionals within the Kohn-Sham framework; the rationale behind and advantages and limitations of four popular classes of orbital-dependent functionals; and the use of orbital-dependent functionals for predicting excited-state properties. For each of these issues, both formal and practical aspects are assessed.

Orbital-dependent density functionals: Theory and applications

The conduction mechanisms in dielectric films are crucial to the successful applications of dielectric materials. There are two types of conduction mechanisms in dielectric films, that is, electrode-limited conduction mechanism and bulk-limited conduction mechanism. The electrode-limited conduction mechanism depends on the electrical properties at the electrode-dielectric interface. Based on this type of conduction mechanism, the physical properties of the barrier height at the electrode-dielectric interface and the effective mass of the conduction carriers in dielectric films can be extracted. The bulk-limited conduction mechanism depends on the electrical properties of the dielectric itself. According to the analyses of bulk-limited conduction mechanisms, several important physical parameters in the dielectric films can be obtained, including the trap level, the trap spacing, the trap density, the carrier drift mobility, the dielectric relaxation time, and the density of states in the conduction band. In this paper, the analytical methods of conduction mechanisms in dielectric films are discussed in detail.

/pdf/a-review-on-conduction-mechanisms-in-dielectric-films-2bpdskdmsp.pdf

A Review on Conduction Mechanisms in Dielectric Films

Experimental and ab initio computational methods are employed to conclusively show that ScN is a semiconductor rather than a semimetal; i.e., there is a gap between the N $2p$ and the Sc $3d$ bands. Previous experimental investigators reported, in agreement with band structure calculations showing a band overlap of 0.2 eV, that ScN is a semimetal while others concluded that it is a semiconductor with a band gap larger than 2 eV. We have grown high quality, single crystalline ScN layers on MgO(001) and on TiN(001) buffer layers on MgO(001) by ultrahigh vacuum reactive magnetron sputter deposition. ScN optical properties were determined by transmission, reflection, and spectroscopic ellipsometry while in-situ x-ray and ultraviolet valence band photoelectron spectroscopy were used to determine the density of states (DOS) below the Fermi level. The measured DOS exhibits peaks at 3.8 and 5.2 eV stemming from the N $2p$ bands and at 15.3 eV due to the N $2s$ bands. The imaginary part of the measured dielectric function ${\ensuremath{\varepsilon}}_{2}$ consists of two primary features due to direct X- and \ensuremath{\Gamma}-point transitions at photon energies of 2.7 and 3.8 eV, respectively. For comparison, the ScN band structure was calculated using an ab initio Kohn--Sham approach which treats the exchange interactions exactly within density-functional theory. Calculated DOS and the complex dielectric function are in good agreement with our ScN valence-band photoelectron spectra and measured optical properties, respectively. We conclude, combining experimental and computational results, that ScN is a semiconductor with an indirect $\ensuremath{\Gamma}--X$ bandgap of $1.3\ifmmode\pm\else\textpm\fi{}0.3\mathrm{eV}$ and a direct X-point gap of $2.4\ifmmode\pm\else\textpm\fi{}0.3\mathrm{eV}.$

/pdf/electronic-structure-of-scn-determined-using-optical-2gevytcm52.pdf

Electronic structure of ScN determined using optical spectroscopy, photoemission, and ab initio calculations

We study metallization of molecular hydrogen under pressure using exact-exchange (EXX) Kohn-Sham density-functional theory in order to avoid well-known underestimates of band gaps associated with standard local-density or generalized-gradient approximations. Compared with the standard methods, the EXX approach leads to considerably (1-2 eV) higher gaps and significant changes in the relative energies of different structures. Metallization is predicted to occur at a density of greater, approximately greater than 0.6 mol/cm(3) (corresponding to a pressure of greater, approximately greater than 400 GPa), consistent with all previous measurements.

Metallization of molecular hydrogen: predictions from exact-exchange calculations.

We investigate theoretically coherent electron tunneling through three-dimensional microscopic Si[100]/SiO2/Si[100] model junctions with oxide thicknesses between 0.4 and 4.6 nm. The transmission probabilities of these structures were calculated using a semiempirical tight-binding scattering method. Our calculations provide a basis for the microscopic understanding of the observed independence of tunneling transmission on the orientation of the bulk silicon and on the nature of inelastic defect-assisted tunneling. We document significant differences between transmission coefficients obtained with the present scheme and with the popular effective-mass-based approaches. The energy dependence of the effective tunneling mass in bulk silicon dioxide is predicted.

Tunneling through ultrathin SiO2 gate oxides from microscopic models

Simulation of nanoscale MOSFETs using modified drift-diffusion and hydrodynamic models and comparison with Monte Carlo results

One-particle wave functions and energies from Kohn-Sham calculations with the exact local Kohn-Sham exchange and the local density approximation (LDA) correlation potential [EXX(c)] are used as input for quasiparticle calculations in the GW approximation (GWA) for eight semiconductors. Quasiparticle corrections to EXX(c) band gaps are small when EXX(c) band gaps are close to experiment. In the case of diamond, quasiparticle calculations are essential to remedy a 0.7 eV underestimate of the experimental band gap within EXX(c). The accuracy of EXX(c)-based GWA calculations for the determination of band gaps is as good as the accuracy of LDA-based GWA calculations. For the lowest valence band width a qualitatively different behavior is observed for medium- and wide-gap materials. The valence band width of medium- (wide-) gap materials is reduced (increased) in EXX(c) compared to the LDA. Quasiparticle corrections lead to a further reduction (increase). As a consequence, EXX(c)-based quasiparticle calculations give valence band widths that are generally 1-2 eV smaller (larger) than experiment for medium- (wide-) gap materials. (c) 2000 The American Physical Society.

M. Stadele

Papers

Electronic structure of ScN determined using optical spectroscopy, photoemission, and ab initio calculations

Metallization of molecular hydrogen: predictions from exact-exchange calculations.

Tunneling through ultrathin SiO2 gate oxides from microscopic models

Simulation of nanoscale MOSFETs using modified drift-diffusion and hydrodynamic models and comparison with Monte Carlo results

Exact-exchange-based quasiparticle calculations