Modeling and simulation is transforming modern materials science, becoming an important tool for the discovery of new materials and material phenomena, for gaining insight into the processes that govern materials behavior, and, increasingly, for quantitative predictions that can be used as part of a design tool in full partnership with experimental synthesis and characterization. Modeling and simulation is the essential bridge from good science to good engineering, spanning from fundamental understanding of materials behavior to deliberate design of new materials technologies leveraging new properties and processes. This Roadmap presents a broad overview of the extensive impact computational modeling has had in materials science in the past few decades, and offers focused perspectives on where the path forward lies as this rapidly expanding field evolves to meet the challenges of the next few decades. The Roadmap offers perspectives on advances within disciplines as diverse as phase field methods to model mesoscale behavior and molecular dynamics methods to deduce the fundamental atomic-scale dynamical processes governing materials response, to the challenges involved in the interdisciplinary research that tackles complex materials problems where the governing phenomena span different scales of materials behavior requiring multiscale approaches. The shift from understanding fundamental materials behavior to development of quantitative approaches to explain and predict experimental observations requires advances in the methods and practice in simulations for reproducibility and reliability, and interacting with a computational ecosystem that integrates new theory development, innovative applications, and an increasingly integrated software and computational infrastructure that takes advantage of the increasingly powerful computational methods and computing hardware.

Using ab initio density-functional total energy and molecular-dynamics simulations, we study the effects of various forms of nitrogen postdeposition anneal (PDA) on the electric properties of hafnia in the context of its application as a gate dielectric in field-effect transistors. We consider the atomic structure and energetics of nitrogen-containing defects which can be formed during PDA in various N-based ambients: N2, N2+, N, NH3, NO, and N2O. We analyze the role of such defects in fixed charge accumulation, electron trapping, and in the growth of the interface SiO2 layer. We find that nitrogen anneal of the oxides leads to an effective immobilization of native defects such as oxygen vacancies and interstitial oxygen ions, which may inhibit the growth of a silica layer. However, nitrogen in any form is unlikely to significantly reduce the fixed charge in the dielectric.

Using classical and ab initio calculations we demonstrate that extra electrons can be trapped in pure crystalline and amorphous SiO${}_2$ (a-SiO${}_2$) in deep band gap states. The structure of trapped electron sites in pure a-SiO${}_2$ is similar to that of Ge electron centers and so-called [SiO${}_4$/Li]${}^0$ centers in $\alpha$ quartz. Classical potentials were used to generate amorphous silica models and density functional theory to characterize the geometrical and electronic structures of trapped electrons in crystalline and amorphous silica. The calculations demonstrate that an extra electron can be trapped at a Ge impurity in $\alpha$ quartz in six different configurations. An electron in the [SiO${}_4$/Li]${}^0$ center is trapped on a regular Si ion with the Li ion residing nearby. Extra electrons can trap spontaneously on pre-existing structural precursors in amorphous SiO${}_2$, while the electron self-trapping in $\alpha$ quartz requires overcoming a barrier of about 0.6 eV. The precursors for electron trapping in amorphous SiO${}_2$ comprise wide ($\ge$132${}^{\circ }$) O–Si–O angles and elongated Si–O bonds at the tails of corresponding distributions. Using this criterion, we estimate the concentration of these electron trapping sites at $\approx 4\times {10}^{19}$ cm${}^{-3}$.

We analyze the mechanisms of contrast formation in noncontact SFM imaging of ionic surfaces and calculate constant frequency shift scanlines of the perfect surfaces of NaCl, MgO, and LiF. The noncontact scanning force microscopy (SFM) operation is modeled by a perturbed oscillator using atomistic static and molecular-dynamics techniques for the force-field calculations. The electrostatic potentials of silicon tips contaminated by various atoms and that of a MgO tip are calculated using a periodic density-functional theory (DFT) method. Their analysis demonstrates that the presence of polar groups or chemisorbed species, such as oxygen atoms, makes the electrostatic forces acting on the surface ions from the Si tip one of the most important contributions to the image contrast. The $(\mathrm{MgO}{)}_{32}$ cube model of the nanotip was found to be representative of a wide class of polar tips and used in the image calculations. The results of these calculations demonstrate that the contrast in noncontact SFM imaging of ionic surfaces is based on an interplay of the electrostatic and van der Waals forces. The main contributions to the contrast formation result from the interaction of the tip with the alternating surface potential and with the surface polarization induced by the electric field of the tip. The results emphasize the importance of the tip-induced relaxation of the surface ions in the tip-surface interaction and in image contrast. The noncontact SFM image of the ${\mathrm{Mg}}^{2+}$-cation vacancy defect on the LiF surface is calculated using the same method.

Despite extensive experimental and theoretical studies, the atomistic mechanisms responsible for dielectric breakdown (BD) in amorphous (a)-SiO₂ are still poorly understood. A number of qualitative physical models and mathematical formulations have been proposed over the years to explain experimentally observable statistical trends. However, these models do not provide clear insight into the physical origins of the BD process. Here, we investigate the physical mechanisms responsible for dielectric breakdown in a-SiO₂ using a multi-scale approach where the energetic parameters derived from a microscopic mechanism are used to predict the macroscopic degradation parameters of BD, i.e., time-dependent dielectric breakdown (TDDB) statistics, and its voltage dependence. Using this modeling framework, we demonstrate that trapping of two electrons at intrinsic structural precursors in a-SiO₂ is responsible for a significant reduction of the activation energy for Si-O bond breaking. This results in a lower barrier for the formation of O vacancies and allows us to explain quantitatively the TDDB data reported in the literature for relatively thin (3–9 nm) a-SiO₂ oxide films.