Graphs are data structures that effectively represent relational data in the real world. Graph representation learning is a significant task since it could facilitate various downstream tasks, such as node classification, link prediction, etc. Graph representation learning aims to map graph entities to low-dimensional vectors while preserving graph structure and entity relationships. Over the decades, many models have been proposed for graph representation learning. This paper aims to show a comprehensive picture of graph representation learning models, including traditional and state-of-the-art models on various graphs in different geometric spaces. First, we begin with five types of graph embedding models: graph kernels, matrix factorization models, shallow models, deep-learning models, and non-Euclidean models. In addition, we also discuss graph transformer models and Gaussian embedding models. Second, we present practical applications of graph embedding models, from constructing graphs for specific domains to applying models to solve tasks. Finally, we discuss challenges for existing models and future research directions in detail. As a result, this paper provides a structured overview of the diversity of graph embedding models.

We present a drain current model and a consistent parameter extraction method for organic field-effect transistors (OFETs) considering the gate voltage-dependent contact resistance and mobility by power-law. The physical origin of the asymptotic power-law dependence of contact resistance is elaborated based on the current crowding model. The parameters of a new model can be completely extracted without ambiguity by the proposed extraction method based on the linear fitting. Pentacene-based OFETs with the Au source/drain contact in a staggered configuration experimentally validate the proposed model and the extraction method, which further reveal the bulk resistivity as the major contribution to contact resistance.

We physically model the injection characteristics at the metal/organic semiconductor (M/O) junctions with a Gaussian density-of-states (GDOS). By both analytical and numerical modelling, the charge carrier concentrations at the M/O junctions in an organic rectifying diode (ORD) are calculated. The results demonstrate a special attention required in the application of the Schottky–Mott rule, which defines the injection barrier (IB) for ideal metal/semiconductor junctions, to M/O junctions. By systematically changing the width of the GDOS that describes the energetic disorder in the organic semiconductor, we show that the edge of the highest-occupied molecular orbitals (HOMO) should be defined as higher rather than from the maximum of the HOMO to keep the consistency of the Schottky–Mott rule. A simple analytical expression for the IB is presented which contains the effect of the disorder in facilitating the charge carrier injection. Simulated current density-voltage characteristics of the ORDs are also presented to support the arguments.

In this review, recent advances in compact modeling of organic field-effect transistors (OFETs) are presented. Despite the inherent strength for printed flexible electronics and the extremely aggressive research conducted over more than three decades, the OFET technology still seems to remain at a relatively low technological readiness level. Among various possible reasons for that, the lack of a standard compact model, which effectively bridges the device-and system-level development, is clearly one of the most critical issues. This paper broadly discusses the essential requirements, up-to-date progresses, and imminent challenges for the OFET compact device modeling toward a universal, physically valid, and applicable description of this fast-developing technology.

Correct parameterization of the Gaussian disorder model (GDM) on spatially random sites is necessary for a complete description of charge transport in disordered materials and concomitant device characteristics. Because the GDM on spatially random sites considers both energetic and spatial disorder, it is superior to the GDM on a cubic lattice. However, analytical arguments and experimental evidence are still lacking for correct parameterization of the model over a wide range of model parameters, energetic and spatial disorder, and electric fields. We show that the model requires a set of parameters to correctly account for high mobility and its charge density dependence, and we develop such a model. The model is implemented in a numerical simulation tool for comparison with the measured device characteristics. Accurate agreement with experimental data, particularly with the high mobility values in organic field-effect transistors, is achieved throughout a wide range of temperature by adjusting both the localization length and the attempt-to-escape frequency.

A nanoarchitectonics approach to high-performance organic multi-valued logic circuits is proposed.