Abstract: Two-dimensional (2D) ultra-thin materials are more crucial than their bulk counterparts for the covalent functionalization of their surface owing to atomic thinness, large surface-to-volume ratio, and high reactivity of surface atoms having unoccupied orbitals. Since the surface of a 2D material is composed of atoms having unoccupied orbitals, covalent functionalization enables one to improve or precisely modify the properties of the ultra-thin materials. Chemical functionalization of 2D materials not only modifies their intrinsic properties but also makes them adapted for nanotechnology applications. Such engineered materials have been used in many different applications with their improved properties. In the present Perspective, we begin with a brief history of functionalization followed by the introduction of functionalized 2D materials. Our Perspective is composed of the following sections: the applications areas of 2D graphene and graphene oxide crystals, transition metal dichalcogenides, and in-plane anisotropic black phosphorus, all of which have been widely used in different nanotechnology applications. Finally, our Perspectives on the future directions of applications of functionalized 2D materials are given. The present Perspective sheds light on the current progress in nanotechnological applications of engineered 2D materials through surface functionalization.

Abstract: We modeled the electron and hole states in Si/SiO2 quantum wells within a basis of standing waves using the 30-band k . p theory. The hard-wall confinement potential is assumed, and the influence of the peculiar band structure of bulk silicon on the quantum-well sub-bands is explored. Numerous spurious solutions in the conduction-band and valence-band energy spectra are found and are identified to be of two types: (1) spurious states which have large contributions of the bulk solutions with large wave vectors (the high-k spurious solutions) and (2) states which originate mainly from the spurious valley outside the Brillouin zone (the extravalley spurious solutions). An algorithm to remove all those nonphysical solutions from the electron and hole energy spectra is proposed. Furthermore, slow and oscillatory convergence of the hole energy levels with the number of basis functions is found and is explained by the peculiar band mixing and the confinement in the considered quantum well. We discovered that assuming the hard-wall potential leads to numerical instability of the hole states computation. Nonetheless, allowing the envelope functions to exponentially decay in a barrier of finite height is found to improve the accuracy of the computed hole states.