Surfaces sputtered by ion beam bombardment have been known to exhibit patterns whose behavior is modeled with stochastic partial differential equations. A widely accepted model is the Cuerno-Barabasi model which is robust in its predictions of sputtered surface morphologies. An understanding of the factors responsible for such surface topographies can be achieved by using scaling arguments on the stochastic model. For such explanations, knowledge of the coefficients is crucial. The more so since these vary with different materials, the sputtering process itself generates non-equilibrium surfaces within some finite timescale, and the implication of recent results of surface topographies unexplained by the continuum theory. We calculate and study these coefficients as functions of the sputtering parameters for yet unreported cases of anisotropic ion energy distribution within the sputtered material. Consequently, we present phase diagrams for the significant case of anisotropic ion straggle. We observe shifts in the phase boundaries when the collision cascade geometry rotates, and we also found saturation behavior in the diagrams; in which case the boundaries become independent of the penetration depths. Our results indicate a possible origin of yet unexplained nanodot topographies arising from oblique incidence ion etching of amorphized surfaces.
The doping exercise has been known to affect the electronic properties of semiconductor materials. However, little is known about the mystery behind what is exactly responsible for this doping effect. In this paper, we report our theoretical findings about a form of gravitation within the lattice and how it can be said to be induced or even responsible for the doping effect. We have observed that the lattice is being grouped into bands of energies by this form of gravitation. We have identified two major types: a-core and a-core-less. It is this form of gravitation that is actually responsible for the selection (or rejection) of atoms into (or from) a band. Hence, we have found out that there seems to be a competition between the electronic effect and this form of gravitation whenever doping occurs. The dopant atom being an impurity atom will contribute to depopulating or populating the band it is located.
Different atoms achieve ionizations at different energies. Therefore, atoms are characterized by different responses to photon absorption in this study. That means there exists a coefficient for their potential for photon absorption from a photon source. In this study, we consider the manner in which molecular constituents (atoms) absorb photon from a photon source. We observe that there seems to be a common pattern of variation in the absorption of photon among the electrons in all atoms on the periodic table. We assume that the electrons closest to the nucleus (En) and the electrons closest to the outside of the atom (Eo) do not have as much potential for photon absorption as the electrons at the middle of the atom (Em). The explanation we give to this effect is that the En electrons are embedded within the nuclear influence, and similarly, Eo electrons are embedded within the influence of energies outside the atom that there exists a low potential for photon absorption for them. Unlike En and Eo, Em electrons are conditioned, such that there is a quest for balance between being influenced either by the nuclear force or forces external to the atom. Therefore, there exists a higher potential for photon absorption for Em electrons than for En and Eo electrons. The results of our derivations and analysis always produce a bell-shaped curve, instead of an increasing curve as in the ionization energies, for all elements in the periodic table. We obtained a huge data of PAPC for each of the several materials considered. The point at which two or more PAPC values cross one another is termed to be a region of conflicting order of ionization, where all the atoms absorb equal portion of the photon source at the same time. At this point, a greater fraction of the photon source is pumped into the material which could lead to an explosive response from the material. In fact, an unimaginable and unreported phenomenon (in physics) could occur, when two or more PAPCs cross, and the material is able to absorb more than that the photon source could provide, at this point. These resulting effects might be of immense materials engineering applications.
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