Abstract
Plasma induces micro/nano roughness on the surface of the polymeric substrates, a factor that has major importance in the surface properties (e.g. wetting behavior, interaction of surfaces with cells). Toward the comprehension and, finally, the control of plasma induced surface roughness, in this dissertation, plasma-surface interactions of rough polymeric substrates are studied from a computational point of view. A hybrid modeling framework, coupling stochastic and deterministic modules, for profile evolution of unconventional, rough polymeric surfaces under plasma etching is developed. To model the temporal evolution of a surface over a short time interval, the framework mainly implements the following three steps: (1) it calculates the fluxes of ions, electrons, neutrals to each point of the surface, (2) it specifies the local etching rate for each surface point from the given fluxes, and (3) it utilizes the local etching rates to predict the surface profile after a short time. Alth ...
Plasma induces micro/nano roughness on the surface of the polymeric substrates, a factor that has major importance in the surface properties (e.g. wetting behavior, interaction of surfaces with cells). Toward the comprehension and, finally, the control of plasma induced surface roughness, in this dissertation, plasma-surface interactions of rough polymeric substrates are studied from a computational point of view. A hybrid modeling framework, coupling stochastic and deterministic modules, for profile evolution of unconventional, rough polymeric surfaces under plasma etching is developed. To model the temporal evolution of a surface over a short time interval, the framework mainly implements the following three steps: (1) it calculates the fluxes of ions, electrons, neutrals to each point of the surface, (2) it specifies the local etching rate for each surface point from the given fluxes, and (3) it utilizes the local etching rates to predict the surface profile after a short time. Although the components of the framework may differ depending on the case study, the cornerstone of the framework is a surface etching model that combines the local flux, energy, and the angle of incidence of the plasma species with the local etching yield and rate. The local etching rate calculated by the surface etching model is then fed to a profile evolution module which computes the successive positions of the profile. The components of the framework are discussed through its application to two different case-studies, namely Argon (Ar) and Oxygen (O2) plasma etching of poly(methyl methacrylate) (PMMA) substrates with an initially sinusoidal profile resembling a rough profile, involving different etching mechanisms. Specifically, Ar plasmas cannot chemically react with the polymer and the interaction is restricted to ion bombardment effects, i.e. energetic ions drive atoms off the surface of a solid material (i.e. physical sputtering). In this case study, the framework consists of: (1) A charging module consisting of models for the calculation of (a) ion and electron trajectories (Newton equations), (b) the surface charge density, and (c) the charging potential (Laplace equation). (2) A model for ion reflection. (3) An original model for the secondary electron-electron emission (SEEE) mechanism, developed for PMMA substrates in the energy range which is of interest in plasma etching. (4) A surface etching model able to calculate the angle and energy dependence of the etching (sputtering) yield of PMMA by Ar ions (Ar+), devised by combining experimental measurements and numerical calculations. (5) A profile evolution module, which is based on a continuum description of the profile and the level set method; the latter module has been used for conventional (microelectronic) structures in previous works not only for plasma etching but also for wet etching and chemical vapor deposition. In this dissertation, it is modified in order to handle also the evolution of unconventional (rough) profiles.The main focus, filling the relevant gap in the literature, is to record how charging is developed on the rough profile being etched and how it affects the evolving roughness of the profile, in the presence of ion reflection and SEEE. This is the first time in the literature that this interplay is examined. Even if plasma induced surface charging on conventional – with respect to the semiconductor industry – structures, i.e., trenches or holes, has been studied in previous works and its artifacts, such as notching, microtrenching, etching lag, and twisting have been examined both experimentally, theoretically, and computationally, there is a lack of studies on surface charging of rough polymeric surfaces. It is revealed, on the one hand, that the surface charging contributes to the suppression of roughness and, on the other hand, that the decrease of the surface roughness induces a decrease of the charging potential. When ion reflection is taken into account, the results show that the surface charging contributes to a faster decrease of the roughness compared to the case without charging. Ion reflection sustains roughness; without ion reflection, roughness is eliminated. Either with or without ion reflection, the effect of SEEE on the evolution of the rms roughness over etching time is marginal. The mutual interaction of the roughness and the charging potential is revealed through the correlation of the charging potential with a parameter suitably combining statistical properties of the profile such as rms roughness and skewness. The charging potential shows an almost monotonic behavior with this parameter, something that reveals the mutual interaction between surface charging and profile roughness.The second model system is plasma etching of PMMA with O2 chemistry. In O2 plasmas, except from mechanical ion induced effects (i.e. sputtering), there are also chemical ion induced effects as ions promote chemical reactions between the O2 reactive species and the polymeric substrate (i.e. ion enhanced etching). Oxygen atoms (O) are combined with oxygen ions (O+) to alter both morphology and composition of polymeric surfaces. Through the implementation of a novel kMC surface etching model, the framework can address both effects of O2 plasma on the PMMA surface. Thus, the framework for O2 plasmas consists of: (1) A kinetic Monte Carlo (kMC) surface etching model, considering the nonlinear synergy of O and O+ for the calculation of the local etching rate in the case of O2 plasma etching, taking into account the surface morphology through the calculation of the trajectories of the species joining the surface reactions. It extends the potential of previous kMC surface models in the literature which assume that the surface is flat. (2) A profile evolution module described above, modified to treat a fundamental weakness of the level set method, and generally of all methods using an implicit representation of the surface profile, namely the tracking of local profile properties during evolution. The first aim is the evaluation of the accuracy of the kMC model through a comparison to the analytical equations describing the ion-enhanced kinetics as well as the proper adjustment of critical parameters of the kMC model in order to cope with computational and accuracy issues. Then, we track how the operating conditions of the reactor, such as the output power (or equivalently the ratio of O flux over the O+ flux at the flat region), the DC bias voltage (or equivalently the ion energy) and the etching time, as well as the model parameters, such as the re-emission of O and the reflection of O+ on the surface, intertwine with the evolution of morphology and, ultimately, how their interwoven effects determine the evolution of roughness. The framework is also able to replicate experimental roughness evolution trends found in the literature in high density plasma reactors under the effect of different operating conditions. For instance, given the output power is large, the roughness is subjected to changes in the growth mode with the etching time and/or it increases with the increase of bias. Given the bias is constant, the roughness increases with the output power. Ultimately, the potential of the modeling framework to address changes of the surface wettability during plasma etching is demonstrated. The framework can simulate changes of surface morphology (roughness) and O surface coverage (linked to O functional groups), the combination of which determines the wetting state of the surface.
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