The Mathematics of Plasma Etching and Deposition: Kinetic Theory, Nonlinear PDEs, and Control for Semiconductor Manufacturing in Python (Computational Mathematics Library)

A rigorous, research-grade treatment that unifies kinetic theory, multiscale PDEs, electromagnetics, inverse problems, and control for modern plasma etching and deposition. Written for advanced graduate students, postdocs, and faculty in applied mathematics, physics, and engineering, it develops models from first principles, key analytical results, and translates them into robust numerical algorithms that connect reactor conditions to feature-scale morphology.You will find a coherent arc from the Boltzmann equation and drift-diffusion-Poisson closures to sheath matching, ion energy and angular distributions, nonlocal electron kinetics, and RF Maxwell coupling. Geometry-driven surface evolution is treated via eikonal and mean-curvature flows with level-set numerics, while metrology and diagnostics are addressed through inverse scattering and Bayesian reconstruction. Control and optimization are presented with adjoints, uncertainty quantification, and large-deviation methods for rare events, complemented by high-order electromagnetic solvers, stiff integrators, and reduced-order modeling.Every chapter ends with a compact Python demonstration that reproduces a central derivation or algorithm using the scientific Python stack. Who it is forGraduate courses and reading groups in plasma physics, applied math, computational science, electrical engineering, materials science, and chemical engineeringResearchers seeking rigorous links between reactor-scale conditions, feature-scale morphology, and metrology-informed controlMethod developers interested in high-order numerics, adjoints, UQ, and data assimilation with reproducible Python examples Read more