Electrostatic potential fluctuation induced by charge discreteness in a nanoscale trench

Abstract

Plasma molding over deep trenches and the resulting ion and energetic neutral distributionsA simplified two-dimensional Monte Carlo simulation is performed to estimate the charging potential fluctuations caused by strong binary Coulomb interactions between discrete charged particles in nanometer scale trenches. It is found that the discrete charge effect can be an important part of the nanoscale trench research, inducing scattering of ion trajectories in a nanoscale trench by a fluctuating electric field. The effect can enhance the ion deposition on the side walls and disperse the material contact energy of the incident ions, among others.

Electrostatic and electromagnetic oscillations of nanoparticles in the presence of magnetic field

“…Liu et al [9] have studied the field emission of electrons from array of carbon nanotubes. Lee et al [10] have carried out simulations to estimate the charging potential fluctuations caused by strong binary Coulomb interactions between discrete charged particles in nanometer scale trenches. Iheludev and Emel'yanov [11] have studied phase matched second harmonic generation from nanostructure metallic surfaces.…”

Simulations of Ion Behaviors in a Photoresist Trench During Plasma Etching Driven by a Radio-Frequency Source

“…In the past few years, the notching effects during etching due to charging and the distortion of ion trajectories have been simulated by using Monte Carlo simulation [5∼8] and other methods [9] . LEE et al found that the width of the trench affected the shapes of the IEDs [10] . MADZIWA-NUSSINOV presented a clear result about the ion trajectories in the photoresist trenches [11,12] .…”

A hybrid modeling framework for simulating plasma-surface interactions of rough polymeric substrates

“…The need to remedy these artifacts has been the motive for several theoretical and computational studies on surface charging. The majority of them focus on dielectric, mainly Silicon dioxide Twisting Etching lag (SiO2) trenches or holes [130][131][132][133][134][135][136][137][138][139][140][141], some of them on Si trenches with a dielectric mask [142][143][144] and/or on SOI wafers [120,145,146].…”

“…Kenney and Hwang [137] investigated the stochastic behavior of charging by studying the oscillation of charging potential in high AR dielectric nanostructures. Lee et al [136] surmised that large electrostatic potential fluctuations due to stochastic charging could lead to profile irregularities as the trench size was reduced to nanometer scale. Zhang et al [158][159][160][161] presented a computational research regarding plasma induced surface charging on the top surface of mask holes.…”

“…The charging module in all previous works included a model for the calculation of the ion and electron trajectories based on the equations of Newton. Except from [136,[159][160][161] where the charging potential was calculated by analytic gathering of the Coulomb interaction fields from discrete surface charges on the microstructure surface, a model for the calculation of the charging potential based on the Laplace equation was used in all previous works. Additionally, all but one [140] of the previous works addressed 2-dimensional (2d) geometries.…”