Numerical solution of a three-dimensional cubic cavity flow by using the Boltzmann equation

A three-dimensional cubic cavity flow has been analyzed for diatomic gases by using the Boltzmann equation with the Bhatnagar-Gross-Krook (B-G-K) model. The method of discrete ordinate was applied, and the diffuse reflection boundary condition was assumed. The results, which show a consistent trend toward the Navier-Stokes solution as the Knudson number is reduced, give us confidence to apply the method to a three-dimensional geometry for practical predictions of rarefied-flow characteristics. The CPU time and the main memory required for a three-dimensional geometry using this method seem reasonable

A numerical analysis applied to high angle of attack three-dimensional inlets

The three-dimensional analytical methods used to analyze subsonic high angle of attack inlets are described. The methods are shown to be in good agreement with experimental results for various three-dimensional high angle of attack inlets. The methods are used to predict aerodynamic characteristics of scarf and slotted-lip inlets

A summary of V/STOL inlet analysis methods

Recent extensions and applications of the methods are emphasized. They include the specification of the Kutta condition for a slotted inlet, the calculation of suction and tangential blowing for boundary layer control, and the analysis of auxiliary inlet geometries at angles of attack. A comparison is made with experiment for the slotted inlet. An optimum diffuser velocity distribution was developed

Pattern-Dependent Charging in Plasmas: Electron Temperature Effects

The differential charging of high-aspect-ratio dense structures during plasma etching is studied by two-dimensional Monte Carlo simulations. Enhanced electron shadowing at large electron temperatures is found to reduce the electron current density to the bottom of narrow trenches, causing buildup of large charging potentials on dielectric surfaces. These potentials alter the local ion dynamics, increase the flux of deflected ions towards the sidewalls, and result in distorted profiles. The simulation results capture reported experimental trends and reveal the physics of charging damage

The influence of mask thickness on charging damage during overetching

Feature-scale charging simulations during gate electrode overetching in high-density plasmas reveal that the thickness of the insulating mask plays a critical role in charging damage. When thinner masks are used, the electron irradiance of the conductive part of the sidewalls increases, causing the charging potentials of the polysilicon lines to decrease, thus reducing the probability for catastrophic tunneling currents through the underlying oxide. Simultaneously, changes in the charging potential distribution at the bottom SiO2 surface cause a significant perturbation in the local ion dynamics which, in turn, adversely affects notching. Notches are predicted to form everywhere in a line-and-space structure, even when the lines are electrically isolated. The results suggest that the trend toward thinner (hard) masks—to keep the aspect ratio low as device dimensions shrink—should reduce oxide failure but at the cost of more severe notching

The Role of the Substrate on Pattern-Dependent Charging

Monte Carlo simulations of charging and profile evolution during plasma etching reveal that the substrate can mediate current imbalance across the wafer. This function couples patterned areas, where the electron shading effect dominates, to substrate areas directly exposed to the plasma. When a net positive current flows through the pattern features to the substrate, increasing the exposed area decreases the substrate potential, thereby causing notching at the connected feature sidewalls to worsen, in agreement with experimental observations

Aspect-ratio-dependent charging in high-density plasmas

The effect of aspect ratio (depth/width) on charge buildup in trenches during plasma etching of polysilicon-on-insulator structures is studied by Monte Carlo simulations. Increased electron shadowing at larger aspect ratios reduces the electron current to the trench bottom. To reach a new charging steady state, the bottom potential must increase, significantly perturbing the local ion dynamics in the trench: the deflected ions bombard the sidewall with larger energies resulting in severe notching. The results capture reported experimental trends and reveal why the increase in aspect ratio that follows the reduction in critical device dimensions will cause more problems unless the geometry is scaled to maintain a constant aspect ratio

The influence of surface currents on pattern-dependent charging and notching

Surface charge dissipation on insulator surfaces can reduce local charging potentials thereby preventing ion trajectory deflection at the bottom of trenches that leads to lateral sidewall etching (notching). We perform detailed Monte Carlo simulations of pattern-dependent charging during etching in high-density plasmas with the maximum sustainable surface electric field as a parameter. Significant notching occurs for a threshold electric field as low as 0.5 MV/cm or 50 V/µm, which is reasonable for the surface of good insulators. The results support pattern-dependent charging as the leading cause of notching and suggest that the problem will disappear as trench widths are reduced