Charging effect simulation model used in simulations of plasma etching of silicon

Abstract

Understanding the consequences of local surface charging on the evolving etching profile is a critical challenge in high density plasma etching. Deflection of the positively charged ions in locally varying electric fields can cause profile defects such as notching, bowing, and microtrenching. We have developed a numerical simulation model capturing the influence of the charging effect over the entire course of the etching process. The model is fully integrated into ViPER (Virtual Plasma Etch Reactor)—a full featured plasma processing simulation software developed at Ilmenau University of Technology. As a consequence, we show that local surface charge concurrently evolves with the feature profile to affect the final shape of the etched feature. Using gas chopping (sometimes called time-multiplexed) etch process for experimental validation of the simulation, we show that the model provides excellent fits to the experimental data and both, bowing and notching effects are captured—as long as the evolving profile and surface charge are simultaneously simulated. In addition, this new model explains that surface scallops, characteristic of gas chopping technique, are eroded and often absent in the final feature profile due to surface charging. The model is general and can be applied across many etching chemistries.

Modeling of Charging on Unconventional Surface Morphologies of PMMA Substrates During Ar Plasma Etching

“…However, the surface has the same shape along the z axis, thus the charging should not vary along that direction. [39,40,48] In such a case, the line and surface charge densities are equivalent.…”

“…[22,39] More precisely, the trajectories of the particles, which abandon the simulation domain and traverse Figure 2. The simulation domain.…”

“…The profile of the surface is constant along the z axis (see Figure 2), thus the surface charging should not vary along that direction. [39,40,48] The latter allows for calculations in 2d for both the particle trajectory and the electric potential. A real rough surface is a 3d surface which is not constant along z axis.…”

“…n is the unit normal vector pointing outside of the simulation domain. Furthermore, the application of the Gauss law between the two media leads to the surface charge density condition [39] imposed on the surface profile, that is,…”

“…[25,27] However, in reality, the surface is floating with a radio frequency bias which is taken into account to the ion energy distribution function (IEDF); the IEDF depends on the sheath potential. [27] In order to mirror the simulation domain, [22,39] the following condition is imposed on both left (x ¼ a) and right (x ¼ b) boundary,…”