Clearing the Dust with VizGrain

Mar 25, 2022

In the fight against airborne particulates, semiconductor manufacturers face the unrelenting threat of contamination within their labs and facilities. Airflow, microfiltration, air ionization, air pressure, humidity controls, polymer toolsets, anterooms / air showers, and cleanroom suits are just a few of the considerations that manufacturers must make, all in the name of isolating lab processes from the outside world. Despite extensive procedures and costly investments, it is nearly impossible to produce an environment completely devoid of pollutants, and the most common of all pollutants is microscopic, fine particles of solid matter known simply as “dust.”

Unlike the dusty plasmas found in the Earth’s mesosphere and among celestial bodies that fascinate astrophysicists, dusty plasmas in labs here on Earth are a constant source of frustration within the semiconductor industry. Their presence within reactors and manufacturing equipment continues to threaten contamination of wafers and other critical components.

Perhaps someday in the future, the presence of dusty plasmas in semiconductor manufacturing facilities will cease to be, either by way of technological innovation or perfection of cleanroom procedure. But until that time, simulations must account for every piece of relevant physics in order to create a realistic model of these environments.

Making the Dust Fly for Semiconductor Manufacturers

 Dust particles are common contaminants of plasma processing discharge chambers used in the semiconductor industry for etching and deposition. These particles can range from several nanometers to several hundred micrometers in size, accrue a relatively large negative charge in the plasma, and consequently are electrostatically trapped in the plasma. Large particles usually accumulate near the sheath edge, while small particles accumulate in the center of the discharge chamber where the electrostatic potential is usually the most positive.

Trajectories of particles (a) with Wafer Bias and (b) without Wafer Bias. Size of particles ranges from 0.15 microns to 0.5 microns. Image Source: Kobayashi et al.

For semiconductor manufacturers, formation of particles within a plasma and the effect of dust particles on a semiconductor’s processing surface are determining factors for overall process quality and yield. Developing macro-particle kinetic models that account for all associated physics (macro-particle growth, charge-up, and transport within a plasma) is a necessity in modern semiconductor processing reactor design.

 As a result, the applications for studies surrounding dusty plasmas focus primarily on particle transport and plasma distribution. This is the case in plasma etching / deposition systems, where particle behavior can be expressed through calculation of measured gas temperature distribution and thermophoretic force. Thermophoretic force can then be controlled using plasma distribution controls, and by changing gas temperature distributions across wafers.

It was only until recently that these breakthroughs in particle control and plasma distribution relied on expensive and elaborate experiments. Now, particle-based simulations through software like VizGrain are able to predict these behaviors while including the core features necessary for creating a computational model:

  1. A multi-subdomain capability, where multiple solids and gas regions can be described simultaneously.
  2. Unstructured meshing for representing complex topologies with fine geometric features.
  3. Modeling of static electric and magnetic fields as well as electromagnetic waves through coupling with an electromagnetics solver.
  4. Treating subsets of the overall gas composition as a continuum through coupling with a classical fluid flow solver and a plasma solver.

VizGrain: A Versatile Computational Tool for Particle Simulations

 A unique aspect of VizGrain is that it allows computational modeling of particle dynamics in a variety of systems, including:

 

  • rarefied gas dynamics
  • gas discharge plasmas
  • macroscopic particle dynamics (e.g., dust particles, droplets, etc.)

VizGrain allows working with atomic-size particles as well as particles with finite macroscopic sizes. The former approach is used to model rarefied gas dynamics and conventional non-equilibrium plasmas, while finite-size macro-particles are considered for models of dusty plasmas, aerosols, and droplets to name a few. In this latter case, there is also consideration for electrical charge-up of particles in a plasma environment. Additionally, these models feature a comprehensive variety of drag forces that can act on both atomic and macro-particles.

 VizGrain solves governing equations that describe the transport (motion and collisions) as well as the generation and destruction of particles in a specified domain. A number of different particle types, both “atomic” and “macro-scale,” can be solved.

Dusty plasma dynamics in a capacitively coupled plasma (CCP) reactor generated using VizGlow™ (fluid) and VizGrain (dust particles).

Electrically neutral species and radicals, as well as electrically charged species like electrons and positive and negative ions are atomic particle types that can be considered simultaneously. Macro-scale particle types, however, include molecular cluster and larger micron-to-millimeter scale dust particles.
All such particles have mass, charge, and size attributes. The mass of atomic particles is immutable, while those of macro-scale particles can change based on governing laws. Similarly, the atomic particle charge is fixed while macro-scale particle charge can change based on charge-up processes.

 

In VizGrain, all the particles in a swarm are classified according to “particle type.”  All particles of a particular type have individual properties such as mass, charge, and size (diameter or cross section). Extensive use of object-oriented programming principles means that implementation is modular, and extending the list of properties is possible whenever necessary.

 

VizGrain also offers flexibility in representing practical applications through complex geometries. Cells can be made from a mesh using triangles and quadrilaterals (for 2D), as well as tetrahedra, hexahedra, prisms, pyramids, or even a mixture of all the aforementioned cell types together.

 

Additionally, meshes can be prepared in a variety of formats that are used commonly by practitioners and imported into VizGrain. The code also outputs the maximum number of particles that exist in a cell over the whole mesh at selected screen output intervals, with warnings for severely skewed cells in the mesh that could portend poor quality solutions (especially in the case of electrostatic potential in PIC simulations). Note that the accuracy of pure particle simulation results are usually insensitive to the quality of the mesh, which has been confirmed in VizGrain simulations.

 

 

Thanks for reading! If you’re still curious about the topics discussed in this article, check out the following journal papers (and ask us for a free copy!):

Levko, Dmitry, et al. “VizGrain: a new computational tool for particle simulations of reactive plasma discharges and rarefied flow physics.” Plasma Sources Science and Technology 30.5 (2021): 055012.

Kobayashi, Hiroyuki, et al. “Investigation of particle reduction and its transport mechanism in UHF-ECR dielectric etching system.” Thin Solid Films 516.11 (2008): 3469-3473.

Merlino, Robert. “Dusty plasmas: from Saturn’s rings to semiconductor processing devices.” Advances in Physics: X 6.1 (2021): 1873859.

Merlino, Robert L., and John A. Goree. “Dusty plasmas in the laboratory, industry, and space.” PHYSICS TODAY. 57.7 (2004): 32-39.

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