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:
A multi-subdomain capability, where multiple solids and gas regions can be described simultaneously.
Unstructured meshing for representing complex topologies with fine geometric features.
Modeling of static electric and magnetic fields as well as electromagnetic waves through coupling with an electromagnetics solver.
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:
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.
Interested in learning more about plasma flow simulations? Click here to take a look at our previous article. Feel free to follow us on Twitter and LinkedIn for more related news, or reach out to us directly at info@esgeetech.com.
Recently, consumers have faced rising prices for semiconductor-powered devices, with shortages affecting the availability of products that serve their daily needs. With increased demand for semiconductors in key areas like the automotive industry, healthcare, and within AI-enabled products, manufacturers are vying to remain competitive while making next-generation breakthroughs in order to meet current demand.
So, the question is: how can industrial researchers continue to innovate in order to boost semiconductor production? And how can simulations relieve the pressure for the semiconductor industry to meet ever-growing global demands?
A joint report authored by Boston Consulting Group (BCG) and The Semiconductor Industry Association (SIA) is aimed at combating semiconductor shortages by profiling risks in the current international supply chain and highlighting semiconductors as a central component of shared economic stability across the globe. Central to the report’s findings are a series of statistics that characterize the current issues the world faces in securing a future where semiconductor demands are met as they continue to grow over the next decade.
The Global Semiconductor Supply Chain at a Glance
The current cooperative structure of the global supply chain for semiconductors is as unique as it is complex, with a web of destinations across the globe from the earliest stages of research and design to the final point of sale. Since the 1970s, specialization within these national and regional stages has contributed to the chain’s ability to produce at the speed of demand, while also innovating and improving the capabilities of semiconductors faster than any one country or region could.
Figure 1 below shows the current global semiconductor market share by region as of 2020. South Korea and the United States account for two-thirds of total market production and sales.
In addition to utilizing the specializations offered by each of the six major regions (Europe, Japan, Mainland China, South Korea, Taiwan, and the United States) that contribute to the global supply chain, the roundabout system also makes use of favorable trade conditions among the participating countries to keep production costs and consumer prices affordable. Figure 2 below shows the usage of semiconductors by industry.
Major risks in disruptions to the current supply chain could lead to a sharp rise in the cost of devices to producers and consumers alike. In a hypothetical situation where the global chain is replaced with self-sufficient regions, the report forecasts up to $900 – 1,225B of upfront investment required to maintain current output and meet rising demands, with an overall cost increase of 35% – 65% for consumers if regional and comparative advantages are ignored.
National policies within key regions, most notably Mainland China – which has massive industrial and manufacturing capabilities – have already placed self-sufficiency as a high priority for their future development in semiconductors.
Similar policies in other nations could leave local markets open to unforeseen factors, including greater competition for materials and additional costs in their securing and transportation. Situations like natural disasters and geopolitical conflict could destabilize systems that seek to decouple from the international chain, leading to regional shortages of semiconductors and additional issues with production for critical communications and security sectors.
Researching and Developing Solutions for the Market
In addition to the current issues that the international supply chain faces, SIA’s report highlights the importance of research and development, which is the primary way that producers maintain state-of-the-art techniques and provide security in their devices.
Although the speed of innovation and change in major market devices like consumer electronics is visible from year-to-year, the time for techniques developed at pre-competition research stages to be utilized at a mass scale and included within the global chain can take decades. As a result, original equipment manufacturers (OEMs) and integrated device manufacturers (IDMs) face upfront costs in both R&D and capital expenditure, with years before seeing a return on investment in these areas.
Despite the delayed turnaround for companies investing and participating in pre-competitive and basic research, cooperation at these early stages enables chips to become smaller while increasing performance. Recent innovations like 5G, internet of things (IoT), and autonomous vehicles all began their journey to widespread use at this stage. Figure 3 below illustrates regional spending in R&D among key regions as a percentage of sales.
SIA’s report also cites the need for utilization of emergent technologies in alleviating risks and constraints in the global chain, with modern inventions like augmented and virtual reality (AR/VR) playing a crucial role in enabling operations to continue remotely throughout the pandemic.
Simulation also provides this principle effect of bridging digital and physical worlds by allowing manufacturers to cut material costs and risk of exposure to hazardous materials, all without sacrificing insights that physical experiments and trials offer.
The use of simulation software and digitally based tools to further minimize risks that current global producers face is both economic and modern, and its viability as an industry-wide solution will only become greater as time continues. Simulations offer additional innovation points through applications for commonly used equipment in the semiconductor industry, such as plasma reactors, with details like simulated angular distribution functions deciding process parameters like excitation frequency and excitation voltage.
Industry leaders like Dr. Peter Ventzek and Dr. Alok Ranjan of Tokyo Electron Ltd. – a global supplier of equipment used to fabricate integrated circuits- have already taken advantage of high-fidelity plasma simulation and processing to develop new techniques with a wide array of applications for the semiconductor industry, using the insights offered by numerical simulations using VizGlow™. Here are a few examples of patented methods and techniques using simulations that are contributing to the semiconductors of today and tomorrow:
· Mode-switching plasma systems and methods that allow manufacturers to reduce minimum-required features and the cost of ICs, while also increasing packing density of components. Manufacturers working at the atomic scale are able to continue scaling semiconductor devices with consideration for constraints like equipment configurability, equipment cost, and wafer throughput.
· Techniques that include formation, patterning, and removal of materials in order to achieve physical and electrical specifications for the current and next generation of semiconductor. Plasma etching and deposition are prone to issues with decoupling source power (SP) and bias power (BP) effects, resulting in reduced control and precision. Decoupling these effects helps reduce cross-talk between a source and bias and in turn enhances control while decreasing complexity.
· Utilizing pulsed electron beams to create new plasma processing methods, which enable reduction of feature size while maintaining structural integrity. As device structures continue to densify and develop vertically, these methods which produce atomic-level precision in plasma processes will be useful for profile control, particularly in controlling deposition and etching processes at timescales associated with growth of a single monolayer of film.
Processes in plasma-assisted etching or deposition rely on the accurate determination of the distribution of the ion energy and angle close to the substrate surface. Precise control over these parameters could be used to manipulate the bombardment of the process surface. However, from a process engineer’s perspective, the incremental changes in geometric design, voltage, power, feed gas composition, and flow rates must be correlated with IEADF (Ion Energy and Angular Distribution functions).
The engineering team at Tokyo Electron Ltd. uses our non-equilibrium plasma solver, VizGlow™, and particle solver, VizGrain™, to understand underlying physics and find the best operating conditions for Tokyo Electron Ltd. products. In a paper published in the Journal of Physics D: Applied Physics, Dr. Rochan Upadhyay, and Dr. Kenta Suzuki, Esgee Technologies along with researchers at The University of Texas at Austin validated the VizGlow™ simulations used to obtain IEADF in a capacitively coupled plasma reactor.
Esgee Technologies uses software products, databases, and consulting projects to solve challenges faced by industrial manufacturers. We are dedicated to the development of plasma and physics simulations for manufacturing applications across a wide range of manufacturing industries, including semiconductors, with a legacy of support for analyzing existing equipment, improving processes, and developing new equipment concepts through the use of our software.
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!):
Upadhyay R., K. Suzuki, L. L. Raja, P.L.G. Ventzek, and A. Ranjan. (2020). Experimentally Validated Computations of Simultaneous Ion and Fast Neutral Energy and Angular Distributions in a Capacitively Coupled Plasma Reactor. Journal of Physics D: Applied Physics. 53. 10.1088/1361-6463/aba068.
Interested in learning more about plasma flow simulations? Click here to take a look at our previous article. Feel free to follow us on Twitter and LinkedIn for more related news, or reach out to us directly at info@esgeetech.com.
Accurate predictions of the Ion Energy and Angular Distributions (IEADFs), are essential for a range of critical applications in thin films deposition and etching. Ion generation and flux is determined by ionization rates that depend on reactor-level parameters. Ion energy and angle depends on the acceleration of the ions across the sheath, driven by potential differences governed by the spatial plasma distribution. The IEADF at the wafer surface sensitively depends on rare collisional events such as charge exchange and ion-neutral collisions during the ion’s transit across the sheath. Using ion transport parameters computed using standard fluid modeling techniques can significantly misrepresent the actual IEADFs at surfaces. In this study we use a hybrid approach where we employ VizGlow, a fluid based plasma solver, to simulate a (pulsed) Inductively Coupled Plasma (ICP) source with a (pulsed) RF bias. Then we use VizGrain, a companion particle solver, to compute the IEADFs using the test-particle approach. We study the effect of pressure, pulse width and duty cycle and the staggering of the source and bias pulsing cycles on the IEADFs using Argon plama. We compare the simulation results to measurements of IEADFs on a test plasma platform for validation purposes.
Join Esgee Tech’s Rochan Upadhyay for his talk on “Computational Modeling and Simulation of a Resonant Plasma Source.” He’ll demonstrate how electrical resonance can be exploited to extend low temperature, unmagnetized plasma sources beyond their typical operating limits.
Esgee also supported the work being presented by Tokyo Electron America’s Peter Ventzek. He will present “Parametric Modeling and Measurements of Pulsed Source and Bias Plasmas.” This talk explores the effects of pulsed and biased plasma sources on ion energy and angular distribution functions (IEDFs) for atomic layer etching applications.
Be sure to stop by the talks and contact us at info@esgeetech.com to learn more.
Figure: Plasma electron number density evolution in helical resonator
Ion beam neutralization is a significant challenge in electric propulsion and is needed to reduce beam electric fields, manage space charge, and reduce ion sputter of the spacecraft. To address these challenges, simulation can be used to investigate ion/electron interactions, predict space charge distributions, and optimize system properties, such as cathode location, beamlet current, ion density, and electron temperature. However, beam neutralization can be a challenging problem to simulate due to the extreme difference in mass between ions and electrons as well as the complex interaction of electromagnetic forces.
VizGrain is used to model the beam neutralization using a full, kinetic particle-in-cell (PIC) modeling approach. Both ions and electrons are modeled as kinetic particles. Typical simulation approaches in literature involve initializing both ion and electron beams from a single, pre-mixed source. This example simulates a configuration in which the electron beam source is located outside of the ion beam. This allows us to investigate the initial mixing and entrainment of the electrons.
The 2D simulation geometry is shown in the Figure 1.
Figure 1: Beam neutralization geometry and simulation setup
The spacecraft, shown in green, is set to a reference of 0 V. The electron beam, shown in blue, is injected with a temperature of 2 eV. The ion beam, shown in red, has a beamlet current of 5mA. To adequately resolve the electrostatic potential required to model ion and electron interaction, the Debye length must be resolved in the mesh. The resulting mesh is ~400K cells using a structured/unstructured mixed meshing approach.
Animations of the results are shown in Figures 2 and 3. Figure 2 shows the electrostatic potential with the interaction of ions (red) and electrons (blue). Figure 3 colors the particles by velocity.
Figure 2: Beam neutralization animation of electrostatic potential, ions = red, electrons = blue
Figure 3: Beam neutralization animation with particles colored by velocity
The electrostatic potential of the ion beam attracts and entrains the electrons. As shown in the velocity plot, the electrons are accelerated as they enter the electrostatic potential well created by the ion beam, then slow down as they exit the beam. Additionally, an instability can be observed in the electron beam in which the electrons begin to oscillate around the ion beam. The magnitude of the oscillations will likely decrease as the neutralization approaches steady state.
Finally, Figure 4 compares the electrostatic potential with and without electron neutralization.
Figure 4: Electrostatic potential with and without electron neutralization
As expected the electron beam greatly reduces the potential, effectively neutralizing the beam. Note that the minimal ion beam divergence for the case without neutralization is attributed to the low beamlet current.
This example demonstrates VizGrain’s PIC modeling capability for electric propulsion applications. VizGrain is the 1D/2D/3D kinetic particle module within the OverViz Simulation Suite that provides scalable parallel simulation for large, complex problems. OverViz is an industrial multiphysics framework for performing hybrid plasma, fluid flow, electromagnetic, particle simulations. For more information, please contact us at info@esgeetech.com.
Ion beam neutralization is a significant challenge in electric propulsion and is needed to reduce beam electric fields, manage space charge, and reduce ion sputter of the spacecraft. To address these challenges, simulation can be used to investigate ion/electron interactions, predict space charge distributions, and optimize system properties, such as cathode location, beamlet current, ion density, and electron temperature. However, beam neutralization can be a challenging problem to simulate due to the extreme difference in mass between ions and electrons as well as the complex interaction of electromagnetic forces.
