Plasma sources capacitively driven at very high frequencies (VHF, e.g.
100MHz) have attracted much interest for semiconductor device fabrication.
These sources have the advantage of high efficiency plasma generation since
power couples efficiently with electrons and with lower ion energy loss
through sheath acceleration. This is beneficial for processes requiring
reduced ion energy, high ion and radical flux. At the same time, spatial
variations in plasma density and sheath voltage can arise leading to
non-uniformities at the wafer. The root cause of VHF plasma non-uniformity
is related to both electromagnetic wave and sheath coupling effects.
Unfortunately, most previous plasma fluid models that include
electromagnetic wave effects have found it challenging to simulate this
physics. Predictive models that can capture these effects are important for
plasma properties and their uniformity in industrial systems. We have
recently developed approaches that have succeeded in reproducing how VHF
power influences plasma uniformity by hybridizing electrostatic and
electromagnetic power delivery in a plasma fluid model with no loss of
self-consistency. These simulations also demonstrate how low frequency added
to VHF impacts uniformity through a sheath-wave interaction mechanism.
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.
Our flagship product, VizGlow, is a powerful, multi-dimensional software tool for simulating industrial, non-equilibrium plasmas. VizGlow can resolve spatial and time accurate plasma discharges with complex reactor geometries in three dimensions using a parallel simulation framework. While it is extremely robust, it is not always the best place to start when implementing a new chemistry mechanism or optimizing a plasma process. For these types of problems, we recommend starting with ChemZone.
ChemZone is a fast, 0-D reactor simulation tool for finite-rate chemistry mechanism and plasma process development. It is based on a well-stirred assumption in which the reactor is represented by a 0-D control volume with a single value for all discharge parameters. The main benefit of this approach is the very fast execution time. A single VizGlow simulation can take hours to days to complete, while a single ChemZone simulation can be completed in seconds. This allows for rapid evaluation of large parametric spaces, sensitivity studies, and uncertainty analyses for complex chemistries requiring thousands of simulations. And these exhaustive simulation approaches are becoming more relevant as semiconductor patterns shrink and process optimization becomes more challenging.
The recommended approach is to first use ChemZone to develop and refine reaction chemistries and explore process sensitivities. Once the mechanism is optimized, VizGlow can be used to spatially resolve the discharge and investigate other performance attributes, such as ion energy and angular distributions at substrates surfaces. This approach improves the accuracy and efficiency of the chemistry mechanism and is ideal for plasma process engineers developing and optimizing reactor processes.
A few examples of how plasma process engineers have used ChemZone for plasma process development include:
Perform simulated design of experiments to refine process controls (e.g. flow rate, pressure, power deposition)
Improve etch recipe through sensitivity analysis of process gas constituents
Explore effects of surface chemistries and heat transfer mechanisms to reduce process variability
ChemZone simulates the generic reactor configuration shown in Figure 1 using a multi-species, multi-temperature, spatially uniform gas mixture formulation. The configuration includes an inlet port with mixture gas, outlet port, volumetric energy source for bulk gas and electrons, volumetric energy loss, and an arbitrary number of surfaces consisting of different areas, materials, and bias voltages. The governing equations consist of species density, bulk temperature, electron temperature, and surface site fractions. Effects of parameters such as flow residence time, initial species concentrations, and external heat loss can also be captured.
Figure 1. Generalized model configuration for simulating plasma reactors in ChemZone
Key model outputs include chemical species densities for ions, electrons, neutrals, electron temperature, bulk gas temperature, net species production rates, forward and backward reaction rate coefficients, and contribution of different reactions to the net production of each species.
Mechanism Evaluation Example
Consider the mechanism evaluation of SF6/O2 plasma chemistry with 35 species and 147 reactions at 25mTorr. Figure 2 shows the transient evolution of dominant charged species and radicals until steady state is reached. F- is the dominant negative species and O2+ is the dominant positive species. The high concentration of negative ions (electronegative plasma) can significantly influence the discharge characteristics and therefore surface processes. Surface biasing or modification to the operating conditions could be used to enhance or suppress negative ion formation.
Figure 2. Generalized model configuration for simulating plasma reactors in ChemZone
Next, Figure 3 shows the contribution to net electron production rates from all 147 reactions at steady state. From this plot, we are able to identify which specific reactions (reactions 16 and 29) contribute more to the production of electrons. To increase production, constituents contained within those reactions can be modified or increased. Reactions can also be enabled/disabled to explore their effects on the production rates. This can be rapidly evaluated through simulation.
Figure 3. Contribution to net electron production rates from all 147 reactions at steady state
Furthermore, the information can be used to design a reduced mechanism. For example, if certain species or reactions are shown to play a negligible role, they can sometimes be excluded from the mechanism. The reduced mechanism can be then used in VizGlow for a full spatially accurate simulation. A reduced mechanism will run much faster than the full mechanism, depending on the total number of reduced species.
ChemZone can perform automated sensitivity analyses for reactor quantities of interest, such as species mass fraction, number densities, wall flux, temperature, and pressure. A user may simply check quantities of interest within the graphical user interface to enable them in the sensitivity study. When ChemZone is executed, the solver will systematically perturb the reaction rate coefficient of each reaction and quantify its effect on the mechanism.
Continuing with the SF6/O2 example, Figure 4 shows a sensitivity analysis of the one-directional wall flux of SF+ ions to the reaction rate coefficients at the wafer surface. The one-directional wall flux of SF+ is dominated by only a few reactions, while the rest play a negligible role. The first dominant reaction, reaction 5, is the electron impact ionization of SF forming SF+. The second, reaction 60, is the collision exchange between SF and O2+ forming SF+ and O2. These reactions are the dominate factors that create SF+ availability for interacting with the wafer surface. A similar investigation can be performed for any quantity of interest.
Figure 4. Sensitivity of the one-directional wall flux of SF+ ions to the reaction rate coefficients at the wafer surface
ChemZone is a fast reactor analysis tool for developing and optimizing chemistry mechanisms and plasma processes. ChemZone can also be used for applications in which the gas is not ionized, such as hydrocarbon combustion in internal combustion engines, gas turbines, and ignition delay timing. The primary benefit of ChemZone is its fast execution, allowing for rapid evaluation of large sensitivity studies, mechanism reductions, forward analyses, and process optimizations. ChemZone is a module within the OverViz Simulation Suite. OverViz is an industrial multiphysics framework for performing hybrid plasma, fluid flow, electromagnetic, particle simulations. For more information, please contact us at email@example.com.
Ion energy and angular distribution functions (IEADFs) characterize the anisotropic impact behavior of ions onto wafer surfaces in cold plasma reactive ion etchers (RIE). IEADFs can be used to quantify the etching performance and guide reactor design in the semiconductor fabrication process. Reducing the angles of ion impact at the wafer surface sharpens the resolution of the etching process, enabling the production of smaller etched features. Controlling the ion energy distributions also offers control over etching rates, shape, and consistency of etched trenches. Improving the ability to quantify IEADFs and their relationships to reactor system parameters will serve the industry’s rapid progression towards fabricating smaller features with faster throughput.
Two modeling approaches are compared to quantify IEADFs for a generic capacitively coupled plasma (CCP) reactor. The differences and advantages are highlighted. The first approach uses a purely fluid/continuum formulation of the plasma governing equations for the non-equilibrium plasma. This includes continuity, species, momentum, and energy. A self-consistent plasma formulation of the electrostatic potential is used to resolve the plasma sheaths. Ion momentum and energies and solved continuously. An external circuit model is used to supply radio-frequency power to the CCP. Boundary surface charging is also included to capture charge build-up on the wafer and dielectric surfaces.
The second approach uses a hybrid, particle-fluid approach that simulates individual ion particle motions over a fluid/continuum background fluid. Particles are dynamically generated and tracked as ions are produced in the plasma. Ion particle motions are solved using Newton’s law and include the Lorentz effects of the local electric and magnetic fields. Particle collisions are also modeled probabilistically using a Direct Simulation Monte Carlo approach.
For this comparison, a generic CCP is assumed. The CCP uses pure argon gas and is operated at 13mTorr. It is powered using a three-circuit fixed voltage waveform of 100V with circuit frequencies of 60MHz, 30MHz, and 2MHz. A multiple frequency design allows higher frequencies to control the plasma while the lower frequency serves to accelerate ions in the sheath. This CCP example is modeled using a 2D axisymmetric geometry. The geometry includes the gas/plasma volume, wafer, and dielectric volumes. The plasma gas phase chemistry is represented by 4 species (electrons E, argon ions Ar+, argon metastable Ar*, and argon neutrals Ar). The 2D finite volume mesh and key model features are shown in Figure 1. The left image shows a model schematic for the fluid approach. The right image shows a model schematic for hybrid approach. Both models used the same axisymmetric structured mesh consisting of approximately 40,000 quadrilateral cells.
Simulations and IEADF calculations were performed using modules within the OverViz Simulation Suite. The self-consistent, non-equilibrium plasma model within VizGlow was used for the fluid/continuum plasma modeling. VizGrain was used for the kinetic particle modeling.
Continuum results for the plasma simulation are given in Figure 2. The cycle averaged electrostatic potential is uniform throughout the plasma with a potential drop across the sheaths. The cycled averaged temperature is also uniform throughout the reactor at approximately 5eV. Adjacent to the powered electrode and wafer surface, the electron temperature reaches 8eV. The cycle averaged electron number density E and cycled averaged ion density AR+ contours (right side of Figure 2) match fairly closely. The plasma structure is uniform across the wafer radius with a peak near the wafer edge.
Figure 3 shows the electron potential with particles for the hybrid approach. A close-up of the wafer edge and sheath region is also shown. Approximately 600,000 particles were simulated.
Figure 4 shows a comparison between the fluid model (left) and the hybrid model (right). Both ion impact energy (top) and impact number flux (bottom) are compared. The ion impact number density agrees well between the two approaches. Both approaches also show a uniform impact energy distribution across the radius with a sharp decrease in energy close to the wafer edge. However, the fluid approach predicts significantly lower impact energy magnitudes. The fluid model is only able to capture average values of the plasma quantities and must assume a velocity distribution for the represented particles. The fluid model accuracy degrades as this assumption breaks down, particularly for low pressure systems where the length scale of the particle mean free path approaches the relevant length scale of the system. The is particularly relevant to the sheath region within this low pressure CCP reactor. Unlike the fluid approach, the hybrid approach correctly represents the statistical velocity distributions within the sheath. This is important for plasma processing applications where wafer surface treatment is dominated by the distributions if ion behavior.
Next, the impact energy and angular distribution functions are explored using the hybrid approach. The impact energy distributions along the wafer radius is shown in Figure 5. A top view of the distribution functions is given on the left side of the figure and a perspective view of the distributions function is given on the right side. A typical bimodal distribution is evident along the wafer radius with a lower peak at approximately 120eV and the higher peak around 200eV. The energy distribution is consistent along the radius. Close to the wafer edge, the impact energies decrease and becomes more diffuse.
The impact angle distributions along the wafer radius is shown in Figure 6, similarly with top and perspective views. The incident angle is close to zero and fairly uniform across the wafer radius with a slight small positive incidence. A more substantial spread in impact angle is found near the wafer edge due to the potential gradient edge effects.
Finally, Figure 7 shows impact energy and angular distributions at five locations along the wafer radius. At the first four locations, the impact bands are consistent and distributed close to 0°. Edge effects are prominent at the fifth location where the impact band becomes wider and less focused with a decrease in impact energies.
Fluid models are typically implemented when the particle mean free path in a plasma is much less than the relevant length scale of the system. At lower pressures, the length scales of the particle motions begin to approach those of the system. In these cases, kinetic particle models are considered more representative. However, kinetic models are considerably more computationally expensive than an equivalent fluid model. Hybrid models offer a compromise between the two, improving the accuracy of fluid simulations where particle length scales become relevant, while requiring less resources than a full kinetic model. The use of these models can help guide plasma reactor design, refine etch process parameters, investigate gas composition effects, explore process anomalies, and offer enhanced engineering insight into physical processes beyond traditional measurement techniques.
Analyses in this study were performed using the OverViz Simulation Suite. OverViz is a multiphysics framework for performing hybrid plasma, fluid flow, electromagnetic, particle simulations. For more information contact us at firstname.lastname@example.org.
The semiconductor industry is one of the most competitive global markets experiencing consistent month-to-month growth with annual global sales approaching $400B. There is a strong demand for integrated circuit technologies across growing markets, such as mobile devices and automotive electronics, with fierce international competition. This is driving an innovation race for enhanced process technologies, increased automation, and reduced product development timelines, in light of increasing development and fabrication costs. A new integrated circuit design can cost tens to hundreds of millions of dollars to develop. A new foundry can cost upwards of $15B to design and build. The need for innovation at a competitive cost presents a significant challenge to the semiconductor equipment and chip makers. This article will discuss how advancements in computational modeling and simulation can help meet some of these challenges.
Plasma reactors offer precise control over processing steps including etching, deposition, cleaning, doping, and surface activation of materials in semiconductor integrated circuit manufacture. All of these rely on complex, highly nonlinear behavior of the plasma and its interaction with surfaces with limitless designs and configurations. They are powered by a variety of excitation sources (e.g. microwave, RF, hybrid DC/RF) and can be driven at one or more frequencies to form and control plasma discharges. The number and complexity of process steps required for a single chip are increasing; upwards of 500 steps in the most advanced memory fabrication. This further drives the need for faster and cheaper methods to evaluate and refine these processes.
Simulation has gained traction to support these efforts, but is underutilized as the industry still relies heavily on iterative testing and engineering judgment. With the continual decline in computational costs, the semiconductor industry stands much to gain from a robust, high-fidelity, scalable industrial simulation solution.
A few applications where modeling and simulation can be leveraged to support plasma reactor design includes:
Refine processes for improved uniformity of ion densities and surface fluxes.
Optimize process design with respect to etch uniformity and rate while controlling temperature to prevent wafer damage.
Select operating conditions to control gas and surface reactions for various materials.
Explore effects of varying feed gas mixtures and flow rates.
Investigate chamber contaminants with simulated particle source methods.
Provide better engineering insight into reactor performance through high fidelity simulation outputs that are not possible through experimental measurement techniques.
This article will discuss three simulation approaches that offer unique solutions to these challenges for a variety of semiconductor applications.
OverViz Simulation Suite
The OverViz Simulation Suite is an industrial, multiphysics framework with coupled plasma-fluid-electromagnetic-particle modeling capabilities with a comprehensive library of process chemistries. Three modeling approaches within OverViz are discussed: (1) reactor-scale modeling, (2) feature-scale modeling, and (3) fast-reactor-scalemodeling. Each approach has unique benefits and applications.
These approaches use a low-temperature, non-equilibrium formulation for multi-species, multi-temperature, self-consistent (and quasi-neutral) plasma systems. The relevant physics that is modeled is shown in Figure 1. A reactor simulation may involve the coupling of non-equilibrium plasma formation, gas chemistries, surface chemistries, compressible gas flow, magnetic field effects, microwaves, external circuit dynamics, ICP induced electromagnetic fields, and kinetic particles. These may be selected and configured to represent a large range of plasma reactor applications, such as a Capacitively Coupled Plasma (CCP) Reactive Ion Etcher, Inductively Coupled Plasma (ICP), and DC magnetron sputtering reactor. The three approaches for these applications is discussed next.
Figure 1. Physics representations for non-equilibrium plasma reactors in OverViz
The reactor-scale model is a high-fidelity representation of the reactor system, as shown in Figure 2. Physical features in this reactor model are on the order of centimeters and millimeters. Features on the order of 10’s of nanometers, such as etched trenches, are not represented in this model, but are represented in a separate feature-scale model. While it may be possible to represent both scales in a single model, it is far more computationally efficient to separate these into two scales. The reactor-scale is discussed first.
VizGlow is used for performing reactor-scale simulations. The reactor is modeled using a finite volume representation that is solved using a well-established continuum/fluid approach. A time accurate formulation for the conservation equations is solved in 1D/2D/3D. Governing equations include species continuity, ion momentum, particle momentum, bulk energy, electron energy, electrostatic potential, electromagnetic wave, surface charge density, bulk flow, and external circuit. Both self-consistent (for resolving plasma sheaths) as well as quasi-neutral (high-density plasmas with negligible sheaths) may be represented. A drift diffusion approach is used for all species with an optional full momentum formulation for ions.
Figure 2. Example simulation domain for reactor-scale model of a CCP. Electron number density shown.
In addition to a continuum/fluid approach, the reactor-scale simulation may be solved using a hybrid approach that includes kinetic particles. Hybrid models combine a fluid model representation for bulk gas characteristics with a particle model representation of ion kinetics. With some additional computational expense, hybrid models provide better physical representation of ion behavior in the sheath region (particularly for lower pressures). These models provide the framework for performing reactor-scale simulations.
A reactor-scale simulation takes of the order of hours to days to run, depending on the reactor complexity and the hardware that is used to execute the simulation (though large simulations can be parallelized offering significant speedup). Model inputs may be varied parametrically to explore system performance or to optimization a design. Sample parametric inputs include:
Feed gas flow rate
Excitation frequency or frequencies
External magnetic field strength
Generation of contaminant (dust) particles
Example results that may be explored in these parametric simulations include:
Uniformity of species densities / fluxes
Electron energies and densities
Plasma chemistry reactions
Surface chemistry interactions
Reactor skin depth
Etch uniformity and rate
Transport of dust particles
Ion energy and angular distribution functions
A simple example of a parametric sensitivity to input power and presence of an external magnetic field is shown in Figure 3. The magnetic field provides higher densities with improved electron confinement.
Figure 3. Example parametric simulations for plasma reactor operating conditions. Electron density shown.
Another set of important outputs from the reactor-scale simulation are ion energy and angular distribution functions (IEADFs). The distribution and angle of ion impact determine how etched features form and evolve. Being able to quantify and control this behavior offers control over the etching process. For example, narrowing the angular distributions to have most ions impact the surface with normal incidence allows for high aspect ratio trench and via features to be etched. Simulated IEADFs at seven locations along a wafer surface are shown in Figure 4. The IEADFs at the first six locations are tightly distributed around 0° (normal incidence). Edge effects become very prominent at the seventh location where significant fraction of the ion impacts with large off-normal angles of incidence, thus compromising the process integrity at these locations.
Figure 4. Ion energy and angular distribution functions along wafer radius.
The feature-scale model is a sub-model of the reactor-scale model that locally resolves the physics around small features in the plasma sheath, such as etched trenches, which can be on the order of tens to hundreds of nanometers. Here mean free paths of the ions and electrons are large compared to the feature dimensions. Ion and electron motion must be represented using particle kinetics. IEADFs are therefore extracted from the reactor-scale model in the region surrounding the small features of interest and then used as boundary conditions for the feature-scale simulation. An example of this is shown in Figure 5. Feature-scale simulation runtime is similar to reactor-scale simulation runtime.
Figure 5. Feature-scale model uses local solution from reactor scale model to resolve features on the order of nanometers.
Feature-scale modeling can be useful to provide design insight into:
IEADF relationship to etched feature geometries (size and aspect ratio)
Surface charge-up and propensity of damage around the etched features
Effects of material properties
Overall relationship between bulk reactor operating conditions and local feature scale processing
Example results from a feature-scale simulation for a dielectric surface exposed to a bias is shown in Figure 6. Ions approach the feature with very narrow off-normal angles and can therefore deposit directly at the bottom surface of the features, thereby imparting a net positive charge at the bottom surfaces. After passing through the sheath, electrons arrive at the trench with low energy and large off-normal incidence angles. Consequently, they deposit a negative charge at the corners of the feature. The differential charge deposition across the feature develops self-induced electric fields that can lead to dielectric breakdown damage.
Figure 6. Example electrostatic potential solution from feature scale model of etched trench.
Reactor-scale models resolve system performance on the length scale of the reactor, millimeters to centimeters. Feature-scale models resolve system performance on the length scale of the surface features, tens to hundreds of nanometers. Next, the fast-reactor-scale model is discussed.
The fast-rector-scale model is a 0-D global representation of the reactor-scale model. ChemZone is used to perform fast-reactor simulation within the OverViz Simulation Suite. It solves the same governing equations for low-temperature, non-equilibrium, multi-species, multi-temperature plasma systems, including chemical reactions. However, the fast-reactor-scale model assumes that the reactor is well stirred, such that reactor gases are perfectly mixed and homogeneous. Reactor properties and constituents are assumed uniform through the reactor, allowing for a 0-D control volume representation. A schematic of a fast-reactor-scale model is given in Figure 7. The reactor is defined by volume V with homogeneous representation of bulk temperature, electron temperature, pressure, and species densities. It can also include mass inflow, mass outflow, energy source term, energy loss, and independent surface reactions. The fast-reactor-scale model provides detailed views of chemistry parameters, such as reaction rates and contributions of individual reactions to specific species. Very large chemistries can be represented, such as plasma discharge, neutral reactions, combustion, and chemical vapor depositions.
Figure 7. Schematic for fast-reactor-scale simulation including inflow, outflow, and surface reactions.
The primary benefit for the fast-reactor-scale modeling approach is its extremely fast runtime, requiring only seconds to minutes for full transient reactor simulations. This allows complex process design studies that involve hundreds or thousands of independent simulations that would not be possible with the standard reactor-scale model.
Specific examples of faster-reactor-scale applications include:
Large parametric studies of process formulations
Design of experiments (DOE) for new fabrication processes
Sensitivity analyses for reaction mechanisms to identify which species/ reactions are dominant
Process optimization for large numbers of chemistries
Troubleshooting and reverse engineering of process issues and defects
This benefits semiconductor design and process engineers that may be responsible for executing extensive DOE experimental studies. What could take months to complete in the lab could be performed on a laptop in minutes. While experiments cannot be completely eliminated (and should not be eliminated, as experiments are critical to validating simulation results and verifying design performance), this provides an upfront analysis capability that could greatly reduce the time and costs required for fabrication process testing.
Sample results for a fast-reactor-scale sensitivity analysis is shown in Figure 8. This study is used to identify which reactions dominate a reactor process. The time evolution of species densities is also shown.
Figure 8. Example outputs for fast-reactor-scale sensitivity analysis.
For well-stirred plasma reactors, the fast-reactor-scale model offers rapid process simulations for reactive flows and finite-rate chemical reaction mechanism development.
Reactor-scale, feature-scale, and fast-reactor-scale modeling are three approaches that can be leveraged for different aspects of semiconductor processing. These simulation approaches can be used very effectively to supplement experiments to reduce time and cost associated with hardware iterations. They can also be used upfront in the design process to refine the design space before executing a single experiment. This accelerates the design and development lifecycle reducing cost. The simulations can also be used to troubleshoot issues in the fabrication process reducing downtime.
Validated simulation can be an important tool in exploring innovation and shortening the development lifecycle. This is particularly useful in the semiconductor industry where the need for innovation and cost of development are growing as fast as the demand for their products.
For more information about these modeling approaches or the OverViz Simulation Suite, please contact us at email@example.com.