Molecular Flow Module

Understand and Predict Free Molecular Flows

The Molecular Flow Module is an add-on to the COMSOL Multiphysics® software that is used to design vacuum systems and understand and predict low-pressure gas flows in the free-molecular-flow regime. Historically, flows in this regime have been modeled by the direct simulation Monte Carlo (DSMC) method. The DSMC method computes the trajectories of large numbers of randomized particles through the system but has the drawback of introducing statistical noise into the modeling process. For low-velocity flows, such as those encountered in vacuum systems, the noise introduced by DSMC renders simulations infeasible. The Molecular Flow Module uses a deterministic approach that is completely free of this statistical noise and provides a fast and convenient method for simulating low-velocity flows.

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A vacuum model showing the molecular flux fraction in the Prism color table.

Accurate Modeling of Low-Pressure, Low-Velocity Gas Flows

The Molecular Flow Module is ideal for the simulation of vacuum systems, including those used in semiconductor processing, particle accelerators, and mass spectrometers. Small channel applications such as shale gas exploration and flow in nanoporous materials can also be addressed.

The angular coefficient method is used in the module to simulate steady-state free molecular flows, allowing for the molecular flux, pressure, and heat flux to be computed on surfaces. The number density can be reconstructed on domains, surfaces, edges, and points from the molecular flux on the surrounding surfaces. It is also possible to model isothermal and nonisothermal molecular flows and calculate the heat flux contribution from the gas molecules.

What You Can Model with the Molecular Flow Module

Design vacuum systems and predict low-pressure gas flows.

A close-up view of a vacuum chamber model in the Disco color table.

Vacuum Systems

Study differentially pumped vacuum systems.

A close-up view of a vacuum model in the Disco color table.

Ultra-High Vacuum Chemical Vapor Deposition (CVD)

Model the growth of silicon wafers using multiple species.

A close-up view of a charge exchange cell model in the Aurora Borealis color table.

Charge Exchange Cells

Simulate the interaction of a proton beam with a charge exchange cell.

A close-up view of an ion implanter model with a wafer.

Ion Implantation

Optimize ion implantation processes for doping of semiconductor wafers.

A close-up view of a thermal evaporator model showing the film thickness.

Thermal Evaporation

Compute the thickness of a thermally evaporated gold film.

A close-up view of a vacuum chamber model in the Thermal Wave color table.

Adsorption and Desorption

Study adsorption and desorption in a vacuum system at low pressures.

Features and Functionality in the Molecular Flow Module

The Molecular Flow Module contains functionality for accurately simulating flows in the free-molecular-flow regime.

A close-up view of the Model Builder with the Free Molecular Flow node highlighted and an ion implanter model in the Graphics window.

Free Molecular Flow

The Free Molecular Flow interface is available for accurate simulation of highly rarefied gas flows. This interface solves for the molecular fluxes at boundaries in the geometry and includes options for computing number density, pressure, and heat flux at boundaries. With this interface, it is possible to run a simulation with a mesh generated only on the boundary. In order to reconstruct the number density inside the domain, a volume mesh can easily be added. With the Free Molecular Flow interface, molecular flow simulations can be performed using authentic CAD models as the basis.

A close-up view of the Free Molecular Flow settings and an s-bend benchmark model in the Graphics window.

Angular Coefficient Method

For highly rarefied flows, the Free Molecular Flow interface uses the angular coefficient method, which is a deterministic approach and faster than particle-based methods. This method is much more accurate than approximate conductance methods for computing the pressure and number density. In addition, multiple species of gas can easily be handled at the same time.

A close-up view of the Electrostatics settings and a charge exchange cell model in the Graphics window.

Extended Multiphysics Analyses

The Molecular Flow Module can be combined with other modules in the COMSOL product suite to expand the functionality for performing multiphysics simulations. By combining modules, data from other modules, such as field variables and parameters, can be used in the Molecular Flow Module via interface couplings. For example, if you combine the Molecular Flow Module with the Particle Tracing Module, the Free Molecular Flow interface — used to compute the background number density — can be coupled with the Charged Particle Tracing interface to simulate collisions between the particles and ambient neutral atoms.

A close-up view of the Model Builder with the Wall node highlighted and an evaporator model in the Graphics window.

Boundary Conditions

The Molecular Flow Module offers a variety of boundary conditions that can be assigned to a model. There are built-in features for specifying the pressure on a boundary due to a large adjacent reservoir or total vacuum. It is also possible to directly specify surface temperature for nonisothermal molecular flows. In addition, the module offers the ability to specify parameters such as the pump flow rate and the fraction of molecules adsorbed or to directly set the adsorption rate on any given surface. The module also offers features for modeling evaporative sources and specifying the flux emitted from a surface using numerical values or arbitrary expressions.

Furthermore, the Molecular Flow Module includes various boundary conditions for modeling different kinds of solid surfaces within vacuum systems. For example, a boundary can be defined with the Wall feature, with which incident molecules are diffusely reflected from the surface. There is also the option to use the Outgassing wall feature, with which incident molecules are diffusely reflected and the additional molecules are outgassed diffusively. The Adsorption/Desorption option can be used so that a fraction of incident molecules is absorbed while the remainder of the molecules are diffusely reflected. Additionally, the Deposition wall type option can be used to model the surface where the molecules will accumulate.

A close-up view of the Model Builder with the Transitional Flow node highlighted and an s-bend geometry model in the Graphics window.

Transitional Flow

The Molecular Flow Module can be used to simulate flows that are slightly less rarefied than free molecular flows but still more rarefied than slip flows. This generally includes rarefied flows spanning from the Navier–Stokes limit to the molecular flow limit. The Transitional Flow interface, designed specifically for these types of rarefied flows, is based on the discrete velocity method. With this approach, a finite set of velocities are chosen to represent all potential velocities of the molecules. Atoms are then assigned to these velocity bins, and the interface calculates the number density in each bin. A convection equation is resolved within the domains, complemented by a scattering term that repositions the molecules between bins. The module also includes various dedicated boundary conditions to streamline the setup. Because transitional flow simulations are computationally demanding and require substantial processing power and time, they are best applied when the CAD geometry model can be simplified.

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