Molecular Flow Module

Software for Modeling Low Pressure Gas Flow in Vacuum Systems

Molecular Flow Module

In an ion implanter, the average number density of outgassing molecules along the beam path is used as a figure of merit to evaluate the design. It must be computed as a function of wafer angle, with rotation about one axis.

Accurate Modeling of Low Pressure, Low Velocity Gas Flows

The Molecular Flow Module is designed to offer previously unavailable simulation capabilities for the accurate modeling of low pressure, low velocity gas flows in complex geometries. It is ideal for the simulation of vacuum systems including those used in semiconductor processing, particle accelerators and mass spectrometers. Small channel applications (e.g. shale gas exploration and flow in nanoporous materials) can also be addressed.

The Molecular Flow Module uses a fast angular coefficient method to simulate steady-state free molecular flows. You can model isothermal and nonisothermal molecular flows, and automatically calculate the heat flux contribution from the gas molecules. The discrete velocity method is also included in the module for the simulation of transitional flows.

Two Methods for Modeling Free Molecular and Transitional Flows

The Molecular Flow Module offers two alternatives to these methods, allowing you to solve for low velocity and low pressure flows in a manageable and accurate fashion. Two specific physics interfaces, configured to receive model inputs via the graphical user interface (GUI) to fully specify a set of equations, are available:

Free Molecular Flows

The Free Molecular Flow interface uses the angular coefficient method to model flows with Knudsen numbers that are greater than ten. This physics interface avoids solving the physics in the volumes of the modeled geometries, and requires meshing only of the surfaces. Completely diffuse scattering (total accommodation) and emission are assumed at all surfaces in the geometry, and flow is computed by integrating the flux arriving at a surface from all other surfaces in its line-of-sight. This means that the dependent variables exist only on the surfaces of the geometry, and the solution process is much faster than the DSMC method. Furthermore, it is not subject to statistical scatter. Number densities are reconstructed using a method included in the Free Molecular Flow interface.

Transitional Flows

The Transitional Flow interface solves the Boltzmann BGK equation by employing a modified form of the Lattice Boltzmann/Discrete Velocity method to solve transitional flows. Unlike the DSMC method, the solutions are not subject to statistical noise. Diffuse reflection of gas molecules is also assumed at all surfaces, with molecules from all directions effectively adsorbed onto the surface and subsequently re-emitted according to Knudsen’s law. In this interface, the model geometry is meshed to discretize the physical space, and a velocity quadrature is chosen, which provides a set of dependent variables that represent a mesh in velocity space. Both the mesh and the quadrature can be independently adjusted to ensure the problem is resolved in both physical and velocity space.

Additional images:

  • Transmission probability through an RF coupler using both the angular coefficient method, available in the Free Molecular Flow interface, and a Monte Carlo method using the Mathematical Particle Tracing interface (requires The Particle Tracing Module). Transmission probability through an RF coupler using both the angular coefficient method, available in the Free Molecular Flow interface, and a Monte Carlo method using the Mathematical Particle Tracing interface (requires The Particle Tracing Module).

Optimized Methods for Fast and Accurate Simulations

Gases at low pressures cannot be modeled using conventional computational fluid dynamics tools. That is due to the fact that kinetic effects become important as the mean free path of the gas molecules becomes comparable to the length scale of the flow. Flow regimes are categorized quantitatively via the Knudsen number (Kn), which represents the ratio of the molecular mean free path to the flow geometry size for gases:

Flow type Knudsen Number
Continuum flow Kn<0.01
Slip flow 0.01<Kn<0.1
Transitional flow 0.1<Kn<10
Free molecular flow Kn>10

While the Microfluidics Module is used for modeling slip and continuum flows, the Molecular Flow Module is designed for accurately simulating flows in the free molecular flow and transitional flow regimes. Historically, flows in this regime have been modeled by the direct simulation Monte Carlo (DSMC) method. This computes the trajectories of large numbers of randomized particles through the system, but introduces statistical noise to the modeling process. For low velocity flows, such as those encountered in vacuum systems, the noise introduced by DSMC renders the simulations unfeasible. COMSOL uses alternative approaches: employing a discrete velocity method for transitional flows (using a Lattice Boltzmann velocity quadrature) and the angular coefficient method for molecular flows.

Ion Implanter Evaluator

Differential Pumping

Molecular Flow Through a Microcapillary

Rotating Plate in a Unidirectional Molecular Flow

Outgassing Pipes

Adsorption and Desorption of Water in a Load Lock Vacuum System

Molecular Flow Through an RF Coupler