Plasma fluid modeling with transient to stochastic transformation
AssigneeTokyo Electron Limited
InventorJozef Brcka
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Abstract
The invention relates to the simulation method and apparatus used in plasma modeling. It includes a method to transform transient formulations of the phenomenological plasma model into a quasi-stochastic spatial formulation. Specifically, the invention aids in decreasing computational time for the modeling of plasma in a plasma processing system, particularly those involving two different time-based parameters. The invention is particularly described in connection with plasma simulations used for the optimization dual-frequency capacitively-coupled plasma etching systems.
Claims31
A computer method for simulating plasma density distribution within a plasma reactor that is responsive to at least two variables of different time bases, the computer method comprising executing computer program codes according to a process comprising:
- approximating transient sheath behavior of the plasma occurring in the plasma reactor in response to a variable having a first time basis, the approximating including:
- defining a model domain that is characteristic of the plasma reactor,
- constructing a probability function for a time dependent variable within the model domain, and
- transferring the time dependent variable into a spatial character based upon the probability function;
- and
- performing, on the spatial character, a time-domain simulation of the transient plasma sheath behavior occurring in the plasma reactor in response to a variable having a second time basis.
A computer method for simulating plasma density distribution within a capacitively coupled plasma reactor having a dual frequency power source coupled to the plasma, the computer method comprising executing computer program codes according to a process comprising:
- approximating transient sheath behavior of the plasma occurring in the plasma reactor at a first frequency of the dual frequency power source by:
- defining a model domain that is characteristic of the plasma reactor,
- constructing a probability function for a time dependent variable within the model domain, and
- transferring the time dependent variable into a spatial character based upon the probability function;
- and
- performing on the spatial character, at a second frequency of the dual frequency power source, a time-domain simulation of the transient plasma sheath behavior occurring in the plasma reactor.
A simulation apparatus for approximating a transient plasma sheath behavior within a plasma reactor, the simulation apparatus comprising:
- a calculating unit that calculates probability function for a time dependent variable within a model domain and that transfers the time dependent variable into a spatial character;
- and
- a simulation unit that performs a simulation of the transient plasma sheath behavior occurring in the plasma reactor based on the spatial character.
Dependencies are inferred from the claim text.