Chemical reduction techniques in PCVD processes

Thin film solar cells also known as thin film photovoltaic cells are made by chemical vapor deposition of thin layer of material on a substrate. Plasma enhanced chemical vapor deposition reactor (peCVD) can be used for the growth of thin film solar cell. Our aim is to study the plasma model containing complex oxygensilane chemistry that is relevant for peCVD.

Numerical description of such plasma models is given by setting up and solving the complex set of equations. These equations are space and time dependent conservation equations (Mass, Momentum and Energy) and the reaction rate equations. The complete simulation to study the behavior of the system involves the solution of all the equations for each species present in the system simultaneously.

Plasma model in general contains large number of chemical species and reactions, which induces a high chemical complexity. In addition to high chemical complexity there are other problems related to plasma state of matter such as ions, electrons, effect of electromagnet interaction etc. One example of such a plasma model is conversion of methane to higher hydrocarbons containing approx. 36 species and 367 reactions. Numerical simulation of such complex mechanism induces a high computational load on the system and the computational time taken to solve the system is very long.

Plasma physics is not the only branch of science that deals with the problem of high computational cost and time. One of the other discipline that encounters a similar problem is combustion research where they try to study the detailed computation of 1D laminar flame. A typical combustion reaction mechanism, when CO is burned in air, contains 67 reaction and 13 species. To overcome the difficulty associated with chemical complexity combustion community employes Chemical Reduction Technique.

A reaction system containing large number of species in general has widely varying time scales for the evolution of the different species in the system. Chemical Reduction Technique simply uses the fact that a system is not evenly sensitive to all the reaction. Variation in system response due to fast time scales is very fast than the variation in system response due to slow time scales. As a matter of fact the densities of species governed by fast time scale will evolve very quickly in the initial period of time that is even less than the time scales of our interest. By decoupling the slow and fast time scales, the fast time scale variation can be assumed to be at steady state for our time of interest. The slow time scales become important and full description of system can be given by the slow time scales without any significant loss in chemical kinetics description.

The chemical reduction techniques commonly employed are ILDM (Intrinsic Low Dimension Manifold), TGLDM (Trajectory Generated Low Dimension Manifold) etc. ILDM method identifies a lower dimensional space (manifold) inside complete state space. After a short time the fast timescale processes will quickly move onto this lower dimensional manifold and the slow timescale processes will move tangential to the manifold. Identification of Low Dimensional Manifold allows a decoupling of the time scales and reducing the number of equations. Full system description can be given by this lower dimensional manifold without loss in chemical kinetics description. ILDM technique will be used to simplify the complexity present in the plasma model and thus reducing the computational load and time required for the numerical simulation of the model.