Modeling, Simulation & Analysis

SC Solutions develops a wide range of numerical models of equipment and processes.

What kinds of models does SC Solutions develop?

At SC Solutions we primarily develop physics-based dynamic models. Our models typically consist of systems of non-linear Ordinary Differential Equations (ODE’s) that approximately describe the underlying physics of the time-varying system. These models range from a few dozen ODE’s to large systems with thousands of ODE’s. Invariably there will be uncertain aspects of the problem, ranging from uncertain material properties to uncertain physics. We typically incorporate physically meaningful adjustable parameters into the model that allow these uncertainties to be reduced by comparing the model to experimental results (validation).

What types of physics are encapsulated in these models?

Typically, our models encompass heat, flow and species transport, chemical kinetics, and solid mechanics. These are key phenomena in many manufacturing processes for semiconductor and advanced materials. We also develop models in cross-disciplinary areas such as electromagnetics, electrochemical processes, optics, and multi-scale phenomena. Some specific applications include hot and cold wall furnaces, thermal stress and deformation, Chemical Vapor Deposition (CVD), Chemical Mechanical Polishing (CMP), Physical Vapor Deposition (PVD), electroplating / electropolishing, and RF inductive heating.

What tools are used to develop such models?

Some of our models are implemented using commercial tools, while others are developed using SC Solutions’ proprietary in-house modeling software. We are a certified consultant for COMSOL, a popular finite-element software package, and also a Matlab Partner.

How would modeling be useful to me?

There are many ways that the models we develop are useful to our customers:

• Control design: Our feedback and feedforward controllers are designed using dynamic physics-based models. High-order models undergo model reduction in order to run simulations in real time while retaining sufficient accuracy for the desired set of states. This approach enables a very efficient control design process, and results in high-performance controllers.
• Equipment design and performance optimization: SC Solutions works with equipment manufacturers from the early stages of design of the next-generation prototype. The designs are tested in closed-loop simulation for performance, and necessary changes are incorporated. The iterative process is continued until an optimal design that meets the performance specifications is obtained before starting the expensive process of building the equipment prototype. Additionally, models are used to determine optimal number of sensors and their locations, and optimal actuator groupings.
• Virtual sensing: The models can be used as virtual sensors where measurements made at some easily accessible location are used to accurately estimate the state at difficult-to-measure points by exploiting the dynamic interrelationship between the states in the equipment model. An added advantage of this approach is that fewer sensors can be used which decreases costs while increasing system robustness.
• Equipment fault diagnostics and health monitoring: An equipment may be characterized by a set of model parameters whose values will be restricted to a determinable range for a properly operating system. Parameter excursion out of that range is a sign of an existing or impending problem. The specific parameter (or parameters) thus becomes an indicator of the subsystem where the problem may have occurred (e.g., burned out heater coil, cooling water supply problem, etc.)

How much would it cost to model my problem?

• The cost depends on the scope of the effort and the complexity of the problem, in terms of both the geometrical complexity and the types of multiphysics involved. Our modeling projects range from those that involve a day or two to ones that require several man-weeks of effort.
• We typically write a proposal that addresses the problem in a systematic manner and ensures that we are on the same page as our customer with regard to the details and assumptions involved in developing the model. A modeling effort is often broken down into multiple tasks and hours assigned to each task in the proposal.
• We work closely with our customers and update them with results of each task as they become available. This approach provides flexibility to our customers to modify the scope and direction of the effort at any stage.

How are modeling results delivered to customers?

For consulting work, we generally provide results of model simulations as presentations with the help of PowerPoint slides. Depending on the scope of the work, we may write a report. In the case of models developed with commercial tools, we can provide the model at the request of the customer.