Analysis of a cooling station for semiconductor wafers illustrates the utility of COSMOS multi-physics in the design process.  The analysis covers three goals:

• reduce the temperature of eighteen hot wafers below a target value of ten minutes or less. 

• minimize the amount of gas used for convective cooling in a cooling chamber that holds a commercially available, multi-axis robot that loads and unloads wafers through a standard interface port. 

• create a manufacturable system.

COSMOS analysis tools integrate with the SolidWorks CAD environment, making it easy to evaluate the performance of new designs or design iterations, within their operating environments.

Kinematics analysis.  The cooling chamber holds the robot and wafers and must accommodate the various robot maneuvers.  The robot picks hot wafers from an inlet port, stacks them in the cooling area, and subsequently, transfers cooled wafers through the outlet port.  We can simulate robot motion to detect any interference among the assembly parts through COSMOSMotion.

In addition to other design constraints, the wafer-cooling station must accommodate the multi-degree-of-freedom maneuvers of the robot as it manipulates the wafers.

Fluid flow analysis of the multi-physics program demonstrated that making the chamber height or width significantly greater than the envelope of the wafer stacks would waste cooling gas.  However, kinematics analysis showed the need for additional height to accommodate the robot linkage during operation.  The compromise was a two-tiered chamber.

Mechanical analysis. Creep analysis of polymer components verified proper function over time and temperature.  Static and dynamic stress analyses confirmed that the mounting interface could handle forces encountered during assembly and operation.  Modal analysis evaluated wafer-positioning accuracy given oscillation of the robot during operation.

Conjugate heat-transfer and fluid-flow analysis.  Once a rough chamber-robot configuration was established, conjugate heat-transfer and fluid-flow analysis showed the wafer-cooling effectiveness.  The objective was to evaluate successive design iterations until we obtained the desired wafer-cooling results. 

These magnified mode shapes of the robot arm in different configurations illustrate the potential effect of oscillation induced during operation.  Additional clearance is required to accommodate the oscillation amplitude when picking and placing wafers.

A key consideration in setting up the problem was to keep runtime manageable without compromising accuracy.  Two aspects of the process that affected runtime were discretization of the governing equations in time and in space.  Spatial discretization began with meshing, which divided the model into cells.  The conjugate analysis involved heat transfer between fluid and solid. The resulting cells are fluid, solid, or partial fluid and solid. 

Temporal discretization involved solving the problem, which had time varying aspects, at discrete time steps.  Underlying physics in this analysis dictated limits on step size.  The cooling time of the wafers was very long compared with the characteristic fluid flow time.  The solver executed a large number of time steps to achieve the desired finish time of ten minutes. 

Automatic time stepping of COSMOS was quite effective for the problem.  However, as is the case with any pre-processing tool, automatically generating the mesh can lead to excessive cells, which can increase runtime.  Discretion is needed to determine where discerning detail is or is not required.  Careful control over the mesh process helps control runtime, allowing multiple design iterations to be evaluated within the allotted project time. 

Flow lines,
among other visualization options, help you evaluate a flow field.  The
top view of the chamber shows fairly even coverage of the three wafer
stacks.

The problem presented a moderate meshing challenge.  Chamber volume is very large compared to local detail; in particular, the wafer stacks.  Thinness and close spacing of the wafers necessitated finer meshing than did the bulk of the chamber.  The most accurate results came from keeping the global mesh relatively coarse while refining the region around the wafers.  Finally, a sensitivity study allowed mesh optimization.  Excessive refinement was eliminated without compromising accuracy.

COSMOS offers many intuitive tools for mesh refinement and viewing.  Refinement can be controlled globally—throughout the model—or in local regions specified through features of the CAD model.  Given this approach, maintaining a meshing scheme in the presence of model changes was straightforward.  Mesh-refinement selections were largely invariant with model changes.  If necessary, they are easily recreated.

Mesh optimization involves a balance between computation time and results accuracy.  Cross-sections through the center of a wafer stack show two different refinement levels.  Both yield comparable accuracy, but the second runs in a fraction of the time.

Successive design iteration resulted in a configuration with two inlet jets that produce reasonably uniform coverage of the eighteen wafers with cooling gas.

Fine-tuning the CAD model and obtaining immediate feedback of the cooling effect of the wafers was an invaluable feature.  Using software, we could “weed” through a variety of system configurations before constructing and testing actual hardware.  Potential benefits of design modifications on cooling performance of the system were readily evident.

Inner and outer views of the chamber illustrate how fine-tuning the design improves flow around the wafers.  A channel cut into the middle of the chamber wall (inner view) helps split the flow to ensure relatively equal distribution of cooling gas among the wafer stacks (outer view).

Reviewing iterations made over the course of the design process underscored the utility of virtual prototyping with a tool like COSMOS.  Major improvements to a design are feasible without having to waste time and money on hardware prototypes. 

Virtual prototyping allows significant improvements to a design without having to construct hardware.

The temperature of each of the eighteen wafers falls below the target temperature within the goal of ten min (600 sec).

The design of the wafer-cooling system meets the original goals.  Specifically, the robot can load and unload the eighteen wafers, and the chamber can reduce the wafer temperatures below the target value within ten minutes.  In addition, combining jets with the specially designed chamber interior uses minimal cooling gas.  Finally, the chamber and other key components can be readily produced by a manufacturing shop. 

Visualization of temperature distribution on wafers reflects comparable cooling among the wafers.  However, significant gradients on each of the wafers are evident.

An advantage offered by multi-physics analysis is the ability to evaluate a design beyond the criteria set by the customer.  For example, examination of wafer surface temperature showed significant gradients, which potentially could be detrimental during cooling.  Given the pattern of the gradients, the cause evidently was contact with the wafer racks.  At this point in the design process, the course of action would be to address the potential concern with the customer.  A possible fix might be design of custom wafer racks.

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