Finite Element Analysis (FEA)

Finite Element Analysis (FEA) is a computer-based numerical technique for obtaining near-accurate solutions to a wide variety of complex engineering problems where the variables are related by sets of algebraic, differential, and integral equations.

Its applications include estimation or prediction of structural strength and behavior, modeling, simulation, and design optimization in engineering branches such as solid mechanics, fluid mechanics, thermodynamics, electromagnetics, acoustics, and the like. State-of-the-art FEA can now be applied to highly non-linear problems involving convoluted geometries, inelastic material dynamics, and fluctuating process conditions.

Finite Element Analysis operates on the principle that the analysis of a large and complex structure can be simplified by breaking down the complex structure into its parts, or "elements".  Each of these elements are then described by a set of relatively simpler equations.  These element-specific sets of equations are then joined together to come up with an extremely large set of inter-related equations that describe the behavior of the entire structure.

A computer is then used to perform the number crunching needed to find solutions to these equations, producing plots to graphically show how the structure behaves against the various excitation or stress conditions of interest.

Figure 1.  Examples of FEA plots generated from board stress analyses

conducted by Everett Charles Technologies; source: www.ectinfo.com

It is said that the use of finite elements to analyze more complex things started as early as over 2,000 years ago, when geometers interested in determining the circumference and area of a circle split the circle into small rectangles that approximately described the area of the circle. Eventually this allowed the determination of the value of pi.

FEA now makes possible the prediction of how a certain design will measure up against specifications even before a prototype is built, allowing quick improvements to the design if necessary.  FEA also prevents the high costs of over-designing a structure, since it provides solutions that are accurate enough to forego of whatever design guardbands were being put in place just a few decades ago.

Finite Element Analysis capability is not cheap.  It needs powerful hardware and software for its effective execution. Commercial FEA software used in the semiconductor industry can cost tens of thousands of dollars.  Furthermore, engineers who are tasked to perform FEA must have a strong foundation in engineering mechanics and should have a basic understanding of finite element methods.  ANSYS and ALGOR are examples of companies that sell FEA software.

Still, companies who can afford to set up FEA capability should do so, because the system cost will be negligible compared to failures that may arise from inadequate design or modeling capability.  Prevention of costly over-designs will also help pay for the FEA system.

Figure 2.  3-D FEA plots showing how a beam of a micromachined

electromechanical system (MEMS) would behave under different excitation

frequency levels; source: www.algor.com

FEA is used extensively in the semiconductor industry. 'Real-life' examples of FEA applications in the industry include but are not limited to the following:

- continuous improvement of IC package designs and material sets;

- stress analysis of adhesive bonding and design of bonded joints;

- fracture mechanics and fatigue analysis of adhesive bonds;

- thermal stress and deformation analysis of solder joints;

- fracture mechanics of solder joints for solder joint reliability studies;

- thermo-mechanical stress analysis of interfaces within a package;

- comparative analyses between flip-chip and wirebonded package configurations;

- thermal, mechanical, and electrical modeling for various leadframe designs and materials;

- simulations of wirebond and die attach fatigue failures;

- selection of the correct wire diameter, arrangement and profile given the current loads;

- reduction of wafer backside waviness through soft pad wafer backgrinding;

- modeling of the vibration responses of beams in micro-machined silicon accelrometers; etc.

 Figure 3.  An FEA contour plot of the electric field surrounding  a TIP field emitter;  source: www.ansys.com