Thermomechanical stresses and deformations are the major contributors to malfunctions of, and failures in, microelectronics and photonics devices, packages and systems. In microelectronics, the most serious consequences of the elevated thermal stresses are usually associated with mechanical (structural) failures (e.g., ductile rupture, brittle fracture, failures due to fatigue, creep, stress relaxation, thermal shock, stress corrosion, etc.). In optoelectronics and photonics, the requirements for the mechanical behavior of the materials and structures are based, in the majority of cases, on their optical performance. It is not the thermal stresses, but rather the thermal strains and displacements that are typically responsible for the viability and reliability of a photonics product or system. Small (i.e., fractions of a micron), but, nevertheless, impermissible, displacements may occur in optoelectronic structures because of various time dependent effects (creep, stress relaxation, materials aging, etc.). If this happens, the long-term optical performance of the device will be compromised.
The ability to understand the sources of the thermally induced stresses and strains, to predict the magnitudes and the distributions of the thermal stresses and displacements, and possibly to minimize them, if necessary, is of obvious practical importance. This can be successfully achieved, if predictive modeling is widely used in addition to – and, desirably, prior to – experimental investigations and reliability testing, whether it is carried on the design stage or during qualification and production of a device.
It is noteworthy that accelerated testing, which is a major experimental approach in microelectronics and photonics, cannot do without a simple and meaningful theoretical model, and microelectronics and photonics cannot do without accelerated testing. It is on the basis of such a model that a reliability engineer decides which parameter he/she should accelerate, how to process the experimental data, and how to bridge the gap between what one “sees” during accelerated testing and what he/she will supposedly “get” in the actual use conditions.
Predictive models represent real phenomena and objects by using abstract notions. Such models usually employ more or less sophisticated mathematical methods of analysis and can be either analytical (“mathematical”) or numerical (computational). Today’s numerical models are, as a rule, computer-aided.
Analytical models can be based on the application of a structural analysis (strength-of-materials) approach or of a theory-of-elasticity method.
The structural analysis (engineering) approach enables one to determine, often with sufficient accuracy, the induced stresses and displacements. This approach results in simple and easy-to-use formulas, and can be (and, actually, has been) successfully employed as a part of a physical design process of a component or device. It can be used to select materials, establish dimensions of the structural elements, compare different designs from the standpoint of the stress level, etc.
The theory of elasticity method is based on rather general assumptions and equations of the elasticity theory and provides a rigorous mechanical treatment of the problem. However, it is not always easy to implement or to make practical. The engineering and the theory-of-elasticity approaches should not be viewed, of course, as “competitors”, but rather as different research tools, which are complementary, have their merits and shortcomings, and, hence, their areas of application.
Finite-element modeling has become the major research tool for theoretical evaluations in mechanical and structural engineering, including the area of microelectronics and photonics. This should be attributed to the availability of powerful and flexible computer programs, which enable one to obtain, within a reasonable time, a solution to almost any stress-strain related problem.
As far as photonics systems are concerned, special effort should be taken to make the existing finite-element analysis (FEA) programs accurate enough to be suitable for the evaluation of the thermomechanical displacements. Another challenge involves the necessity to consider viscoelastic and time-dependent behavior of photonic materials.
|“The practical value of mathematics is, in effect, a possibility to obtain, with its help, results simpler and faster.”
|Andrey Kolmogorov, Russian mathematician
Certainly, broad application of computers has, by no means, made analytical solutions unnecessary or even less important, whether exact, approximate, or asymptotic. Analytical modeling can be very useful to select and to master the preprocessing model. Simple and easy-to-use analytical relationships have invaluable advantages, due to the clarity and “compactness” of the obtained information and to the direct indication on the role of various factors affecting the given phenomenon or the behavior of the given system.
Probabilistic models can be used successfully in situations in which the “fluctuations” from the mean values are significant and in which the variability, change and uncertainty play a vital role. In the majority of such situations the product will most likely fail if these uncertainties are ignored. Probabilistic models enable one to establish the scope and the limits of the application of deterministic models, provide a solid basis for a substantiated and goal-oriented accumulation and effective use of empirical data, and enable one to assess quantitatively the degree of uncertainty in various factors, which determine the performance of a product. This allows a reliability engineer to design a product with a predictable and sufficiently low probability of failure.
|“An equation longer than three inches is most likely wrong.”
- Predictive modeling is an effective tool for the evaluation and prevention of thermomechanical structural and functional failures in microelectronics and photonics materials and structures.
- Analytical (“mathematical”) numerical (computer-aided) models should be viewed as important and indispensable to the design of a viable, reliable and cost-effective product.
- An analytical model should be simple enough to be useful in accelerated life testing or in mastering a preprocessing finite-element model.
- Special effort should be taken to make the existing finite-element analysis programs accurate enough to be suitable for the evaluation of the thermal stresses and displacements in photonics structures.
- Application of the probabilistic approach enables one to assess quantitatively the role of various uncertainties in the materials properties, geometrical characteristics and loading conditions, and, owing to that, to design and manufacture a viable and reliable product.