Predictive Analytical Thermal Stress Modeling in Electronics and Photonics

Abstract

We discuss the role and the attributes of, as well as the state-of-the-art and some major findings in, the area of predictive analytical (“mathematical”) thermal stress modeling in electronic, opto-electronic, and photonic engineering. The emphasis is on packaging assemblies and structures and on simple meaningful practical models that can be (and actually have been) used in the mechanical (“physical”) design and reliability evaluations of electronic, opto-electronic, and photonic assemblies, structures, and systems. We indicate the role, objectives, attributes, merits, and shortcomings of analytical modeling and discuss its interaction with finite-element analysis (FEA) simulations and experimental techniques. Significant attention is devoted to the physics of the addressed problems and the rationale behind the described models. The addressed topics include (1) the pioneering Timoshenko’s analysis of bimetal thermostats and its extension for bimaterial assemblies of finite size and with consideration of the role of the bonding layer of finite compliance; this situation is typical for assemblies employed in electronics and photonics; (2) thermal stresses and strains in solder joints and interconnections; (3) attributes of the “global” and “local” thermal expansion (contraction) mismatch and the interaction of the induced stresses; (4) thermal stress in assemblies adhesively bonded at the ends and in assemblies (structural elements) with a low-modulus bonding layer at the ends (for lower interfacial stresses); (5) thin film systems; (6) thermal stress induced bow and bow-free assemblies subjected to the change in temperature; (7) predicted thermal stresses in, and the bow of, plastic packages of integrated circuit devices, with an emphasis on moisture-sensitive packages; (8) thermal stress in coated optical fibers and some other photonic structures; and (9) mechanical behavior of assemblies with thermally matched components (adherends). We formulate some general design recommendations for adhesively bonded or soldered assemblies subjected to thermal loading and indicate an incentive for a wider use of probabilistic methods in physical design for reliability of “high-technology” assemblies, including those subjected to thermal loading. Finally, we briefly address the role of thermal stress modeling in composite nanomaterials and nanostructures. It is concluded that analytical modeling should be used, whenever possible, along with computer-aided simulations (FEA) and accelerated life testing, in any significant engineering effort, when there is a need to analyze and design, in a fast, inexpensive, and insightful way, a viable, reliable, and cost-effective electronic, opto-electronic, or photonic assembly, package, or system.

Predicted Response of the Die-Carrier Assembly in Flexible Electronics to the Combined Action of Tension and Bending Applied to the Carrier

“…The approach enables one to separate the roles of the material and geometry factors (considered by the external loading independent interfacial compliance) and the external-loading factors (accounted for by the magnitude and distribution of the thermal and/or mechanical loading). The attributes, merits, and shortcomings of this engineering approach has been discussed in detail in Ref, [30],…”

Thermal stresses in the discrete joints of sandwiched structures

“…Examples of this approach are Goland and Reissner in modeling flexible bond [1], Taylor and Yuan [11], Ojalvo and Eidinoff [12], Grimado [13], Chen and Nelson [14], Delale et al [15], Willams [16], Suhir [17,18], Pao and Eisele [19], Jiang et al [20], Ru [21], Wen and Basaran [22] and Wong et al [23]. More examples could be found in the articles of Suhir [24] and Silva et al [25]. The strength-of-material approach gives rise to closedform solutions that facilitates adoptions by practicing engineers.…”

Bow-free tri-component assembly for aerospace optoelectronics applications: Predicted thermal stresses

“…One obvious and a straightforward way is by simply introducing a third, "surrogate", material [6]. An alternative way is by making the bonding material stiff enough in its plane, so that the bonding layer becomes "an equal member/partner" with the two other components of the assembly [32][33][34]. If this approach is applied, the bonding material should be able to produce and to withstand a sufficiently large axial force, needed to create a bending moment that would be significant enough to equilibrate the moment caused by the forces acting in the adherends.…”