Multi-objective topology optimization of porous microstructure in die-bonding layer of a semiconductor

Figures & data

Figure 1. Process of constructing representative volume elements. (a) Generation of the first seed on the surface of $Y_3$ = 0. (b) Generation of abundant seeds. (c) Radius distribution of seeds to obtain interconnected pores. (d) Random generation of separated pores.

Figure 2. Control of pore connectivity and anisotropy in porous microstructures.

Figure 3. (a) Generated representative volume element. (b) Geometric periodicity on one side face and the corresponding opposite face of the cube.

Figure 4. Shear modulus of the generated representative volume elements using high-throughput evaluation.

Figure 5. Representative volume elements (RVEs) with identical volume fractions ($\mathit{V}$ $\approx$ 50%) but different pore connectivity.

Figure 6. Thermal conductivity of generated representative volume elements using high-throughput evaluation.

Figure 7. Relationship between the shear modulus and thermal conductivity.

Figure 8. Flowchart of the multi-objective topology optimization process.

Figure 9. Multi-objective topology optimization using different volume fraction constraints: optimized structures and their properties for $w_1$ = $w_2$ = 0.5.

Figure 10. Convergence history of multi-objective topology optimization using different weight factors: (a) Objective function (b) Shear compliance (c) Thermal compliance, and (d) Volume fraction.

Figure 11. Multi-objective topology optimization using different weight factors: optimized structures and their properties under orthotropic assumptions.

Figure 12. Effect of weight factor on von mises stress of the optimized microstructures under the imposed macroscopic strain mode ${\overline{ϵ}}_5$.

Figure 13. Effect of weight factor on component of heat flux $q_3$ of the optimized microstructures under the applied macroscopic temperature mode ${\bar{G}}_3$.

Figure 14. Comparison between the generated RVEs and optimized microstructures in terms of the shear modulus and thermal conductivity.