Case ID: M23-116P

Published: 2023-07-28 08:56:45

Last Updated: 1690534605


Marc Mignolet
Xiaoquan (Julian) Wang

Technology categories

Advanced Materials/NanotechnologyComputing & Information TechnologyManufacturing/Construction/MechanicalPhysical Science

Licensing Contacts

Physical Sciences Team

ThermEla/Subs – Thermoelastic Analysis of Substrates


Heating-based semiconductor packaging processes, e.g., thermal compression bonding, induce significant deformations in the substrates which must be accurately determined to avoid failure. This effort can be carried out using standard finite element software, but it is computationally very intensive. Significant reductions in this cost would allow the use of more refined models that would lead to better prediction of deformations. In turn, that would reduce uncertainty and tighten process conditions that would lead to an increased manufacturing yield and possibly to operating at lower temperatures creating directly an energy saving and a reduced risk of warping.

Invention Description

Researchers at Arizona State University have developed the software ThermEla/Subs, combining two novel computational strategies to determine the deformations of heated substrates much more computationally efficiently than currently while still relying on an underlying finite element model. The first approach views the semiconductor substrate as a weakly coupled chain of substructures which allows a computation of the displacements by groups of layers vs. the determination of the response of all layers at the same time. This strategy led to reductions of the CPU time by a factor of 3 and of the required memory by a factor of 15. These two reductions could be combined by running multiple jobs in parallel for a total reduction by a factor of up to 45.

The second approach models each component of the assembly, e.g., each layer of the substrate, in a reduced order model (ROM) format leading to a much lower number of degrees of freedom per layer and thus overall. The typical system considered (21 layers) has 433,000 nodal values of displacements in the finite element model but only 525 unknowns in the reduced order model, thus leading to a dramatic reduction in CPU time and memory. This second option does require the upfront cost of selecting the ROM basis functions.

Potential Applications

  • Analysis of deformations caused by heating of substrates
  • Optimization of process to increase yield and reduce energy cost

Benefits & Advantages

  • Reduced computational time for displacements prediction (32% of standard solutions with option #1, less than 1% + upfront cost for option 2)
  • Reduced necessary memory (4-7% of standard solutions with option #1, less than 1% for option 2)
  • Low memory usage allows parallel computations to determine response to substrate to all temperature loadings at the same time
  • Reduced computational time and memory allows more representative description of substrate heterogeneity for increased accuracy or process optimization