Physics-Based Acoustic Wave Modeling and Subsurface Warpage Reconstruction for Advanced Semiconductor Packages

/ Physics-Based Acoustic Wave Modeling and Subsurface Warpage Reconstruction for Advanced Semiconductor Packages

Physics-Based Acoustic Wave Modeling and Subsurface Warpage Reconstruction for Advanced Semiconductor Packages

Advance Physics-Based Digital Twins for Non-Destructive Characterization of Next-Generation Semiconductor Packages.

Title: Physics-Based Acoustic Wave Modeling and Subsurface WarpageReconstruction for Advanced Semiconductor Packages

Technical Description:

Astransistor scaling approaches its physical limits, advanced packaging hasbecome essential to drive semiconductor performance, system integration, andreliability beyond traditional Moore's Law. These dense architectures subjectthin silicon dies to severe thermo-mechanical stresses, leading to packagewarpage, solder fatigue, and interfacial delamination. Standard industrialwarpage metrology tools, such as mechanical stylus profilometers and opticalinterferometers (e.g., shadow moiré), are strictly limited to measuring theexterior topside surface of the package. They remain blind to buried,subsurface interfaces, such as the silicon‑to‑underfill junction.

ScanningAcoustic Microscopy (SAM) is highly used in the industry for non‑destructivedefect screening, but it can also be used as a powerful metrology tool. Recent studieshave demonstrated that high‑frequency time‑of‑flight (ToF) acoustic data can beleveraged beyond defect identification to reconstruct full three‑dimensionalcurvature maps of both topside and subsurface die interfaces in Flip‑Chip BallGrid Array (FCBGA) packages. While topside acoustic reconstructions show closeagreement with high‑precision stylus profilometry, significant measurementuncertainties emerge near die‑underfill boundaries. Furthermore, a systematicdifference observed between the extracted topside and backside warpage profileswarrants deeper physical investigation. Resolving whether this divergence stemsprimarily from asymmetric thermo‑mechanical stresses or from acoustic beamrefraction across curved interfaces requires a comprehensive forward acousticsimulation framework that models non‑perpendicular wave incidence andtransducer physics.

Objectives:

Currentacoustic warpage reconstruction models assume planar, normal incidence wavepropagation evaluated via one‑dimensional Transfer Matrix Method (TMM). Thissimplification breaks down when physical acoustic artifacts are introduced(e.g., edge scattering, lens aberrations, non‑normal incidence). Key objectivesfor this project include:

• Extend current 1D forward acoustic simulation framework intoa multi‑dimensional wave propagation model that accounts for focused beamgeometry, lens aberrations, non‑normal incidence angles, and interfacialrefraction.
• Quantitatively decouple acoustic path distortion(refraction/lens effects) from thermo‑mechanical stress effects (metallizationlayers and underfill‑induced asymmetric strain).
• Develop an edge‑correction post‑processing algorithm torecover valid ToF warpage maps across the full die perimeter without excessiveboundary trimming.
• Evaluate method accuracy and limitations for measuringsub‑surface warpage in different types of packages

References:

[1]M. Gomes Abrantes, J. Gutierrez, U. Raia, K. Baumans, P. De Pauw, and H.Zahedmanesh, "Beyond Defect Detection: Using Scanning Acoustic Microscopy(SAM) to Measure Subsurface Warpage in Flip‑Chip Packages," presented atthe 37th European Symposium on Reliability of Electron Devices, Failure Physicsand Analysis (ESREF), Sep. 2026.

[2]A. Atalar, “An angular‑spectra approach to contrast in reflection,” Journal ofApplied Physics, vol. 49, no. 10, pp. 5130–5139, 1978.

[3]C. S. Lee, G.-M. Zhang, D. M. Harvey, and H.-W. Ma, “Development of c‑line plottechnique for the characterization of edge effects in acoustic imaging: A casestudy using flip chip package geometry,” Microelectronics Reliability, vol. 55,no. 12, Part B, pp. 2762– 2768, 2015. [Online]. Available:https://www.sciencedirect.com/science/ article/pii/S0026271415301414.

[4]C. H. Hsueh, S. Lee, and T. J. Chuang, “An alternative method of solvingmultilayer bending problems,” Journal of Applied Mechanics, vol. 70, no. 1, pp.151–154, 2003.

[5]J. S. S. T. Association, “Jesd22‑b112c: Package warpage measurement ofsurface‑mount integrated circuits at elevated temperature,” JEDEC, Arlington,VA, USA, Tech. Rep., 2023.

Desired Qualifications:

• Strong mathematical foundation in wave propagation,acoustics, or physical optics.
• Proficient in Python (NumPy, SciPy, Matplotlib); experiencewith vector acoustics or finite‑difference time‑domain (FDTD) simulation is an asset.
• Interest in hands‑on cleanroom/lab metrology (SAM, surfaceprofilometry).

Type of internship: Master internship, PhD internship

Durat