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

Title: Physics-Based Acoustic Wave Modeling and Subsurface Warpage Reconstruction for Advanced Semiconductor Packages Technical Description: As transistor scaling approaches its physical limits, advanced packaging has become essential to drive semiconductor performance, system integration, and reliability beyond traditional Moore's Law. These dense architectures subject thin silicon dies to severe thermo-mechanical stresses, leading to package warpage, solder fatigue, and interfacial delamination. Standard industrial warpage metrology tools, such as mechanical stylus profilometers and optical interferometers (e.g., shadow moiré), are strictly limited to measuring the exterior topside surface of the package. They remain blind to buried, subsurface interfaces, such as the silicon-to-underfill junction. Scanning Acoustic Microscopy (SAM) is highly used in the industry for non-destructive defect screening, but it can also be used as a powerful metrology tool. Recent studies have demonstrated that high-frequency time-of-flight (ToF) acoustic data can be leveraged beyond defect identification to reconstruct full three-dimensional curvature maps of both topside and subsurface die interfaces in Flip-Chip Ball Grid Array (FCBGA) packages. While topside acoustic reconstructions show close agreement with high-precision stylus profilometry, significant measurement uncertainties emerge near die-underfill boundaries. Furthermore, a systematic difference observed between the extracted topside and backside warpage profiles warrants deeper physical investigation. Resolving whether this divergence stems primarily from asymmetric thermo-mechanical stresses or from acoustic beam refraction across curved interfaces requires a comprehensive forward acoustic simulation framework that models non-perpendicular wave incidence and transducer physics. Schematic illustration of the basic operating principles of scanning acoustic microscopy (SAM). The transmitted waves are identified by the letter T, and the reflected waves by the letter R. The initial transducer pulse is identified by Pin. Figure extracted from [1] (a) Dektak measurements (20 mm span) and best-fit curve extrapolated to full die diagonal span (22.62 mm). (b) Diagonal cross-section of Dektak best-fit vs. SAM best-fit. Figure extracted from [1]. Objectives: Current acoustic warpage reconstruction models assume planar, normal incidence wave propagation evaluated via one-dimensional Transfer Matrix Method (TMM). This simplification breaks down when physical acoustic artifacts are introduced (e.g., edge scattering, lens aberrations, non-normal incidence). Key objectives for this project include: Extend current 1D forward acoustic simulation framework into a multi-dimensional wave propagation model that accounts for focused beam geometry, lens aberrations, non-normal incidence angles, and interfacial refraction. Quantitatively decouple acoustic path distortion (refraction/lens effects) from thermo-mechanical stress effects (metallization layers and underfill-induced asymmetric strain). Develop an edge-correction post-processing algorithm to recover valid ToF warpage maps across the full die perimeter without excessive boundary trimming. Evaluate method accuracy and limitations for measuring sub-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 at the 37th European Symposium on Reliability of Electron Devices, Failure Physics and Analysis (ESREF), Sep. 2026. [2] A. Atalar, “An angular-spectrum approach to contrast in reflection,” Journal of Applied 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 plot technique for the characterization of edge effects in acoustic imaging: A case study 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 solving multilayer 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 of surface-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); experience with vector acoustics or finite-difference time-domain (FDTD) simulation is an asset. Interest in hands-on cleanroom/lab metrology (SAM, surface profilometry). Contact: Jeffrey.gutierrez@imec.be Type of internship : Master internship, PhD internship Duration : 6 months to 1 year Required educational background : Electromechanical engineering, Electrotechnics/Electrical Engineering, Materials Engineering, Mechanical Engineering, Nanoscience & Nanotechnology, Physics, Other University promotor : Houman Zahedmanesh (KU Leuven) Supervising scientist(s) : For further information or for application, please contact Jeffrey Gutierrez ( Jeffrey.Gutierrez@imec.be ) The reference code for this position is 2026-INT-329 . Mention this reference code in your application. Imec allowance will be provided. Applications should include the following information: resume motivation current study Incomplete applications will not be considered