Fig. 6: Quantitative model precision analysis of IMC-layer growth and Kirkendall pore area increase for real and generated images, comprising seen, unseen and unknown datapoints.

a Physics-based validation workflow for -DDPM generated microstructural images of unknown sample conditions. Three images are generated for each unknown sample condition. Since the C-DDPM generates images from random noise, the three generated images are not identical for each sample condition, resulting in some degree of variation. The microstructural features are manually labelled, extracted based on those labels, and quantified in terms of IMC-layer thickness and Kirkendall pore area. These quantities are further utilised for the C-DDPM validation. The physics-based model validation is elaborated in b–e for all sample conditions, i.e. seen, unseen and unknown. Therein, the microstructural evolution at Cu–SAC305 interfaces during isothermal ageing at 150 °C is quantitatively analysed. The IMC-layer growths and Kirkendall pore area increases, dependent on the impurity content in the Cu metallisation, are plotted and the parabolic growth rates are determined and compared for real and generated images. PVD-Cu is plotted in green, ECD1-Cu in blue, ECD2-Cu in purple and ECD3-Cu in pink. b, d Cumulative (Cu₆Sn₅ + Cu₃Sn) layer growth. c, e Kirkendall pore area increases. b, c Mean values of the real images are shown as squares, square-root fits of these mean values as dashed lines and standard deviations as shaded areas versus the ageing time. The respective values of the three generated images for each sample condition are shown as circles (seen conditions) and triangles (unseen and unknown conditions). d, e Separate linear fitting of mean data from real and generated images and determination of parabolic growth rates versus the square root of ageing time.