Fine grinding of silicon wafers: a mathematical model for grinding marks

The majority of today’s integrated circuits are constructed on silicon wafers. Fine-grinding process has great potential to improve wafer quality at a low cost. Three papers on fine grinding were previously published in this journal. The first paper discussed its uniqueness and special requirements. The second one presented the results of a designed experimental investigation. The third paper developed a mathematical model for the chuck shape, addressing one of the technical barriers that have hindered the widespread application of this technology: difficulty and uncertainty in chuck preparation. As a follow up, this paper addresses another technical barrier: lack of understanding on grinding marks. A mathematical model to predict the locus of the grinding lines and the distance between two adjacent grinding lines is first developed. With the developed model, the relationships between grinding marks and various process parameters (wheel rotational speed, chuck rotational speed, and wheel diameter) are then discussed. Finally, results of pilot experiments to verify the model are discussed.