# Material Removal Model for Lapping Process Based on Spiral Groove Density
## 1 Introduction  
Semiconductors are manufactured by depositing an epitaxial layer on single-crystal wafers through the metal-organic chemical vapor deposition (MOCVD) process and fabricating electrically functional components on the epitaxial layer [1]. As the demand continues to grow for single-crystal wafers, such as SiC and GaN wafers used in power semiconductors, sapphire wafers used in LEDs, and silicon wafers used in memory, the manufacturing processes for semiconductor wafers are becoming more important [2]. To manufacture wafers for semiconductors, the raw material is melted at a high temperature and grown into single-crystal ingots. The grown ingots are then cut into thin wafers through the multiwire sawing process and polished flat through the double-sided and single-sided lapping processes. Subsequently, the defect layers made in the previous lapping processes are eliminated through chemical-mechanical polishing (CMP) to prepare epi-ready wafers [3; 4; 5; 6; 7]. In the single-sided lapping process, material is removed as abrasive particles in a slurry pass over and scratch the surface of the wafer during the relative rotational motion of the wafer and platen while pressure is applied to the wafer [8; 9]. The lapping process is the last process that determines the thickness and thickness variation of a wafer. If the thickness variation of the wafer is large, it will be out of the depth of field (DOF) in the lithography process. Therefore, a thickness variation that satisfies the DOF is essential. On the other hand, the dimensional accuracy required for a 100 mm diameter wafer is now much stricter at 1-2 \(\upmu\)m, compared to the previous requirement of 5 \(\upmu\)m. As wafers increase in diameter, further improvements in thickness variation and material removal rate arerequired to ensure price competitiveness of wafers; consequently, the lapping process has gained the attention of researchers. It is difficult to control and improve lapping characteristics such as thickness variation and material removal rate because they are affected by various parameters [10]. Therefore, it is necessary to identify and study the most influential lapping parameters and find a method to control these parameters to improve the lapping characteristics. [PERSON] [11] presented a material removal model by investigating the material removal mechanism based on parameters such as the abrasive size, abrasive shape, and hardness of platens and workpieces. [PERSON] [12] conducted a study on the relationship between abrasive size and material removal rate during the polishing process for quartz crystals, while [PERSON] [13] and [PERSON] [14] studied the effect of the platen material on the material removal rate and surface roughness in the lapping process. [PERSON] [15] and [PERSON] [16] suggested a modified model of the Preston equation for the material removal rate. [PERSON] [17] presented a distribution model for hydrodynamic pressure and contact pressure based on pad grooves in the CMP process using the Reynolds equation and reported that the movement of the slurry and the number of participating abrasives varied with different pad grooves, which in turn affected the material removal rate. Studies related to grooves are mostly limited to the process conditions or slurry movement based on the grooves used in the CMP process. As a result, it is difficult to understand the effect of grooves on the lapping process through these studies, and there is insufficient research on the effect of platen grooves. In this study, the parameters to describe grooves were defined in order to understand their influence on the lapping process, and a material removal model was suggested based on the indentation theory that was then experimentally validated. The probability of abrasive participation in the lapping process was introduced by observing the changes in the frictional force and oil film thickness at the contact interface between the wafer and platen as a function of the platen groove.