A calculating method for the fewest cutting passes on sapphire substrate at a certain depth using specific down force energy with an AFM probe

This paper proposes the innovative concept of specific down force energy (SDFE) and applies it to nanoscale multi-pass cutting using an atomic force microscopy (AFM) probe as a cutting tool. This paper defines SDFE as the down force energy dividing the volume of material removed of the workpiece by the AFM probe. Experimental data and the calculation results indicate that the SDFE values of different down forces and in different cutting passes are close to a constant value. Adopting the SDFE theory, this paper calculates objective functions through step-by-step adjustments of the increased cutting depth under some constraint conditions. These conditions require that the shape of probe is already known and is within the range of machinable down force of probe, and that the requirement of convergence error functions of SDFE and objective cutting depth are met. This paper uses the proposed method to identify the fewest cutting passes that can achieve the objective cutting depth under suitable down force action. Finally, this paper reports experiments using an AFM probe cutting tool to carry out nanoscale cutting experiments on the surface of sapphire substrate for cutting nanoscale V-shaped grooves in different cutting passes under different down force actions. This study compares the cutting depth values of different nanoscale grooves in the central area with the theoretically calculated results. A comparison of these results shows that the down force and cutting passes required to achieve the objective cutting depth using the proposed method are very close to experimental results using the same down force and cutting passes. These results verify the feasibility of the proposed method in finding the fewest cutting passes for cutting a specific depth using an AFM probe.