Study On Uniformity Of Particle Trajectories With Irrational Rotational Ratio In Lapping And Polishing

As an important method to obtain high precision surface such as optical element,sapphire substrate and single crystal silicon substrate,lapping and polishing have been widely used in the fields of electronic communication,computer and laser.With the increase of the size of the silicon wafer and the increasing of the degree of integration,the flatness of the silicon wafer and the requirement of the global planarization are also getting higher and higher.In order to improve the accuracy of the surface shape of silicon wafer,this study put forward a new kind of driving mode in lapping and polishing process,namely,a method for lapping and polishing with irrational rotating ratio.The machining method breaks the periodicity of particle track,and improves the surface quality of silicon wafer.Aiming to the problem that particle sliding trajectories with rational rotational speed ratio is periodic,the trajectory simulations are carried out based on the kinematic analysis.Numerical simulations of particle sliding trajectories are performed to examine the influence of the kinematic parameters on the polishing uniformity of typical rotary-type lapping equipment.A method of plane lapping with irrational rotational speed ratio was presented.The kinematic analysis and numerical calculation were used to discuss the effect of the rotating speed ratio on the trajectory uniformity and the lapping plate with preferred helix arrangement of fixed particle was selected.The results indicate that,the trajectory distribution with irrational rotational speed ratio is more intensive and complicate than that with rational rotational speed ratio.For different irrational rotational speed ratio,the uniformity of trajectory distribution increases with increasing of rotational speed ratio gradually but it is more uniform with increasing of lapping time.The research provides theoretical guide to the design and development of new plan lapping equipment with condition of irrational rotating speed ratio.The method of region girding is improved;a distorting the film edge is solved;a new statistical method is put forward,namely,the total trajectory length of all particles sliding over one mesh area of the wafer is calculated;variation coefficient CV is used to evaluate the trajectory uniformity.The paper provides theoretical guide to the design and development of new plan lapping equipment with condition of irrational rotating speed ratio.