Preston Equation Research Articles

Softness consolidation abrasives material removal characteristic oriented to laser hardening surface

The high hardness and irregular characteristics of laser hardening free-form surface bring many problems into the finishing process. A new autofinishing method based on softness consolidation abrasives (SCA), oriented to laser hardening surface, is brought forward. Abrasives are consolidated on the rubber bonnet by the polymer binder, which have micromovement under the elastic restraint to form stress concentration for cutting. By the modification of coefficients and stress, the material removal model is given by the modified Preston equation. According to a series of simulation and practical experiments, the size of abrasive, hardness of abrasive, and hardness of surface were derived as important factors for the material removal. The empirical results showed that the modified Preston equation is propitious to avoid errors for calculation. Compared with free abrasive methods, it demonstrated that SCA can help to improve at least 13.6 % of efficiency.

Ultrasmooth reaction-sintered silicon carbide surface resulting from combination of thermal oxidation and ceria slurry polishing

An ultrasmooth reaction-sintered silicon carbide surface with an rms roughness of 0.424 nm is obtained after thermal oxidation for 30 min followed by ceria slurry polishing for 30 min. By SEM-EDX analysis, we investigated the thermal oxidation behavior of RS-SiC, in which the main components are Si and SiC. As the oxidation rate is higher in the area with defects, there are no scratches or cracks on the surface after oxidation. However, a bumpy structure is formed after oxidation because the oxidation rates of Si and SiC differ. Through a theoretical analysis of thermal oxidation using the Deal-Grove model and the removal of the oxide layer by ceria slurry polishing in accordance with the Preston equation, a model for obtaining an ultrasmooth surface is proposed and the optimal processing conditions are presented.

Polisher density into Preston equation

For the polishing process, Preston (1927) [1] proposed wear, h, is proportional to the work given by a frictional force, ffr, on the glass. He assumed ffr does not depend on relative velocity, v, between the glass and the tool. Téllez et al. (2007) [2] found frictional force depends on v. We have experimentally found that fdr depends on relative velocity, v, and concentration, ρ, of the polisher suspension. Then Preston equation has to be modified i.e. h=h(ffr(v), ρ).

Soft-Consolidation Abrasives Pneumatic Wheel Technology Oriented to Finishing of High-Hardness Free-Form Surface

In order to improve the efficiency of high-hardness laser strengthening mold polishing, especially to the free-form surface, a new precision finishing method based on soft-consolidation abrasives pneumatic wheel is brought forward. The pneumatic wheel is constituded by flexible rubber maxtrix, combined with the robbet control. The abrasives group is bond to the rubber matrix by the polymer binder. In the way, compared with those free abrasives used in other polishing method, the soft-consolidation abrasives can get more stable surpport from nearby polymer to form effective cutting. On the other hand, it is unlike the abrasive of rigid grinding wheel because the flexibility of pneumatic wheel can have self-adaptation according to the changes in local curvature and achieve large scale copying contact between tools and work piece. Combined with the lay elastic system theory and Preston equation and coefficients, the mechanics model of polishing is given. The results of experiment shows the Ra of workpiece can be reached to 0.09um and the efficiency of process can be improved three times more than free abrasive machining. It will show its wild prospects in the process of polishing.

Impact of Pad Conditioning on Thickness Profile Control in Chemical Mechanical Planarization

Chemical mechanical planarization (CMP) has been proven to be the best method to achieve within-wafer and within-die uniformity for multilevel metallization. Decreasing device dimensions and increasing wafer sizes continuously demand better planarization, which necessitates better understanding of all the variables of the CMP process. A recently highlighted critical factor, pad conditioning, affects the pad surface profile and consequently the wafer profile; in addition, it reduces defects by refreshing the pad surface during polishing. This work demonstrates the changes in the postpolish wafer profile as a function of pad wear. It also introduces a wafer material removal rate profile model based on the locally relevant Preston equation by estimating the pad thickness profile as a function of polishing time. The result is a dynamic predictor of how the wafer removal rate profile shifts as the pad ages. The model helps fine-tune the pad conditioner operating characteristics without the requirement for costly and lengthy experiments. The accuracy of the model is demonstrated by experiments as well as data from a real production line. Both experimental data and simulations indicate that the smaller conditioning disk size and extended conditioning sweep range help improve the post-CMP wafer planarization. However, the defectivity tends to increase when the conditioning disk sweeps out of the pad radius; hence, the pad conditioning needs to be designed by considering the specific requirements of the CMP process conducted. The presented model predicts the process outcomes without requiring detailed experimentation.

Ballonet Polishing of Aspheric Part Based on MRF Torque Servo

This paper proposed a new ballonet polishing method for the precise polishing of aspheric parts. The method is based on the integration of a MRT (Magnetorheological fluid Torque servo)-based ballonet polishing tool system and a CNC lathe. By using this method, the decoupling control of force-position-posture can be realized in polishing process. The structure and working principle of the polishing tool system were introduced. The material removal model for ballonet polishing was established according to Preston Equation. The main factors affecting the material removal were discussed, and the control model of uniform removal was put forward.

Exploration on chemical mechanical planarization of ZnO functional thin films for novel devices

Zinc oxide (ZnO) is an attractive material for its application in the electronics, optics, acoustics, and sensor field. With the shrinking of minimum feature size of the devices and the increasing of devices function layers, surface planarization of each layer is demanded in the devices manufacturing. However, ZnO thin films deposited directly have high surface roughness which could cause device performance degradation. Therefore, ZnO thin films must be planarized in order to obtain high density and high integration devices. In this paper, chemical mechanical polishing (CMP) was used for ZnO thin films planarization, these films were deposited on 4inch Si blanket wafer by RF magnetron sputtering. The influence of the process parameters on CMP removal rate including pressure, platen speed was discussed, and the results demonstrated that removal rate still exist when there is no pressure and velocity, hence Preston equation was slightly modified. The effect of slurry pH on CMP removal rate was also investigated in detail after considering different corrosion rate of ZnO films in different solution. After optimizing CMP process parameter, the removal rate of ZnO films was up to 165.1nm/min, and the surface root mean square roughness was reduced from 16 to 1.9A.

Optimization of Slurry and Technological Parameter on Chemical Mechanical Polishing of Titanium Dioxide Film for IC

Titanium dioxide (TiO2) has shown a great potential to be used in resistive random access memory, capacitor, solar cell and sensor. However, the surface topography as-deposited TiO2 film cannot meet the requirement of IC. Therefore, TiO2 film must be flattened before apply into semiconductor device. In this paper, chemical mechanical polishing (CMP) was used for polishing TiO2 film. We studied the effect of slurry pH of polishing from the viewpoint of chemical we found the removal rate with acid slurry is lower than the removal rate obtained by alkali slurry. The effect of the process parameter such as down force, platen rotation rate were also studied in detail and found the removal rate still exist when there is no pressure and velocity, hence Preston equation was slightly modified. Final, the surface roughness was reduced from 36Aå to 1.2Aå, and the removal rate was up to 38.2nm/min.

Application of Multi-Mode Combined Polishing to Optical Manufacturing

The object of this study is the application of Multi-mode combined polishing, which is combination of polishing technology mode and current high-end CNC machining technology, to optical manufacturing. Detailed analysis and explanation of application of multi-mode combined polishing to optical manufacturing are made, from the perspectives of basic information and Preston equation of multi-mode combined polishing. And thus demonstrate the crucial role and significance of application of this technology in further promote and enhance the precision of optical processing operation efficiency.

An Analytical Model of Contact Pressure Caused by 2-D Wafer Topography in Chemical-Mechanical Polishing Process

Topography on wafer surface affects chemical-mechanical polishing (CMP) greatly. In this paper, wafer topography's effects on the contact pressure in CMP are investigated and calculated. It is found that the wafer can be treated as a rigid punch and pad as an elastic half space when the main frequencies of the topography on the wafer surface are high. Based on the linear small strain theory of elasticity, the formula of calculating the contact pressure between the wafer and the pad is given. The performance of CMP system is shown to be a linear time invariant (LTI) system in a mathematical way. The magnitude spectra and phase spectra of the system are obtained exactly by the formula. The result is consistent with numerical result obtained by finite element (FE) model. The removal rate at any point on the wafer surface is calculated by Preston's equation. The pattern structures with fixed line width and different line space is simulated based on the formula during overpolishing time. The simulation results fit the experimental data very well.

Effects of Curvature on Material Removal in NC Polishing of Aspheric Part

The objective of this paper is to investigate the effect of radius of curvature on the material removal in the NC polishing of aspheric part. The models of polishing pressure and material removal rates were established based on Preston equation and Hertz theory. The material removal rates was analyzed. Experiments were carried out. Results showed that the material removal rate varies with the variations of the curvature under a constant polishing force and velocity, and the part can not be polished uniformly.

Analytical method of softness abrasive two-phase flow field based on 2D model of LSM

To solve the precision machining problem in the structural surface mould manufacturing process, a new no-tool precision machining method based on softness abrasive flow machining (SAFM) is proposed. The key technology of SAFM is the characteristic analysis of two-phase flow. To solve this problem, a two-dimensional model of the two-phase flow is established by the topological structure transformation of level set method. This mechanics model is used to simulate the motion of the turbulent flow and work out the characteristic parameters of abrasive two-phase flow. The simulation results show that this model can preferably simulate the motion of the two-phase flow and calculate velocity and pressure with k- model and Preston equation. Therefore the feasibility of SAFM can be confirmed and a good reference can be provided for the further research.

Chemical Mechanical Planarization of Ruthenium with Oxone as Oxidizer

Potassium peroxymonosulfate (Oxone) was investigated as an oxidizing agent in silica based slurries for chemical mechanical planarization of Ru. Upon addition of oxone, the Ru removal rate increases significantly in the pH range of 1‐6. The slurry stability is poor at pH 3 and higher. At pH 2, oxone enhances the Ru removal rate even in the absence of abrasive, indicating that a soft film is formed on the Ru surface. Ru dissolution experiments show that the static etch rate is low. The Ru removal rate variation with pressure and velocity does not follow the Preston equation.

A Model of Chemical Mechanical Planarization to Predict Impact of Pad Conditioning on Process Performance

ABSTRACTThis study presents an effort to couple a wafer removal rate profile model based on the locally relevant Preston equation to the change in pad thickness profile which reflects to post polish profile of the wafers after Chemical Mechanical Planarization. The result is a dynamic predictor of how the wafer removal rate profile shifts as the pad ages. These predictions can be used to fine tune the conditioner operating characteristics without having to carry out high cost and time consuming experiments. The accuracy of the predictions is demonstrated by individual confirmation experiments in addition to the evaluation of the defectivity performance with the varied pad conditioning profiles.

Research on Parameters of Bonnet Polishing Based on FEA

In this paper, according to the bonnet polishing technology, in order to get the change regularity of the bonnet’s deformation, the inflated deformation model of the bonnet, which is made all of rubber or made of rubber but with a nylon enhancement layer, is established and analyzed by using the FEA simulation. And then, by simulating the process of the bonnet polishing the plane wafer, it achieves the contact pressure curve which varies with the bonnet decrement. According to the Preston equation, k can be acquired through the experiment, v can be achieved through mathematical modeling, and p has been achieved in this paper. Thus, the removal function based on FEA will be acquired.

A Study on Mathematical Modeling Technology for Magnetic-Fluid Grinding

The paper introduces the precision processing technology of grinding using magnetic fluid and presents the working mechanism of magnetic-fluid grinding. Based on Preston Equation, it also establishes a mathematical modeling for magnetic-fluid grinding, which is used to study the relationships between the effects of grinding and the variation of such technological parameters as the revolving speed of work-piece, the intensity of magnetic field, the distance between work-piece surface and magnetic center, the size of the magnetic fluid and grinding time, etc. Analysis on the grinding of Si3N4 ceramic-balls proves that the model has been well established.

Effect of Shape and Size of Polishing Pad on Material Removal Characteristic

The objective of this paper is to investigate the effect of shape and size of polishing pad on the material removal characteristics in the NC polishing. The material removal model was established based on Preston equation. The law of the effect of shape and size of polishing pad on the model was simulated. Experiments were carried out. Results showed that both of the shape and size of polishing pads influence the shape of material removal curves, polishing efficiency, and surface roughness. The amount of removed material increases with the increasing of size of polishing pad.

Investigation on Supersmooth Surface Machining with Stable Eccentric Immersed Polishing

In this paper stable eccentric immersed polishing is investigated according to Preston equation. The polishing trace, speed, density of polishing fluid etc were analyzed in detail. The polishing practicability of the technology was verified for polishing a piece of zerodur and the supersmooth surface with the flatness of PV0.04μm was obtained. The roughness of the surface has decreased to Ra0.37nm from initial Ra1.5nm after polishing 120 minutes.

Research on Material Removal Characteristics in Plane Lapping Method for Aspherical Surface Using Elastic Deformation

Plane lapping method using the elasticity of materials has many advantages comparing with current machining method for aspherical surface machining. Due to the deformation of the workpiece, the material removal characteristics of this method are different from the traditional lapping process of flat surface. In this paper, based on the Preston equation and plate theory, the theoretical model of the material remove rate is built in the case of proving experiment. Then the proving experiment of elastic deformation method is carried out, the recorded values fit well with theoretical ones, which shows that the theoretical model of material removal property is valid and the variation of MRR is related to the deformed profile of workpiece.

Effect of mechanical process parameters on friction behavior and material removal during sapphire chemical mechanical polishing

The effect of mechanical process parameters such as down force and rotation speed on friction behavior and material removal rate (MRR) was investigated during chemical mechanical polishing (CMP) of sapphire substrate. It was found that the increase in both rotation speed and down force can enhance the MRR and friction force almost linearly depends on the down force and rotation speed. The coefficient of friction (COF) decreases with increasing rotation speed under a fixed down force but keeps constant regardless of variation in down force under a fixed rotation speed. Moreover, the relationship between friction force and MRR was obtained. MRR was proportional to friction force with increasing down force whereas converse proportional to that with increasing the rotation speed. In addition, MRR data are fitted to the Preston equation in the sapphire CMP.