{'fraction_non_alphanumeric': 0.018832391713747645, 'fraction_numerical': 0.0049435028248587575, 'mean_word_length': 5.184861717612809, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A Material Removal Model for CMP Based on the Contact Mechanics of Pad, Abrasives, and Wafer

Applied pressure in chemical mechanical polishing CMP is shared by the two-body pad–wafer and the three-body pad–abrasive– wafer contacts. The fraction of applied pressure transferred through the particle contacts is a significant factor as most of the material removal is due to abrasive particles trapped in the pad–wafer interface. In this work, the contact of a rough, deformable pad and a smooth, rigid wafer with rigid particles in the contact interface is investigated by using contact mechanics and finite element modeling. The interactions between the pad, wafer, and abrasive particles are modeled at different scales of contact, starting from the particle–pad level and gradually expanding to the multiasperity contact of the pad and the wafer. Wear rate due to each abrasive particle is calculated based on the wafer–abrasive particle contact force and by considering adhesive and abrasive wear mechanisms. A thin passivated layer on the wafer surface is modeled to consider the effect of chemical reactions between slurry and wafer. Good agreement between the model and the experimental literature is found for the relationships between material removal rate and applied pressure, pad elastic modulus and porosity, particle size and concentration, and pad roughness and wafer hardness. Chemical mechanical polishing CMP is a polishing method commonly used in the manufacturing of wafer-based integrated circuits ICs. Since CMP was first introduced to the IC manufacturing in the mid-1980s by IBM, CMP became a key technology in generating planar surfaces for several semiconductor manufacturing processes. 1 CMP operation involves forcing a rotating wafer attached to a wafer carrier against a rotating polishing pad. The polishing pad is covered with liquid slurry, which contains abrasive particles. The chemical reactions between the CMP slurry and the wafer are the primary driver for preparing the surface for polishing. The chemical composition of the surface is modified by the chemically reactive slurry to favor higher wear rates. In addition to the chemical interactions, the pad–wafer interface experiences the effects of contact and lubrication. Three-body contact due to the abrasive particles caught between the pad and the wafer and two-body contact between the pad and the wafer provide the necessary physical force to remove the material from the wafer surface. While solidbody contact is taking place, the pad–wafer interface experiences the lubricating effect of the slurry flow. The abrasive particles used in conventional polishing techniques are 2.5–3 times harder than the workpiece material. These techniques cause scratches and pitting on the surface and cracks in the subsurface of the workpiece. The passivation of the surface layer of the wafer workpiece is important to achieve smooth and planarized surfaces without any surface and subsurface defects. 2 For this reason, an effective CMP process should provide a balance between the chemical and mechanical effects. The Preston equation is widely used to calculate the material removal rate MRR, which is given as follows 3 RR = kPPoVr 1 where RR is the removal rate with units of material depth/time, kP is the Preston constant, Po is the average push-down pressure, and Vr is the relative sliding velocity of the surfaces. The Preston equation indicates a linear variation in MRR with respect to applied pressure and relative velocity. There are various experimental studies indicating both linear and nonlinear applied pressure Po relationships. 4-10 Also, kP is typically determined experimentally, and it conveniently includes the effects of other parameters that influence the outcome of polishing. In this paper, we present a mechanistic model of the MRR in CMP. A hierarchical model of the particle–wafer–pad interactions, presented recently, 11 was combined with abrasive and adhesive wear models to obtain a wafer-level MRR model based on particle-level interactions. The predictions of the model were compared with published experimental data. Material removal models were developed by considering a contact regime in the pad–wafer interface. 2,12-14