A 3D EHL Simulation of CMP

Abstract

The extensive application of chemical mechanical polishing ͑CMP͒ in the semiconductor industry requires an understanding of the fundamental mechanisms involved. This paper integrates a group of mechanical models to give a framework for CMP modeling: a mixed three-dimensional ͑3D͒ soft elastohydrodynamic lubrication ͑EHL͒ model with asperity contact considered. The soft-pad mechanics, asperity-contact analysis, and slurry film description are three major components of this framework. Based on the results of a thin-layer contact analysis, the Winkler foundation model is selected to evaluate the pad deformation in bulk. By applying the macro-micro approach, the macroscopic view of the average fluid film thickness ͑average clearance͒ is related to microasperity contact. When CMP is implemented in a mixed lubrication regime, the soft polishing pad usually undergoes a displacement of the same scale as the slurry film, which may change the lubrication boundary considerably. Considering this effect, a modified Reynolds equation is derived, and a stronger coupling is found in the global force and moment balances. Finally, an effective iterative scheme is proposed and modeling results examined.Chemical mechanical polishing ͑CMP͒ is currently used to achieve global planarization over a long length/thickness scale and is being widely applied in the semiconductor industry. During a CMP process, a rotating wafer is pressed face down onto a moving, resilient thin polishing pad, while a polishing slurry containing abrasive particles and chemical reagents flows between the wafer and pad. The extensive utilization of CMP in integrated circuit ͑IC͒ manufacturing requires deep understanding of the CMP mechanisms.Nanz and Camilletti 1 presented a critical review of the CMP models developed prior to 1995 for pad bending, nonplanarity of a wafer, the effect of pad asperities, and slurry flow. Whereas various working conditions may weigh differently due to the factors mentioned previously, it is axiomatic that the contact between the polishing pad and the wafer is determined by the clearance between them. Bhushan et al. 2 pointed out that three contact scenarios, namely, direct contact, nondirect contact, and semidirect contact, may appear at the pad-wafer interface in CMP. Chekina et al. 3 developed an analytical solution for wafer surface evolution in a steady state on the basis of elastic contact mechanics. Zhao and Chang 4 developed an abrasive wear model for CMP on the basis of elastic-plastic microcontact mechanics. They first estimated a relationship among the real area of contact, the number of particles participating in wafer material removal, and the particle indentation depth into the wafer surface, and then derived a closed-form formula to address the material removal rate ͑MRR͒. Runnels and Eyman presented a nondirect-contact model for CMP based on a waferscale slurry flow analysis. 5 Supposing the wafer is completely separated from the polishing pad by the flowing slurry, the slightly tilted wafer with a curvature allows a...

Modeling and calculation of slurry-chemistry effects on chemical–mechanical planarization with a grooved pad

“…So, strictly speaking, the wafer-surface tilting has to be taken into account in the model to ensure that the resultant moment with respect to the ball joint due to the contact stress, fluid pressure, and friction acting on the wafer surface is zero. However, since the tilting angle of the wafer surface usually is extremely small (on the order of a few micro radians in the calculations of Jin et al [12]), for simplicity we will not explicitly consider the moment balance here.…”

“…A number of other theoretical models exist in the literature (e.g., [10][11][12]), each considering certain aspects of the CMP process. To our knowledge, one of the simplest models that calculates the contact stress on the pad-wafer interface, which then determines the slurry-film thickness, was proposed by Shan et al [11] for CMP with a flat pad.…”

Modelling of delamination of ultra low-k material during chemical mechanical polishing

“…Most existing models e.g. [12,[19][20][21][22] have treated the polishing pad according to the Greenwood-Williamson theory [23] as a rough engineering surface with protruding asperities whose heights follow the Gaussian distribution. The asperities are assumed to be capped with spherical peaks of uniform radius.…”

“…Equation (20) shows that the probability P 0 that no defects in the wafer fail is a function only of the critical number of contacts n c , the mean number of asperity contacts k and the total number of defects N w . Alternatively, the mean number of asperity contacts k required for a given probability of delamination (here taken for the polishing tests as 50%), can be found given n c and N w .…”

“…Then the micro-tribometer test, with a Hertz pressure p m the same as " p gives the critical number of contacts to failure n c , while equation (15) provides the defect density q d . Equation (20) is used to calculate the mean number of asperity contacts k to give a 50% chance of delamination failure, and equation (21) gives the corresponding time t. The defect length ' is the only parameter that has to be obtained by estimation in this statistical model. Figure 14 summarises the above algorithm, showing the calculation procedure for predicting the polishing time to delamination in the polishing experiments based on the micro-tribometer experimental results.…”