Abrasive size distribution and active abrasives 

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... of the material removal mechanism in chemical mechanical polishing (CMP) should be based on understanding the roles of the cutting tools, or namely, the abrasives, and their interactions with other important input values such as the pad, chemical and wafer materials. The effect of abrasive size distribution in the chemical-mechanical polishing has long been observed ([1]- [4]). Experimental results show that there is a reversal proportional relationship between the abrasive size and the material removal rate ( MRR ) when the abrasive weight concentration is constant ([2]–[3]). Connections between the size distribution and the scratching of wafer surface have also been observed and reported [4]. Although qualitative explanations of the roles of abrasive size distribution in CMP have been proposed, however, to clarify their roles, a quantitative explanation is needed. Recently, a comprehensive model to explain the fundamental mechanism and interactions ([5]-[6]) of consumable parameters in solid-solid contact of CMP, including the abrasive size and size distribution, has been developed by Luo and Dornfeld [5]. It is principally based on three assumptions: a regular pad topography, normal distribution of abrasive size and plastic deformations over the wafer-abrasive and pad-abrasive interfaces (two-body abrasion). One core idea of the model is that the effects of the consumables on material removal can be attributed to two sources, one the number of active abrasive number, and the other the material removed by a single abrasive. The later is a function of the abrasive size. According to the model, only part of abrasives, or namely, the active abrasives are involved in the material removal process, Figure 1 [5-6]. For an abrasive to be ‘ active’, there are two conditions to be satisfied. First, it should be located on the contact area between the wafer and pad. The number of abrasives there is proportional to the weight concentration of abrasives in the slurry. Secondly, the abrasive should be large enough. When the force is applied on the wafer top surface, the wafer will contact with the largest abrasives first. A gap is formed between the pad and wafer surface in the neighborhood of the larger abrasives. Only abrasives larger than this gap can participate in material removal. Apparently, the distribution function affects both the size of active abrasives, and therefore the volume removed by a single abrasive, and the number of active abrasives. In [5-6], material removal formulations as functions of the process parameters including the down pressure and velocity as well as consumable parameters including the abrasive size distribution have been proposed. The non-linear down pressure dependence of material removal rate is attributed to the abrasive size distribution and elastic deformations of the polishing pad. The model predictions correlate with the experimental results of MRR as a function of down pressure quite well [5]. To fully verify the roles of the abrasive size distributions proposed in the material removal model, however, experimental results of MRR as a function of abrasive size distribution are preferred. Recently, tungsten (W) CMP experiments have been done by Bielmann et. al. [3]. They measured five different kinds of abrasive size distribution and obtained MRR under these five size distributions. In this paper, we discuss how the model prediction correlates with these experimental results. A detailed view of wafer-abrasive-pad contact is proposed to explain the roles of the abrasive size distribution. Material removal rate formulation as a function of abrasive size distribution has been developed and verified using the published experimental results. We propose the following detailed view of wafer-pad- abrasive contact, which has been discussed briefly in [5-6]. First, it is proposed that only part of the pad contacts the wafer directly. This part of pad is called the contact area. This view of wafer-pad contact is shown schematically in Fig. 2 (a). The relationship between the down pressure P 0 , contact pressure P and contact area A can be obtained based on contact model as shown in [5-6]. The contact area A and contact pressure P are determined by the down pressure, pad topography and pad materials. The active abrasives involved in the two-body abrasion will be sitting on the contact area, Fig. 2(b)-(e). Since the nano-scale active abrasives are much smaller than the micro-scale feature of the pad topography and the pad surface is quite soft, the final effective contact area A and contact pressure P in the situations where abrasives are embedded into the contact area, should be approximately equal to that without abrasives embedded in, Fig. 2 (e). We call the trend for this contact, which makes the effective contact area between the wafer and pad as close as possible to that without abrasives, the ‘stable contact”. From that the wafer begins to contact the pad and abrasives to that the final ‘stable contact’ is realized, there are four stages, Figs. 2 (b) – (d). Before the down pressure is applied on the wafer top surface, the abrasives with different sizes disperse on the pad contact area randomly, Fig. 2 (b). The number of abrasives located on the contact area is proportional to the abrasive weight concentration in the slurry [5-6]. Since no down pressure is applied on the wafer top surface, the wafer and pad are separated by abrasives and the gap g between them is equal to the size of the largest abrasives, Fig. 2 (b). Once down pressure is applied on the wafer top surface, it will be supported by abrasives only at first, Fig. 2 (c). The effective contact area is approximately equal to 0.25 π x avg 2 n , where n is the number of abrasives and x avg the average size of abrasives. The forces applied on each single abrasive are quite large in this stage and all the abrasives are embedded into the pad deeply. A very small gap is formed between the pad and wafer, Fig. 2 (c), which is determined by the pad hardness and force applied on the abrasives. The trend for wafer and pad to contact directly will push the abrasives to come together so that the effective contact area becomes closer to that without abrasives in, Fig. 2 (d). In this stage, some part of pad contact area is the direct contact between the wafer and pad, while other part of contact area is occupied by abrasives with closer relative locations, Fig. 2 (d). The force applied on each single abrasive becomes smaller and therefore the gap g’ between the wafer and pad in this area becomes larger. The abrasives smaller than this gap g’ will be pushed off the contact area. In this stage, however, the effective contact area, which is equal to the abrasive number times their average size plus the direct contact area A 1 , is still smaller than A , Fig. 2 (d). Therefore, the process to increase the direct contact between wafer and pad will continue until that all the abrasives finally comes together closely without gap existing between them, as shown in Fig. 2 (e). In this stage, the effective contact area, A 1 + A 2 , between wafer and pad is approximately equal to that without abrasives in. The direct contact area A 1 will not increase any more and a stable gap g is finally formed, Fig. 2 (e). The abrasives smaller than this gap have been pushed off the contact area in the process of Fig. 2 (b)-(e). From the above discussion, it can be seen that only part of abrasive is involved in the material removal process and the portion of these active abrasives is determined by the gap g, which is the bottom bound of the active abrasive size. In most situations the distribution of abrasive particles sizes (i.e. diameters), x , satisfies normal probability density functions as shown in earlier studies ...