Slurry film thickness

Sundararajan et al. [131] in 1999 calculated the slurry film thickness and hydrodynamic pressure in CMP by solving the Re5molds equation. The abrasive particles undergo rotational and linear motion in the shear flow. This motion of the abrasive particles enhances the dissolution rate of the surface by facilitating the liquid phase convective mass transfer of the dissolved copper species away from the wafer surface. It is proposed that the enhancement in the polish rate is directly proportional to the product of abrasive concentration and the shear stress on the wafer surface. Hence, the ratio of the polish rate with abrasive to the polish rate without abrasive can be written as... 

Coppeta et al. [10] made slurry film measurements during using laser-induced fluorescence. By addition of a fluorescent dye to the polishing slurry film thickness was experimentally from the fluorescence intensity of the lubrication film as measured through a transparent substrate. Film thickness measurements were in good agreement with those of Levert et al. [7,8]. This technique can also be used to study slurry transport across the wafer surface, diameter variation in lubrication film thickness, and slurry mixing effects [11]. 

Levert, J., Mess, F., Grote, L., Dmytrychenko, M., Cook, L., Danyluk, S. (1995). Slurry film thickness measurements in float and semipermeable and permeable polishing pad geometries. Proc. Int. TYiboiogy Conf., Yokahama. 

Lu J, Rogers C, Manno VP, Philipossian A, Anjur S, Moinpour M. Measurements of slurry film thickness and wafer drag during CMP. Electrochem Soc 2004 151 (4) G241-G247. 

Figure 1.5 Illustration of CMP with different slurry film thickness [8]. (a) CMP with thinner slurry film and (b) CMP with thicker slurry film.

Y. Moon, D.A. Domfeld, The effect of slurry film thickness variation in chemical mechanical polishing (CMP), Proc. Am. Soc. Precision Eng. 18 (1998) 591—596. G.S. Grover, H. Liang, S. Ganeshkumar, W. Foitino, Effect of slurry viscosity modification on oxide and tungsten CMP, Wear 214 (1) (1997) 10—13. 

It is therefore necessary to determine the slurry film thickness under the various sawing conditions. The hydrodynamic behavior of slurry films has been studied in lubrication or polishing processes, where many fundamental aspects have been derived from experimental and theoretical results [15, 16]. An important aspect is that the wire, and to some extent the crystal, can deform elastically in response to the slurry pressure. Considering that the wires are thin and long it is very likely that mainly the elastic response of the wire has to be considered when the slurry transport is analyzed. In the following the main aspects of the problem are derived from a one-dimensional treatment of the hydrodynamic slurry transport below a flexible wire. 

Fig. 18.6 Numerical calculation of the slurry film thickness h x) along the wire length. The parameters are given in the text.

For a given slurry film thickness the total applied force is the sum of both terms Ftot(ho) = F j(Ho) + Ffo((ho) according to Eq. (18.17). Depending on the distance, either the particles or the slurry carries the main load of the wire. It is assumed that the best sawing conditions occur in the region where both curves intersect, since this allows both high material-removal rates due to particle contact and good particle transport in the slurry. 

Particles with a diameter I greater than the slurry film thickness ho are in contact both with the crystal and the workpiece surface. Their number m can be calculated in the same way as before from Eq. (18.19). Therefore, one obtains the same equation (Eq. (18.21)) for the material-removal rate. However, the number of particles that are in direct contact, the effective total force Ff, and thus the material-removal rate will be different from the wire-sawing case. 

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