Modeling the Effects of Polishing Pressure and Speed on CMP Rates
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MODELING THE EFFECTS OF POLISHING PRESSURE AND SPEED ON CMP RATES Ed Paul Stockton College, Pomona NJ 08240 Abstract: In a previous CMP model, the effects of the slurry concentration of chemicals and abrasives on the polishing rate were quantitatively explained, for constant polishing pressure and velocity. That model is extended here to consider specific descriptions of mechanical abrasion, involving polishing pressures and speeds. Predictions of behavior are compared to literature data, leading to an improved understanding of the abrasive process in CMP. Introduction: A theory of Chemical Mechanical Polishing (CMP) has been developed1 which treats the overall process as a series of 4 steps: (1) formation of a surface complex through a chemical reaction between the workpiece surface and components of the slurry, (2) the reverse reaction of decomposition of the surface complex, (3) dissolution of the surface complex into the slurry, and (4) mechanical abrasion of the surface complex. This theory has led to an expression for the polishing rate as a function of various chemical kinetic and mechanical parameters. The elementary reactions and reaction rates involved in this process are shown in Table 1. Table 1. Elementary Reactions and Rate Equations
Å Å Å
WC* W+C W+C WC* WC* W + WC(aq) W + A-WC(aq) WC* + A
r1f = k1f nW [C] r1r = k1r nWC* rD = kD nWC* rM = τ kM nA nWC*
Å
(1) (2) (3) (4)
Here W is the workpiece material, [C] is the concentration of chemical in the slurry and WC* is the surface complex formed in the reaction. A is an abrasive particle on the surface of the pad while both WC(aq) and A-WC(aq) represent complexes that have separated from the workpiece and are in the slurry either freely or associated with an abrasive particle. ri is the rate and ki is the rate constant of step i. The subscript notation 1f and 1r stands for forward and reverse chemical reaction, D is for dissolution, and M is for mechanical abrasion. The mechanical parameter τ is for the thickness of material removed in this step. The number of surface particles is nW for workpiece atoms, nWC* for chemical complexes on the workpiece and nA for active abrasive particles on the pad. Using standard methods of chemical kinetics, the removal rate per unit area R is the sum of the dissolution and mechanical abrasion rates, and is proportional to the number of surface complexes nWC*. Using the relationship no = nW + nWC* = A/Ao between the total number of workpiece sites no, the total workpiece area A, and the area per site Ao, leads to steady state expressions for nWC* and the polishing rate R. R = ( kD nWC* + τ kM nA nWC* ) / A
and
nWC* =
k1f no [C] k1f [C]+ k1r + kD + kM nA
This leads to an expression for R as a function of experimental variables [C] and kM nA M4.8.1
(5)
R=
(1 / Ao )(kD + τ kM nA ) k1f[C] k1f[C] + kD + k1r + kM nA
= Ro +
a[C ] b + [C ]
(6)
Previous work1 successfully compared this theory of the dependence of polishing rate R on the slurry concentrations of chemical and abrasive to literature data for tungsten C
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