Copper CMP Removal Rate: Preston Equation, Key Variables & Practical Optimization

1. Why Copper CMP Removal Rate Matters

In a high-volume 300 mm fab, the CMP module is typically one of the top three throughput bottlenecks in the BEOL process flow. A copper CMP Step 1 process that must remove 600 nm of copper at 200 nm/min will occupy a polishing head for three minutes — while a process achieving 400 nm/min completes the same job in 90 seconds, doubling effective tool capacity. At a production scale of tens of thousands of wafer starts per month, this difference translates directly into capital expenditure (fewer CMP tools needed) and operational cost (lower cost per wafer).

However, removal rate cannot be maximized in isolation. Three coupled performance metrics constrain the operating envelope:

• Within-wafer non-uniformity (WIWNU): A higher removal rate achieved through excessive pressure often comes at the cost of worse WIWNU — the radial and azimuthal variation in copper thickness remaining after polishing.
• Defect count: Aggressive polishing conditions (high pressure, high velocity, excess oxidizer) increase surface scratch density and micro-roughness.
• Dishing and erosion: Over-fast Step 1 processes that over-shoot the endpoint leave too little copper for Step 2 to clear uniformly, or — if the endpoint is mistimed — expose the barrier metal prematurely, causing topographic disturbance.

The practical optimization goal is to find the highest removal rate that keeps all three secondary metrics within their process specifications simultaneously.

2. The Preston Equation: Foundation and Limitations

The Preston equation, originally developed for glass polishing in the 1920s, remains the foundational model for CMP removal rate:

where RR is the material removal rate (nm/min), K_p is the Preston coefficient (a material- and slurry-specific proportionality constant, units of nm·min⁻¹·kPa⁻¹·(m/s)⁻¹), P is the applied downforce pressure (kPa), and V is the relative velocity between the wafer and pad surface (m/s).

For copper CMP, the Preston equation is useful as a first-order model but fails in several important regimes:

• Chemical saturation: Above a threshold oxidizer concentration, the copper surface becomes fully oxidized between asperity contact events, and further increasing oxidizer concentration does not increase RR — only static etch rate. The model predicts linear RR increase with oxidizer concentration, which is not observed experimentally.
• High-pressure non-linearity: Above approximately 5 psi (34 kPa), the pad’s elastic contact mechanics change, the slurry hydrodynamic film between pad and wafer collapses, and RR increases more slowly than the Preston model predicts.
• Low-pressure chemical dominance: Below approximately 0.5 psi (3.5 kPa) — required for ELK dielectric compatibility at advanced nodes — chemical dissolution becomes rate-limiting rather than mechanical abrasion, and the mechanical term in the Preston equation underweights the chemical contribution.

A more accurate model for copper CMP uses a modified Langmuir-Hinshelwood kinetic framework that treats the oxidation, passivation, and mechanical removal as parallel rate processes, each with its own concentration and pressure dependence. In practice, however, the Preston equation remains the standard for first-pass process window estimation and fab-to-fab transfer because of its simplicity and the limited availability of kinetic constants for the full mechanistic model.

3. Chemical Contribution to Removal Rate

The chemical component of copper CMP removal rate is determined primarily by the slurry’s oxidizer concentration, complexing agent activity, and corrosion inhibitor loading. These three parameters define the chemical removal rate envelope — the maximum rate achievable at any given mechanical condition.

Oxidizer Concentration Effects

Within the optimal range (typically 1–3 wt% H₂O₂ for most copper CMP formulations), increasing oxidizer concentration increases both static etch rate and dynamic removal rate proportionally. The optimal oxidizer concentration is defined as the point where dynamic RR is maximized without static etch rate exceeding the dishing specification — typically <1 nm/min SER.

The oxidizer optimum shifts with other formulation parameters: higher BTA loading requires higher H₂O₂ to overcome the passivation layer’s resistance, and lower pH generally allows lower oxidizer concentrations to achieve the same removal rate due to enhanced Cu²⁺ solubility in acidic conditions.

BTA Loading and Its Inverse Relationship with RR

BTA acts as a removal rate suppressant as well as a corrosion inhibitor — by forming a mechanically resistant passivation layer, it effectively requires greater mechanical energy to disrupt and achieve material removal. This inverse relationship between BTA concentration and removal rate is one of the most important process knobs in copper CMP:

• At low BTA loading (0.001–0.005 wt%): high removal rate, high static etch rate, poor dishing control
• At optimal BTA loading (0.01–0.05 wt%): balanced removal rate, SER <1 nm/min, good dishing control
• At high BTA loading (>0.1 wt%): low removal rate, very low SER, but process becomes throughput-limited

Complexing Agent Influence

Higher complexing agent (glycine) concentration increases removal rate by driving the Cu ion dissolution equilibrium forward more aggressively. However, as noted in the chemistry cluster article, glycine competes with BTA for copper surface sites, so increasing glycine concentration effectively shifts the optimal BTA concentration upward. In practical formulation work, glycine and BTA concentrations are co-optimized as a pair rather than as independent variables.

4. Mechanical Parameters: Pressure, Velocity & Pad State

The mechanical parameters of the CMP process — downforce pressure, rotation speeds, and pad condition state — directly control the K_p × P × V product in the Preston equation and are the primary tools available to the process engineer for in-fab removal rate adjustment without reformulating the slurry.

Downforce Pressure

Downforce is the most direct lever for removal rate adjustment. In the Preston-linear regime (0.5–5 psi for most copper CMP slurries), every 10% increase in downforce produces approximately a 10% increase in removal rate. Multi-zone carrier heads on production 300 mm CMP tools allow independent pressure control across 4–7 concentric wafer zones, enabling non-uniform pressure profiles that compensate for radial removal rate gradients and reduce WIWNU.

At advanced nodes with ELK dielectric stacks, the maximum allowable downforce is constrained to <1 psi (6.9 kPa) to prevent dielectric cracking and delamination. This constraint fundamentally limits throughput and requires slurry chemistry to compensate through enhanced chemical activity — a significant formulation challenge that has driven the development of JEEZ’s CuELK low-pressure slurry series.

Rotational Velocity

Both platen and carrier rotation speeds contribute to the relative velocity V. Standard copper CMP operates at 60–120 rpm for both. The velocity distribution across a 300 mm wafer is inherently non-uniform due to the kinematics of orbital motion — the wafer center experiences lower relative velocity than the edge for any fixed platen and carrier RPM combination. This velocity non-uniformity is a primary contributor to WIWNU and is managed through:

• Differential platen and carrier RPM settings that optimize the velocity uniformity profile
• Multi-zone carrier pressure profiling that compensates for velocity-driven removal rate gradients
• Slurry formulations with reduced K_p pressure-sensitivity that minimize the amplification of velocity non-uniformity into removal rate non-uniformity

Pad Condition State and Conditioning

The polishing pad’s effective hardness and asperity height distribution — its “condition state” — is a major determinant of K_p and therefore of removal rate at any given P and V. A freshly conditioned pad has high asperity density and relatively high K_p; a glazed pad (asperities flattened by sustained polishing without conditioning) has a much lower effective K_p and reduced slurry transport capacity.

In-situ conditioning with a rotating diamond disk maintains pad condition state during polishing, but the aggressive conditioning needed for high removal rate stability accelerates pad wear and increases pad debris — a defect risk. The optimal conditioning recipe balances removal rate stability against pad lifetime and defect count: typically expressed as a conditioning sweep rate (mm/s), disc RPM, and disc downforce. These parameters must be co-optimized with the slurry formulation, as different slurry chemistries produce different pad surface interactions and wear characteristics.

5. Slurry Flow Rate & POU Delivery

Slurry flow rate determines the replenishment of fresh oxidizer and complexing agent at the pad-wafer interface and the removal rate of polishing byproducts (Cu²⁺ ions, BTA-Cu complex, abraded particle debris). Slurry starvation — insufficient flow to maintain fresh chemistry at the interface — is one of the most common causes of unexplained removal rate loss and WIWNU degradation in production copper CMP processes.

Signs of slurry starvation include: removal rate that is lower at wafer center than edge (center of the wafer is the last point reached by freshly dispensed slurry), WIWNU that improves when flow rate is increased, and removal rate drift over the course of a polishing run as pad grooves become filled with slurry byproducts.

Typical optimal slurry flow rates for 300 mm copper CMP are 150–250 mL/min at the pad surface. For H₂O₂-based slurries, POU mixing systems combine the slurry base concentrate and oxidizer at the dispense arm. The POU mixing ratio (slurry base : H₂O₂ : DIW) is a critical process parameter that must be precisely controlled through mass-flow controllers rather than volumetric flow control, as the density difference between concentrated H₂O₂ and slurry base can cause metering errors if volumetric measurement is used.

6. WIWNU Optimization Strategies

Within-wafer non-uniformity (WIWNU) in copper CMP is measured as the standard deviation of copper thickness (or removal depth) across all measured sites on the wafer, normalized to the mean, expressed as a percentage: WIWNU (%) = σ / mean × 100. Production targets are typically WIWNU <3% (1σ) for 300 mm copper CMP.

WIWNU is driven by a combination of factors that must be addressed systematically:

APC (advanced process control) run-to-run control is the most powerful tool for maintaining WIWNU within specification across a production lot. By measuring post-CMP copper thickness profiles after each wafer and feeding back adjustments to carrier zone pressures and polishing time, APC systems can compensate for tool-to-tool variation, pad aging effects, and lot-to-lot slurry concentration variation — maintaining <3% WIWNU even as process conditions drift.

7. Advanced-Node Constraints on Removal Rate

At 7 nm and below, the freedom to tune removal rate through pressure is severely constrained by ELK dielectric fragility. This forces slurry formulators to compensate chemically — and creates a different optimization problem than conventional copper CMP.

At <1 psi polishing pressure, removal rate in a Preston-regime slurry drops to <100 nm/min — far below what is needed for economically viable throughput on 600+ nm copper overburden. JEEZ’s CuELK series addresses this by using enhanced chemical activity formulations: slightly higher H₂O₂ concentration (3–5 wt%), optimized glycine loading, and reduced BTA concentration at the lower end of the dishing-safe window. These formulations achieve 180–250 nm/min removal rate at 0.7 psi by increasing the chemical contribution to K_p — effectively boosting the “chemical Preston coefficient” while keeping mechanical pressure below the ELK damage threshold.

The tradeoff is tighter process window: with higher oxidizer and lower BTA loading, the margin between optimal and excessive dishing is narrower, requiring tighter endpoint detection (typically eddy-current APC rather than friction-based endpoint) and more precise run-to-run time control.

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8. Frequently Asked Questions