Lesson 1 named CMP as the step that planarizes a layer so the next layer's lithography has a flat surface to focus on, and lesson 1's worked example showed copper damascene relying on CMP to remove overburden copper. This lesson covers how CMP actually works, the equation that predicts how fast it removes material, and the two defect modes, dishing and erosion, that every CMP process has to control.
Reading time: about 8 minutes.
9.1 What CMP does
Chemical-mechanical planarization polishes the wafer surface using a combination of mechanical abrasion and chemical reaction together: the wafer, held face-down in a carrier, is pressed against a rotating polishing pad while a slurry, a liquid carrying fine abrasive particles and reactive chemicals, flows between pad and wafer. The chemistry softens or reacts with the surface film (for example, oxidizing copper into a more easily abraded compound), and the mechanical abrasion from the pad and slurry particles then removes that softened material. Neither half works well alone: pure mechanical abrasion without the right chemistry can scratch and damage the surface; the chemistry alone, without mechanical removal, would simply etch, not planarize.
The result, done correctly, is a surface flat enough across both small (die-scale) and large (wafer-scale) distances that the next layer's lithography can hold its depth-of-focus budget (lesson 3), which is the whole reason CMP exists in the per-layer loop.
9.2 The Preston equation
The material removal rate in CMP is commonly modeled by the Preston equation:
RR = Kp * P * Vwhere RR is the polish (removal) rate, P is the pressure the wafer is pressed against the pad with, V is the relative velocity between wafer and pad, and Kp is the Preston coefficient, an empirical constant that bundles together everything about the pad, slurry chemistry, and film material that is not already captured by pressure and velocity. Preston's equation was originally derived for glass polishing long before CMP existed, and it is an approximation, not an exact physical law for every material and condition, but it captures the first-order behavior CMP process engineers actually tune against: increase pressure or relative velocity, and removal rate goes up roughly proportionally, within the range where the approximation holds.
9.3 Pad and slurry
The polishing pad is a textured polymer (commonly polyurethane) with a pattern of grooves cut into its surface; the grooves carry fresh slurry in and spent slurry and removed material out from under the wafer as it polishes. Pads wear with use, and their surface texture (conditioned periodically with a diamond conditioning disk during polishing) directly affects removal rate and uniformity, which is why pad condition is itself a controlled process variable, not just a consumable swapped on a fixed schedule.
Slurry composition is tuned per application: a copper slurry is formulated to chemically soften and remove copper (and, for a barrier/liner film beneath it, is often switched to a different slurry formulation for a second polish step) while being far less aggressive toward the surrounding dielectric, so that polishing stops cleanly at the dielectric surface rather than continuing to remove it; a shallow-trench-isolation (STI) slurry for oxide polishing is tuned the opposite way, aggressive toward oxide, far less aggressive toward the nitride film commonly used as a polish-stop layer in STI.
9.4 Dishing and erosion
Real patterns are not uniformly one material; a copper damascene layer, for example, has wide copper lines next to narrow ones, and dense arrays of lines next to isolated ones. Two related defect modes appear when polish rate is not perfectly uniform across these different local patterns:
- Dishing: over-polishing of a wide feature (for example a wide copper line or bond pad), where the soft copper in the middle of a wide feature erodes faster than the surrounding, harder dielectric, leaving the center of the feature polished lower than its edges, a dish-shaped depression.
- Erosion: thinning of the dielectric itself in a densely patterned region, where the higher fraction of soft copper in a dense array causes the local effective removal rate to be higher than in a sparse or all-dielectric region, eroding the dielectric surface lower in dense areas than in sparse ones.
Both effects leave a non-flat surface exactly where CMP was supposed to produce a flat one, which both degrades the next layer's lithography depth-of-focus margin, and, for copper specifically, can thin the copper line enough to raise its resistance measurably, a timing and reliability concern, not just a cosmetic flatness one.
| Aspect | Dishing | Erosion |
|---|---|---|
| Where it happens | Within one wide feature | Across a densely patterned region |
| Cause | Soft copper center polishes faster than harder dielectric edges | Higher local copper fraction raises effective removal rate |
| What thins | Center of the wide copper line/pad | The dielectric between dense lines |
9.5 Worked example: Preston equation sensitivity
Assumptions: illustrative numbers only, Preston coefficient and velocity held fixed while pressure is varied, within the pressure range where the linear Preston approximation holds for this film and slurry.
- Starting removal rate at pressure P: RR = Kp x P x V.
- Doubling pressure to 2P, holding Kp and V fixed: RR_new = Kp x 2P x V = 2 x RR, so removal rate roughly doubles.
- In practice, CMP process engineers rarely push pressure as the main lever for a large rate increase, because higher pressure also tends to worsen dishing and erosion (the same pressure that removes copper faster in the field also presses harder into a soft, wide copper feature's center); rate is more often tuned through slurry chemistry and pad conditioning instead, trading Kp rather than P, precisely to avoid that trade-off.
9.6 Interview questions
Write the Preston equation and explain each term. RR = Kp x P x V: RR is polish removal rate, P is the pressure pressing the wafer against the pad, V is the relative wafer-pad velocity, and Kp is an empirical coefficient bundling pad, slurry and film-specific effects.
Why does CMP need both chemistry and mechanical abrasion, not just one? Chemistry alone would etch the surface without planarizing it; mechanical abrasion alone, without the chemistry softening or reacting with the film, risks scratching and surface damage. The combination removes material through softened, mechanically-abraded material.
What is dishing, and what causes it? A depression in the center of a wide soft feature (for example a wide copper line), caused by the center polishing faster than the surrounding harder dielectric at its edges.
What is erosion, and how does it differ from dishing? Thinning of the dielectric surface specifically in densely patterned regions, caused by a higher local fraction of soft material raising the effective removal rate there; dishing happens within a single wide feature, erosion happens across a dense pattern region.
Why might a process engineer prefer tuning slurry chemistry over pressure to raise removal rate? Raising pressure tends to worsen dishing and erosion, since the same higher pressure that speeds removal in the field also presses harder into soft, wide features; tuning the Preston coefficient through slurry chemistry or pad conditioning can raise rate without that same trade-off.
Key takeaways
- CMP combines chemistry (softening/reacting with the film) and mechanical abrasion (pad and slurry particles) to remove material and flatten the surface.
- The Preston equation, RR = Kp x P x V, models removal rate as proportional to pressure and velocity, through an empirical coefficient.
- Slurry chemistry is tuned to be selective: fast on the target film (copper, or oxide for STI), slow on the surrounding or stop-layer material.
- Dishing over-polishes the center of wide soft features; erosion thins the dielectric in densely patterned regions; both degrade flatness and, for copper, raise resistance.
- CMP's whole purpose in the per-layer loop is protecting the next layer's lithography depth-of-focus budget.