Eddy Current

Eddy-current metrology uses electromagnetic coupling to examine a conductive film without electrical probe contact. An alternating current in a coil produces a changing magnetic field. That field induces circulating currents in a nearby conductor, whose response alters the electrical behavior measured by the sensing system. A calibrated model relates this response to properties such as sheet conductance or film thickness.

The method does not directly count nanometers. Its response can depend on conductivity, thickness, probe spacing, frequency, substrate, and geometry. Reliable measurement requires separating the property of interest from other influences, not simply assuming that every signal change means a thickness change.

The conductor becomes part of a coupled system. The induced currents generate a secondary magnetic field that reacts against the change that produced them. Depending on the instrument, the measured quantity may involve coil impedance or a receive-coil response. Both amplitude and phase can contain information. The currents reverse as the excitation alternates; they are not a steady flow in one fixed direction.

A coil above a conductive film couples electromagnetically to induced circulating currents Sense the film without touching it Schematic perspective, not a field simulation AC coil Lift-off Induced currents circulate in the conductive film Current direction reverses during the AC cycle

The gap between the sensor and specimen is called lift-off. Changes in that gap can change coupling even when the film is unchanged. Wafer bow, positioning, probe geometry, and edge proximity can therefore matter. Calibration or compensation must cover the intended setup; there is no universal stand-off distance that applies to every eddy-current instrument.

Sheet resistance is not thickness by itself. For a uniform film of resistivity ρ and thickness t, sheet resistance is Rs = ρ/t, and sheet conductance is Gs = σt = 1/Rs, where σ = 1/ρ. In an appropriate thin-film regime, the response is strongly related to this conductance. Converting it into thickness requires a justified resistivity value or additional independent information.

A thin film with higher conductivity can have the same sheet conductance as a thicker film with lower conductivity One conductance, two thicknesses Ideal uniform films, both in the thin-film regime Conductivity σ Conductivity σ/2 Thickness t Thickness 2t σ × t = (σ/2) × 2t Same sheet conductance does not prove equal thickness

Film resistivity can differ from a bulk handbook value because of microstructure, composition, temperature, and size-related scattering. If the assumed resistivity changes, the inferred thickness changes even at the same measured sheet resistance. Report whether a map represents an electrical property or a thickness inferred using a particular material model.

Frequency changes how deeply the field penetrates. In the ideal homogeneous, thick-conductor approximation, skin depth is δ = 1/√(πfμσ), where f is frequency, μ magnetic permeability, and σ conductivity. The current-density amplitude falls to about 37% of its surface value at one skin depth. Skin depth is a decay scale, not a sharp boundary beyond which the signal disappears.

Normalized current amplitude decays more rapidly with depth at higher frequency in the same homogeneous conductor Frequency changes the depth scale Ideal thick conductor; amplitude normalized at surface Current amplitude Lower frequency Higher frequency Depth into conductor → Higher f → smaller δ, for fixed μ and σ

When a film is much thinner than the relevant penetration scale, its finite thickness and underlying stack must be treated explicitly. The thick-conductor exponential is not a complete model for every wafer film. Multiple frequencies can add information, but do not guarantee that several unknown layer thicknesses and conductivities can be uniquely separated.

The current paths depend on the sample geometry. A continuous blanket metal film is different from a patterned network of narrow, isolated features. Patterning can interrupt or redirect the circulating currents. Conductive underlayers or a conductive substrate can contribute to the response, while finite sample edges alter the field and current distribution. A blanket-film calibration should not be applied blindly to a patterned multilayer stack.

An insulating layer does not itself support the same conduction-current response as a metal film, but it can change separation from an underlying conductor. Thus, “not directly measuring an insulating film” does not mean that insulating layers are irrelevant to the measurement setup.

Useful applications need a defined measurement model. Eddy-current techniques can support conductive-film mapping and metal-thickness monitoring, including suitable CMP applications. An in-situ sensor follows changing process conditions, while an ex-situ mapper measures selected wafer locations after processing. Their calibration, environmental constraints, and interpretation are not automatically interchangeable.

A map also has a spatial footprint and sampling plan. The sensor integrates a response over a region rather than measuring an infinitesimal point. Site spacing, edge exclusion, and probe footprint determine which variations can be resolved. A smooth interpolated wafer map is not evidence that every point was measured.

Non-contact is an advantage, not a blanket accuracy guarantee. Removing contact tips avoids one source of surface marking and contact variability. It does not eliminate lift-off error, drift, stack sensitivity, or model bias. Qualification should establish the useful range, repeatability, calibration stability, and comparison with an appropriate independent reference for the actual material system.

The key idea: eddy-current metrology senses a conductor's electromagnetic response. Thickness becomes a trustworthy result only when conductivity, geometry, spacing, and the layer stack are sufficiently known or independently constrained.

Sources: KLA Filmetrics eddy-current methodology and metal-film mapping documentation; Eddyfi skin-depth explanation; research on equivalent thin-structure eddy-current responses. Illustrations are model explanations, not measured wafer data or operating settings.

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