Etch Depth Uniformity Budget

# Etch Depth Uniformity Budget

An etch depth uniformity budget checks both spatial depth variation and distance from the required depth limits. It defines the sampling plan and the reported metric, then asks whether the measured result and its uncertainty support acceptance.

The loading-budget entry concerns pattern-dependent clearing. This guide focuses on depth measurements across a defined wafer sample. A depth map can reveal spatial differences without, by itself, proving their physical cause.

## Keep the map, not just the mean

Record the depth at each specified site together with its wafer position and feature geometry. A useful comparison holds the intended structure and measurement definition consistent; otherwise layout differences can be mixed with wafer-position effects.

For these invented equally weighted measurements, the values are 96, 98, 100, 102 and 104 nm. Their arithmetic mean is 100 nm, the minimum is 96 nm, and the maximum is 104 nm. The map is a teaching example rather than a recommended five-site production sampling plan.

An equal-weight sample mean is not automatically an area-weighted wafer mean. Unmeasured sites may contain excursions, and a few radial points may miss an azimuthal or localized pattern. Record the sampling coverage and any excluded edge region explicitly.

## Define the uniformity formula

One possible sampled nonuniformity metric is 100 × (maximum - minimum) / (2 × sample mean). With the example values, this is 100 × 8 / 200 = 4%. Here 4% describes the sampled half-range normalized to its mean.

Other documents may quote full range divided by mean, a standard-deviation-based statistic, or a different site set. These are not interchangeable. State the formula, site count, edge exclusion and measured quantity whenever reporting a uniformity percentage. Depth uniformity also differs from etch-rate uniformity when incoming thickness, time or measurement conditions differ.

## Uniformity alone does not establish a pass

Suppose the illustrative depth specification is 95-105 nm. All five initial measurements lie inside that interval. Now shift every sample upward by 2 nm, producing 98, 100, 102, 104 and 106 nm.

The shifted mean is 102 nm and the absolute range remains 8 nm. Using the same half-range formula, normalized nonuniformity is about 3.92%, slightly smaller than before. Nevertheless, the 106 nm sample exceeds the assumed upper limit. A favorable relative uniformity statistic cannot replace checking the absolute specification.

Conversely, centering the mean on target does not prove that the shallowest and deepest sites pass. Track both the location of the sampled range and its width. The numbers here establish only the arithmetic of the stated sample, not a wafer-level pass probability or process capability.

## Allocate an absolute depth window

For a deterministic sampled check, compare the minimum and maximum with the lower and upper limits. Account for the relevant measurement uncertainty and the acceptance rule used by the process; a nominal point just inside a limit may not provide enough evidence for acceptance.

Incoming structure variation, etch response, recipe transitions and measurement effects may contribute to the result. Do not add an incoming-thickness variation term blindly to a measured etched-depth range if that influence is already included in the final measurement or if the depth definition is independent of it. Define the measurement model first.

A fixed tolerance should not be divided into mean shift and spatial variation without stating how the allocations are applied. If statistical models are used instead of bounded intervals, define the populations, correlations and sampling assumptions explicitly.

## Investigate and verify spatial behavior

Compare maps across wafers, runs and relevant pattern classes. Center-to-edge trends, left-to-right differences and local excursions call for different evidence; none should be diagnosed solely from a single scalar uniformity value. Tool state, incoming conditions, pattern loading and thermal or plasma conditions can be possible influences, depending on the integration.

Check profile, CD and protected-layer integrity alongside depth when they are acceptance requirements. A depth map cannot establish sidewall quality or electrical behavior by itself.

A useful depth budget preserves the measured map, defines its statistic and checks the absolute limits. Keep sampling and uncertainty visible in the conclusion.

## Sources and scope

• [Lam Research — Evolution of Uniformity Control](https://newsroom.lamresearch.com/Evolution-of-Uniformity-Control-Looking-Back-and-Peeking-Ahead): within-wafer and edge uniformity context.
• [Lam Research — Edge Control Solutions](https://newsroom.lamresearch.com/Lam-Extends-Leadership-in-Edge-Control-Solutions): wafer-edge control considerations.
• [NIST-hosted research — Plasma etching uniformity control for large and thick dual-focus zone plates](https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=905958): an application-specific example of cross-substrate measurements and uniformity control.

Original wafer map, comparison graph and arithmetic examples. Site positions, depths and limits are illustrative rather than a qualified metrology or manufacturing plan.