Etch Sidewall Angle Budget

# Etch Sidewall Angle Budget

An etch sidewall angle budget connects opening depth and wall taper to the bottom critical dimension that must remain usable. It complements a top-CD budget: two openings with the same top width can have different bottom widths when their wall angles differ.

## Define the geometry first

This guide considers a symmetric trench cross-section with straight walls that narrow inward with depth. The wall angle is measured relative to the wafer plane, so 90 degrees means vertical. Some documents instead report deviation from vertical; state the convention before using any angle value.

The drawing is an opening in surrounding material, not a retained material line. A tapered material pillar can have a different top-to-bottom width relationship. Top width, bottom width and depth must refer to specified measurement locations; corner rounding can make an unspecified edge location ambiguous.

## Calculate the bottom-width change

For this symmetric straight-wall opening, each wall moves inward by depth divided by tan(angle). Therefore:

Bottom width = top width - 2 × depth / tan(angle).

Use a consistent angle unit when evaluating the tangent. The factor of two counts both walls. The expression applies to the defined geometry, not to every etched profile.

For a 120 nm top opening and a 500 nm depth, a vertical wall leaves a 120 nm bottom opening. At 89 degrees, each wall moves inward about 8.73 nm and the bottom width becomes about 102.5 nm. At 88 degrees, the bottom width falls to about 85.1 nm. These values come from geometry, not a measured etch recipe.

If the example requires at least 100 nm at the bottom, the total narrowing allowance is 20 nm, or 10 nm per wall under symmetry. The angle must be at least arctan(500/10), approximately 88.85 degrees, within this model. That result holds only for the assumed 120 nm top width and 500 nm depth.

## Carry top width and depth into the budget

A smaller incoming top width or greater depth reduces the bottom width at the same inward taper. If those quantities vary, calculate the combinations allowed by the stated bounds rather than using only their nominal values. Do not assume variation in top CD, depth and angle is independent without evidence.

Do not treat a nominal 89-degree angle as a demonstrated pass simply because the nominal calculated width is 102.5 nm. The remaining 2.5 nm above the illustrative minimum must also accommodate the relevant geometry variation and uncertainty. A specification may require other dimensions or electrical behavior as well.

## Know when a single angle is insufficient

Bowing, footing, notching, roughness and left/right asymmetry are not captured by one symmetric straight-wall angle. A local minimum opening can matter more than the angle fitted over the full depth. If the equation predicts a zero or negative width, the assumed open straight-wall geometry is no longer physically available; a negative result is a model warning, not a real opening size.

Profile-sensitive measurements are needed to check the model. Top-down CD alone does not establish a buried bottom width. Cross-section imaging or suitable three-dimensional/profile metrology can provide additional information, subject to preparation, accessibility, calibration and uncertainty.

## Connect the budget to the next step

A contact opening needs a usable landing and a geometry compatible with subsequent liner and fill. A trench may require a particular taper for deposition, isolation or mechanical reasons. There is no universal sidewall angle that is ideal for every integration.

Budget the bottom opening that the next step actually needs, then verify the complete profile. Angle is a useful descriptor only when its definition and the geometry behind it are clear.

## Sources and scope

• [NIST — Atomic-force microscopy](https://www.nist.gov/programs-projects/atomic-force-microscopy): dimensional and sidewall-profile metrology.
• [NIST — Contour Metrology using Critical Dimension Atomic Force Microscopy](https://www.nist.gov/publications/contour-metrology-using-critical-dimension-atomic-force-microscopy): extraction of sidewall and contour data.
• [Oxford Instruments — Profile Control for Slanted Etching](https://plasma.oxinst.com/media-centre/wp/augmented-reality-profile-control-for-slanted-etching): an example where a deliberately angled profile is part of the process objective.

Original diagrams and calculated geometry example. Dimensions and limits are teaching values, not a production specification.