Measuring Resistivity and Film Thickness

Using Resistivity to Estimate Film Thickness

Relationship Between Resistivity and Thickness

Some applications require tracking how etching or polishing changes the thickness of a coating or metal film on a substrate. For example, engineers may need to compare copper or aluminum structures on silicon before and after etching. If they want to avoid damaging the sample with a contact-based film-thickness profiler such as an alpha-step instrument, electrical measurements may provide another way to estimate thickness.

The Delcom resistivity measurement instrument represented by Fulcrum Technology does not directly measure bulk resistivity. It measures the sheet conductance of a conductive layer.

When a material has a uniform thickness and that thickness is known, the measured sheet conductance can be used to calculate resistivity. The instrument can measure, record, display, and map the electrical response across the material.

Conversely, the instrument does not directly measure thickness. If the material has uniform resistivity and its resistivity is known, sheet-conductance measurements can be used to estimate thickness and create a thickness map.

For a uniform conductive film, sheet resistance Rs is related to bulk resistivity ρ and thickness t by:

Rs = ρ / t

Sheet conductance is the reciprocal of sheet resistance, so:

t = ρ × sheet conductance

This calculation is meaningful only when the material properties and measurement conditions are suitable and sufficiently uniform. Confirm the resistivity value for the specific material, composition, temperature, and process before using the result as a thickness estimate.

Reference Resistivity Values

The following values are reproduced from the source article as approximate reference data at 20°C. Actual values can vary with purity, composition, processing, and test conditions; verify the appropriate value for your sample before using it in calculations.

Material — Resistivity (Ω·m)
Graphene — 1.00 × 10⁻⁸
Silver — 1.59 × 10⁻⁸
Copper — 1.7 × 10⁻⁸
Gold — 2.44 × 10⁻⁸
Aluminum — 2.82 × 10⁻⁸
Tungsten — 5.6 × 10⁻⁸
Brass — 8 × 10⁻⁸
Iron — 1.0 × 10⁻⁷
Platinum — 1.1 × 10⁻⁷
Lead — 2.2 × 10⁻⁷
Mercury — 9.8 × 10⁻⁷
Nichrome — 1.10 × 10⁻⁶
Germanium — 4.6 × 10⁻¹
Silicon — 6.40 × 10²

Reference condition: 20°C.

Need help estimating conductive-film thickness?

Contact Fulcrum Technology to discuss your material, known resistivity, measurement conditions, and whether a Delcom sheet-conductance measurement can support your application.