Kitstead Labs
Electroplating
Copper Electroplating: Thickness, Charge, and Faraday's Law
A copper electroplating thickness calculation needs a geometry model, an electrochemical basis and clear units. This guide derives charge from a target deposit, then adds explicitly supplied current density and area to estimate time. A synthetic round-pillar example makes each conversion visible and separates the general law from the narrower inputs offered by PlatingMate Web.
Quick answer
Faraday’s law converts charge into copper mass through molar mass, electron count and current efficiency. Density converts mass into volume; geometry converts volume into thickness. Time additionally needs current, and an assumed efficiency does not establish actual bath performance.
From electron transfer to deposited volume
For Cu²⁺ + 2e⁻ → Cu, two moles of electrons deposit one mole of copper at ideal efficiency. Faraday's law relates total charge to deposited mass. It does not by itself predict local current distribution, roughness or the detailed shape of a deposit.
Let Q be charge in coulombs (C), I current in amperes (A), t time in seconds, M = 0.063546 kg/mol the copper molar mass, z = 2 the electron count, F = 96485.33212 C/mol the rounded Faraday constant, and η the current efficiency as a fraction. Here 95% means 0.95, not 95. Use bulk copper density ρ = 8960 kg/m³ as a modeling assumption.
Q = ρVzF / (ηM); Q = It (constant current)
Thickness, charge and time equations
For a uniform planar layer over deposited area Adeposit, V = Adeposith. Substitution gives the forward and inverse thickness formulas below. The units must remain consistent: meters and square meters with SI density and molar mass.
Q = ρAdeposit h zF / (ηM)
t = Q / I; h = ηItM / (ρAdeposit zF)
For ideal round pillars of diameter D, deposited height H and count N, use V = NπD²H/4 instead. Neither formula automatically defines the effective area used by the current-density recipe. Keep geometry and electrical drive inputs explicit.
Worked example: synthetic copper round pillars
Assume 100,000 identical ideal cylinders, each 50 µm in diameter with 20 µm of new copper height. Assume η = 0.95, constant current, bulk density and all modeled copper charge assigned to this population. These are synthetic planning inputs, not a measured bath calibration or process recipe.
| Input | Engineering value | SI value |
|---|---|---|
| Count N | 100,000 pillars | 100,000 |
| Diameter D | 50 µm | 50 × 10⁻⁶ m |
| Height H | 20 µm | 20 × 10⁻⁶ m |
| Efficiency η | 95% | 0.95 |
| Operating current density J | 2 A/dm² (2 ASD) | 200 A/m² |
| Effective plating area Aeff | 0.5 dm² (50 cm²) | 0.005 m² |
V = 3.926991 × 10⁻⁹ m³ = 3.926991 mm³
m = 8960 × V = 3.518584 × 10⁻⁵ kg = 0.035186 g
Q ≈ 112.473 C = 0.0312424 Ah
I = J × Aeff = 2 × 0.5 = 1.0 A
t = Q / I ≈ 112.473 s = 1.87455 min
Check the result by inserting I × t back into the mass equation, then dividing by density and the total pillar cross-sectional area. This recovers the requested 20 µm height. One ampere-hour is 3600 C. One ASD is 1 A/dm² = 100 A/m².
The 0.5 dm² effective area is a separately supplied electrical input, not an area inferred from pillar diameters. This result requires the entered ASD and area to imply the current delivered to the modeled deposition population. If current also plates unmodeled surfaces, or the equipment's ASD area basis differs, reconcile that allocation before using the time. The result is a charge budget and conditional time estimate, not a uniformity guarantee.
Why actual thickness can differ
Total mass can agree with Faraday's law while edge and center thicknesses differ. Current distribution, shielding, transport, evolving geometry and side reactions can change local deposition. Efficiency may vary with operating conditions. A nominal efficiency setting is an assumption until measurement supports it.
The ideal-cylinder model describes newly deposited copper. Counting an existing seed or underlayer as new plated height overstates the charge demand. Diameter errors matter strongly because cylinder volume depends on D². Do not report many decimal places as evidence of physical accuracy.
Current density and optional time estimation
Charge follows the specified copper volume and efficiency. Supplying ASD and effective area adds a current estimate and therefore a time estimate; increasing ASD alone does not reduce the modeled required charge. For variable current, Q is the time integral of current, and a constant-current duration may not represent ramped or pulsed operation.
Use the released PlatingMate Web scope
PlatingMate Web Plan supports Cu round pillars, with Required Charge as its primary output. Optional time needs explicitly supplied operating current density and effective plating area. Plan offers a Faraday basis with explicit current efficiency or an empirical Bath Rate basis; these are alternative calculation bases.
The planar equations above explain the physical law, not an arbitrary-shape interface in the released app. Analyze is a separate measured-rate workflow using measured deposit geometry and actual accumulated charge. It does not automatically calibrate Plan. Do not infer support for arbitrary shapes, film stacks or bath recipes from the general formulas.
Sources and further reading
- OpenStax Chemistry 2e: Electrolysis — electron, charge and deposition stoichiometry.
- Royal Society of Chemistry: Copper — molar mass and density.
For measurements after plating, see I-MR control charts for ordered process monitoring. Monitoring observed variation is a different task from estimating theoretical charge.