- Alristech Ltd

300 mm Wafer ECD Cell Simulation

Multiphysics Simulation of a 300 mm Wafer Electrochemical Deposition Cell

Coupled current-density, electrolyte-flow and copper-ion transport modelling for deposition-uniformity prediction.

Converged deposition-rate map across the 300 mm wafer surface, combining the coupled current-density and concentration fields.

Overview

This case study presents coupled multiphysics simulation work for a representative 300 mm semiconductor wafer electrochemical deposition (ECD) cell. The work combines electrostatic current-density modelling, electrolyte flow simulation and copper-ion species-transport modelling to assess deposition-rate uniformity across the wafer surface.

The model links the current-density field, local copper-ion concentration and electrolyte flow behaviour into a coupled simulation workflow, allowing changes in ion availability and flow-driven transport to influence the predicted deposition-rate distribution.

Engineering Challenge

Electrochemical deposition uniformity across a 300 mm wafer depends on the combined behaviour of three interacting physical fields: the electric current distribution through the electrolyte, the bulk electrolyte flow pattern, and the local copper-ion concentration at the wafer surface. These fields cannot be assessed in isolation: current density depends on local ion concentration, ion concentration depends on both current consumption and convective transport by the flow, and the flow field governs how effectively fresh electrolyte reaches different regions of the wafer. Predicting deposition uniformity therefore requires a coupled simulation rather than three separate, independent analyses.

Engineering Approach

Modelled a representative 300 mm wafer ECD cell geometry, including the silicon wafer (cathode), copper counter-electrode (anode), PTFE retaining ring and tangential electrolyte inlet/outlet ducts.
Generated a 5.8-million-element tetrahedral mesh (1,047,427 nodes) suitable for resolving the coupled electrostatic, flow and species-transport fields.
Solved Stage 1 (electrostatics): current density distribution through the electrolyte, wafer, retaining ring and electrode, giving a flat bulk current density of approximately 2.15–2.2 A/m² with approximately 5% edge enhancement under uniform-conductivity conditions.
Solved Stage 2 (Navier-Stokes flow): electrolyte velocity field driven by a tangential inlet duct, producing a swirl-dominated recirculating flow.
Solved Stage 3 (species transport): copper-ion concentration field, advected by the Stage 2 flow field and two-way coupled to Stage 1 through concentration-dependent electrolyte conductivity and surface reaction kinetics at the wafer.
Developed an open-source multiphysics workflow covering geometry preparation, meshing, coupled finite-element solving, deposition-rate post-processing and visualisation.

Wafer Cell Geometry

The model geometry comprises four main bodies: the silicon wafer cathode, the copper counter-electrode anode (top), a PTFE retaining ring and the surrounding electrolyte fluid domain. The electrolyte inlet and outlet ducts are positioned on the same side of the chamber, offset from one another, producing a tangential entry flow rather than a simple straight-through flow. This tangential arrangement is the primary driver of the swirl-dominated flow pattern discussed below.

Wafer cell geometry, showing the electrolyte fluid domain and the same-side inlet/outlet duct arrangement.

Coupled Electrostatic-Flow-Species Transport Model

The core of the work is the coupling between the electrostatic, flow and species-transport fields. The electrostatic model provides the current-density distribution driving copper deposition at the wafer surface; the Navier-Stokes flow model provides the electrolyte velocity field that transports fresh copper ions toward the wafer; and the species-transport model computes the resulting ion-concentration field, consuming ions at a rate set by the local current density and replenishing them by advection from the flow field.

Species transport was governed by the advection-diffusion equation, using the converged velocity field to carry copper ions through the electrolyte. At the wafer surface, ion consumption was set by Faraday’s law, proportional to the local current density; electrolyte conductivity was made a function of local ion concentration, closing the loop back into the electrostatic charge-conservation equation.

Coupled Field Behaviour

The coupled species-transport solve converged within five outer iterations, with copper-ion concentration settling between approximately 212 and 217 mol/m³ across the wafer surface and current density redistributing in response to local ion availability. As concentration evolved, conductivity and current density updated with it, and the model converged to a single, mutually consistent electrostatic/species-transport solution rather than three independent results.

Numerical Workflow

The numerical workflow used an open-source simulation stack for geometry preparation, meshing, coupled finite-element solving and post-processing. Elmer FEM was used for the coupled electrostatic, flow and species-transport equations, with ParaView and Python used for visualisation, deposition-rate post-processing and statistical analysis.

The coupled electrostatic/species-transport workflow converged successfully, allowing the current-density and copper-ion concentration fields to reach a mutually consistent solution.

Engineering Relevance

The work demonstrates capability in coupled electrochemical-flow multiphysics simulation, species-transport modelling, mass-transfer and reaction-kinetics modelling, deposition-uniformity analysis and open-source multiphysics workflow development.

This type of approach can support semiconductor wet-process equipment design, electrochemical deposition chamber development, inlet/outlet geometry comparison, wafer-fixture and retaining-ring design, process-window investigation and deposition-uniformity troubleshooting before physical tooling or process trials are committed.

Simulation Results and Visualisation

Stage 1: converged current-density distribution across the wafer surface (left) and current-density magnitude profile across the wafer diameter (right), showing a flat bulk region of approximately 2.15–2.2 A/m² with edge enhancement of approximately 5% at both edges.

Electrolyte velocity field 5 mm above the wafer surface, showing the swirl-dominated flow pattern driven by the tangential inlet duct.

Electrolyte velocity field at a horizontal section nearer the inlet/outlet duct height, showing both duct cross-sections and the resulting jet structure feeding the swirl below.

Converged copper-ion concentration field at the wafer surface, showing the asymmetric depletion pattern driven by the coupled flow and current-density fields.

Copper-ion concentration profile across the full 300 mm wafer diameter, showing a smooth, flow-driven gradient from the inlet side to the far side.

Deposition-rate map across the wafer surface, combining the converged current-density and concentration fields, showing both bulk asymmetry and edge enhancement.

Deposition-rate profile across the wafer diameter, quantifying bulk non-uniformity and edge-enhancement effects.

Outcome

Developed a fully coupled electrostatic-flow-species-transport simulation workflow for a 300 mm wafer ECD cell.
Demonstrated two-way coupling between current density and copper-ion concentration through concentration-dependent electrolyte conductivity and surface reaction kinetics.
Quantified deposition-rate non-uniformity across the wafer, identifying approximately 3% bulk variation and approximately 8% edge enhancement driven by the interaction of flow pattern and current distribution.
Established a reusable, open-source-based coupled multiphysics workflow applicable to alternative cell geometries and process conditions.

Future Development Direction

This work forms the foundation for future geometry comparison studies, including alternative electrolyte inlet/outlet duct arrangements, to quantify the influence of flow pattern on deposition uniformity. It also provides a basis for later investigation of process-enhancement techniques such as acoustic agitation, if required for more detailed process-development work.

Confidentiality Note

This case study is based on representative wafer ECD cell simulation work developed as part of ongoing simulation capability development. No client-specific, proprietary or confidential project data is disclosed.