Fluid Transport
Wet chemical processing in printed circuit board manufacturing involves simultaneous momentum transfer and molecular mass diffusion within liquid reagents. Schmidt number defines the dimensionless ratio of momentum diffusivity to mass diffusivity within a fluid flow field. Process engineers use this fluid parameter to analyze boundary layer dynamics in plating and etching baths.
Boundary Dynamics
Chemical reactions at copper-fluid interfaces depend on how fast fresh reactant molecules diffuse across stagnant fluid layers relative to liquid momentum transport. High Schmidt numbers indicate that momentum diffuses much faster than mass, resulting in hydrodynamic boundary layers that are significantly thicker than concentration boundary layers. Aqueous electroplating baths exhibit high Schmidt number values, meaning mass transfer limits metal deposition rates inside microvias.
Agitation systems and ultrasonic transducers increase liquid shear to overcome slow mass diffusion rates in high-viscosity chemical baths. Schmidt number values guide fluid flow modeling inside narrow copper microvias during electroplating. Controlling fluid properties and bath temperature optimizes chemical mass transport relative to fluid drag forces.
Etch Rate
Copper etching chemical solutions require rapid mass transport to clear metal from narrow spaces between dense signal traces. Slow mass diffusion causes localized etchant depletion, leading to incomplete copper removal in tight spaces. Higher bath temperatures increase mass diffusivity, lowering the dimensionless ratio and improving etching uniformity.
