COMSOL 6.4 - Chemical Etching

This example illustrates the principle of wet chemical etching. Wet chemical etching is particularly important for microelectronics industry for patterning of integrated circuits, MEMS devices, and optoelectronic and pressure sensors. Wet etching processes use solution based (“wet”) etchants, where the substrate to be etched is immersed in a controlled flow of etchant. Wet etching process is selective isotropic, fast (usually reaction rate limited) and reproducible. Due to its reproducibility the technique is often used for micropatterning of substrates.

A wet etching process involves chemical reaction that consume the original reactant and produce new reactant. The wet etch process can be described by three basic steps:

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Transport of the liquid etchant to the structure that is to be removed.

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The reaction between the liquid etchant and the material being etched away. A reduction-oxidation (redox) reaction usually occurs. This reaction entails the oxidation of the material followed by dissolution.

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Transport of the by products in the reaction from the reacted surface.

The purpose of this tutorial is to examine how the copper substrate material is depleted and how the cavity shape evolves during the wet etching process. The rate of the etching reaction depends on the local concentration of a reactant, which is transported to the surface by coupled convection–diffusion. The laminar flow profile of the etchant fluid changes due to the shape evolution of the etched cavity.

Model Definition

The simplified 2D model geometry consists of a masked copper substrate with an exposed surface which is to be wet etched. The geometry is shown in Figure 1. The top rectangular domain has fluid flowing over the exposed copper substrate as marked in the x direction. The fluid reacts only with the unmasked copper as the etching proceeds.

Figure 1: Schematic diagram of the chemical etching under a laminar flow of the etchant.

Transport of Chemical Species

The mass flux of the etching species is governed by diffusion and convection according to

(1)

where D (SI unit: m2/s) denotes the diffusion coefficient and c (SI unit: mol/m3) is the concentration. The modeled species has a diffusion coefficient of 1 · 10−9 m2/s. At the inlet and top boundaries of the flow, the concentration is equal to the bulk concentration of the etchant solution. At the etching surface (moving boundary), the flux condition is considered as in:

(2)

where k (SI unit: m/s) is the forward rate constant for linear kinetics of the etching species, and n is the normal vector. k is assumed to be independent of the position on the surface. A No Flux condition is used for all other boundaries except the moving boundary.

Laminar Flow

At the cavity, the flow field can be calculated by the Navier–Stokes equations

(3)

along with the continuity equation

(4)

Here ρ is the fluid density (SI unit: kg/m3), p is the pressure (SI unit: Pa), μ is the dynamic viscosity (SI unit: Pa·s), F is the volume force vector (indicated as the boundary stress in the modeling instructions), and u is the fluid velocity (SI unit: m/s).

Along the moving wall, a no slip condition is applied.

Deformed Geometry

The movement of the boundary is defined by an interfacial condition on the boundary

(5)

where v is velocity of the moving mesh in the normal direction; r, M, and ρ are the reaction rate (SI unit: mol/(m2 ·s), which is the right side −k c in Equation 2 above, molar mass (SI unit: kg/mol), and density (SI unit: kg/m3) of the etching species, respectively.

Results and Discussion

Figure 2 shows the concentration of etchant species CuCl2 at t = 10,800 s for an initial cavity radius of 0.5 mm. The etch profile is asymmetric owing to the fluid flow in the x direction. The etch rate is higher around the area where laminar flow first encounters the boundary layer in fluid direction. Concentration becomes uniform deeper into the cavity as laminar flow can no longer transport reactant to the boundary layer owing to larger aspect ratio. (See also the velocity profile in Figure 3.)

Figure 2: Concentration profile of CuCl2 etchant at t = 10,800 s over unmasked copper cavity.

Figure 3 shows the velocity profile for etchant flow at t = 10,800 s. The velocity is zero close to the moving boundary. The fluid flow eventually becomes weak deeper as the aspect ratio of cavity increases with time.