Because there is relative motion between the glass pipette and the conductive substrate in the deposition process, and the deposition process is a dynamic process changing with time, the multi-physical field finite element analysis software COMSOL Multiphysics was used to simulate the physical processes of electrodeposition, fluid dynamics, and mass and heat transfer in the MCED process to further explore the influence of water vapor evaporation on the dynamic process of MCED.
3.1. Geometry
In this study, the FE analysis was based on the experimental parameters. Among them, the meniscus shape of MCED geometric model is described by formula (2)[37].
(2)
where R is the radius of deposited metal microstructure; r0 is the radius of glass pipette nozzle; φ0 is the growth angle, that is, the angle between the tangent line of the meniscus and the upper surface of the deposited metal microstructure; α0=90°- φ0.
Because of the symmetry of the geometric model, a two-dimensional axisymmetric FE simulation model was used in the simulation process (Fig. 3a). The geometric model represents a glass pipette filled with metal salt solution and connected to the upper surface of the deposited metal microstructure through the metal salt solution meniscus. In this study, the metal salt solution used to deposit metal microstructure was CuSO4. The two-dimensional axisymmetric cylindrical coordinate system and the Z axis were used in the vertical direction.
3.2. Boundary condition
The simulation model consisted of an electrolyte (copper ion (Cu2+) and sulfate ion (SO42-)), which was placed in a glass pipette in an air environment with controllable humidity. The ion transfer in the electrolyte region was controlled by the Nernst-Plank formula of the electrolyte and the Navier-Stokes formula of convection. The boundary conditions are shown in Fig. 3b.
In order to make the simulation results more in line with the actual situation, the dynamic process of deposition was carefully observed, according to the experimental conditions, the diameter of the deposited metal microstructure was designed to be 70 μm, the diameter of the glass pipette nozzle was designed to be 100 μm, the electrolyte concentration was 0.5 M, the ambient temperature was 25°C, the ambient relative humidity was 40%, and the deposition time was set to 600 s. In addition, in the humidity-controlled environment, there is no environmental change in the electrodeposition process, so the simulated evaporation process is regarded as a time-independent process.
3.3. Simulation results
The multi-physical field simulation results are shown in the figure. Fig. 4 shows the variation of relative humidity near meniscus with time during MCED. Fig. 5 indicates the variation of evaporation flux near meniscus with time during MCED. Fig. 6 illustrates the variation of total flux in meniscus area with time during MCED. As can be seen from the relative humidity cloud map, when the external environmental humidity was 40%, the relative humidity near the meniscus was not uniform. Specifically, there was a certain relative humidity gradient, and the relative humidity near the meniscus was larger, close to 100%. Because the electrodeposition process was in a humidity-controlled environment, the relative humidity did not change obviously with time. When the deposition time was 0 s, there was an evaporation flux near the meniscus due to the relative humidity gradient, which would cause convection on the meniscus surface, among them, the evaporation flux near the solid-liquid-gas three-phase contact angle of the meniscus was more significant, with a peak value of 7.94 × 10-8 kg/(m2s). Thus, the total flux in the edge region was 19.12 × 10-3 mol/(m2s), slightly higher than that in the central region. When the deposition time was 180 s, with the glass pipette moving up slowly, the evaporation flux increased to 9.01 × 10-8 kg/(m2s). Due to the short evaporation time, the total flux only fluctuated slightly, the peak value was 19.65 × 10-3 mol/(m2s), and the distribution did not change obviously. Therefore, the deposited metal microstructure (red frame area) showed growth with a flat-top. By contrast, when the deposition time was 600s, the evaporation flux increased significantly as high as 23.90 × 10-8 kg/(m2s), especially near the solid-liquid-gas contact angle of the meniscus. Thus, the total flux in the central region of the meniscus decreased, and the total flux in the edge region increased to 23.07 × 10-3 mol/(m2s). The deposited metal microstructure (red frame region) showed the trend of edge preferential growth. In addition, the results show that although evaporation takes away water from the surface of the meniscus over time, the dynamic deposition process does not change the shape of the liquid surface, and the overall deposition structure grows vertically.