Home

# Mathematical Modeling of a Copper-Deposition System for Integrated Circuits

### A unique process for making flip-chip IC receptacles required optimization through modeling.

Advanced packaging techniques are the key to utilizing state-of-the-art microelectronic devices. The flip-chip method has become a cost-effective means of erasing many packaging and thermal issues that could spell disaster for high-density, high-power integrated circuits (ICs). Making flip-chip receptacles presents significant engineering challenges. To overcome those challenges, Replisaurus developed a unique process that required mathematical modeling to better understand and optimize the patented process.

A flip chip eliminates the need for wire bonds between the silicon die and the package. Instead, the final wafer-processing step deposits solder beads on the chip pads, so the die package must have pads whose positions line up with those beads. Creating these carrier substrates with photolithography can involve almost as many manufacturing steps as creating the IC itself. Electrochemical pattern replication (ECPR) employs a reusable patterned patterned master electrode as a template and provides for direct metalization on a variety of substrates. Compared to lithography- based metalization, which takes as long as 120 minutes, the ECPR process requires between 1 and 5 minutes. Further, it achieves higher precision for the plating/etching reaction and is far more economical, primarily because it requires less capital equipment than photolithographic techniques.

The ECPR process starts with two elements: a flat cathode substrate with a thin metal seed layer on which the pads and traces are to be deposited, and a master anode consisting of an electrically conducting electrode layer and a patterned insulating material. In the pattern’s gaps, the operator predeposits an anode material — usually copper. An electrolyte is then placed between the two layers and squeezed together. The sandwich goes into a pressure vessel to hold in the electrolyte. When given a voltage across the layers, the metal migrates to the cathode yielding a deposition rate of between 1 and 4 µm per minute. The final step etches away the metal seed layer from the cathode, leaving only the pattern of metal traces and pads exactly corresponding to that on the master electrode.

To push the limits and optimize the process, the research team needed a quantitative understanding of it. Previously, basic calculations were done by hand in one dimension. Results and understanding were derived experimentally, not analytically, so a numerical model was needed that would explain the theory behind the phenomena observed. While the engineers can measure electrolyte concentrations and can control voltages, the ECPR process takes place inside the enclosed cavities, where it is impossible to put in any test instrumentation to monitor the process.

FEMLAB software was used to create a model of the process. The initial model assumed a constant current, and variability was added to refine the simulation. The model determines flux using a material balance in combination with the electroneutrality condition. The model was built using the Nernst-Planck equation, which describes transport of copper ions in the electrolyte by diffusion and migration. Next, the normal flux at the model boundaries, the cathode and the anode, follows the Butler-Volmer equation. It describes the current density at the electrode as a function of the overpotential, which in turn is given by the difference between the electrode’s surface potential and the potential in the electrolyte closest to the electrode surface.

With an accurate model, the ways to refine ECPR could be investigated. Using the model, a large number of parameters such as different voltage levels, warpage, or unevenness in the substrate or electrolyte properties, could be tested.

One effect that required investigation was the effect of uneven surfaces such as imperfections on the cathode surface. Using the model, the operator was able to rule out issues that might cause a non-uniform current-density distribution. Figure 2 compares growth at the level of the substrate to that at the tip of the protuberance.

Using this and similar models, analytical research can be performed that helps find the optimum voltage to use in the process. An unacceptably low voltage can result in a slow deposition rate, whereby only a few crystallization sites have enough energy so that the copper can crystallize, leading to irregularities in the plating. On the other hand, an unacceptably high voltage can result in deposits that are too porous, so fast plating can lead to poor quality.

The ECPR has not yet been introduced to the market, but research institutes and manufacturers have shown considerable interest in the technology. The company is working with equipment manufacturers to develop an industrial ECPR machine, which it expects to demonstrate in the second half of this year.

This work was done by Mikael Fredenberg, manager of R&D, for Replisaurus, using FEMLAB software from COMSOL. For more information, visit http://info.ims.ca/5215-125