Modeling a copper-deposition system where measurements are impossible
The founders of Replisaurus Technologies AB (left to right): Patrik Möller, CEO; Mikael Fredenberg, CTO; Peter Wiwen-Nilsson; CFO.
By Paul G. Schreier
Only through advanced packaging techniques can we take advantage of 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. Finding a way to make flip-chip receptacles presents significant engineering challenges, but Replisaurus Technologies AB (www.replisaurus.com), based in Kista, Sweden, has developed a unique method to overcome them. Their process has some interesting twists and turns that required mathematical modeling to better understand and optimize the patented process. COMSOL and the Chemical Engineering Module, with ready-made interfaces already optimized for electrochemical engineering, were the obvious choice.
Flip it over and solder
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 itself have pads whose positions line up with those beads. Creating these carrier substrates with photolithography can involve almost as many manufacturing steps as when creating the IC itself. Replisaurus, however, has developed electrochemical pattern replication (ECPR), which employs a reusable 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.
Figure 1: In the ECPR process, the operator predeposits an anode material in the graps of a pattern that matches that of an integrated circuit (Step 1). When the anode and cathode are put together (Step 2) enclosed cavities result. A voltage migrates the metal from the anode to the cathode (Step3). Removing the seed layer leaves only a replica of the original pattern (Step 4).
The ECPR process starts with two elements (Figure 1): 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 pre-deposits an anode material, usually copper. Then the operator places an electrolyte between the two layers and squeezes them 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.
Figure 2: The coiled device on the left demonstrates that the ECPR process can reproduce objects with unusual shapes; the device on the right helps in assessing the quality of the metal being used in the process.
Figure 2 shows some results of Replisaurus´ work. The coil (left) serves as a demo of the process´ capabilities, and the other device (right) allows measurement of the copper´s resistivity and thus the metal's quality. Comments Replisaurus´ manager of R&D Mikael Fredenberg, "We started at a 5-µm feature size adequate to prove the process and sufficient for our existing applications, and we´re certain we can reach much finer resolutions."
Software peeks inside an enclosed cavity
To push the limits and optimize the process, the research team needed a quantitative understanding of it. "Before we started working with COMSOL," explains Mikael, "we could only do some basic calculations by hand in one dimension. We derived our results and understanding experimentally, not analytically, so we wanted a numerical model that would explain the theory behind the phenomena we observed.”While the engineers can measure electrolyte concentrations and can control voltages, the ECPR process takes place inside the enclosed cavities, where it´s impossible to put in any test instrumentation to monitor the process. When he decided to create a model, Mikael started with the experience he gained with COMSOL during his studies at the Lund Institute of Technology (Lund, Sweden), but he had never before modeled an electrochemical process. Thus, he first had to study this process and learn to model how the electrical fields and chemical transport interact inside the electrolyte. Here the COMSOL support team proved invaluable because they have considerable experience in electrochemical engineering and so provided extensive help.
Figure 3: This uneven surface geometry represents effects such as imperfections on the cathode surface.
Mikael's initial model assumed a constant current, then he added variability 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 in the ready-made modeling interface that comes with the Chemical Engineering Module. The Nernst-Planck equation describes transport of copper ions in the electrolyte by diffusion and migration. The mass transport by diffusion follows the concentration gradient that appears when copper ions are created at the anode and consumed at the cathode. The migration represents ion transport according to electrical charge, where the positively charged copper ions move towards the more negative cathode surface. Next, the normal flux at the model boundaries, the cathode and the anode, follows the Butler-Volmer equation. The Butler-Volmer equation 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 (applied with an external power source) and the potential in the electrolyte closest to the electrode surface. Mikael was able to enter these equations for the electrode kinetics directly into COMSOL's graphical user interface. With an accurate model, the company could then investigate ways to refine ECPR. "Using it," explains Mikael, "we can play with a large number of parameters such as different voltage levels, warpage or unevenness in the substrate, or electrolyte properties. For example, we were able to test hundreds of electrolyte compositions in software before taking the time and expense of running a laboratory experiment in the clean room. Thanks to COMSOL we can try out all sorts of ideas, no matter how wild, and get a first estimation of the results, enough to let us know if they're worth pursuing."
A particular problem in the modeling process deals with moving boundaries. As material grows on the cathode, a nonuniform current-density distribution can lead to changes in the geometry of the cells. Areas on the cathode with higher deposition rate grow faster and get closer to the anode, causing the current density to increase as the gap decreases. Mikael's initial COMSOL models didn´t account for such an effect, and again the COMSOL support team came to his aid, showing him how to solve a moving-boundary problem using COMSOL's implementation of the Arbitrary Lagrangian Eulerian (ALE) method, a powerful method not found in convetional mathematical-modeling codes.
A look at uneven surfaces
Figure 4: The plot on the right compares growth at the level of the substrate (dashed line) and at the tip of the protuberance (solid line). Note that differences in the growth rate by location is negligibly small. The figure below shows the modulus of the current-density vector (color plot) and the displaced mesh on the XY plane as computed with the moving-boundary method in COMSOL. The thickness of the deposited copper layer appears as the distance between the boundaries of the model domain and the displaced finite-element mesh.
One effect Mikael wanted to investigate in particular was the effect of uneven surfaces such as imperfections on the cathode surface, which he examined with the geometry in Figure 3. Thanks to the model he ruled out some issues he though might cause a non-uniform current-density distribution. Figure 4 compares growth at the level of the substrate to that at the tip of the protuberance. Mikael was quite surprised to see that the growth rate isn�t terribly higher at the tip. Based on this finding, he was able to shift his focus to searching for the real causes of non-uniform deposition. He also looked at current density along the substrate at a specific point in time (Figure 5). Recall that current density sets the speed of the plating process. As he surmised, growth is higher at the tip of the protrusion, but an examination of the figure�s y-axis shows that the difference is quite small, again much less so than he had expected.
Using this and similar models Mikael can perform analytical research that helps him 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 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. Thus Mikael spends a considerable time finding the best balance between deposition rate and quality.
"With these COMSOL models we can start to explain the different phenomena we´ve seen in the lab and can better track how the process works." Mikael explains. "That information is invaluable in debugging the ECPR process and helps us study new effects such as the plating of an uneven surface, what happens if the distance between the master electrode and the anode varies, or if the two surfaces are not in perfect contact."
Figure 5: Current density along the substrate after 18 sec. Finding out that the current densities are only negligibly higher at the tip than at the substrate freed Mikael to look for the true causes of non-uniform current densities.
A bright future for ECPR
Replisaurus has not yet introduced its ECPR to the market, but already research institutes and manufacturers have shown considerable interest in the technology. In fact, the company is working with equipment manufacturers to develop an industrial ECPR machine, which it expects to demonstrate later this year. "We hope ECPR will become the leading manufacturing process for the advanced metallization industry," says Mikael, "replacing more costly photolithography-based metallization. Because the technology is unexplored, COMSOL is proving to be a powerful tool for understanding the electrochemical process aspects that ECPR enables. These models will also prove very valuable in helping potential customers understand the process, which will make it easier for them to purchase our equipment with confidence."