Crystallization kinetics during layer exchange of 28Si implanted Al films for fabrication of quantum computers: A theoretical model

We are investigating a novel enrichment process that could allow the use of industrial complementary metal-oxide-semiconductor implanters to manufacture "quantum grade" Si-28 layers for use in quantum computers. Our implanted layer exchange enrichment process leverages conventional deposition-based layer exchange approaches but replaces a step of depositing a Si layer above an Al layer with a Si-28 implant into the top of an Al layer. A subsequent anneal dissolves Si into Al beneath the implanted region where Si diffuses and either epitaxially grows onto the substrate or forms poly-crystals in the Al [Schneider and England, ACS Appl. Mater. Interfaces 15, 21609 (2023)]. We have developed a qualitative model using simple assumptions and boundary conditions to estimate characteristic times and rates of epitaxy or poly-crystallization for this novel layer exchange process. We have used the model to explain crystallization outcomes reported in this paper and previously. We find that the absence of an oxide boundary layer separating Si and Al allows Si diffusion to become established within the first second of all the anneals studied and that crystallization actually completes during the temperature ramp of most of the anneals. The rapid evolution of Si supersaturation in Al beneath the implanted layer explains the ratios of epitaxial growth to poly-crystallization observed after these anneals. We use this understanding to propose the implant layer exchange conditions that could produce the highest quality mono-crystalline quantum grade Si.