A fitting algorithm for optimizing ion implantation energies and fluences

We describe a method to automatically generate an ion implantation recipe, a set of energies and fluences, to produce a desired defect density profile in a solid using the fewest required energies. We simulate defect density profiles for a range of ion energies, fit them with an appropriate function, and interpolate to yield defect density profiles at arbitrary ion energies. Given $N$ energies, we then optimize a set of $N$ energy-fluence pairs to match a given target defect density profile. Finally, we find the minimum $N$ such that the error between the target defect density profile and the defect density profile generated by the $N$ energy-fluence pairs is less than a given threshold. Inspired by quantum sensing applications with nitrogen-vacancy centers in diamond, we apply our technique to calculate optimal ion implantation recipes to create uniform-density 1 $\mu$m surface layers of $^{15}$N or vacancies (using $^4$He).