Error Rates in Deterministic Ion Implantation for Qubit Arrays

The theoretical error rates in deterministic ion implantation when using an ion beam governed by a Poisson point process with a detector that counts the impacts are investigated. It is concluded that if the error rates are small, then for spots with nominally one implanted ion the probability of failure to implant the correct number is ≈ for a synchronous (i.e., pulsed) system or for an asynchronous (i.e., continuous beam) system, where is the probability that the detector misses an ion impact, and and are the number of ions (dark counts) per unit time and per pulse, respectively. ts is the system reaction time for an asynchronous system. This approximation allows easy identification of the greatest need for engineering effort. Some experimental efforts to measure these parameters and their uncertainties are examined.