The technique of accelerator mass spectrometry has been used extensively in recent years as a method for detecting low levels (< 1 part per trillion atomic) of radioactive isotopes in solid materials. The technique consists of a Secondary Ion Mass Spectrometer (SIMS) system in which the conventional mass spectrometer has been replaced by a particle accelerator. We have applied this method to the study of stable elements, primarily semiconductor dopants, using the Univ. of Arizona tandem accelerator mass spectrometer. The use of tandem accelerators allows molecular interferences to be removed due to dissociation of the molecules. Particle energies of several MeV are produced, and energy spectroscopy removes the background due to scattered particles, detector noise, etc. to provide positive particle identification. The current detection limits (-10 parts per billion atomic) are primarily due to ion source contamination and their origin is discussed. Removal of this contamination will allow parts per trillion level detection of stable elements.