We have studied the initial stages of Li adsorption onto the Si(001) surface with scanning tunneling microscopy and spectroscopy (STM/S). On p-type silicon samples, STS on the Li sites shows a region of strong negative differential resistance (NDR). In addition, with the tip held stationary above the Li sites, a digital switching is observed in the tunneling current, which we attribute to the existence of thermally activated electron traps. The changing occupation statistics of these traps as the voltage changes causes the NDR. Screening of the traps means that weaker NDR is also observed when the tip is positioned over unmodified Si dimers. Thus, Very small amounts of Li have a dramatic effect on both local and extended length scales.