  We use electrostatic force microscopy to spatially resolve random telegraph
noise at the Si/SiO$_2$ interface. Our measurements demonstrate that two-state
fluctuations are localized at interfacial traps, with bias-dependent rates and
amplitudes. These two-level systems lead to correlated carrier number and
mobility fluctuations with a range of characteristic timescales; taken together
as an ensemble, they give rise to a $1/f$ power spectral trend. Such individual
defect fluctuations at the Si/SiO$_2$ interface impair the performance and
reliability of nanoscale semiconductor devices, and will be a significant
source of noise in semiconductor-based quantum sensors and computers. The
fluctuations measured here are associated with a four-fold competition of
rates, including slow two-state switching on the order of seconds and, in one
state, fast switching on the order of nanoseconds which is associated with
energy loss.
