  We show that random telegraph signals in metal-oxide-silicon transistors at
millikelvin temperatures provide a powerful means of investigating tunneling
between a two-dimensional electron gas and a single defect state. The tunneling
rate shows a peak when the defect level lines up with the Fermi energy, in
excellent agreement with theory of the Fermi-edge singularity at finite
temperature. This theory also indicates that defect levels are the origin of
the dissipative two-state systems observed previously in similar devices.
