Imaging the percolation of localized states in a multisubband two-dimensional electronic system subject to a disorder potential

The electronic local density of states (LDOS) in an In_0.53Ga_0.47As surface quantum well (QW) grown by molecular beam epitaxy was measured by low-temperature scanning tunneling spectroscopy under ultrahigh vacuum. The LDOS in the conduction band has a clear steplike energy dependence, revealing that several subbands are formed in the QW. At a given energy, the LDOS shows strong spatial fluctuations in the QW plane due to the presence of a disorder potential. Percolation of localized states with increasing energy is observed in each subband tail. The percolation threshold is determined for each subband by using a semiclassical model. The origin of the disorder potential is discussed, and is ascribed to a random distribution of native point defects located at the QW surface.