Imaging of localized electronic states in the quantum Hall regime.

The concept of electron localization has long been accepted to be essential to the physics of the quantum Hall effect in a two-dimensional electron gas. The exact quantization of the Hall resistance and the zero of the diagonal resistance over a range of filling factors close to integral are attributed to the localization of electronic states at the Fermi level in the interior of the gas. As the electron density is changed, charging of the individual localized states may occur by single-electron jumps, causing associated oscillations in the local electrostatic potential.

Scanning Single-Electron Transistor Microscopy: Imaging Individual Charges.

A single-electron transistor scanning electrometer (SETSE)-a scanned probe microscope capable of mapping static electric fields and charges with 100-nanometer spatial resolution and a charge sensitivity of a small fraction of an electron-has been developed. The active sensing element of the SETSE, a single-electron transistor fabricated at the end of a sharp glass tip, is scanned in close proximity across the sample surface. Images of the surface electric fields of a GaAs/AlxGa1-xAs heterostructure sample show individual photo-ionized charge sites and fluctuations in the dopant and surface-charge distribution on a length scale of 100 nanometers.