  Noise is usually a hindrance to signal detection. As stressed by Landauer,
however, noise can be an invaluable signal that reveals kinetics of charge
particles. Understanding local non-equilibrium electron kinetics at nano-scale
is of decisive importance for the development of miniaturized electronic
devices, optical nano-devices, and heat management devices. In non-equilibrium
conditions electrons cause current fluctuation (excess noise) that contains
fingerprint-like information about the electron kinetics. A crucial challenge
is hence a local detection of excess noise and its real-space mapping. However,
the challenge has not been tackled in existing noise measurements because the
noise studied was the spatially integrated one. Here we report the experiment
in which the excess noise at ultra-high-frequency(21.3THz), generated on
GaAs/AlGaAs quantum well (QW) devices with a nano-scale constriction, is
locally detected and mapped for the first time. We use a sharp tungsten tip as
a movable, contact-free and noninvasive probe of the local noise, and achieved
nano-scale spatial resolution (~50nm). Local profile of electron heating and
hot-electron kinetics at nano-scales are thereby visualized for the first time,
disclosing remarkable non-local nature of the transport, stemming from the
velocity overshoot and the intervalley hot electron transfer. While we
demonstrate the usefulness of our experimental method by applying to mesoscopic
conductors, we emphasize that the method is applicable to a variety of
different materials beyond the conductor, and term our instrument a scanning
noise microscope (SNoiM):In general non-equilibrium current fluctuations are
generated in any materials including dielectrics, metals and molecular systems.
The fluctuations, in turn, excite fluctuating electric and magnetic evanescent
fields on the material surface, which can be detected and imaged by our SNoiM.
