High-resolution numerical study of conductance and noise imaging of mesoscopic devices

Advanced high-vacuum, ultra-low-temperature scanning probe techniques have allowed imaging of the current flow in mesoscopic devices based on a 2-dimensional electron gas (2DEG). The basic concept behind these very successful experiments consists in the observation of how conductance through the device varies as a negatively charged probe is scanned over the semiconductor surface, locally depleting the 2DEG. Besides conductance, the shot noise power spectral density is another quantity that could be taken into consideration for imaging purposes. The power spectral density of shot noise is related to the transmission matrix through Buttiker´s relationship: S/sub I/ = 4q/sup 3//h|V|Tr[t/sup /spl dagger/t/(I - t/sup /spl dagger//t)], where q is the electron charge, h is Planck´s constant, V the potential drop across the device, and t is the transmission matrix. Thus the depleted spot due to the scanning probe, through its action on the transmission matrix, will also affect the shot noise level. Based on an optimized recursive Green´s function formalism, we can treat, within reasonable computational time limits, a 2D scan on a grid of at least 200 /spl times/ 300 points (larger grids up to 600 /spl times/ 1000 should be accessible) and, if needed, we can model the actual potential due to the scanning probe over an area of about 200 mesh points. We have also added the possibility of treating impurities and dopants, with an approach based on the generation of a random distribution of point charges, whose contribution to the potential at the 2DEG level is computed with the inclusion of screening via a semi-analytical expression.