Simulations of imaging of the local density of states by a charged probe technique for resonant cavities

We simulate scanning probe imaging of the local density of states related to scattering Fermi level wave functions inside a resonant cavity. We calculate the potential landscape within the cavity, taking into account the Coulomb charge of the probe and its screening by deformation of the two-dimensional electron gas using the local density approximation. Approximation of the tip potential by a Lorentz function is discussed. The electron transfer problem is solved with a finite difference approach. We look for stable work points for the extraction of the local density of states from conductance maps. We find that conductance maps are highly correlated with the local density of states when the Fermi energy level enters into Fano resonance with states localized within the cavity. Generally outside resonances the correlation between the local density of states and conductance maps is low.