Angstrom resolved imaging of charge percolation through the interface between phosphorous doped crystalline silicon and silicon dioxide*

Using a high resolution ($\approx$100fm/$\sqrt{\mathrm{Hz}}$ spectral noise density) scanning probe at T$\approx$4K, we measure currents through the interface between phosphorus doped ([P] $\approx$ 10$^{17}$-10$^{18}$ cm$^{-3}$) crystalline silicon and a native silicondioxide layer as a function of either the lateral cantilever position or the applied cantilever bias voltage (c-AFM imaging). These measurements visualize the percolation of charge through the interface and they show that local current maxima exist in patch-like structures of $\approx$30nm diameter, randomly distributed with an average distance between the centers of 30-40 nm. We associate these with P donor electron states. Within the patch-like structures, we observe additional, extremely localized ($\approx$5{\AA}), current maxima. We associate those to silicon dangling bonds at the interface or within the silicondioxide. The hypothesized association of these very reproducible features is tested by current-voltage (I-V) measurements. For any randomly chosen surface position, these measurements reveal one of only four qualitatively distinct I-V responses, each of which is identified with charge percolation from P donors to the cantilever either with or without different kinds of silicon dangling bond involvement.