STM Topographic Imaging Lab: Constant-Current vs Constant-Height (2D)

This 2D companion runs the same core tunneling relation as the 3D lab — I(x,y) = C·V·exp(−2κ·d(x,y)), where d is the local vacuum gap — but exposes both scan modes an operator actually chooses between on a real instrument. In constant-current mode the feedback loop is solved analytically: because I depends only on the gap d, holding I fixed forces d to a single constant everywhere, so the tip-height trace z_tip(x,y) = d_const + h(x,y) reconstructs the true corrugation almost exactly no matter what κ or V is set to. In constant-height mode the tip is frozen at a fixed plane and the measured image is the raw exponential current itself — small bumps get wildly amplified, and if the local gap collapses below about 0.15 Å the simulation flags a genuine tip crash. A reference pane renders the true synthesized surface (hexagonal graphite-like, square metal-like, or hexagonal with a vacancy defect) next to the measured image and a cross-section line plot, so the distortion — or lack of it — is directly comparable.