Retrieving derivative information from tunneling current errors in scanning tunneling microscopy

Noise and errors in signal are a common hindrance in experiments. When the source of noise or error is understood, new experimental strategies can be employed to either reduce the error or measure the error as a new source of signal. In constant-current mode scanning tunneling microscopy (STM), despite the active feedback loop, one such error as observed experimentally is a current offset from its setpoint that occurs when the tunneling junction is subject to external pertubations. We show through low-temperature STM imaging and spectroscopy, as well as phenomenological modeling, that this current offset contains local tunneling barrier height information from a d²I/dz² dependence and local density of states information from a (dI/dV)² dependence when the tip-sample distance and sample bias voltage are periodically perturbed, respectively. This new source of signal enables a faster and simpler method for measuring these quantities than traditional lock-in amplifier methods. We further demonstrate evidence of the generalizability of our method in other negative feedback systems.