Resolving voltage hysteresis in low temperature RF-STM I(V) curves on terminated Si (100) samples

Recently, our group has been measuring the voltage dependent tip-sample capacitance C_TS(V) using an RF tank circuit on Cl terminated Si (100) samples in a milli Kelvin scanning tunneling microscope (mK-STM). These curves show hysteresis with respect to the voltage sweep direction (forward (+ to -) and backward (- to +)). Alongside, we have been measuring I(V_bias) data which also show a large hysteresis. Notably, both sets of curves show little change with the sweep time within 1 second to 2 minutes but depend on the voltage range of the sweep. As such, the apparent hysteresis can likely be attributed to slow charge motion inside the silicon sample which significantly distorts the actual tip-sample voltage (V_TS = s(V_bias)). By constraining the tunnel junction resistance to be fixed, we can construct a voltage scaling function to map the current from the forward sweep onto the backward sweep and vice versa. However, this only removes the relative hysteresis. The global scaling function can be estimated by the mean of s_forw and s_backw. Our main application is to align the simultaneously measured C_TS(V) curves. The C_TS hysteresis remains under the voltage correction and is subject of further study. The scaling method will be described in excruciating detail.