Theoretical Analysis of Apparent Barrier Height on an Al Surface: Difference by Measurement Methods

Abstract

We have analyzed the difference in apparent barrier height (ABH) by the approach and modulation methods, using the boundary-matching scattering-state density functional method, in which electric states under an applied bias voltage are self-consistently calculated. We found that the approach and modulation methods provide nearly the same calculated ABH values for a wide range of tunneling conductances from 10-11 to 10-5 Ω-1. The change in ABH in the tunneling conductance range from 10-11 to 10-7 Ω-1 is smaller than that in the tunneling conductance range from 10-7 to 10-5 Ω-1, suggesting that some of the observed discrepancies between the two methods may be due to the difference in tip-sample distance. Furthermore, we also found that the change in modulation amplitude, which is caused by the force acting on the tip atom due to the applied bias voltage, can account for the observation that the modulation method provides a smaller ABH value than the approach method.