The phantom force

Abstract

While atomic resolution in an AFM image is usually assumed to originate from the formation of a chemical bond or Pauli repulsion, it can also be caused by a phenomenon we called the phantom force. When there is an electric potential difference between tip and sample, they will be attracted to one another. It is quite common in AFM experiments to apply a voltage between the tip and the sample. At distances required for atomic resolution, this can result in a tunneling current. If there is a tunneling current, then there will also be a potential difference within the sample (as charge carriers do not accumulate after they have tunnelled). The magnitude of this potential difference within the sample is related to the resistivity of the sample. The total potential difference between the sample bulk and the tip is fixed by the applied voltage, so any potential difference within the sample reduces the potential drop in the junction between the tip and sample. This phantom force is an apparently repulsive force caused by a decrease in the electrostatic attraction between tip and sample. If the total resistance within the tip or sample is high enough, then the phantom force can be the dominant contrast mechanism in AFM images. It can also dominate features in bias and distance spectroscopy. This chapter includes a comprehensive description of our theory of the phantom force and data which demonstrate this effect.