Tunneling current, in STM

As we have shown in Chapters 2 and 3, under the normal operating conditions of STM, the tunneling current can be calculated from the wavefunctions a few A from the outermost nuclei of the tip and the sample. The wavefunctions at the surfaces of solids, rather than the wavefunctions in the bulk, contribute to the tunneling current. In this chapter, we will discuss the general properties of the wavefunctions at surfaces. This is to fill the gap between standard solid-state physics textbooks such as Kittel (1986) and Ashcroft and Mermin (1985), which have too little information, and monographs as well as journal articles, which are too much to read. For more details, the book of Zangwill (1988) is helpful. 

The purpose of doing STM is to learn about surface structures, and the tip as such is regarded as an uninteresting probe. In this sense, it is a problem that the electronic structure of the tip is contained in the formula for the tunnel current in the original work by Bardeen 58). Tersoff and Hamann 59,60), however, extended Bardeen s formalism and showed by simple, yet relevant approximations that the impact of the unwanted electronic structure of the tip is in many cases less pronounced for typical tunneling parameters. Fortunately, the Tersoff-Hamann model provides a simple conceptual framework for interpreting STM images, and therefore it is still the most widely used model. 

EC-STM consists in performing standard STM imaging, therefore based on a measure of the tunneling current, in an electrolytic solution so as to allow electrochemical control of the imaged substrate. When applied to an eleclronically conducting polymer, this... 

For STM, both electrodes, the probe and the sample, must be conductive. A sharp tip is used as a probe, and it is usually produced by electrochemical etching of a tungsten wire in KOH or NaOH solution (see Section 5.1.1). The tip is brought close to the sample surface by piezoelements until a tunnel current in the nA-range flows through the vacuum or air gap. 

At a surface, not only can the atomic structure differ from the bulk, but electronic energy levels are present that do not exist in the bulk band structure. These are referred to as surface states . If the states are occupied, they can easily be measured with photoelectron spectroscopy (described in section A 1.7.5.1 and section Bl.25.2). If the states are unoccupied, a teclmique such as inverse photoemission or x-ray absorption is required [22, 23]. Also, note that STM has been used to measure surface states by monitoring the tunnelling current as a fiinction of the bias voltage [24] (see section BT20). This is sometimes called scamiing tuimelling spectroscopy (STS). 

The teclmique of scaiming electrochemical microscopy (SECM) [62] uses the same apparatus as in electrochemical STM, but instead of measuring tunnelling currents, the reaction O + ue —> R (where O and R... 

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