Quantum tunneling current

Because STM measures a quantum-mechanical tunneling current, the tip must be within a few A of a conducting surface. Therefore any surface oxide or other contaminant will complicate operation under ambient conditions. Nevertheless, a great deal of work has been done in air, liquid, or at low temperatures on inert surfaces. Studies of adsorbed molecules on these surfaces (for example, liquid crystals on highly oriented, pyrolytic graphite ) have shown that STM is capable of even atomic resolution on organic materials. 

Classically there should not be a current between the sample and the tip, but as the distance becomes below 0.5 nm quantum mechanics takes over and electrons may tunnel through the gap, giving rise to a tunnel current on the order of 1 nA, which can then be measured. The experimental set-up is shown schematically in Fig. 4.27. 

In a quantum mechanical treatment the tunnel current is given as a function of distance d between tip and surface as ... 

Figure 19b displays the 2D histogram of the experimentally obtained conductance of N4 plotted vs distance [63]. The distance scale z is normalized with respect to z = 0 at G = 0.7 G0, to a common point. The chosen procedure is justified, because of the steep decay of the tunneling current after breaking of the last atomic contact. The histogram counts the occurrence of [log(G/Go), z ] pairs in a 2D field. Figure 19b exhibits the features of gold quantum contacts at G > Go, and a second cloud-like pattern in [10 5 10 4 G0, 0 0.5 nm]. We attribute the latter to the formation of single-molecule junctions of only one type. The center of the cloud is located at G = 3.5 4.5 x 10 5 Go, close to the peak position in the ID histogram (Fig. 19a). The extension of the cloud along the distance scale is around 0.5 nm, close to the typical length of the plateaus (the inset of Fig. 19a).

The scanning tunneling microscope uses an atomically sharp probe tip to map contours of the local density of electronic states on the surface. This is accomplished by monitoring quantum transmission of electrons between the tip and substrate while piezoelectric devices raster the tip relative to the substrate, as shown schematically in Fig. 1 [38]. The remarkable vertical resolution of the device arises from the exponential dependence of the electron tunneling process on the tip-substrate separation, d. In the simplest approximation, the tunneling current, 1, can be simply written in terms of the local density of states (LDOS), ps(z,E), at the Fermi level (E = Ep) of the sample, where V is the bias voltage between the tip and substrate... 

In the s-wave-tip model (Tersoff and Hamann, 1983, 1985), the tip was also modeled as a protruded piece of Sommerfeld metal, with a radius of curvature R, see Fig. 1.25. The solutions of the Schrodinger equation for a spherical potential well of radius R were taken as tip wavefunctions. Among the numerous solutions of this macroscopic quantum-mechanical problem, Tersoff and Hamann assumed that only the s-wave solution was important. Under such assumptions, the tunneling current has an extremely simple form. At low bias, the tunneling current is proportional to the Fermi-level LDOS at the center of curvature of the tip Pq. 

The local modification of sample wavefunctions due to the proximity of the tip, and consequently the involvement of the Bloch functions outside the energy window Er eV in the tunneling process, has an effect on the limit of the energy resolution of scanning tunneling spectroscopy. This effect is discussed in detail by Ivanchenko and Riseborough (1991). First, if the tunneling current is determined by the bare wavefunctions of the sample and the tip, the process is linear, and there is no effect of quantum uncertainty. The effect of quantum uncertainty is due to the modification or distortion of the sample wavefunction due to the existence of the tip. Here, we present a simple treatment of this problem in terms of the MBA. 

It is believed that surface localized electron-hole pairs produced under light in SC nanoparticles participate in photo-induced processes of charge transfer between nanoparticles. These processes most probably of quantum tunnel type determine photoconductivity of composite films containing SC nanoparticles in a dielectric matrix. The photocurrent response time in this case should correspond to the lifetime ip of such pairs, which is of the order nanosecond and even more [6]. This rather long ip makes photo-induced tunnel current in composite film possible. 

In all cases of electron transport, whether it be hopping, thermal emission, or quantum tunneling, the effect of the electric field in the oxide film is extremely important. In fact, the electric field effect on ion motion is the primary reason the electronic species must be considered at all in most real metal oxidation reactions. This can be understood better when we discuss the coupled-currents approach [10,11] in Sect. 1.15. 

To understand how STM works, it is vital to know what is tunneling current, and how it is related to all the experimental observations. Tunneling current is originated from the wavelike properties of particles (electrons, in this case) in quantum mechanics. When an electron is incident upon a vacuum barrier with potential energy larger than the kinetic energy of the electron, there is still a non-zero probability that it may traverse the forbidden region and reappear on the other side of the barrier. It is shown by the leak out electron wave function in Fig. 2. 

Quantum mechanics allows a few electrons to traverse the barrier if the thickness z is small. The probability that an electron will cross the barrier is the tunneling current (7) flowing across the vacuum gap, and it decays exponentially with the barrier width z as... 

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