Introduction to STM

The Scanning Tunneling Microscope

The Scanning Tunneling Microscope (STM) gained instant international fame both in the scientific community as well as in the mainstream culture by revealing images of atomic structure in real space for the first time. Since its invention by Binnig and Rohrer at the IBM laboratories in 1981 the STM has been a core tool of nanoscience not only for imaging but also for probing the electronic structure of surfaces with incomparable energy resolution. It is also reknowned for building and manipulating nanostructure one atom at a time. In this short introduction to STM we will present the theoretical foundations and typical modes of operation of the STM. This page will give a brief outline if the underlying tunneling effect along with some details on various applications.

Tunneling 101:

At the foundation of the STM is the tunneling effect. Its most basic and important properties can be easily derived from the direct application of the Schrodinger equation onto a plane wave travelling through a square potential as shown in Figure 1. In this model, the electrons or holes (represented here as a single particle planar wavefunction) will be able to flow between the sample and the tip across the barrier via the overlap of the evanescent wave function inside the vacuum.

Figure 1: Plane wave travelling trough a energy barrier defined by the work function of the sample from the sample to the tip separated by an external bias eV.

It can be shown that the tunneling current (I) follows as

under a small applied potential (U), particle mass (m), and separation distance D. One can readily see that the tunneling barrier is Ohmic and linear to the first approximation. The most central result in the above current expression is that the tunneling current will decay exponentially with an increasing barrier width. The characteristic decay length is linked to the height of the barrier (work function of the surface) as well as the electron/holes tunneling properties. In standard cases the characteristic length of separation distance is in the order of few Angstrom, 10^-10m, or simply put, the size of an atom! Those two characteristics (the exponential dependence of the tunneling current and a nominal atomic decay length) confer the STM its ability of probing condensed matter down to its most fundamental elements, the atoms.

STM operation:

Figure 2: Operating diagram of a scanning tunneling microscope.

The main control for operating the STM is to set the tunneling impedance which determines the tip ? sample distance. The larger the impedance is the larger the sample-tip separation will be (and the less the resolution of the measurement). The experimentalist first polarizes the tunneling junction by applying an electric potential ranging from a few meV to a few V. The tip is then gently approached towards the sample until the tunneling current reaches a pre-determined value, typically in the few pA to few nA range. The tunneling impedance can be continually adjusted from 1MOhms up to 100GOhms by controlling actively the width D of the vacuum barrier by adjusting the tip height.

The nature of the probe is point-like in nature. In order to get spatial information the tip is mounted on a XYZ piezoelectric actuator and raster across the surface. During the course of the scan the tunneling current is kept constant by adjusting the height of the tip which is recorded and then process to form a tri-dimensional dataset. An example of representation of such a dataset can be seen in Figure 3. Here we used both tridimensional surface plot and false colors to emphasizes four consecutive single atomic steps from a single crystal of Silver (40*40 nm) oriented along its [111].

Figure 3: 40*40nm STM image of the Silver 111 surface shows four distinct atomic terraces.

Tunneling 201:

The application of Schrodinger? s equation to a simple tunneling problem enabled us to understand how the STM can access the topography of a surface at the atomic level. The second power of the STM is the capability of performing local spectroscopy. To understand its origin one need to include a more detailed description of the effect of varying biases upon the tunneling current.

Prior to the invention of STM the tunneling of particles between two planar (semi-, super-, metallic) conductors separated by a thin insulating layer was a well studied problem both experimentally and theoretically. The model of Bardeen state that the tunneling current between two reservoir u and v derived trough first order perturbation theory is:

Here, the current is the sum over all the possible tunneling events between the discrete tip and sample states time the tunneling matrix Muv. For most practical purposes some simplifications are made to the above equation. First, we move from the concept of discrete electronic states to the idea of a band structure and its density of states (DOS) which is more adapted to describe crystalline materials. Furthermore we can assume that the DOS is constant at the Fermi energy (EF), for the tip, since its metallic. Unfortunately, a quantitative evaluation of the tunneling matrix is most often avoided because the exact shape of the tip is still difficult to characterize and even more to control. Under those assumptions one can write,

where d is the tunneling distance and rho(E) is the DOS of the sample. This expression is a very powerful approximation since it links the tunneling current to the DOS of the sample which is central information in condensed matter physics.

Figure 4: A: Topography of Ag(111) surface overlaid with a dI/dV STS map in order to enhance the standing wave pattern of the surface state electrons reflected at the step edges. B: STS of the Ag surface state revealing the stepwise onset in the density of states typical for a 2D electron gas. C: Regular methionine grating on Ag(111) self-assembled at room temperature. D: Tunneling spectrum taken in between the molecular chains demonstrating the 1D confinement of surface state electrons. E: Chain of Fe monomers in a molecular resonator. F: Tunneling spectrum taken at Ag patches between Fe atoms revealing quantum corral formation. There is a continuous increase of the surface state onset with increasing confinement.

Figure 4 shows the stunning validity of the STM scan approach when applied to an exquisitely simple and controlled quantum system: the confinement of the Shockley surface state; a two dimensional electron gas (2DEG). The upper left hand side (A) shows a STM image of the surface of bare silver 111. This medium supports the 2DEG. The upper right side shows its DOS measured with the STM overlaid with its theoretical expectation, a step function. In the second row the initial 2DEG have been confined to a one dimensional channel by the addition of electronic reflectors (here some methionine based molecular nanowires). The measured DOS now presents sharp Van Hove singularities characteristics of a 1DEG that can be model within a simple Fabry-Perot resonator description. In a last stage, additional electronic mirrors are added inside the one dimensional trench in the form of single Fe atoms. Now the electron gas is fully confine in the three direction of space. Once again, the theoretical Lorentzian shape for the DOS of a quantum dot can be mapped onto the experimental spectroscopy.