Scanning tunneling microscope
Its development in 1981 earned its inventors, Gerd Binnig and Heinrich Rohrer, then at IBM Zürich, the Nobel Prize in Physics in 1986.
When the tip is brought very near to the surface to be examined, a bias voltage applied between the two allows electrons to tunnel through the vacuum separating them.
The resulting tunneling current is a function of the tip position, applied voltage, and the local density of states (LDOS) of the sample.
[5] A refinement of the technique known as scanning tunneling spectroscopy consists of keeping the tip in a constant position above the surface, varying the bias voltage and recording the resultant change in current.
[7] This is sometimes performed in high magnetic fields and in presence of impurities to infer the properties and interactions of electrons in the studied material.
Scanning tunneling microscopy can be a challenging technique, as it requires extremely clean and stable surfaces, sharp tips, excellent vibration isolation, and sophisticated electronics.
This mode is relatively slow, as the electronics need to check the tunneling current and adjust the height in a feedback loop at each measured point of the surface.
When the surface is atomically flat, the voltage applied to the z-scanner mainly reflects variations in local charge density.
But when an atomic step is encountered, or when the surface is buckled due to reconstruction, the height of the scanner also have to change because of the overall topography.
The image formed of the z-scanner voltages that were needed to keep the tunneling current constant as the tip scanned the surface thus contain both topographical and electron density data.
In constant-height mode, the z-scanner voltage is kept constant as the scanner swings back and forth across the surface, and the tunneling current, exponentially dependent on the distance, is mapped.
This mode of operation is faster, but on rough surfaces, where there may be large adsorbed molecules present, or ridges and groves, the tip will be in danger of crashing.
The images produced by STM are therefore grayscale, and color is only added in post-processing in order to visually emphasize important features.
[4] This type of measurement is called scanning tunneling spectroscopy (STS) and typically results in a plot of the local density of states as a function of the electrons' energy within the sample.
Every so often the tips can be conditioned by applying high voltages when they are already in the tunneling range, or by making them pick up an atom or a molecule from the surface.
The outer surface is divided into four long quadrants to serve as x and y motion electrodes with deflection voltages of two polarities applied on the opposing sides.
[5] Due to the extreme sensitivity of the tunneling current to the separation of the electrodes, proper vibration isolation or a rigid STM body is imperative for obtaining usable results.
In video-rate microscopes, frame rates of 80 Hz have been achieved with fully working feedback that adjusts the height of the tip.
The expression can be further simplified, as follows: In STM experiments, typical barrier height is of the order of the material's surface work function W, which for most metals has a value between 4 and 6 eV.
[5] Because of this, even when tunneling occurs from a non-ideally sharp tip, the dominant contribution to the current is from its most protruding atom or orbital.
The current due to an applied voltage V (assume tunneling occurs from the sample to the tip) depends on two factors: 1) the number of electrons between the Fermi level EF and EF − eV in the sample, and 2) the number among them which have corresponding free states to tunnel into on the other side of the barrier at the tip.
[16] His model takes two separate orthonormal sets of wave functions for the two electrodes and examines their time evolution as the systems are put close together.
Consequently, the time evolution of the coefficients is given by Because the potential UT is zero at the distance of a few atomic diameters away from the surface of the electrode, the integration over z can be done from a point z0 somewhere inside the barrier and into the volume of the tip (z > z0).
The fraction, as written above, is a representation of the delta function, so Solid-state systems are commonly described in terms of continuous rather than discrete energy levels.
for those that will actually tunnel: Typical experiments are run at a liquid-helium temperature (around 4 K), at which the Fermi-level cut-off of the electron population is less than a millielectronvolt wide.
Bardeen's tunneling matrix element is an integral of the wave functions and their gradients over a surface separating the two planar electrodes: The exponential dependence of the tunneling current on the separation of the electrodes comes from the very wave functions that leak through the potential step at the surface and exhibit exponential decay into the classically forbidden region outside of the material.
With such a simplification, their model proved valuable for interpreting images of surface features bigger than a nanometre, even though it predicted atomic-scale corrugations of less than a picometre.
In sub-nanometre-resolution experiments, the convolution of the tip and sample surface states will always be important, to the extent of the apparent inversion of the atomic corrugations that may be observed within the same scan.
Such effects can only be explained by modeling of the surface and tip electronic states and the ways the two electrodes interact from first principles.
IBM researchers famously developed a way to manipulate xenon atoms adsorbed on a nickel surface.
