Scanning tunneling microscope

A scanning tunneling microscope is a type of scanning probe microscope used for imaging surfaces at the atomic level. Its development in 1981 earned its inventors, Gerd Binnig and Heinrich Rohrer, then at IBM Zürich, the Nobel Prize in Physics in 1986. STM senses the surface by using an extremely sharp conducting tip that can distinguish features smaller than 0.1 nm with a 0.01 nm depth resolution. This means that individual atoms can routinely be imaged and manipulated. Most scanning tunneling microscopes are built for use in ultra-high vacuum at temperatures approaching absolute zero, but variants exist for studies in air, water and other environments, and for temperatures over 1000 °C.
STM is based on the concept of quantum tunneling. 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 of the sample. Information is acquired by monitoring the current as the tip scans across the surface, and is usually displayed in image form.
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. Using this technique, the local density of the electronic states can be reconstructed. 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, for example from quasiparticle interference imaging.
Scanning tunneling microscopy can be a challenging technique, as it requires extremely clean and stable surfaces, sharp tips, excellent vibration isolation, and sophisticated electronics. Nonetheless, many hobbyists build their own microscopes.

Procedure

The tip is brought close to the sample by a coarse positioning mechanism that is usually monitored visually. At close range, fine control of the tip position with respect to the sample surface is achieved by piezoelectric scanner tubes whose length can be altered by a control voltage. A bias voltage is applied between the sample and the tip, and the scanner is gradually elongated until the tip starts receiving the tunneling current. The tip–sample separation w is then kept somewhere in the 4–7 Å range, slightly above the height where the tip would experience repulsive interaction but still in the region where attractive interaction exists The tunneling current, being in the sub-nanoampere range, is amplified as close to the scanner as possible. Once tunneling is established, the sample bias and tip position with respect to the sample are varied according to the requirements of the experiment.
As the tip is moved across the surface in a discrete x–''y matrix, the changes in surface height and population of the electronic states cause changes in the tunneling current. Digital images of the surface are formed in one of the two ways: in the constant-height mode changes of the tunneling current are mapped directly, while in the constant-current mode the voltage that controls the height of the tip is recorded while the tunneling current is kept at a predetermined level.
In constant-current mode, feedback electronics adjust the height by a voltage to the piezoelectric height-control mechanism. If at some point the tunneling current is below the set level, the tip is moved towards the sample, and conversely. 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 some cases it may not be clear whether height changes came as a result of one or the other.
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 raster scan of the tip is anything from a 128×128 to a 1024×1024 matrix, and for each point of the raster a single value is obtained. The images produced by STM are therefore grayscale, and color is only added in post-processing in order to visually emphasize important features.
In addition to scanning across the sample, information on the electronic structure at a given location in the sample can be obtained by sweeping the bias voltage and measuring current change at a specific location. This type of measurement is called scanning tunneling spectroscopy and typically results in a plot of the local density of states as a function of the electrons' energy within the sample. The advantage of STM over other measurements of the density of states lies in its ability to make extremely local measurements. This is how, for example, the density of states at an impurity site can be compared to the density of states around the impurity and elsewhere on the surface.

Instrumentation

The main components of a scanning tunneling microscope are the scanning tip, piezoelectrically controlled height and lateral scanner, and coarse sample-to-tip approach mechanism. The microscope is controlled by dedicated electronics and a computer. The system is supported on a vibration isolation system.
The tip is often made of tungsten or platinum–iridium wire, though gold is also used. Tungsten tips are usually made by electrochemical etching, and platinum–iridium tips by mechanical shearing. The resolution of an image is limited by the radius of curvature of the scanning tip. Sometimes, image artefacts occur if the tip has more than one apex at the end; most frequently double-tip imaging is observed, a situation in which two apices contribute equally to the tunneling. While several processes for obtaining sharp, usable tips are known, the ultimate test of quality of the tip is only possible when it is tunneling in the vacuum. 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.
In most modern designs the scanner is a hollow tube of a radially polarized piezoelectric with metallized surfaces. 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. The tube material is a lead zirconate titanate ceramic with a piezoelectric constant of about 5 nanometres per volt. The tip is mounted at the center of the tube. Because of some crosstalk between the electrodes and inherent nonlinearities, the motion is calibrated, and voltages needed for independent x, y and z motion applied according to calibration tables.
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 the first STM by Binnig and Rohrer, magnetic levitation was used to keep the STM free from vibrations; now mechanical spring or gas spring systems are often employed. Additionally, mechanisms for vibration damping using eddy currents are sometimes implemented. Microscopes designed for long scans in scanning tunneling spectroscopy need extreme stability and are built in anechoic chambers—dedicated concrete rooms with acoustic and electromagnetic isolation that are themselves floated on vibration isolation devices inside the laboratory.
Maintaining the tip position with respect to the sample, scanning the sample and acquiring the data is computer-controlled. Dedicated software for scanning probe microscopies is used for image processing as well as performing quantitative measurements.
Some scanning tunneling microscopes are capable of recording images at high frame rates. Videos made of such images can show surface diffusion or track adsorption and reactions on the surface. In video-rate microscopes, frame rates of 80 Hz have been achieved with fully working feedback that adjusts the height of the tip.

Principle of operation

Quantum tunneling of electrons is a functioning concept of STM that arises from quantum mechanics. Classically, a particle hitting an impenetrable barrier will not pass through. If the barrier is described by a potential acting along z direction, in which an electron of mass m_e acquires the potential energy U, the electron's trajectory will be deterministic and such that the sum E of its kinetic and potential energies is at all times conserved:
The electron will have a defined, non-zero momentum p only in regions where the initial energy E is greater than U. In quantum physics, however, the electron can pass through classically forbidden regions. This is referred to as tunneling.

Rectangular barrier model

The simplest model of tunneling between the sample and the tip of a scanning tunneling microscope is that of a rectangular potential barrier. An electron of energy E is incident upon an energy barrier of height U, in the region of space of width w. An electron's behavior in the presence of a potential U, assuming one-dimensional case, is described by wave functions that satisfy the Schrödinger equation
where ħ is the reduced Planck constant, z is the position, and m_e is the electron mass. In the zero-potential regions on two sides of the barrier, the wave function takes on the forms
where. Inside the barrier, where E < U, the wave function is a superposition of two terms, each decaying from one side of the barrier:
where.
The coefficients r and t provide measure of how much of the incident electron's wave is reflected or transmitted through the barrier. Namely, of the whole impinging particle current only is transmitted, as can be seen from the probability current expression
which evaluates to. The transmission coefficient is obtained from the continuity condition on the three parts of the wave function and their derivatives at z = 0 and z = w. This gives where. 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. The work function is the minimum energy needed to bring an electron from an occupied level, the highest of which is the Fermi level, to vacuum level. The electrons can tunnel between two metals only from occupied states on one side into the unoccupied states of the other side of the barrier. Without bias, Fermi energies are flush, and there is no tunneling. Bias shifts electron energies in one of the electrodes higher, and those electrons that have no match at the same energy on the other side will tunnel. In experiments, bias voltages of a fraction of 1 V are used, so is of the order of 10 to 12 nm⁻¹, while w is a few tenths of a nanometre. The barrier is strongly attenuating. The expression for the transmission probability reduces to The tunneling current from a single level is therefore
where both wave vectors depend on the level's energy E, and
Tunneling current is exponentially dependent on the separation of the sample and the tip, typically reducing by an order of magnitude when the separation is increased by 1 Å. 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.