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A scanning tunneling microscope (STM) is a type of scanning probe microscope used for imaging
surface A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is ...
s at the
atom Atoms are the basic particles of the chemical elements. An atom consists of a atomic nucleus, nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished fr ...
ic level. Its development in 1981 earned its inventors, Gerd Binnig and
Heinrich Rohrer Heinrich Rohrer (6 June 1933 – 16 May 2013) was a Swiss physicist who shared half of the 1986 Nobel Prize in Physics with Gerd Binnig for the design of the scanning tunneling microscope (STM). The other half of the Prize was awarded to Ernst R ...
, then at IBM Zürich, the
Nobel Prize in Physics The Nobel Prize in Physics () is an annual award given by the Royal Swedish Academy of Sciences for those who have made the most outstanding contributions to mankind in the field of physics. It is one of the five Nobel Prizes established by the ...
in 1986. STM senses the surface by using an extremely sharp
conducting Conducting is the art of directing a musical performance, such as an orchestral or Choir, choral concert. It has been defined as "the art of directing the simultaneous performance of several players or singers by the use of gesture." The primary d ...
tip that can distinguish features smaller than 0.1  nm with a 0.01 nm (10  pm) 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 Ultra-high vacuum (often spelled ultrahigh in American English, UHV) is the vacuum regime characterised by pressures lower than about . UHV conditions are created by pumping the gas out of a UHV chamber. At these low pressures the mean free path of ...
at temperatures approaching
absolute zero Absolute zero is the lowest possible temperature, a state at which a system's internal energy, and in ideal cases entropy, reach their minimum values. The absolute zero is defined as 0 K on the Kelvin scale, equivalent to −273.15 ° ...
, 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 In physics, a quantum (: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a property can be "quantized" is referred to as "the hypothesis of quantization". This me ...
. When the tip is brought very near to the surface to be examined, a
bias Bias is a disproportionate weight ''in favor of'' or ''against'' an idea or thing, usually in a way that is inaccurate, closed-minded, prejudicial, or unfair. Biases can be innate or learned. People may develop biases for or against an individ ...
voltage applied between the two allows
electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...
s to tunnel through the
vacuum A vacuum (: vacuums or vacua) is space devoid of matter. The word is derived from the Latin adjective (neuter ) meaning "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressur ...
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. 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. Scanning tunneling microscopy can be a challenging technique, as it requires extremely clean and stable surfaces, sharp tips, excellent
vibration isolation ''Vibration isolation'' is the prevention of transmission of vibration from one component of a system to others parts of the same system, as in Building, buildings or mechanical systems. Vibration is undesirable in many domains, primarily engineere ...
, 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 Piezoelectricity (, ) is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as bone, DNA, and various proteins—in response to applied stress (mechanics), mechanical s ...
scanner tubes whose length can be altered by a control voltage. A bias
voltage Voltage, also known as (electrical) potential difference, electric pressure, or electric tension, is the difference in electric potential between two points. In a Electrostatics, static electric field, it corresponds to the Work (electrical), ...
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 (0.4–0.7  nm) 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 (''z'') 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 Reconstruction may refer to: Politics, history, and sociology *Reconstruction (law), the transfer of a company's (or several companies') business to a new company *''Perestroika'' (Russian for "reconstruction"), a late 20th century Soviet Union ...
, 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 A raster scan, or raster scanning, is the rectangular pattern of image capture and reconstruction in television. By analogy, the term is used for raster graphics, the pattern of image storage and transmission used in most computer bitmap image s ...
of the tip is anything from a 128×128 to a 1024×1024 (or more) matrix, and for each point of the raster a single value is obtained. The images produced by STM are therefore
grayscale In digital photography, computer-generated imagery, and colorimetry, a greyscale (more common in Commonwealth English) or grayscale (more common in American English) image is one in which the value of each pixel is a single sample (signal), s ...
, 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 (along with a small AC modulation to directly measure the derivative) and measuring current change at a specific location. This type of measurement is called scanning tunneling spectroscopy (STS) and typically results in a plot of the local
density of states In condensed matter physics, the density of states (DOS) of a system describes the number of allowed modes or quantum state, states per unit energy range. The density of states is defined as where N(E)\delta E is the number of states in the syste ...
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 In chemistry and materials science, impurities are chemical substances inside a confined amount of liquid, gas, or solid. They differ from the chemical composition of the material or compound. Firstly, a pure chemical should appear in at least on ...
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 (''z'' axis) and lateral (''x'' and ''y'' axes) 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 Tungsten (also called wolfram) is a chemical element; it has symbol W and atomic number 74. It is a metal found naturally on Earth almost exclusively in compounds with other elements. It was identified as a distinct element in 1781 and first ...
or platinum–iridium wire, though
gold Gold is a chemical element; it has chemical symbol Au (from Latin ) and atomic number 79. In its pure form, it is a brightness, bright, slightly orange-yellow, dense, soft, malleable, and ductile metal. Chemically, gold is a transition metal ...
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 In differential geometry, the radius of curvature, , is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius ...
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 Magnetic levitation (maglev) or magnetic suspension is a method by which an object is levitation (physics), suspended with no support other than magnetic fields. Lorentz force, Magnetic force is used to counteract the effects of the gravitation ...
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 chamber An anechoic chamber (''an-echoic'' meaning "non-reflective" or "without echoes") is a room designed to stop reflection (physics), reflections or Echo (phenomenon), echoes of either sound or electromagnetic waves. They are also often isolate ...
s—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 An image or picture is a visual representation. An image can be two-dimensional, such as a drawing, painting, or photograph, or three-dimensional, such as a carving or sculpture. Images may be displayed through other media, including a pr ...
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 Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical p ...
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 Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
. 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''(''z''), the electron's trajectory will be deterministic and such that the sum ''E'' of its kinetic and potential energies is at all times conserved: : E = \frac + U(z). The electron will have a defined, non-zero momentum ''p'' only in regions where the initial energy ''E'' is greater than ''U''(''z''). 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''(''z''), assuming one-dimensional case, is described by
wave function In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters and (lower-case and capital psi (letter) ...
s \psi(z) that satisfy the
Schrödinger equation The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. It is named after E ...
: -\frac \frac + U(z)\,\psi(z) = E\,\psi(z), where ''ħ'' is the
reduced Planck constant The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a ...
, ''z'' is the position, and ''m''e is the
electron mass In particle physics, the electron mass (symbol: ) is the mass of a stationary electron, also known as the invariant mass of the electron. It is one of the fundamental constants of physics. It has a value of about or about , which has an energy ...
. In the zero-potential regions on two sides of the barrier, the wave function takes on the forms : \psi_L(z) = e^ + r\,e^ for ''z'' < 0, : \psi_R(z) = t\,e^ for ''z'' > ''w'', where k = \tfrac \sqrt. Inside the barrier, where ''E'' < ''U'', the wave function is a superposition of two terms, each decaying from one side of the barrier: : \psi_B (z) = \xi e^ + \zeta e^ for 0 < ''z'' < ''w'', where \kappa = \tfrac \sqrt. 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 j_i = \hbar k/m_\text only j_t = , t, ^2\, j_i is transmitted, as can be seen from the probability current expression : j_t = -i \frac \left\, which evaluates to j_t = \tfrac \vert t \vert^2. 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'' (detailed derivation is in the article Rectangular potential barrier). This gives , t, ^2 = \big + \tfrac \varepsilon^(1 - \varepsilon)^ \sinh^2\kappa w\big, where \varepsilon = E/U. 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 In solid-state physics, the work function (sometimes spelled workfunction) is the minimum thermodynamic work (i.e., energy) needed to remove an electron from a solid to a point in the vacuum immediately outside the solid surface. Here "immediately" ...
''W'', which for most metals has a value between 4 and 6 eV. The
work function In solid-state physics, the work function (sometimes spelled workfunction) is the minimum thermodynamic work (i.e., energy) needed to remove an electron from a solid to a point in the vacuum immediately outside the solid surface. Here "immediately" ...
is the minimum energy needed to bring an electron from an occupied level, the highest of which is the
Fermi level The Fermi level of a solid-state body is the thermodynamic work required to add one electron to the body. It is a thermodynamic quantity usually denoted by ''μ'' or ''E''F for brevity. The Fermi level does not include the work required to re ...
(for metals at ''T'' = 0 K), 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 \kappa 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 , t, ^2 = 16\,\varepsilon(1 - \varepsilon)\,e^. The tunneling current from a single level is therefore : j_t = \left frac\right2 \, \frac\,e^, where both wave vectors depend on the level's energy ''E'', k = \tfrac \sqrt, and \kappa = \tfrac\sqrt. 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 (0.1 nm). 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.


Tunneling between two conductors

As a result of the restriction that the tunneling from an occupied energy level on one side of the barrier requires an empty level of the same energy on the other side of the barrier, tunneling occurs mainly with electrons near the Fermi level. The tunneling current can be related to the density of available or filled states in the sample. 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 ''E''F and ''E''F − ''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. The higher the density of available states in the tunneling region the greater the tunneling current. By convention, a positive ''V'' means that electrons in the tip tunnel into empty states in the sample; for a negative bias, electrons tunnel out of occupied states in the sample into the tip. For small biases and temperatures near absolute zero, the number of electrons in a given volume (the electron concentration) that are available for tunneling is the product of the density of the electronic states ''ρ''(''E''F) and the energy interval between the two Fermi levels, ''eV''. Half of these electrons will be travelling away from the barrier. The other half will represent the
electric current An electric current is a flow of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is defined as the net rate of flow of electric charge through a surface. The moving particles are called charge c ...
impinging on the barrier, which is given by the product of the electron concentration, charge, and velocity ''v'' (''I''i = ''nev''), : I_i = \tfrac e^2 v\,\rho(E_\text)\,V. The tunneling electric current will be a small fraction of the impinging current. The proportion is determined by the transmission probability ''T'', so\ : I_t = \tfrac e^2v\,\rho(E_\text)\,V\,T. In the simplest model of a rectangular potential barrier the transmission probability coefficient ''T'' equals , ''t'', 2.


Bardeen's formalism

A model that is based on more realistic wave functions for the two electrodes was devised by
John Bardeen John Bardeen (; May 23, 1908 – January 30, 1991) was an American solid-state physicist. He is the only person to be awarded the Nobel Prize in Physics twice: first in 1956 with William Shockley and Walter Houser Brattain for their inventio ...
in a study of the metal–insulator–metal junction. 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. Bardeen's novel method, ingenious in itself, solves a time-dependent perturbative problem in which the perturbation emerges from the interaction of the two subsystems rather than an external potential of the standard Rayleigh–Schrödinger perturbation theory. Each of the wave functions for the electrons of the sample (S) and the tip (T) decay into the vacuum after hitting the surface potential barrier, roughly of the size of the surface work function. The wave functions are the solutions of two separate Schrödinger equations for electrons in potentials ''U''S and ''U''T. When the time dependence of the states of known energies E^\text_\mu and E^\text_\nu is factored out, the wave functions have the following general form : \psi^\text_\mu(t) = \psi^\text_\mu \exp\left(-\frac E^\text_\mu t\right), : \psi^\text_\nu(t) = \psi^\text_\nu \exp\left(-\frac E^\text_\nu t\right). If the two systems are put closer together, but are still separated by a thin vacuum region, the potential acting on an electron in the combined system is ''U''T + ''U''S. Here, each of the potentials is spatially limited to its own side of the barrier. Only because the tail of a wave function of one electrode is in the range of the potential of the other, there is a finite probability for any state to evolve over time into the states of the other electrode. The future of the sample's state ''μ'' can be written as a linear combination with time-dependent coefficients of \psi^\text_\mu(t) and all \psi^\text_\nu(t): : \psi(t) = \psi^\text_\mu(t) + \sum_\nu c_\nu(t) \psi^\text_\nu(t) with the initial condition c_\nu(0) = 0. When the new wave function is inserted into the Schrödinger equation for the potential ''U''T + ''U''S, the obtained equation is projected onto each separate \psi^\text_\nu (that is, the equation is multiplied by a ^* and integrated over the whole volume) to single out the coefficients c_\nu. All \psi^\text_\mu are taken to be ''nearly orthogonal'' to all \psi^\text_\nu (their overlap is a small fraction of the total wave functions), and only first-order quantities retained. Consequently, the time evolution of the coefficients is given by : \frac c_\nu(t) = -\frac \int \psi^\text_\mu \,U_\text\, ^* \,\mathrmx\,\mathrmy\,\mathrmz\,\exp\left \frac (E^\text_\mu - E^\text_\nu) t\right Because the potential ''U''T 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 ''z''0 somewhere inside the barrier and into the volume of the tip (''z'' > ''z''0). If the tunneling matrix element is defined as : M_ = \int_ \psi^\text_\mu \,U_\text\, ^* \,\mathrmx\,\mathrmy\,\mathrmz, the probability of the sample's state ''μ'' evolving in time ''t'' into the state of the tip ''ν'' is : , c_\nu (t), ^2 = , M_, ^2 \frac. In a system with many electrons impinging on the barrier, this probability will give the proportion of those that successfully tunnel. If at a time ''t'' this fraction was , c_\nu (t), ^2, at a later time ''t'' + d''t'' the total fraction of , c_\nu(t + \mathrmt), ^2 would have tunneled. The ''current'' of tunneling electrons at each instance is therefore proportional to , c_\nu(t + \mathrmt), ^2 - , c_\nu(t), ^2 divided by \mathrmt, which is the time derivative of , c_\nu(t), ^2, : \Gamma_\ \overset\ \frac , c_\nu(t), ^2 = \frac , M_, ^2\frac. The time scale of the measurement in STM is many orders of magnitude larger than the typical femtosecond time scale of electron processes in materials, and t/\hbar is large. The fraction part of the formula is a fast-oscillating function of (E^\text_\mu - E^\text_\nu) that rapidly decays away from the central peak, where E^\text_\mu = E^\text_\nu. In other words, the most probable tunneling process, by far, is the elastic one, in which the electron's energy is conserved. The fraction, as written above, is a representation of the delta function, so : \Gamma_ = \frac , M_, ^2 \delta(E^\text_\mu - E^\text_\nu). Solid-state systems are commonly described in terms of continuous rather than discrete energy levels. The term \delta(E^\text_\mu - E^\text_\nu) can be thought of as the
density of states In condensed matter physics, the density of states (DOS) of a system describes the number of allowed modes or quantum state, states per unit energy range. The density of states is defined as where N(E)\delta E is the number of states in the syste ...
of the tip at energy E^\text_\mu, giving : \Gamma_ = \frac , M_, ^2 \rho_\text(E^\text_\mu). The number of energy levels in the sample between the energies \varepsilon and \varepsilon + \mathrm\varepsilon is \rho_\text(\varepsilon)\,\mathrm\varepsilon. When occupied, these levels are spin-degenerate (except in a few special classes of materials) and contain charge 2e \cdot \rho_\text(\varepsilon)\,\mathrm\varepsilon of either spin. With the sample biased to voltage V, tunneling can occur only between states whose occupancies, given for each electrode by the Fermi–Dirac distribution f, are not the same, that is, when either one or the other is occupied, but not both. That will be for all energies \varepsilon for which f(E_\text - eV + \varepsilon) - f(E_\text + \varepsilon) is not zero. For example, an electron will tunnel from energy level E_\text - eV in the sample into energy level E_\text in the tip (\varepsilon = 0), an electron at E_\text in the sample will find unoccupied states in the tip at E_\text + eV (\varepsilon = eV), and so will be for all energies in between. The tunneling current is therefore the sum of little contributions over all these energies of the product of three factors: 2e \cdot \rho_\text(E_\text - eV + \varepsilon)\,\mathrm\varepsilon representing available electrons, f(E_\text - eV + \varepsilon) - f(E_\text + \varepsilon) for those that are allowed to tunnel, and the probability factor \Gamma for those that will actually tunnel: : I_t = \frac \int_^ (E_\text - eV + \varepsilon) - f(E_\text + \varepsilon)\, \rho_\text(E_\text - eV + \varepsilon) \, \rho_\text(E_\text + \varepsilon) \, , M, ^2 \, d \varepsilon. 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. The allowed energies are only those between the two step-like Fermi levels, and the integral becomes : I_t = \frac \int_0^ \rho_\text(E_\text - eV + \varepsilon) \, \rho_\text(E_\text + \varepsilon) \, , M, ^2 \, d \varepsilon. When the bias is small, it is reasonable to assume that the electron wave functions and, consequently, the tunneling matrix element do not change significantly in the narrow range of energies. Then the tunneling current is simply the convolution of the densities of states of the sample surface and the tip: : I_t \propto \int_0^ \rho_\text(E_\text - eV + \varepsilon) \, \rho_\text(E_\text + \varepsilon) \, d \varepsilon. How the tunneling current depends on distance between the two electrodes is contained in the tunneling matrix element : M_ = \int_ \psi^\text_\mu \,U_\text\, ^* \,\mathrmx\,\mathrmy\,\mathrmz. This formula can be transformed so that no explicit dependence on the potential remains. First, the U_\text\, ^* part is taken out from the Schrödinger equation for the tip, and the elastic tunneling condition is used so that : M_ = \int_ \left(^* E_\mu \psi^\text_\mu + \psi^\text_\mu \frac \frac^*\right) \,\mathrmx\,\mathrmy\,\mathrmz. Now E_\mu\, is present in the Schrödinger equation for the sample and equals the kinetic plus the potential operator acting on \psi^\text_\mu. However, the potential part containing ''U''S is on the tip side of the barrier nearly zero. What remains, : M_ = -\frac \int_ \left(^* \frac - \frac^*\right) \,\mathrmx\,\mathrmy\,\mathrmz, can be integrated over ''z'' because the integrand in the parentheses equals \partial_z\left(^* \, \partial_z \psi^\text_\mu - \, \partial_z ^*\right). Bardeen's tunneling matrix element is an integral of the wave functions and their gradients over a surface separating the two planar electrodes: : M_ = \frac \int_ \left( \frac^* - ^* \frac \right) \,\mathrmx\,\mathrmy. 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. The tunneling matrix elements show appreciable energy dependence, which is such that tunneling from the upper end of the ''eV'' interval is nearly an order of magnitude more likely than tunneling from the states at its bottom. When the sample is biased positively, its unoccupied levels are probed as if the density of states of the tip is concentrated at its Fermi level. Conversely, when the sample is biased negatively, its occupied electronic states are probed, but the spectrum of the electronic states of the tip dominates. In this case it is important that the density of states of the tip is as flat as possible. The results identical to Bardeen's can be obtained by considering adiabatic approach of the two electrodes and using the standard time-dependent perturbation theory. This leads to
Fermi's golden rule In quantum physics, Fermi's golden rule is a formula that describes the transition rate (the probability of a transition per unit time) from one energy eigenstate of a quantum system to a group of energy eigenstates in a continuum, as a result of a ...
for the transition probability \Gamma_ in the form given above. Bardeen's model is for tunneling between two planar electrodes and does not explain scanning tunneling microscope's lateral resolution. Tersoff and Hamann used Bardeen's theory and modeled the tip as a structureless geometric point. This helped them disentangle the properties of the tip—which are hard to model—from the properties of the sample surface. The main result was that the tunneling current is proportional to the local density of states of the sample at the Fermi level taken at the position of the center of curvature of a spherically symmetric tip (''s''-wave tip model). 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. These are well below the microscope's detection limit and below the values actually observed in experiments. 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 In philosophy and science, a first principle is a basic proposition or assumption that cannot be deduced from any other proposition or assumption. First principles in philosophy are from first cause attitudes and taught by Aristotelians, and nuan ...
.


Gallery of STM images

File:Scanning tunneling microscope (STM) 250 nm by 250 nm image of one-atom-thick silver islands grown on palladium (111) surface.png, One-atom-thick silver islands grown on terraces of the (111) surface of palladium. Image size is 250 nm by 250 nm. File:Atomic resolution Au100.JPG, The characteristic reconstruction fringes on the (100) surface of gold are 1.44  nm wide and consist of six atomic rows that sit on top of five rows of the crystal bulk. Image size is approximately 10 nm by 10 nm. File:Chiraltube.png, A 7 nm long part of a single-walled
carbon nanotube A carbon nanotube (CNT) is a tube made of carbon with a diameter in the nanometre range ( nanoscale). They are one of the allotropes of carbon. Two broad classes of carbon nanotubes are recognized: * ''Single-walled carbon nanotubes'' (''S ...
. File:Silicium-atomes.png, Atoms on the surface of a crystal of
silicon carbide Silicon carbide (SiC), also known as carborundum (), is a hard chemical compound containing silicon and carbon. A wide bandgap semiconductor, it occurs in nature as the extremely rare mineral moissanite, but has been mass-produced as a powder a ...
(SiC) are arranged in a hexagonal lattice and are 0.3 nm apart. File:Cens nanomanipulation3d Trixler.jpg, STM nanomanipulation of PTCDA molecules on
graphite Graphite () is a Crystallinity, crystalline allotrope (form) of the element carbon. It consists of many stacked Layered materials, layers of graphene, typically in excess of hundreds of layers. Graphite occurs naturally and is the most stable ...
to inscribe the logo of the Center for NanoScience (CeNS), Munich.


Early invention

An earlier invention similar to Binnig and Rohrer's, the ''Topografiner'' of R. Young, J. Ward, and F. Scire from the
NIST The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical s ...
, relied on field emission. However, Young is credited by the Nobel Committee as the person who realized that it should be possible to achieve better resolution by using the tunnel effect.


Other related techniques

Many other microscopy techniques have been developed based upon STM. These include photon scanning microscopy (PSTM), which uses an optical tip to tunnel photons; scanning tunneling potentiometry (STP), which measures electric potential across a surface; spin-polarized scanning tunneling microscopy (SPSTM), which uses a
ferromagnetic Ferromagnetism is a property of certain materials (such as iron) that results in a significant, observable magnetic permeability, and in many cases, a significant magnetic coercivity, allowing the material to form a permanent magnet. Ferromagne ...
tip to tunnel spin-polarized electrons into a magnetic sample; multi-tip scanning tunneling microscopy, which enables electrical measurements to be performed at the nanoscale; and
atomic force microscopy Atomic force microscopy (AFM) or scanning force microscopy (SFM) is a very-high-resolution type of scanning probe microscopy (SPM), with demonstrated resolution on the order of fractions of a nanometer, more than 1000 times better than the opti ...
(AFM), in which the
force In physics, a force is an influence that can cause an Physical object, object to change its velocity unless counterbalanced by other forces. In mechanics, force makes ideas like 'pushing' or 'pulling' mathematically precise. Because the Magnitu ...
caused by interaction between the tip and sample is measured. STM can be used to manipulate atoms and change the topography of the sample. This is attractive for several reasons. Firstly the STM has an atomically precise positioning system, which enables very accurate atomic-scale manipulation. Furthermore, after the surface is modified by the tip, the same instrument can be used to image the resulting structures.
IBM International Business Machines Corporation (using the trademark IBM), nicknamed Big Blue, is an American Multinational corporation, multinational technology company headquartered in Armonk, New York, and present in over 175 countries. It is ...
researchers famously developed a way to manipulate
xenon Xenon is a chemical element; it has symbol Xe and atomic number 54. It is a dense, colorless, odorless noble gas found in Earth's atmosphere in trace amounts. Although generally unreactive, it can undergo a few chemical reactions such as the ...
atoms adsorbed on a
nickel Nickel is a chemical element; it has symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel is a hard and ductile transition metal. Pure nickel is chemically reactive, but large pieces are slo ...
surface. This technique has been used to create electron ''corrals'' with a small number of adsorbed atoms and observe Friedel oscillations in the electron density on the surface of the substrate. Aside from modifying the actual sample surface, one can also use the STM to tunnel electrons into a layer of electron-beam
photoresist A photoresist (also known simply as a resist) is a light-sensitive material used in several processes, such as photolithography and photoengraving, to form a patterned coating on a surface. This process is crucial in the electronics industry. T ...
on the sample, in order to do
lithography Lithography () is a planographic method of printing originally based on the miscibility, immiscibility of oil and water. The printing is from a stone (lithographic limestone) or a metal plate with a smooth surface. It was invented in 1796 by ...
. This has the advantage of offering more control of the exposure than traditional
electron-beam lithography Electron-beam lithography (often abbreviated as e-beam lithography or EBL) is the practice of scanning a focused beam of electrons to draw custom shapes on a surface covered with an electron-sensitive film called a resist (exposing). The electron ...
. Another practical application of STM is atomic deposition of metals (gold, silver, tungsten, etc.) with any desired (pre-programmed) pattern, which can be used as contacts to nanodevices or as nanodevices themselves.


See also

*
Scanning probe microscopy Scanning probe microscopy (SPM) is a branch of microscopy that forms images of surfaces using a physical probe that scans the specimen. SPM was founded in 1981, with the invention of the scanning tunneling microscope, an instrument for imaging ...
*
Atomic force microscope Atomic force microscopy (AFM) or scanning force microscopy (SFM) is a very-high-resolution type of scanning probe microscopy (SPM), with demonstrated resolution on the order of fractions of a nanometer, more than 1000 times better than the diffr ...
* Electrochemical scanning tunneling microscope *
Microscopy Microscopy is the technical field of using microscopes to view subjects too small to be seen with the naked eye (objects that are not within the resolution range of the normal eye). There are three well-known branches of microscopy: optical mic ...
*
Electron microscope An electron microscope is a microscope that uses a beam of electrons as a source of illumination. It uses electron optics that are analogous to the glass lenses of an optical light microscope to control the electron beam, for instance focusing it ...
* Multi-tip scanning tunneling microscopy * IBM (atoms)


References


Further reading

* * * * * * * * * * * * *


External links


A scanning tunelling microscope filmed during operation by an electron microscope


WeCanFigureThisOut.org

* ttp://toutestquantique.fr/en/microscopy/ Animations and explanations on various types of microscopes including electron microscopes(Université Paris Sud)
Introduction to STM in plain English
(Harvard University) {{DEFAULTSORT:Scanning Tunneling Microscope Scanning probe microscopy Swiss inventions German inventions Microscopes 1981 introductions Articles containing video clips 20th-century inventions