[LEFT]Electron tunneling& application of Electron tunneling
By 1928, George Gamow had solved the theory of the alpha decay of a nucleus via tunneling. Classically, the particle is confined to the nucleus because of the high energy requirement to escape the very strong potential. Under this system, it takes an enormous amount of energy to pull apart the nucleus. In quantum mechanics, however, there is a probability the particle can tunnel through the potential and escape. Gamow solved a model potential for the nucleus and derived a relationship between the half-life of the particle and the energy of the emission.
Alpha decay via tunneling was also solved concurrently by Ronald Gurney and Edward Condon. Shortly thereafter, both groups considered whether particles could also tunnel into the nucleus.
After attending a seminar by Gamow, Max Born recognized the generality of quantum-mechanical tunneling. He realized that the tunneling phenomenon was not restricted to nuclear physics, but was a general result of quantum mechanics that applies to many different systems. Today the theory of tunneling is even applied to the early cosmology of the universe
Quantum tunneling was later applied to other situations, such as the cold emission of electrons, and perhaps most importantly semiconductor and superconductor physics. Phenomena such as field emission, important to flash memory, are explained by quantum tunneling. Tunneling is a source of major current leakage in Very-large-scale integration (VLSI) electronics, and results in the substantial power drain and heating effects that plague high-speed and mobile technology.
Another major application is in electron-tunneling microscopes which can resolve objects that are too small to see using conventional microscopes. Electron tunneling microscopes overcome the limiting effects of conventional microscopes (optical aberrations, wavelength limitations) by scanning the surface of an object with tunneling electrons.
It has been found that quantum tunneling may be the mechanism used by enzymes to speed up reactions in lifeforms to millions of times their normal speed.
Electron tunneling model of bond the covalent
Chemical bonding occurs when one or more electrons can be simultaneously close to two nuclei. But how can this are arranged? The conventional picture of the shared electron bond places the bonding electrons in the region between the two nuclei. This makes a nice picture, but it is not consistent with the principle you probably, that opposite charges attract. This would imply that the electrons would be "happiest" (at the lowest potential energy) when they are very close to a nucleus, not half a bond-length away from two of them!
This plot shows how the potential energy of an electron in the hydrogen atom varies with its distance from the nucleus. Notice how the energy falls without limit as the electron approaches the nucleus, represented here as a proton, H+. If potential energy were the only consideration, the electron would fall right into the nucleus where its potential energy would be minus infinity.
When an electron is added to the proton to make a neutral hydrogen atom, it tries to get as close to the nucleus as possible. The Heisenberg Indeterminacy ("uncertainty") principle requires the total energy of the electron energy to increase as the volume of space it occupies diminishes. As the electron gets closer to the nucleus, the nuclear charge confines the electron to such a tiny volume of space that its energy rises, allowing it to "float" slightly away from the nucleus without ever falling into it.
The shaded region above shows the range of energies and distances from the nucleus the electron is able to assume within the 1s orbital. The electron can thus be regarded as a fluid that occupies a vessel whose walls conform to the red potential energy curves shown inside *Note that as the potential energy falls, the kinetic energy increases, but only half as fast (this is called the virial theorem.) Thus close to the nucleus, the kinetic energy is large and so is the electron's effective velocity. The top of the shaded area defines the work required to raise its potential energy to zero, thus removing it from the atom; this corresponds, of course, to the ionization energy.
A quantum particle can be described by a waveform which is the plot of a mathematical function related to the probability of finding the particle at a given location at any time. If the particle is confined to a box, it turns out that the wave does not fall to zero at the walls of the box, but has a finite probability of being found outside it. This means that a quantum particle is able to penetrate, or "tunnel through" its confining boundaries. This remarkable property is called the tunnel effect.
In terms of the electron fluid model introduced above, the fluid is able to "leak out" of the atom if another low-energy location can be found nearby.
Electron tunneling in the simplest molecule
Suppose we now bring a bare proton up close to a hydrogen atom. Each nucleus has its own potential well, but only that of the hydrogen atom is filled, as indicated by the shading in the leftmost potential well.
But the electron fluid is able to tunnel through the potential energy barrier separating the two wells; like any liquid, it will seek a common level in the two sides of the container as shown below. The electron is now "simultaneously close to two nuclei" while never being in between them. Bear in mind that this would be physically impossible for a real liquid composed of real molecules; this is purely a quantum effect that is restricted to a low-mass particle such as the electron.
Because the same amount of electron fluid is now shared between the two wells, its level in both is lower. The difference between what it is now and what is before corresponds to the bond energy of the hydrogen molecule ion.
The dihydrogen molecule
Now let's make a molecule of dihydrogen. We start with two hydrogen atoms, each with one electron. But there is a problem here: both potential energy wells are already filled with electron fluid; there is no room for any more without pushing the energy way up. But quantum theory again comes to the rescue! If the two electrons have opposite spins, the two fluids are able to interpenetrate each other, very much as two gases are able to occupy the same container. This is depicted by the double shading in the diagram below.
When the two hydrogen atoms are within tunneling distance, half of the electron fluid (really the probabability of finding the electron) from each well flows into the other well. Because the two fluids are able to interpenetrate, the level is not much different from what it was in the H2+ ion, but the greater density of the electron-fluid between the two nuclei makes H2 a strongly bound molecule.
So why does dihelium not exist?
If we tried to join two helium atoms in this way, we would be in trouble. The electron well of He already contains two electrons of opposite spin. There is no room for more electron fluid (without raising the energy), and thus no way the electrons in either He atom can be simultaneously close to two nuclei.
application of Electron tunneling
Resonant tunneling diode
A resonant tunnel diode (RTD) is a device which uses quantum effects to produce negative differential resistance (NDR). As an RTD is capable of generating a terahertz wave at room temperature, it can be used in ultra high-speed circuitry. Therefore The RTD is extensively studied.
RTDs are formed as a single quantum well structure surrounded by very thin layer barriers. This structure is called a double barrier structure. Carriers such as electrons and holes can only have discrete energy values inside the quantum well. When a voltage is placed across an RTD, a terahertz wave is emitted which is why the energy value inside the quantum well is equal to that of the emitter side. As voltage increased, the terahertz stops because the energy value in the quantum well is outside the emitter side energy.
This structure can be grown by molecular beam heteroepitaxy. GaAs and AlAs in particular are used to form this structure. AlAs/InGaAs or InAlAs/InGaAs can be used.
A double-barrier potential profile with a particle incident from left with energy less than the barrier height.
In quantum tunneling through a single barrier, the transmission coefficient, or the tunneling probability, is always less than one (for incoming particle energy less than the potential barrier height). Consider a potential profile which contains two barriers (which are located close to each other), one can calculate the transmission coefficient (as a function of the incoming particle energy) using any of the standard methods. It turns out that, for certain energies, the transmission coefficient is equal to one, i.e. the double barrier is totally transparent for particle transmission. This phenomenon is called resonant tunneling. It is interesting that while the transmission coefficient of a potential barrier is always lower than one (and decreases with increasing barrier height and width), two barriers in a row can be completely transparent for certain energies of the incident particle.
Resonant tunneling also occurs in potential profiles with more than two barriers
[LEFT] The potential profiles required for resonant tunneling can be realized in semiconductor system using heterojunctions which utilize semiconductors of different types to crease potential barriers or wells in the conduction band or the valence band. It is worth noting that resonant tunnel diodes are intraband tunnel diodes; see also resonant interband tunnel diodes.
V Resonant Tunnel Diodes
Resonant tunnel diodes are typically realized in III-V compound material systems, where heterojunctions made up of various III-V compound semiconductors are used to create the double or multiple potential barriers in the conduction band or valence band. Reasonably high performance III-V resonant tunnel diodes have been realized. But such devices have not entered mainstream applications yet because the processing of III-V materials is incompatible with Si CMOS technology and the cost is high.
Si/SiGe Resonant Tunnel Diodes
[LEFT] Resonant tunnel diodes can also be realized using the Si/SiGe materials system. But the performance of Si/SiGe resonant tunnel diodes was limited due to the limited conduction band and valence band discontinuities between Si and SiGe alloys.
Resonant tunneling of holes through Si/SiGe heterojunctions was attempted first because of the typically relatively larger valence band discontinuity in Si/SiGe heterojunctions than the conduction band discontinuity. This has been observed, but negative differential resistance was only observed at low temperatures but not at room temperature
Resonant tunneling of electrons through Si/SiGe heterojunctions was obtained later, with a limited peak-to-valley current ratio (PVCR) of 1.2 at room temperature
Subsequent developments have realized Si/SiGe RTDs (electron tunneling) with a PVCR of 2.9 with a PCD of 4.3 kA/cm2 and a PVCR of 2.43 with a PCD of 282 kA/cm2 at room temperature
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