Term Paper: Quantum Tunneling

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Quantum tunneling is a function of quantum-mechanical activity in the instance where a particle moves against potential energy and appears on the other side of the energy barrier. At least the wave function describing the particle is extended to the other side. These wave functions are the means by which the particle is found, so it is assumed that the particle has made it to the other side of the barrier. This behavior on the part of a particle is called tunneling, as there is no other means by which it can be described, as the particle has not penetrated the barrier nor does it have the energy to break through a barrier (Barrier 1).

This phenomenon could not happen in other than the nanoscopic realm; therefore a person could not tunnel through the chair upon which they are sitting, unless an exorbitant amount of time is involved. And in order to observe the phenomena, one would need a nanoscopic microscope.

Solutions where total energy (E-V) is positive will be harmonic as was the case inside the infinite square well.

Solutions where total energy is negative result in a complex value of k and will become a negative exponential in 'x'.

The general solution to the time independent Shrodinger Equation

Negative energies are not allowed within the barrier of the nucleus and a particle could never enter into a region where the total energy was less than zero in the classical case. If a marble is in a spherical depression and has less total energy than is required to overcome the potential energy at an elevation equal to the rim of the depression, it will remain contained within the depression indefinitely, never being able to escape unless it had external assistance (Barrier 1).

In the quantum case, a particle has some exponentially declining probability of entering a region where the total energy of the marble is less than zero. Particles do not normally appear within their negative energy region but have a finite probability of appearing on the other side of a potential energy barrier, a feat which would be insurmountable in the classical case.

The phenomena of magically appearing on the other side of a barrier is known as tunneling and has important electronic applications in semiconductor electronics, where tunneling devices control currents. An explanation of important applications of the tunneling phenomena follows:

It was known that radioactive materials had characteristic exponential decay rates or half lives in the early 1900s. It was also known that radiation emissions had certain characteristic energies. By 1928, the theory of the alpha decay of a nucleus via tunneling had solved by George Gamow. It takes a lot of energy for a particle confined to the nucleus to escape the strong potential. It also takes a huge amount of energy to split the nucleus. Quantum mechanics said that a particle can tunnel through the potential and escape, so Ganow created a model potential and derived the relationship between the half-life of the particle and the energy of the emission needed to escape.

Concurrently Ronald Gurney and Edward Condon solved the Alpha decay via tunneling. Indeed, it occurred to both groups that particles could also tunnel into the nucleus.

Max Born recognized the generality of quantum-mechanical tunneling after attending a seminar by Gamow. He realized that the tunneling phenomena was a general result of Quantum mechanics and was not restricted to nuclear physics, but could be applied to many different systems. Today the tunneling theory is even applied to the universe during its early cosmology.

Other situations, such as the cold emission of electrons and semiconductor and superconductor physics, have found the quantum tunneling theory applicable to them. Field emission phenomena can be explained by quantum tunneling, which is important to flash memory. Tunneling is also a source of major current leakage in very-large-scale integration (VLSI) electronics, and is the explanation for substantial power drain or heating effects in high-speed and mobile technology.

Another application for quantum tunneling is in electron-tunneling microscopes or scanning tunneling microscopes, which can see objects too small to see using conventional microscopes. Electron tunneling microscopes have overcome the limited effects of conventional microscopes, such as optical aberrations and wavelength limitations, by scanning the surface of an object with tunneling electrons (Quantum 1).

Schrodinger equation concepts say that a particle of energy (E) less than the height (U0) of a barrier could not penetrate the region inside the barrier, which is classically forbidden. But in order to penetrate, the wave function must be continuous that is associated with a free particle at the barrier and show an exponential decay inside the barrier. There is a finite probability that the particle will tunnel through the barrier if the wave function is continuous on the far side of the barrier.

As the particle approaches the barrier, a free particle wave function defines it. In a real or imaginary application, part of this function would be appropriate. In general one speaks of free particles within some kind of boundary, with conditions of some kind of potential set. When it reaches the barrier, it must satisfy the Schrodinger equation, as mentioned above (Barrier 1).

The tunnel or Esaki diode is a very fast operating diode, speeding into the microwave region GHz. Leo Esaki discovered the effect that is used in these diodes and for this received the Nobel Prize in Physics in 1973. The diode was developed in conjunction with efficiency improvements at Sony laboratories when the 2T5 transistor in Sony radios were being upgraded. They developed a smaller diode, called the 2T7 and set up their factories for mass production. However, the new, smaller diode worked less efficiently than the older one, and experiments were set up to determine why. Theoretically it should have worked much more efficiently.

Leo Esaki was called from the Research Department of Sony to measure concentration levels to determine the maximum acceptable levels of phosphorous the base was doped with. It was suspected that the phosphorus levels had destroyed the PN junction during the bonding process. Esaki set about to determine the cause and measure how much phosphorous could be used, assisted by Yuriko Kurose, a college student, and Takashi Suzuki, a trainee at Sony, who took the measurements.

After he began to take measurements, Esaki noticed what happened when high concentrations of phosphorous crystals were applied to this tiny diode. Usually current tended to flow forward when the voltage was applied to the PN junction diode, but when Suzuki plotted the graph, he found that the diode displayed current flow in the reverse direction with a curve and unusual peak appearing in the forward flow. Unable to believe this, Suzuki tested the diode several times and reported this to Esaki.

Using a cathode tube, the two reproduced the phenomena on the graph and, after repeating the tests, realized they were onto something new. However, Esaki had already realized that reducing the phosphorous concentration corrected the original problem and Sony was able to manufacture a high quality transistor. This was all well and good, but then Esaki began to think about the reverse diode and went back to experiment with it, to try to determine the cause of the negative resistant represented by the peak in the graph. His assistant, Suzuki, suggested that the cause might be "forward bias tunneling," as all matter, reduced to waves, energy is concentrated at the peak of these waves. Particles tunnel through these waves of energy and the "tunneling effect" occurred. Up until this time, reverse bias tunneling had been the subject of research by other scientists, but Esaki realized he had discovered a forward bias tunneling effect.

Esaki and his team worked to develop the new diode that had negative resistance and current diminishing as voltage increased. Finally, in 1957, Esaki and his team perfected the diode and reported it to the Physics Society. The following year the details were published in national and international journals and it was announced at the International Conference on Solid State Physics held in Brussels. Although widely acclaimed throughout the world, the Japanese at Sony disregarded Esaki's experiments and accomplishments at the time (Sony 2007).

The Esaki diodes have a heavily doped p-n junction only 10 nm (100 a) wide. The p-n junction is an interface between two regions in the semiconductor crystal which have been treated so that one is a p-type semiconductor and the other is an n-type semiconductor; it contains a permanent dipole charge layer. The heavy doping in the Esaki diode creates a broken band gap, where" conduction band electron states on the n-side are more or less aligned with valence band hole states on the p-side" (Tunnel 7).

During the normal operation of forward bias, as there is an increase in voltage, electrons tunnel through the p-n barrier because they are in states in the conduction band on the n-side that are aligned with valence band hole states on the p-side of the p-n junction. Then, as voltage increases, the… [END OF PREVIEW]

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Quantum Tunneling.  (2007, April 28).  Retrieved April 25, 2019, from https://www.essaytown.com/subjects/paper/quantum-tunneling/610301

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