Quantum Tunneling and Field Electron Emission Theories by Shi-Dong Liang

By Shi-Dong Liang

Quantum tunneling is a necessary factor in quantum physics. specifically, the swift improvement of nanotechnology lately can provide loads of functions in condensed topic physics, floor technology and nanodevices, that are growing to be pursuits in basic concerns, computational suggestions and strength purposes of quantum tunneling.

The e-book includes proper subject matters. One is quantum tunneling conception in condensed subject physics, together with the fundamental techniques and strategies, in particular for contemporary advancements in mesoscopic physics and computational formula. the second one half is the sphere electron emission idea, which covers the fundamental box emission strategies, the Fowler Nordheim idea, and up to date advancements of the sector emission idea particularly in a few primary thoughts and computational formula, resembling quantum confinement results, Dirac fermion, Luttinger liquid, carbon nanotubes, coherent emission present, quantum tunneling time challenge, spin polarized box electron emission and non-equilibrium Green's functionality strategy for box electron emission.

This e-book provides in either educational and pedagogical types, and is as attainable as self-complete to make it appropriate for researchers and graduate scholars in condensed subject physics and vacuum nanoelectronics.

Readership: Graduate scholars and researchers in vacuum nanoelectronics and physics.

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The scattering process is also described by ψL = MψR , where ψL (ψR ) is the wave function in the left (right) side of the scattering potential. They are a vector describing the incident and scattering components of the wave function. M is called the transfer matrix. β’ α S β α’ M Fig. 1 Schematics of scattering and transfer matrices of quantum tunneling. Potential scattering model: Suppose a wave enters a local potential with two components (α, β) and go out from the local potential with (α , β ), which is shown in Fig.

It should be pointed out that the unitary U cannot guarantee the probability current density conservation, namely, the probability conservation, in principle, is not equivalent to the probability current density conser2 p and H = − 2m ∇2 + V , where V is vation. In the special case, v = m spatial-independent potential. It is easy to verify that [v, H] = 0, namely the probability conservation is equivalent to the probability current density convervation. 5 Quantum Physics versus Classical Physics Physical phenomena can be understood by two different natures, quantum physics and classical physics.

For a given system with the average distance a between particles, the degenerate temperature T0 is given by Eq. 23). Any system in equilibrium state with temperature T exhibits quantum characteristic when T < T0 . For common solids and liquids, the degenerate temperature of electrons T0 ∼ 105 K. Therefore, in room temperature electrons in solid, in principle, exhibit quantum characteristic (wave behavior). However, it is not easy to observe quantum interference and tunneling phenomena for solids in room temperature and macroscopic scale even though the wave behavior of electrons in principle exists because the inelastic scattering of electron-electron or electron-phonon breaks the phase coherence of electron wave.

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