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Klein Tunneling, Graphene, Bipolar Junctions, Quantum Physics
* On the quantum scale, objects exhibit wave-like characteristics.
* Quanta moving against a potential hill can be described by their wave function.
* The wave function represents the probability amplitude of finding the object in a particular location.
* If this wave-function describes the object as being on the other side of the potential hill, then there is a probability that the object has moved through the potential hill.
* This transmission of the object through the potential hill is termed as tunneling.
> In quantum mechanics, an electron can tunnel from the conduction into the valence band.
> Such tunneling from an electron-like to hole-like state is called as interband tunneling or Klein tunneling.
> Here, electron avoids backscattering
> Here, electrons avoid backscattering because the carrier velocity is independent of the energy.
> The absence of backscattering is responsible for the high conductivity in carbon nanotubes (Ando et al, 1998).
Let?s consider a linear electrostatic potential
Absence of backscattering
* For py = 0, no backscattering.
* The electron is able to propagate through an infinitely high potential barrier because it makes a transition from the conduction band to the valence band.
* In this transition from conduction band to valence band, its dynamics changes from electron-like to hole-like.
* The equation of motion is thus,
at energy E with
* It shows that in the conduction band (U < E) and in the valence band (U > E).
* Electrical conductance through the interface between p-doped and n-doped graphene: Klein tunneling.
* The Fermi wave vector for typical carrier densities of is > 10-1 nm-1.
* Under these conditions kFd >1, p-n and n-p junctions are smooth on the Fermi wavelength.
* The tunneling probability expression can be used.
* The result of integration ?:
Applications of tunneling
* Atomic clock
* Scanning Tunneling Microscope
* Tunneling diode
* Tunneling transistor
Who got the Nobel prize (1973) in Physics for his pioneering work on electron tunneling in solids?