Download: >> Powerpoint Presentation Keywords: Klein Tunneling, Graphene, Bipolar Junctions, Quantum Physics 
Presentation Transcript:
Classical Picture
* On the quantum scale, objects exhibit wavelike 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 wavefunction 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 electronlike to holelike 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. Band structure * In this transition from conduction band to valence band, its dynamics changes from electronlike to holelike. * 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).
Klein tunneling Transmission resonance Bipolar junctions * Electrical conductance through the interface between pdoped and ndoped graphene: Klein tunneling.
* The Fermi wave vector for typical carrier densities of is > 101 nm1. * Under these conditions kFd >1, pn and np 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? 
