Resonant tunneling of electrons in a crossed-field nanogap

Summary form only given. In the emerging fields of nano-technology, electrode gaps with scales down to nanometer regime can be easily be fabricated. On such a nanoscopic scale., quantum effects such as electron tunneling will become important in the beam-gap interaction when the gap spacing is smaller than the electron wavelength. In this paper, we study the resonant tunneling of electrons in a crossed-field nanogap. By ignoring the space-charge effects, the combination of the magnetic field and the DC electrostatic field will produce a barrier-well-barrier like potential field. By solving the 1D time-independent Schrodinger equation, we find that the energy levels of the electrons are quantized, and resonant tunneling occurs when the emission energy of the electrons equals to the discrete energy levels. The transmission coefficient (T) of the electron is formulated as a function of normalized parameters, which depends on the gap spacing, DC gap voltage, magnetic field, emission energy, and surface potential energy of the cathode. Our results show that there is an optimum magnetic field for perfect electron transmission (T=1) from the cathode to the anode. The application of this work will be discussed.