An analytical solution of the one-dimensional Schrodinger equation with a potential in the form of a quadratic function of the coordinate and a fourth-order function of the coordinate is obtained. An analytical expression has been found for the transparency of the diode as a function of the electron energy and the anode voltage. The explicit analytical volt-ampere characteristic of the diode is determined as a function of the anode voltage and temperature. The tunneling current in the diode is calculated taking into account the temperature and its volt-ampere characteristics are constructed. Keywords: thermionic-field emission, Schrodinger equation, tunneling, diode.
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