Resonant tunneling of electrons of one or two degrees of freedom

Analytical expressions for the tunneling current of electrons with one or two degrees of freedom (DOF), due to additional quantum confinement transverse to the electron transport direction, are explicitly derived, analyzed, and implemented into computer simulations. The results are compared with the well-known case in which 3-DOF electrons tunnel through a one-dimensional double-barrier well. The results show that the singularity of the density of states in a one-dimensional system will not manifest sharp features in tunneling current, and that when the spacing between the Fermi energy and bottom of conduction band is the same, the tunneling current peak becomes broader and the peak-to-valley ratio becomes smaller as the number of degrees of freedom of the electrons is reduced. The results also show that when scattering is neglected, the energy quantization due to transverse confinement in 1- or 2-DOF systems will not contribute any additional peaks to the tunneling current.