Symmetry selected quantum dynamics of few electrons in nanopillar transistors

Study on single electron tunnel using current-voltage characteristics in nanopillar transistors at 298 K show that the mapping between the N_th electron excited in the central box ∼8.5 × 8.5 × 3 nm³ and the N_th tunnel peak is not in the one-to-one correspondence to suggest that the total number N of electrons is not the best quantum number for characterizing the quality of single electron tunnel in a three-dimensional quantum box transistor. Instead, we find that the best number is the sub-quantum number n_z of the conduction z channel. When the number of electrons in n_z is charged to be even and the number of electrons excited in the n_x and n_y are also even at two, the adding of the third electron into the easy n_x/n_y channels creates a weak symmetry breaking in the parity conserved x-y plane to assist the indirect tunnel of electrons. A comprehensive model that incorporates the interactions of electron-electron, spin-spin, electron-phonon, and electron-hole is proposed to explain how the excited even electrons can be stabilized in the electric-field driving channel. Quantum selection rules with hierarchy for the n_i (i = x, y, z) and N = Σn_i are tabulated to prove the superiority of n_z over N.