Ballistic current - voltage model in depletion all around operation of silicon on insulator four - gate transistor

Abstract

Two dimensional Poisson-Schrödinger equation is solved numerically in depletion all around (DAA) operation of n-channel four gate transistor (G4-FET) by finite element method. Potential distribution is obtained by solving 2-D Poisson equation. The influence of different gate bias voltages on the location and size of the conducting channel is studied, which also includes fully depleted condition for certain gate bias voltages. The developed model is used to investigate the gradual change of the size of the conducting channel from drain to source, when drain is positively biased. Conduction band profile is studied and shallow n-well region is found. By solving 2D Schrödinger equation, Eigen energy at various cross sections between drain and source, subband profiles from source to drain and wave function distribution are observed. Weak energy quantization is found by observing small energy difference (less than kT) between subsequent subband profiles and noticing wave function distribution extending beyond neutral n-well and into the depletion region. Using the outputs of 2D Poisson-Schrödinger solver, a ballistic currentvoltage model is developed by mode-space approach and modified Tsu-Esaki equation. Finally, effect of gate bias on current-voltage characteristics is investigated.