Transmission and Dwell Time Oscillations Caused by Coexistence of Tunneling and Propagating in a Trapezoidal Barrier

A refined one of our exactly solvable trapezoidal barrier potential model [Thin Solids Films, 414 (2002) 136)] for metal-insulator-metal tunnel junctions has been presented. According to the refined model, the longitudinal kinetic energy (E_(xL)) and the effective mass (m_L~*) of the electrons in the electrode on the left of the barrier distinguish from that on the right. It is found that as E_(xL) is greater than the shorter side of the resultant trapezoidal barrier potential, there will be a coexistence of the tunneling and propagating in the barrier. The results demonstrate that the damped oscillating electron waves localized in the propagating barrier subregion lead to the oscillation and enhancement in the transmission coefficient DT and dwell time τ_D. For the barrier height φ_1= 2.6 eV and φ_2= 1.4 eV, the width d= 22 A and E_(xL0=1.0 eV, D_T and τ_D have a maximum of 0.054 and 0.58×10~(-15) s at V= 2.04 V and 2.18 V, respectively. This suggests that a real tunneling may be a hybrid.