ANALYTICAL EXPRESSIONS FOR TUNNELING TIME THROUGH SINGLE AND DOUBLE-BARRIER STRUCTURES

In the past, the quantum mechanical tunneling time through simple rect angular barrier has been obtained by various theoretical approaches in cluding the dwell time, the phase delay time, the Larmor clock time an d also using the numerical analysis of wave packets. The agreement amo ng these approaches over a range of incident electron energy is far fr om satisfactory. In this manuscript, analytical expressions for the tu nneling time are derived based on the group velocity approach (referre d hereafter as the Average Particle Time, tau(APT)) for single and dou ble rectangular potential barriers under zero bias. The results of the single barrier case, including the limiting value of the tunneling ti me for various energy limits, are compared with these previous tunneli ng time calculations, The tau(APT) results provide physically meaningf ul tunneling times for zero and infinite incident energy limits of the electron. The tau(APT) for the double barrier structure is computed f rom the analytical solution as a function of the incident energy of th e electron for two experimentally studied resonant tunneling structure s. For both the single and double barrier cases, the effect of the str ucture parameters such as barrier width, height, and well width on the tau(APT) are obtained and reported.