P. Thanikasalam et al., ANALYTICAL EXPRESSIONS FOR TUNNELING TIME THROUGH SINGLE AND DOUBLE-BARRIER STRUCTURES, IEEE journal of quantum electronics, 29(9), 1993, pp. 2451-2458
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.