Comparison of Electron Direct Tunneling Time in a Heterostructure with a Nanometer-Thick Trapezoidal Barrier Calculated Using Exponential and Airy Wavefunctions

Abstract

Analytical expressions of electron direct transmittance and tunneling time in a heterostructure with a nanometer-thick trapezoidal barrier have been derived by using the Airy wavefunctions. The analytic expressions are applied to the Si (100)/SiO₂/Si (100) heterostructure. It has been found that the electron direct transmittance and tunneling time are suitably calculated by employing the Airy wavefunction as compared to those obtained under the exponential wavefunction. It has also been found that the calculated electron direct transmittance and tunneling time under the Airy wavefunction are the same as those under the exponential wavefunction for very low bias voltage and low electron incident energy.