Application of Fourier series methods for studying tunnelling of electrons out of quantum wells in an electric field

Abstract

The electron energy shifts and mean tunnelling lifetimes in a quantum well with different potential profiles under an applied electric field are calculated using Fourier series methods. In the present work, single-rectangular, symmetric double, and diffusion-modified quantum wells have been taken into account. The mean lifetime at high field strength obtained from the time evolution of the wave packets is found to be lower than that obtained from the conventional standing-wave approach.

Analytic methods for field induced tunneling in quantum wells with arbitrary potential profiles

“…The effect of the effective mass is quite significant on both Ö and . The quasi-bound energies agree well with our previous Fourier series [15] and finite difference [34] methods. The resonance widths estimated in the present analytic methods do not agree with our previous work based on the finite difference method [34] which solves time-dependent effective mass equations.…”

“…We have shown Ö and at different field strengths in table 2. As observed before [15], Ö decreases rapidly with increasing electric field strength, while increases slowly with that due to the barrier present between two single RQWs.…”

“…The Airy function methods are also efficient in calculating the mean tunneling lifetimes´ µ. Recently Panda et al [15] have presented accurate numerical methods based on the Fourier series expansion techniques for calculating in quantum wells with arbitrary form of the potential profile. The analytic method is always preferred for its simplicity and requirement of modest computational facilities.…”

Density of states in an electrically biased quantum well

“…The field when applied along the growth direction produces a shift in the quasi-bound levels of the QW. The quasi-bound Stark states for the QW were calculated [1,2,5,8] and it was reported that the ground state energy for both the infinite and finite QW decreases with the increase of intensity of electric field whereas the first excited level raises [1,2,8]. This shows that the field along the growth direction changes the degree of quantum confinement along the growth direction.…”

“…Since the last two decades the electronic properties of quantum well (QW) in the presence of electric field have been studied with increasing interest [1][2][3][4][5][6][7][8] owing to their numerous device applications. Due to small dimensions of these devices, a small bias of even 0.1 V will produce a field of 10 8 V/m in the devices.…”