Stark shifts and mean lifetimes for AlxGa1−xAs/GaAs single quantum wells

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

“…Moreover, the diagonalization method fails to include the zero-field structure. It was demonstrated earlier using our finite-difference scheme [14,15] that the inverse-power method (IPM), which solves for the energy and wavefunction iteratively, produces correct results. However, in the finitedifference method the wavefunction is obtained in position space.…”

“…In this way we need only three iterations to get converged results. The mean tunnelling lifetime at high electric field can be calculated from the probability of the electrons tunnelling out of the well [13][14][15]. The bias is suddenly applied at t = 0.…”

“…The Stark shifts and resonance widths have been thoroughly studied in the single-RQW using different analytic and numerical techniques [9,10,[12][13][14][15][16][18][19][20]. We therefore calculate the mean tunnelling lifetimes for this well to verify the correctness of our calculation.…”

“…Several alternative numerical approaches such as the finite-difference method [13][14][15], finite-element method [16], complex-coordinate approach [17], and Fourier series method [18,19] have been successfully applied to calculate energies and wavefunctions for any form of the QW. In these methods, the solution is obtained over a distance L which is the sum of the well widths and barrier widths.…”

“…In our earlier work, the finite-difference scheme was employed to obtain energies, wavefunctions, and lifetimes in different QW structures [14,15]. Since the plane waves are orthonormalized, the Fourier series in the plane-wave basis set is an attractive method for solving eigenvalue equations in different physical problems.…”