Binding energy of excitons in cylindrical quantum dots

Excitons in semiconductor quantum discs

“…Figure 2 shows the calculated exciton binding energy as a function of the radius of the quantum disc R for widths L of 70 Å and 100 Å. We choose to compare these two values of L with the results of Susa [7], as it was explained by Le Goff and Stebe [5,6] that the separable wavefunction, φ 2 , is expected to be a good approximation in the limit of strong quantum confinement and when L/R < 1. From figure 2, we see that both φ 1 and φ 3 yield consistently higher binding energies than φ 2 .…”

“…For the full 3D motion, the product f c (r c )g c (z c ) is no longer a solution of the 3D effective-mass Schrödinger equation since the actual 3D finite confinement potential is not straightforwardly the sum of the finite confinements V c + V ⊥ c . Using the perturbational approach suggested by the Le Goff and Stebe [5,6], we write the 3D finite confinement potential as…”

“…It should be noted that even with this simplified wavefunction, the variational treatment required numerical evaluation of fourfold integrals before the single-parameter energy minimization (with respect to α), which hence imposes a heavy computational burden. Later, Le Goff and Stebe [5,6] introduced a two-parameter relative variational wavefunction:…”

“…Advances in nanoscale fabrication techniques have further brought about the reduction of the effective dimension of excitonic states-from quasi-two-dimensional (2D) down to the quasi-one-dimensional (1D) and 'zero'-dimensional (0D) states. The question of whether excitonic states are even more enhanced and the extent of the enhancement in these reduced-dimensional (<2D) structures has thus been a topic of much interest in the past few years [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. In view of the rapid development in crystal growth and fabrication techniques, as we progress from microtechnologies to nanotechnologies whereby devices are designed in the nanometre range, it becomes increasingly necessary to address the concern of the exciton losing its enhanced effects in the ultrasmall quantum structures, due to the increased penetration of the exciton wavefunction into the barrier regions in the direction of diminishing spatial confinement.…”

“…Here, we are also interested in the dimensionality crossover in the critical confinement limit where quantum confinement effects are rapidly overwhelmed by the bulk effect. Although previous work [5][6][7] has been done on the variational calculation of the exciton in the quantum disc, the authors have used different trial wavefunctions which have their individual limitations for certain geometries of the disc. Also there seems to be a lack as regards comparison and justification of these wavefunctions employed in quantum disc calculations, as the success and accuracy of results based on variational methods often depend on the parameters chosen and the functional form of the trial wavefunction used.…”